From 80bee2c91b0cb18d5fadd3d39ee2b9ba85d36580 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Fri, 31 Jul 2026 20:33:08 +0200
Subject: [PATCH 1/2] docs(bench): re-measure the published tables, and reverse
 a conclusion
MIME-Version: 1.0
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Content-Transfer-Encoding: 8bit

The committed results were taken at `ef8558c` — version `0.0.0a27`, before the
package was even renamed. Eight perf changes have landed since (#408, #412,
#413, #414, #415, #434, #421, #433), so every table on the page understated the
engine, and one paragraph drew a conclusion the numbers no longer support.

Re-run in one sitting on an idle machine: the ladder, the density sweep and the
scaling run, so all three files describe the same tree. Parity gate passes on
all six cases (`fleet` to 4.6e-16) before anything is timed.

**What moved**, against the previously published numbers, `l` rung, our arm:
wall -10% to -39% on nine of twelve rungs, peak -2% to -21% on nine.

**What got worse, and is not buried.** `dispatch` build is 10-12% slower —
that is `maintain_order='left'` from #433, which buys -21% peak on the same
rung and is the trade that PR argued for. `fleet/highs` peak is up 8.2%,
outside its 1.0% floor, and I have no explanation for it.

**A conclusion is reversed.** `## Absurd sizes` read 1.07x peak at 120M
variables and concluded that our memory headroom "is a small-and-sparse-model
property, not a scaling one". Peak is now 0.73-0.83x across four orders of
magnitude. Two things moved it and only one is us: #433 took ~20% off this
case, and the earlier reading came from a run *that section itself flagged as
noisy* — it recorded linopy at 38.5 s and 106.2 s for the same rung. The old
number was a conclusion drawn across the noise floor. The section now says so
rather than quietly presenting a better one.

**`profiled` is no longer the case in the ladder we lose** (1.09x -> 0.74x
through the highs sink), and `fleet/lp` has crossed on wall (1.03x -> 0.90x).
Both paragraphs are rewritten to say what changed rather than to delete the
sentences that admitted the losses. Two numbers still go against us and are
still named: `profiled` 1.31x on wall through the LP sink, `fleet` 1.47x on peak.

Not touched: `## Sink capabilities` still says Gurobi's row wants a spike before
it is relied on. #418 shipped a real Gurobi sink since, so that caveat is
probably obsolete — but exercising it is not this change, and asserting
capabilities I have not run is how that table would come to lie.
---
 bench/results/density.jsonl  | 166 ++----
 bench/results/latest.jsonl   | 998 ++++++++++++-----------------------
 bench/results/scaling.jsonl  |  74 +--
 docs/benchmarks-scaling.html |   2 +-
 docs/benchmarks.md           | 246 ++++-----
 5 files changed, 552 insertions(+), 934 deletions(-)

diff --git a/bench/results/density.jsonl b/bench/results/density.jsonl
index 1c1675b15..6a03fe256 100644
--- a/bench/results/density.jsonl
+++ b/bench/results/density.jsonl
@@ -1,109 +1,57 @@
-{"record": "run", "platform": "macOS-26.2-arm64-arm-64bit-Mach-O", "machine": "arm64", "processor": "arm", "python": "3.13.2", "versions": {"lpspec": "0.0.0a27.dev30+g771c5f403", "linopy": "0.8.0.post1.dev140+g346943317", "duckdb": "1.5.5", "highspy": "1.15.1", "polars": "1.43.0", "pandas": "3.0.5", "numpy": "2.5.1", "xarray": "2026.7.0", "pyarrow": "25.0.0"}, "commits": {"lpspec": "ef8558c-dirty", "duckdb": "4a13d38"}}
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diff --git a/bench/results/latest.jsonl b/bench/results/latest.jsonl
index 923cd7272..392613c3c 100644
--- a/bench/results/latest.jsonl
+++ b/bench/results/latest.jsonl
@@ -1,655 +1,343 @@
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diff --git a/bench/results/scaling.jsonl b/bench/results/scaling.jsonl
index 374e8451e..7e433b998 100644
--- a/bench/results/scaling.jsonl
+++ b/bench/results/scaling.jsonl
@@ -1,49 +1,25 @@
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+{"case": "dispatch", "size": "xs", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 100}, "nominal_variables": 10000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 733385, "phases": {"import": 0.20211295795161277, "build": 0.19540149997919798, "emit": 0.00810987502336502}, "counts": {"columns": 10000, "rows": 100, "nonzeros": null}, "wall_seconds": 0.203511375002563, "live_fraction": 1.0, "peak_rss_bytes": 221904896, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "s", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 1000}, "nominal_variables": 100000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 7346570, "phases": {"import": 0.10136437497567385, "build": 0.013775375089608133, "emit": 0.012658999999985099, "teardown": 5.166977643966675e-06}, "counts": {"columns": 100000, "rows": 1000, "nonzeros": 100000}, "wall_seconds": 0.0264395420672372, "live_fraction": 1.0, "peak_rss_bytes": 209715200, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "s", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 1000}, "nominal_variables": 100000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 7346570, "phases": {"import": 0.1031743329949677, "build": 0.013054749928414822, "emit": 0.01291487505659461, "teardown": 5.750101990997791e-06}, "counts": {"columns": 100000, "rows": 1000, "nonzeros": 100000}, "wall_seconds": 0.02597537508700043, "live_fraction": 1.0, "peak_rss_bytes": 209485824, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "s", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 1000}, "nominal_variables": 100000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 7646573, "phases": {"import": 0.20055591606069356, "build": 0.19690654193982482, "emit": 0.018495582975447178}, "counts": {"columns": 100000, "rows": 1000, "nonzeros": null}, "wall_seconds": 0.215402124915272, "live_fraction": 1.0, "peak_rss_bytes": 269320192, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "s", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 1000}, "nominal_variables": 100000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 7646573, "phases": {"import": 0.2035621249815449, "build": 0.19687470805365592, "emit": 0.021992750000208616}, "counts": {"columns": 100000, "rows": 1000, "nonzeros": null}, "wall_seconds": 0.21886745805386454, "live_fraction": 1.0, "peak_rss_bytes": 264306688, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "m", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 10000}, "nominal_variables": 1000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 76375489, "phases": {"import": 0.10157858300954103, "build": 0.030991583946160972, "emit": 0.09160854108631611, "teardown": 5.375011824071407e-06}, "counts": {"columns": 1000000, "rows": 10000, "nonzeros": 1000000}, "wall_seconds": 0.12260550004430115, "live_fraction": 1.0, "peak_rss_bytes": 438435840, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "m", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 10000}, "nominal_variables": 1000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 76375489, "phases": {"import": 0.10058554098941386, "build": 0.0305287919472903, "emit": 0.09771470807027072, "teardown": 4.665926098823547e-06}, "counts": {"columns": 1000000, "rows": 10000, "nonzeros": 1000000}, "wall_seconds": 0.12824816594365984, "live_fraction": 1.0, "peak_rss_bytes": 436731904, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "m", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 10000}, "nominal_variables": 1000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 79375492, "phases": {"import": 0.20470212493091822, "build": 0.20543604204431176, "emit": 0.1422153749736026}, "counts": {"columns": 1000000, "rows": 10000, "nonzeros": null}, "wall_seconds": 0.34765141701791435, "live_fraction": 1.0, "peak_rss_bytes": 582483968, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "m", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 10000}, "nominal_variables": 1000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 79375492, "phases": {"import": 0.210925874998793, "build": 0.2028352910419926, "emit": 0.13125012500677258}, "counts": {"columns": 1000000, "rows": 10000, "nonzeros": null}, "wall_seconds": 0.3340854160487652, "live_fraction": 1.0, "peak_rss_bytes": 575160320, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "l", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 100000}, "nominal_variables": 10000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 796454817, "phases": {"import": 0.10155683301854879, "build": 0.1719499999890104, "emit": 0.9183232079958543, "teardown": 1.4041084796190262e-05}, "counts": {"columns": 10000000, "rows": 100000, "nonzeros": 10000000}, "wall_seconds": 1.090287249069661, "live_fraction": 1.0, "peak_rss_bytes": 1586151424, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "l", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 100000}, "nominal_variables": 10000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 796454817, "phases": {"import": 0.10115187498740852, "build": 0.1654730000300333, "emit": 0.9520032909931615, "teardown": 9.541981853544712e-06}, "counts": {"columns": 10000000, "rows": 100000, "nonzeros": 10000000}, "wall_seconds": 1.1174858330050483, "live_fraction": 1.0, "peak_rss_bytes": 1574043648, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "l", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 100000}, "nominal_variables": 10000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 826454820, "phases": {"import": 0.20129970810376108, "build": 0.2662983339978382, "emit": 1.384374332963489}, "counts": {"columns": 10000000, "rows": 100000, "nonzeros": null}, "wall_seconds": 1.6506726669613272, "live_fraction": 1.0, "peak_rss_bytes": 2152464384, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "l", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 100000}, "nominal_variables": 10000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 826454820, "phases": {"import": 0.20416991598904133, "build": 0.26440395903773606, "emit": 1.408610500046052}, "counts": {"columns": 10000000, "rows": 100000, "nonzeros": null}, "wall_seconds": 1.673014459083788, "live_fraction": 1.0, "peak_rss_bytes": 2253520896, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "xl", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 400000}, "nominal_variables": 40000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 3285751292, "phases": {"import": 0.10006733401678503, "build": 0.588497166056186, "emit": 4.019390708999708, "teardown": 1.3833981938660145e-05}, "counts": {"columns": 40000000, "rows": 400000, "nonzeros": 40000000}, "wall_seconds": 4.607901709037833, "live_fraction": 1.0, "peak_rss_bytes": 5420695552, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "xl", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 400000}, "nominal_variables": 40000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 3285751292, "phases": {"import": 0.10066075006034225, "build": 0.5781799589749426, "emit": 3.9573320409981534, "teardown": 1.0958989150822163e-05}, "counts": {"columns": 40000000, "rows": 400000, "nonzeros": 40000000}, "wall_seconds": 4.535522958962247, "live_fraction": 1.0, "peak_rss_bytes": 5422514176, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "xl", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 400000}, "nominal_variables": 40000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 3405751295, "phases": {"import": 0.20385670801624656, "build": 0.5029340420151129, "emit": 6.542074249940924}, "counts": {"columns": 40000000, "rows": 400000, "nonzeros": null}, "wall_seconds": 7.045008291956037, "live_fraction": 1.0, "peak_rss_bytes": 6515064832, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "xl", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 400000}, "nominal_variables": 40000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 3405751295, "phases": {"import": 0.2039495409699157, "build": 0.47699212504085153, "emit": 6.4347698339261115}, "counts": {"columns": 40000000, "rows": 400000, "nonzeros": null}, "wall_seconds": 6.911761958966963, "live_fraction": 1.0, "peak_rss_bytes": 7255490560, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "2xl", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 1200000}, "nominal_variables": 120000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 9971142786, "phases": {"import": 0.10166595806367695, "build": 1.9270675419829786, "emit": 18.30700670799706, "teardown": 0.0001909160055220127}, "counts": {"columns": 120000000, "rows": 1200000, "nonzeros": 120000000}, "wall_seconds": 20.234265165985562, "live_fraction": 1.0, "peak_rss_bytes": 7284588544, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "2xl", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 1200000}, "nominal_variables": 120000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 9971142786, "phases": {"import": 0.1499241249402985, "build": 2.0317505840212107, "emit": 16.352403500000946, "teardown": 0.0004467080580070615}, "counts": {"columns": 120000000, "rows": 1200000, "nonzeros": 120000000}, "wall_seconds": 18.384600792080164, "live_fraction": 1.0, "peak_rss_bytes": 7928315904, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "2xl", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 1200000}, "nominal_variables": 120000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 10331142789, "phases": {"import": 0.32708783401176333, "build": 1.0432504579657689, "emit": 52.408572792075574}, "counts": {"columns": 120000000, "rows": 1200000, "nonzeros": null}, "wall_seconds": 53.45182325004134, "live_fraction": 1.0, "peak_rss_bytes": 9288663040, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "2xl", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 1200000}, "nominal_variables": 120000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 10331142789, "phases": {"import": 0.28709195903502405, "build": 1.0065649580210447, "emit": 37.641629667021334}, "counts": {"columns": 120000000, "rows": 1200000, "nonzeros": null}, "wall_seconds": 38.64819462504238, "live_fraction": 1.0, "peak_rss_bytes": 12301271040, "threads": 8, "record": "timing", "repeat": 1}
diff --git a/docs/benchmarks-scaling.html b/docs/benchmarks-scaling.html
index 2e50f895f..ec800590e 100644
--- a/docs/benchmarks-scaling.html
+++ b/docs/benchmarks-scaling.html
@@ -197,7 +197,7 @@ <h2>The numbers</h2>
 </style>
 
 <script>
-const DATA = {"scaling": {"vars": [10000, 100000, 1000000, 10000000, 40000000, 120000000], "wall": {"polars": [0.015, 0.027, 0.128, 1.123, 5.989, 35.358], "linopy": [0.21, 0.218, 0.34, 1.538, 8.805, 106.226]}, "peak": {"polars": [0.17, 0.212, 0.468, 2.04, 5.978, 8.301], "linopy": [0.214, 0.261, 0.564, 2.134, 7.922, 7.775]}}, "cases": {"dispatch": {"vars": [10000, 100000, 1000000, 10000000], "wall": {"polars": [0.017, 0.022, 0.084, 0.687], "linopy": [0.207, 0.219, 0.374, 1.93]}, "peak": {"polars": [0.168, 0.208, 0.52, 3.127], "linopy": [0.201, 0.229, 0.495, 3.304]}}, "fleet": {"vars": [12000, 120000, 1200000, 12000000], "wall": {"polars": [0.044, 0.057, 0.177, 1.481], "linopy": [0.288, 0.322, 0.578, 3.404]}, "peak": {"polars": [0.174, 0.231, 0.653, 3.764], "linopy": [0.203, 0.246, 0.703, 4.871]}}, "nodal": {"vars": [3000, 30000, 300000, 3000000], "wall": {"polars": [0.017, 0.02, 0.048, 0.491], "linopy": [0.213, 0.232, 0.298, 1.339]}, "peak": {"polars": [0.167, 0.186, 0.333, 1.42], "linopy": [0.202, 0.213, 0.352, 1.709]}}, "profiled": {"vars": [12000, 120000, 1200000, 12000000], "wall": {"polars": [0.022, 0.044, 0.228, 2.843], "linopy": [0.286, 0.281, 0.459, 2.613]}, "peak": {"polars": [0.174, 0.261, 0.836, 4.114], "linopy": [0.205, 0.247, 0.642, 4.73]}}, "sector": {"vars": [1000, 10000, 100000, 1000000], "wall": {"polars": [0.02, 0.025, 0.049, 0.38], "linopy": [0.225, 0.232, 0.333, 1.248]}, "peak": {"polars": [0.168, 0.19, 0.342, 0.946], "linopy": [0.203, 0.22, 0.493, 2.978]}}, "transport": {"vars": [9800, 98000, 980000, 9800000], "wall": {"polars": [0.024, 0.035, 0.142, 1.552], "linopy": [0.243, 0.26, 0.469, 2.61]}, "peak": {"polars": [0.174, 0.221, 0.596, 3.089], "linopy": [0.204, 0.234, 0.565, 3.952]}}}, "caseNames": ["dispatch", "fleet", "nodal", "profiled", "sector", "transport"], "rungs": ["xs", "s", "m", "l"]};
+const DATA = {"scaling": {"vars": [10000, 100000, 1000000, 10000000, 40000000, 120000000], "wall": {"polars": [0.015, 0.026, 0.123, 1.09, 4.536, 18.385], "linopy": [0.2, 0.215, 0.334, 1.651, 6.912, 38.648]}, "peak": {"polars": [0.169, 0.209, 0.437, 1.574, 5.421, 7.285], "linopy": [0.222, 0.264, 0.575, 2.152, 6.515, 9.289]}}, "cases": {"dispatch": {"vars": [10000, 100000, 1000000, 10000000], "wall": {"polars": [0.017, 0.022, 0.075, 0.585], "linopy": [0.203, 0.22, 0.361, 1.902]}, "peak": {"polars": [0.17, 0.204, 0.496, 2.886], "linopy": [0.206, 0.233, 0.499, 3.313]}}, "fleet": {"vars": [12000, 120000, 1200000, 12000000], "wall": {"polars": [0.042, 0.051, 0.145, 1.119], "linopy": [0.284, 0.307, 0.556, 3.148]}, "peak": {"polars": [0.174, 0.223, 0.61, 4.072], "linopy": [0.207, 0.251, 0.706, 5.377]}}, "nodal": {"vars": [3000, 30000, 300000, 3000000], "wall": {"polars": [0.018, 0.021, 0.046, 0.299], "linopy": [0.212, 0.217, 0.298, 1.08]}, "peak": {"polars": [0.169, 0.187, 0.331, 1.329], "linopy": [0.207, 0.218, 0.36, 1.775]}}, "profiled": {"vars": [12000, 120000, 1200000, 12000000], "wall": {"polars": [0.019, 0.033, 0.193, 1.83], "linopy": [0.211, 0.23, 0.466, 2.47]}, "peak": {"polars": [0.176, 0.263, 0.818, 3.909], "linopy": [0.209, 0.252, 0.643, 4.739]}}, "sector": {"vars": [1000, 10000, 100000, 1000000], "wall": {"polars": [0.02, 0.023, 0.045, 0.31], "linopy": [0.223, 0.229, 0.33, 1.485]}, "peak": {"polars": [0.17, 0.187, 0.307, 0.947], "linopy": [0.207, 0.227, 0.501, 2.971]}}, "transport": {"vars": [9800, 98000, 980000, 9800000], "wall": {"polars": [0.024, 0.032, 0.117, 1.098], "linopy": [0.233, 0.248, 0.432, 2.479]}, "peak": {"polars": [0.175, 0.223, 0.571, 2.923], "linopy": [0.208, 0.24, 0.56, 3.894]}}}, "caseNames": ["dispatch", "fleet", "nodal", "profiled", "sector", "transport"], "rungs": ["xs", "s", "m", "l"]};
 
 /* Two categorical slots, validated all-pairs in both modes (worst CVD dE 24.7
    light / 26.8 dark, worst normal-vision 33.6 / 31.8, both clear of the surface
diff --git a/docs/benchmarks.md b/docs/benchmarks.md
index 86f70beed..08b9b7270 100644
--- a/docs/benchmarks.md
+++ b/docs/benchmarks.md
@@ -43,10 +43,10 @@ while the laptop was doing other work and it inflated `profiled` by 55% —
 enough to turn "level" into "the one case we lose". Best of three, nothing else
 running.
 
-macOS-26.2-arm64-arm-64bit-Mach-O, python 3.13.2, 26 GB · polars 1.43.0 ·
-linopy 0.8.0.post1.dev140+g346943317 (the v1-semantics build, PyPSA/linopy#717)
-· highspy 1.15.1 · numpy 2.5.1. Parity gate: all six cases agree to 0.0e+00
-relative (`fleet` to 4.6e-16) before anything is timed.
+macOS-26.2-arm64-arm-64bit-Mach-O, python 3.13.2, 26 GB · lpspec 0.0.1a55 ·
+polars 1.43.0 · linopy 0.8.0.post1.dev140+g346943317 (the v1-semantics build,
+PyPSA/linopy#717) · highspy 1.15.1 · numpy 2.5.1. Parity gate: all six cases
+agree to 0.0e+00 relative (`fleet` to 4.6e-16) before anything is timed.
 
 *This lane replaced a duckdb engine, and the three-way comparison that decided
 it — speed against a settable memory ceiling — is in
@@ -62,10 +62,10 @@ Both arms end holding a populated `highspy.Highs` with `run()` never called: lps
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 10k | 100% | 100 | 0.02 s | 0.21 s | 0.08x | 0.17 GB | 0.20 GB | 0.83x | — |
-| 100k | 100% | 1k | 0.02 s | 0.22 s | 0.10x | 0.21 GB | 0.23 GB | 0.91x | — |
-| 1M | 100% | 10k | 0.08 s | 0.37 s | 0.23x | 0.52 GB | 0.50 GB | 1.06x | — |
-| 10M | 100% | 100k | 0.69 s | 1.93 s | 0.36x | 3.14 GB | 3.30 GB | 0.95x | — |
+| 10k | 100% | 100 | 0.02 s | 0.20 s | 0.08x | 0.17 GB | 0.21 GB | 0.83x | — |
+| 100k | 100% | 1k | 0.02 s | 0.22 s | 0.10x | 0.20 GB | 0.23 GB | 0.87x | — |
+| 1M | 100% | 10k | 0.08 s | 0.36 s | 0.21x | 0.50 GB | 0.50 GB | 0.99x | — |
+| 10M | 100% | 100k | 0.58 s | 1.90 s | 0.31x | 2.89 GB | 3.31 GB | 0.87x | — |
 
 ### dispatch — lp sink
 
@@ -73,10 +73,10 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 10k | 100% | 100 | 0.01 s | 0.21 s | 0.07x | 0.17 GB | 0.21 GB | 0.79x | 1 MB |
-| 100k | 100% | 1k | 0.03 s | 0.22 s | 0.13x | 0.21 GB | 0.26 GB | 0.81x | 7 MB |
-| 1M | 100% | 10k | 0.13 s | 0.35 s | 0.37x | 0.47 GB | 0.59 GB | 0.80x | 76 MB |
-| 10M | 100% | 100k | 1.11 s | 1.55 s | 0.72x | 2.02 GB | 2.25 GB | 0.90x | 796 MB |
+| 10k | 100% | 100 | 0.01 s | 0.21 s | 0.07x | 0.17 GB | 0.22 GB | 0.76x | 1 MB |
+| 100k | 100% | 1k | 0.03 s | 0.22 s | 0.12x | 0.21 GB | 0.27 GB | 0.77x | 7 MB |
+| 1M | 100% | 10k | 0.12 s | 0.34 s | 0.36x | 0.43 GB | 0.59 GB | 0.73x | 76 MB |
+| 10M | 100% | 100k | 1.09 s | 1.64 s | 0.67x | 1.58 GB | 2.20 GB | 0.72x | 796 MB |
 
 ### fleet — highs sink
 
@@ -84,10 +84,10 @@ Both arms end holding a populated `highspy.Highs` with `run()` never called: lps
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 12k | 100% | 6.02k | 0.04 s | 0.29 s | 0.15x | 0.17 GB | 0.20 GB | 0.86x | — |
-| 120k | 100% | 60.2k | 0.06 s | 0.32 s | 0.18x | 0.23 GB | 0.25 GB | 0.94x | — |
-| 1.2M | 100% | 602k | 0.18 s | 0.58 s | 0.31x | 0.65 GB | 0.70 GB | 0.93x | — |
-| 12M | 100% | 6.02M | 1.48 s | 3.40 s | 0.44x | 4.38 GB | 5.24 GB | 0.84x | — |
+| 12k | 100% | 6.02k | 0.04 s | 0.28 s | 0.15x | 0.17 GB | 0.21 GB | 0.84x | — |
+| 120k | 100% | 60.2k | 0.05 s | 0.31 s | 0.17x | 0.22 GB | 0.25 GB | 0.89x | — |
+| 1.2M | 100% | 602k | 0.15 s | 0.56 s | 0.26x | 0.61 GB | 0.71 GB | 0.86x | — |
+| 12M | 100% | 6.02M | 1.12 s | 3.15 s | 0.36x | 4.07 GB | 5.38 GB | 0.76x | — |
 
 ### fleet — lp sink
 
@@ -95,10 +95,10 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 12k | 100% | 6.02k | 0.04 s | 0.30 s | 0.14x | 0.18 GB | 0.22 GB | 0.82x | 1 MB |
-| 120k | 100% | 60.2k | 0.06 s | 0.32 s | 0.19x | 0.24 GB | 0.25 GB | 0.98x | 9 MB |
-| 1.2M | 100% | 602k | 0.24 s | 0.47 s | 0.51x | 0.67 GB | 0.45 GB | 1.49x | 89 MB |
-| 12M | 100% | 6.02M | 1.99 s | 1.93 s | 1.03x | 2.78 GB | 1.66 GB | 1.68x | 920 MB |
+| 12k | 100% | 6.02k | 0.04 s | 0.29 s | 0.14x | 0.18 GB | 0.22 GB | 0.79x | 1 MB |
+| 120k | 100% | 60.2k | 0.06 s | 0.31 s | 0.18x | 0.24 GB | 0.26 GB | 0.95x | 9 MB |
+| 1.2M | 100% | 602k | 0.21 s | 0.45 s | 0.46x | 0.63 GB | 0.46 GB | 1.39x | 89 MB |
+| 12M | 100% | 6.02M | 1.79 s | 1.99 s | 0.90x | 2.39 GB | 1.60 GB | 1.49x | 920 MB |
 
 ### nodal — highs sink
 
@@ -106,10 +106,10 @@ Both arms end holding a populated `highspy.Highs` with `run()` never called: lps
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 3k | 25% | 1k | 0.02 s | 0.21 s | 0.08x | 0.17 GB | 0.20 GB | 0.83x | — |
-| 30k | 25% | 10k | 0.02 s | 0.23 s | 0.09x | 0.19 GB | 0.21 GB | 0.87x | — |
-| 300k | 25% | 100k | 0.05 s | 0.30 s | 0.16x | 0.34 GB | 0.35 GB | 0.95x | — |
-| 3M | 25% | 1M | 0.49 s | 1.34 s | 0.37x | 1.42 GB | 1.71 GB | 0.83x | — |
+| 3k | 25% | 1k | 0.02 s | 0.21 s | 0.08x | 0.17 GB | 0.21 GB | 0.82x | — |
+| 30k | 25% | 10k | 0.02 s | 0.22 s | 0.10x | 0.19 GB | 0.22 GB | 0.86x | — |
+| 300k | 25% | 100k | 0.05 s | 0.30 s | 0.15x | 0.33 GB | 0.36 GB | 0.92x | — |
+| 3M | 25% | 1M | 0.30 s | 1.08 s | 0.28x | 1.35 GB | 1.78 GB | 0.76x | — |
 
 ### nodal — lp sink
 
@@ -117,10 +117,10 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 3k | 25% | 1k | 0.02 s | 0.21 s | 0.07x | 0.17 GB | 0.21 GB | 0.79x | 0 MB |
-| 30k | 25% | 10k | 0.02 s | 0.23 s | 0.09x | 0.19 GB | 0.24 GB | 0.81x | 2 MB |
-| 300k | 25% | 100k | 0.07 s | 0.28 s | 0.25x | 0.32 GB | 0.45 GB | 0.71x | 25 MB |
-| 3M | 25% | 1M | 0.63 s | 0.84 s | 0.74x | 1.19 GB | 1.46 GB | 0.82x | 264 MB |
+| 3k | 25% | 1k | 0.02 s | 0.21 s | 0.07x | 0.17 GB | 0.22 GB | 0.76x | 0 MB |
+| 30k | 25% | 10k | 0.02 s | 0.22 s | 0.09x | 0.19 GB | 0.25 GB | 0.77x | 2 MB |
+| 300k | 25% | 100k | 0.07 s | 0.28 s | 0.25x | 0.32 GB | 0.46 GB | 0.69x | 25 MB |
+| 3M | 25% | 1M | 0.52 s | 0.84 s | 0.62x | 1.06 GB | 1.57 GB | 0.68x | 264 MB |
 
 ### profiled — highs sink
 
@@ -128,10 +128,10 @@ Both arms end holding a populated `highspy.Highs` with `run()` never called: lps
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 12k | 100% | 1k | 0.02 s | 0.29 s | 0.08x | 0.17 GB | 0.21 GB | 0.85x | — |
-| 120k | 100% | 10k | 0.04 s | 0.28 s | 0.16x | 0.26 GB | 0.25 GB | 1.06x | — |
-| 1.2M | 100% | 100k | 0.23 s | 0.46 s | 0.50x | 0.84 GB | 0.64 GB | 1.30x | — |
-| 12M | 100% | 1M | 2.84 s | 2.61 s | 1.09x | 4.15 GB | 4.73 GB | 0.88x | — |
+| 12k | 100% | 1k | 0.02 s | 0.21 s | 0.09x | 0.18 GB | 0.21 GB | 0.84x | — |
+| 120k | 100% | 10k | 0.03 s | 0.23 s | 0.14x | 0.26 GB | 0.25 GB | 1.04x | — |
+| 1.2M | 100% | 100k | 0.19 s | 0.47 s | 0.41x | 0.82 GB | 0.65 GB | 1.27x | — |
+| 12M | 100% | 1M | 1.83 s | 2.47 s | 0.74x | 3.91 GB | 4.74 GB | 0.82x | — |
 
 ### profiled — lp sink
 
@@ -139,10 +139,10 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 12k | 100% | 1k | 0.02 s | 0.22 s | 0.09x | 0.18 GB | 0.22 GB | 0.81x | 1 MB |
-| 120k | 100% | 10k | 0.04 s | 0.25 s | 0.17x | 0.26 GB | 0.30 GB | 0.88x | 9 MB |
-| 1.2M | 100% | 100k | 0.33 s | 0.51 s | 0.64x | 0.71 GB | 0.72 GB | 0.99x | 95 MB |
-| 12M | 100% | 1M | 4.48 s | 3.06 s | 1.46x | 3.19 GB | 3.14 GB | 1.02x | 986 MB |
+| 12k | 100% | 1k | 0.02 s | 0.21 s | 0.08x | 0.18 GB | 0.23 GB | 0.78x | 1 MB |
+| 120k | 100% | 10k | 0.04 s | 0.23 s | 0.17x | 0.26 GB | 0.30 GB | 0.87x | 9 MB |
+| 1.2M | 100% | 100k | 0.28 s | 0.42 s | 0.66x | 0.73 GB | 0.69 GB | 1.07x | 95 MB |
+| 12M | 100% | 1M | 2.88 s | 2.20 s | 1.31x | 2.44 GB | 3.14 GB | 0.78x | 986 MB |
 
 ### sector — highs sink
 
@@ -150,10 +150,10 @@ Both arms end holding a populated `highspy.Highs` with `run()` never called: lps
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 1k | 6% | 1k | 0.02 s | 0.23 s | 0.09x | 0.17 GB | 0.20 GB | 0.83x | — |
-| 10k | 6% | 10k | 0.02 s | 0.23 s | 0.11x | 0.19 GB | 0.22 GB | 0.86x | — |
-| 100k | 6% | 100k | 0.05 s | 0.33 s | 0.15x | 0.34 GB | 0.49 GB | 0.69x | — |
-| 1M | 6% | 1M | 0.38 s | 1.25 s | 0.30x | 0.95 GB | 2.98 GB | 0.32x | — |
+| 1k | 6% | 1k | 0.02 s | 0.22 s | 0.09x | 0.17 GB | 0.21 GB | 0.82x | — |
+| 10k | 6% | 10k | 0.02 s | 0.23 s | 0.10x | 0.19 GB | 0.23 GB | 0.83x | — |
+| 100k | 6% | 100k | 0.04 s | 0.33 s | 0.14x | 0.31 GB | 0.50 GB | 0.61x | — |
+| 1M | 6% | 1M | 0.31 s | 1.48 s | 0.21x | 0.96 GB | 2.97 GB | 0.32x | — |
 
 ### sector — lp sink
 
@@ -161,10 +161,10 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 1k | 6% | 1k | 0.02 s | 0.23 s | 0.07x | 0.17 GB | 0.21 GB | 0.79x | 0 MB |
-| 10k | 6% | 10k | 0.02 s | 0.24 s | 0.09x | 0.19 GB | 0.24 GB | 0.79x | 1 MB |
-| 100k | 6% | 100k | 0.07 s | 0.31 s | 0.24x | 0.34 GB | 0.52 GB | 0.65x | 12 MB |
-| 1M | 6% | 1M | 0.62 s | 1.14 s | 0.55x | 0.93 GB | 2.91 GB | 0.32x | 120 MB |
+| 1k | 6% | 1k | 0.02 s | 0.22 s | 0.08x | 0.17 GB | 0.22 GB | 0.77x | 0 MB |
+| 10k | 6% | 10k | 0.02 s | 0.23 s | 0.09x | 0.19 GB | 0.25 GB | 0.75x | 1 MB |
+| 100k | 6% | 100k | 0.05 s | 0.31 s | 0.16x | 0.30 GB | 0.53 GB | 0.58x | 12 MB |
+| 1M | 6% | 1M | 0.39 s | 1.28 s | 0.30x | 0.94 GB | 2.91 GB | 0.32x | 120 MB |
 
 ### transport — highs sink
 
@@ -172,10 +172,10 @@ Both arms end holding a populated `highspy.Highs` with `run()` never called: lps
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 9.8k | 100% | 1.4k | 0.02 s | 0.24 s | 0.10x | 0.17 GB | 0.20 GB | 0.85x | — |
-| 98k | 100% | 14k | 0.03 s | 0.26 s | 0.13x | 0.22 GB | 0.23 GB | 0.95x | — |
-| 980k | 100% | 140k | 0.14 s | 0.47 s | 0.30x | 0.60 GB | 0.57 GB | 1.05x | — |
-| 9.8M | 100% | 1.4M | 1.55 s | 2.61 s | 0.59x | 3.14 GB | 3.95 GB | 0.80x | — |
+| 9.8k | 100% | 1.4k | 0.02 s | 0.23 s | 0.10x | 0.18 GB | 0.21 GB | 0.84x | — |
+| 98k | 100% | 14k | 0.03 s | 0.25 s | 0.13x | 0.22 GB | 0.24 GB | 0.93x | — |
+| 980k | 100% | 140k | 0.12 s | 0.43 s | 0.27x | 0.57 GB | 0.56 GB | 1.02x | — |
+| 9.8M | 100% | 1.4M | 1.10 s | 2.48 s | 0.44x | 2.99 GB | 3.90 GB | 0.77x | — |
 
 ### transport — lp sink
 
@@ -183,38 +183,38 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 9.8k | 100% | 1.4k | 0.02 s | 0.23 s | 0.10x | 0.18 GB | 0.22 GB | 0.81x | 1 MB |
-| 98k | 100% | 14k | 0.04 s | 0.25 s | 0.15x | 0.23 GB | 0.29 GB | 0.81x | 8 MB |
-| 980k | 100% | 140k | 0.27 s | 0.50 s | 0.55x | 0.55 GB | 0.66 GB | 0.84x | 79 MB |
-| 9.8M | 100% | 1.4M | 2.37 s | 2.49 s | 0.95x | 2.20 GB | 1.85 GB | 1.19x | 820 MB |
+| 9.8k | 100% | 1.4k | 0.02 s | 0.23 s | 0.10x | 0.18 GB | 0.23 GB | 0.78x | 1 MB |
+| 98k | 100% | 14k | 0.04 s | 0.24 s | 0.15x | 0.23 GB | 0.29 GB | 0.80x | 8 MB |
+| 980k | 100% | 140k | 0.19 s | 0.40 s | 0.47x | 0.54 GB | 0.67 GB | 0.82x | 79 MB |
+| 9.8M | 100% | 1.4M | 1.76 s | 2.14 s | 0.82x | 1.90 GB | 1.78 GB | 1.07x | 820 MB |
 
 ## What this says
 
-**Ahead on peak on all six models and on wall on five**, at the `l` rung through
-the sink most callers use:
+**Ahead on both, on all six models**, at the `l` rung through the sink most
+callers use:
 
 | | dispatch | fleet | nodal | profiled | sector | transport |
 |---|---|---|---|---|---|---|
-| wall | **0.36x** | **0.44x** | **0.37x** | 1.09x | **0.30x** | **0.59x** |
-| peak | **0.95x** | **0.77x** | **0.83x** | **0.87x** | **0.32x** | **0.78x** |
-
-**`profiled` is the case in the ladder to be lost.** It is level here — 2.84 s
-against 2.61, from a case whose own repeats span 2.33–2.84 s at ~4 GB resident —
-and an unambiguous 1.46x through the LP sink, where no HiGHS copy dilutes it. A
-parameter dense over the whole variable product is the array xarray already
-wants and a full-size join for us. It is in the set on purpose.
-
-**The LP file is the weaker route.** Three numbers are against us there:
-`profiled` 1.46x and `fleet` 1.03x on wall, `fleet` 1.64x and `transport` 1.19x
-on peak. What is left is structural in two ways — most of an LP write is turning
+| wall | **0.31x** | **0.36x** | **0.28x** | **0.74x** | **0.21x** | **0.44x** |
+| peak | **0.87x** | **0.76x** | **0.75x** | **0.82x** | **0.32x** | **0.75x** |
+
+**`profiled` is no longer the case in the ladder we lose**, and it is worth
+saying why rather than deleting the sentence that said we did. It was level
+through this sink (1.09x) and an unambiguous loss through the LP one; it is now
+0.74x and 1.31x. A parameter dense over the whole variable product is the array
+xarray already wants and a full-size join for us — the shape has not changed,
+the joins got cheaper. It stays in the set for the same reason it was put there.
+
+**The LP file is still the weaker route**, and two numbers are against us there:
+`profiled` **1.31x** on wall, and `fleet` **1.47x** on peak with `transport` at
+1.07x. What is left is structural in two ways — most of an LP write is turning
 doubles into text, work neither lane avoids, so the wall ratio compresses toward
 1.00 however fast the build gets; and COO carries a `(row, col, coeff)` triple
-per nonzero where a dense array carries one float, which is `fleet`'s 1.64x.
-The many-declaration shape is the one that shows it, which is why that case
-exists.
+per nonzero where a dense array carries one float, which is `fleet`'s 1.47x. The
+many-declaration shape is the one that shows it, which is why that case exists.
 
 **Sparsity is what separates the peak numbers**, not size. At the same rung
-`sector` is 0.32x of linopy's peak and `dispatch` 0.95x: a coordinate that does
+`sector` is 0.32x of linopy's peak and `dispatch` 0.87x: a coordinate that does
 not exist is an absent row here and a NaN in a dense array there, so the gap
 tracks how much of the coordinate product a model actually uses.
 
@@ -231,30 +231,30 @@ Build only, repeated in one process. **first** is what a caller pays who builds
 
 | case | vars | lpspec: first | lpspec: steady | linopy: first | linopy: steady | steady vs linopy |
 |---|---|---|---|---|---|
-| transport | 9.8k | 28.8 ms | **13.7 ms** | 289.9 ms | 34.7 ms | 0.39x |
-| dispatch | 10k | 166.1 ms | **5.7 ms** | 449.0 ms | 13.8 ms | 0.41x |
-| profiled | 12k | 14.9 ms | **7.8 ms** | 205.7 ms | 19.4 ms | 0.40x |
-| nodal | 12k | 14.3 ms | **7.1 ms** | 224.0 ms | 19.1 ms | 0.37x |
-| fleet | 12k | 43.8 ms | **32.1 ms** | 293.4 ms | 95.5 ms | 0.34x |
-| sector | 17k | 108.6 ms | **9.4 ms** | 455.4 ms | 23.9 ms | 0.39x |
-| transport | 98k | 24.3 ms | **18.0 ms** | 228.8 ms | 37.7 ms | 0.48x |
-| dispatch | 100k | 15.3 ms | **7.9 ms** | 199.9 ms | 14.3 ms | 0.56x |
-| profiled | 120k | 26.3 ms | **18.0 ms** | 217.5 ms | 21.2 ms | 0.85x |
-| nodal | 120k | 15.1 ms | **8.6 ms** | 211.0 ms | 20.8 ms | 0.41x |
-| fleet | 120k | 44.6 ms | **37.5 ms** | 283.8 ms | 98.1 ms | 0.38x |
-| sector | 170k | 19.7 ms | **12.6 ms** | 221.4 ms | 28.4 ms | 0.44x |
-| transport | 980k | 78.6 ms | **69.4 ms** | 251.6 ms | 62.4 ms | 1.11x |
-| dispatch | 1M | 28.2 ms | **18.3 ms** | 209.0 ms | 21.0 ms | 0.87x |
-| profiled | 1.2M | 150.8 ms | **130.6 ms** | 238.5 ms | 39.1 ms | 3.34x |
-| fleet | 1.2M | 90.4 ms | **78.5 ms** | 294.2 ms | 105.7 ms | 0.74x |
-| nodal | 1.2M | 27.9 ms | **20.5 ms** | 220.5 ms | 30.2 ms | 0.68x |
-| sector | 1.7M | 38.3 ms | **31.7 ms** | 267.1 ms | 62.5 ms | 0.51x |
-| transport | 9.8M | 783.1 ms | **933.5 ms** | 654.9 ms | 406.4 ms | 2.30x |
-| dispatch | 10M | 157.9 ms | **137.0 ms** | 280.1 ms | 85.9 ms | 1.60x |
-| profiled | 12M | 1868.8 ms | **2059.1 ms** | 581.3 ms | 269.3 ms | 7.65x |
-| fleet | 12M | 651.4 ms | **668.9 ms** | 507.5 ms | 206.2 ms | 3.24x |
-| nodal | 12M | 178.0 ms | **182.8 ms** | 410.7 ms | 140.5 ms | 1.30x |
-| sector | 17M | 265.9 ms | **287.9 ms** | 878.9 ms | 573.9 ms | 0.50x |
+| transport | 9.8k | 23.0 ms | **15.3 ms** | 262.7 ms | 38.3 ms | 0.40x |
+| dispatch | 10k | 11.0 ms | **6.0 ms** | 208.2 ms | 13.9 ms | 0.44x |
+| fleet | 12k | 40.5 ms | **33.8 ms** | 308.6 ms | 101.9 ms | 0.33x |
+| nodal | 12k | 14.9 ms | **9.1 ms** | 231.0 ms | 18.8 ms | 0.49x |
+| profiled | 12k | 14.4 ms | **7.6 ms** | 199.6 ms | 18.5 ms | 0.41x |
+| sector | 17k | 13.7 ms | **9.0 ms** | 212.2 ms | 23.6 ms | 0.38x |
+| transport | 98k | 29.0 ms | **22.6 ms** | 320.9 ms | 54.3 ms | 0.42x |
+| dispatch | 100k | 15.0 ms | **9.1 ms** | 214.9 ms | 14.8 ms | 0.61x |
+| profiled | 120k | 25.8 ms | **17.9 ms** | 206.6 ms | 20.0 ms | 0.90x |
+| fleet | 120k | 47.1 ms | **38.0 ms** | 305.5 ms | 102.3 ms | 0.37x |
+| nodal | 120k | 15.3 ms | **8.8 ms** | 208.8 ms | 19.4 ms | 0.46x |
+| sector | 170k | 16.4 ms | **11.2 ms** | 213.0 ms | 28.4 ms | 0.39x |
+| transport | 980k | 264.5 ms | **183.2 ms** | 454.7 ms | 110.7 ms | 1.66x |
+| dispatch | 1M | 33.8 ms | **25.0 ms** | 217.0 ms | 20.6 ms | 1.22x |
+| fleet | 1.2M | 88.0 ms | **73.9 ms** | 314.3 ms | 108.8 ms | 0.68x |
+| nodal | 1.2M | 28.9 ms | **19.3 ms** | 222.1 ms | 29.9 ms | 0.65x |
+| profiled | 1.2M | 134.6 ms | **117.8 ms** | 225.5 ms | 35.1 ms | 3.35x |
+| sector | 1.7M | 35.6 ms | **28.3 ms** | 285.6 ms | 78.2 ms | 0.36x |
+| transport | 9.8M | 1596.5 ms | **1675.4 ms** | 966.3 ms | 601.4 ms | 2.79x |
+| dispatch | 10M | 190.1 ms | **184.2 ms** | 318.3 ms | 75.8 ms | 2.43x |
+| profiled | 12M | 1233.5 ms | **1251.1 ms** | 478.2 ms | 198.6 ms | 6.30x |
+| fleet | 12M | 511.0 ms | **489.3 ms** | 437.4 ms | 182.4 ms | 2.68x |
+| nodal | 12M | 165.2 ms | **150.6 ms** | 363.9 ms | 140.5 ms | 1.07x |
+| sector | 17M | 264.4 ms | **314.3 ms** | 1039.9 ms | 559.4 ms | 0.56x |
 
 ## Absurd sizes
 
@@ -264,28 +264,34 @@ plotted in [benchmarks-scaling.html](benchmarks-scaling.html):
 
 | variables | lpspec | linopy | wall | peak |
 |---|---|---|---|---|
-| 10k | **0.02 s** / 0.17 GB | 0.21 s / 0.21 GB | **0.07x** | **0.79x** |
-| 100k | **0.03 s** / 0.21 GB | 0.22 s / 0.26 GB | **0.12x** | **0.81x** |
-| 1M | **0.13 s** / 0.47 GB | 0.34 s / 0.56 GB | **0.38x** | **0.83x** |
-| 10M | **1.12 s** / 2.04 GB | 1.54 s / 2.13 GB | **0.73x** | **0.96x** |
-| 40M | **5.99 s** / 5.98 GB | 8.80 s / 7.92 GB | **0.68x** | **0.75x** |
-| 120M | **35.36 s** / 8.30 GB | 106.23 s / 7.77 GB | **0.33x** | 1.07x |
+| 10k | **0.01 s** / 0.17 GB | 0.20 s / 0.22 GB | **0.07x** | **0.76x** |
+| 100k | **0.03 s** / 0.21 GB | 0.22 s / 0.26 GB | **0.12x** | **0.79x** |
+| 1M | **0.12 s** / 0.44 GB | 0.33 s / 0.58 GB | **0.37x** | **0.76x** |
+| 10M | **1.09 s** / 1.57 GB | 1.65 s / 2.15 GB | **0.66x** | **0.73x** |
+| 40M | **4.54 s** / 5.42 GB | 6.91 s / 6.52 GB | **0.66x** | **0.83x** |
+| 120M | **18.38 s** / 7.28 GB | 38.65 s / 9.29 GB | **0.48x** | **0.78x** |
 
 **Nothing falls over**, on either lane, at a 9.97 GB LP file. The wall ratio
-does not decay with size — it is 0.33x at 120M against 0.73x at 10M, because
-linopy's curve steepens above 10M and this one does not.
-
-**Peak is where the advantage runs out.** 1.07x at 120M: past a certain size
-both lanes are holding the same model, and the representation stops deciding
-anything. Whatever memory headroom this lane has over the eager one is a
-small-and-sparse-model property, not a scaling one — which is the honest
-reading of the `sector`-against-`dispatch` spread above, at a size where it can
-no longer hide.
-
-*The `2xl` rung is noisy between runs* — this lane read 20.6 s once and 35.4 s
-another time, linopy 38.5 s and 106.2 s — because 8-10 GB of peak on a 26 GB
-machine is where other things start to matter. Read the ordering, not the
-seconds.
+does not decay with size — 0.48x at 120M against 0.66x at 10M, because linopy's
+curve steepens above 10M and this one does not.
+
+**Peak does not run out, and this page used to say it did.** The previous
+version of this section read 1.07x at 120M and concluded that "whatever memory
+headroom this lane has over the eager one is a small-and-sparse-model property,
+not a scaling one". That conclusion does not survive re-measurement: peak is
+0.73-0.83x across four orders of magnitude, 0.78x at the top rung.
+
+Two things moved it, and only one of them is us. `cols` became positional
+([#433](https://github.com/FBumann/lpspec/pull/433)) and took ~20% off this
+case's peak. The rest is that the earlier reading was taken in a run *this
+section itself flagged as noisy* — it recorded linopy at 38.5 s and 106.2 s for
+the same rung. The honest summary is that the old 1.07x was a conclusion drawn
+across the noise floor, and the caveat below was already telling the reader not
+to trust it.
+
+*The `2xl` rung is still the noisiest* — 8-10 GB of peak on a 26 GB machine is
+where other things start to matter, and it is best-of-two rather than
+best-of-three. Read the ordering, not the seconds.
 
 ## The density sweep, and the claim it used to refuse
 
@@ -297,13 +303,13 @@ the 12 technologies each node has installed.
 
 | case | live | variables | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak |
 |---|---|---|---|---|---|---|---|---|
-| nodal | 100% | 1.2M | 0.22 s | 0.44 s | 0.50x | 0.58 GB | 0.64 GB | 0.91x |
-| nodal | 50% | 600k | 0.12 s | 0.31 s | 0.38x | 0.43 GB | 0.59 GB | 0.72x |
-| nodal | 25% | 300k | 0.07 s | 0.29 s | 0.23x | 0.32 GB | 0.45 GB | 0.72x |
-| nodal | 8% | 100k | 0.04 s | 0.25 s | 0.17x | 0.26 GB | 0.34 GB | 0.78x |
+| nodal | 100% | 1.2M | 0.17 s | 0.39 s | 0.45x | 0.55 GB | 0.65 GB | 0.84x |
+| nodal | 50% | 600k | 0.11 s | 0.31 s | 0.34x | 0.42 GB | 0.61 GB | 0.69x |
+| nodal | 25% | 300k | 0.07 s | 0.27 s | 0.25x | 0.32 GB | 0.46 GB | 0.70x |
+| nodal | 8% | 100k | 0.04 s | 0.24 s | 0.16x | 0.26 GB | 0.35 GB | 0.74x |
 
-**It now does, and it did not before.** Wall time falls from 0.50x to 0.17x as
-density drops, and peak improves at every rung — 0.91x, 0.72x, 0.72x, 0.78x.
+**It now does, and it did not before.** Wall time falls from 0.45x to 0.16x as
+density drops, and peak improves at every rung — 0.84x, 0.69x, 0.70x, 0.74x.
 The previous run of this sweep had linopy's peak *below* ours at the sparsest
 rung, and the note here said so.
 

From 42fdd013285d16b48d6fa6904186b9710dab3177 Mon Sep 17 00:00:00 2001
From: FBumann <117816358+FBumann@users.noreply.github.com>
Date: Fri, 31 Jul 2026 20:49:20 +0200
Subject: [PATCH 2/2] docs(bench): re-measure at 98f382d, and correct a claim
 the harness bug made
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Every number on the page now comes from one run at `98f382d` on a clean tree,
and the page says so — the fingerprint hash is what makes a published number
traceable to the code that produced it, and the previous one recorded
`782f76b-dirty`, which identifies nothing.

**The `highs` comparison was not like for like, and it flattered us.** #438
found that linopy's `to_highspy()` was being timed *with* variable naming, which
neither of our solver sinks does — 82% of its hand-off, and memory as well as
time. Corrected:

    highs sink, l rung        was      now
    dispatch  peak           0.87x    1.46x
    fleet     peak           0.76x    1.10x
    profiled  peak           0.82x    1.27x
    transport peak           0.75x    1.10x

So the summary changes from "ahead on both, on all six" to **ahead on wall on
five of six, and behind on peak on four of six through `highs`**. HiGHS's own
dense model dominates both arms there and our COO triples are what is left. The
`lp` sink barely moved, because that comparison was already like for like, and
it is where the representation actually pays: ahead on peak on four of six.

`profiled` is the case in the ladder we lose, on both sinks (1.27x, 1.07x).
Said plainly rather than left to the tables.

The scaling section's reversal stands and is re-measured: peak 0.68-0.78x from
10k to 120M variables, against the 1.07x this page used to conclude the
advantage "runs out" from. That section now also says it is the LP sink, and
therefore not evidence for the `highs` peak row.
---
 bench/results/density.jsonl  | 166 ++----
 bench/results/latest.jsonl   | 998 ++++++++++++-----------------------
 bench/results/scaling.jsonl  |  74 +--
 docs/benchmarks-scaling.html |   2 +-
 docs/benchmarks.md           | 275 +++++-----
 5 files changed, 575 insertions(+), 940 deletions(-)

diff --git a/bench/results/density.jsonl b/bench/results/density.jsonl
index 1c1675b15..7d22c69df 100644
--- a/bench/results/density.jsonl
+++ b/bench/results/density.jsonl
@@ -1,109 +1,57 @@
-{"record": "run", "platform": "macOS-26.2-arm64-arm-64bit-Mach-O", "machine": "arm64", "processor": "arm", "python": "3.13.2", "versions": {"lpspec": "0.0.0a27.dev30+g771c5f403", "linopy": "0.8.0.post1.dev140+g346943317", "duckdb": "1.5.5", "highspy": "1.15.1", "polars": "1.43.0", "pandas": "3.0.5", "numpy": "2.5.1", "xarray": "2026.7.0", "pyarrow": "25.0.0"}, "commits": {"lpspec": "ef8558c-dirty", "duckdb": "4a13d38"}}
-{"case": "nodal", "size": "d100", "arm": "lpspec", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": null, "lp_bytes": 94886786, "phases": {"import": 0.19804308301536366, "build": 0.12666383397299796, "emit": 0.1572495410218835, "teardown": 3.029097570106387e-05}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": 1200000}, "wall_seconds": 0.2839436659705825, "live_fraction": 1.0, "peak_rss_bytes": 582238208, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d100", "arm": "lpspec", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": null, "lp_bytes": 94886786, "phases": {"import": 0.10722787503618747, "build": 0.04435220896266401, "emit": 0.17545595800038427, "teardown": 8.533301297575235e-05}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": 1200000}, "wall_seconds": 0.21989349997602403, "live_fraction": 1.0, "peak_rss_bytes": 579911680, "threads": 8, "record": "timing", "repeat": 1}
-{"case": "nodal", "size": "d100", "arm": "lpspec", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": null, "lp_bytes": 94886786, "phases": {"import": 0.10384145803982392, "build": 0.04481033398769796, "emit": 0.1988297079806216, "teardown": 4.470802377909422e-05}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": 1200000}, "wall_seconds": 0.24368474999209866, "live_fraction": 1.0, "peak_rss_bytes": 588890112, "threads": 8, "record": "timing", "repeat": 2}
-{"case": "nodal", "size": "d100", "arm": "linopy", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "memory_limit": null, "lp_bytes": 98486789, "phases": {"import": 0.26903583301464096, "build": 0.48749174998374656, "emit": 0.21823574998416007}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.7057274999679066, "live_fraction": 1.0, "peak_rss_bytes": 618119168, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d100", "arm": "linopy", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "memory_limit": null, "lp_bytes": 98486789, "phases": {"import": 0.18759308301378042, "build": 0.2225050840061158, "emit": 0.2193499580025673}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.4418550420086831, "live_fraction": 1.0, "peak_rss_bytes": 616349696, "threads": 8, "record": "timing", "repeat": 1}
-{"case": "nodal", "size": "d100", "arm": "linopy", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "memory_limit": null, "lp_bytes": 98486789, "phases": {"import": 0.18992425000760704, "build": 0.22027145797619596, "emit": 0.21994270803406835}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.4402141660102643, "live_fraction": 1.0, "peak_rss_bytes": 639942656, "threads": 8, "record": "timing", "repeat": 2}
-{"case": "nodal", "size": "d100", "arm": "duckdb", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": "-1", "lp_bytes": 94886786, "phases": {"import": 0.11163175001274794, "build": 0.6335797919891775, "emit": 0.1857317910180427, "teardown": 0.032159750000573695}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.8514713330077939, "live_fraction": 1.0, "peak_rss_bytes": 343654400, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d100", "arm": "duckdb@1GB", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": "1GB", "lp_bytes": 94886786, "phases": {"import": 0.07223258295562118, "build": 0.4596203750115819, "emit": 0.17623845802154392, "teardown": 0.04668983398005366}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.6825486670131795, "live_fraction": 1.0, "peak_rss_bytes": 327434240, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d100", "arm": "duckdb", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": "-1", "lp_bytes": 94886786, "phases": {"import": 0.0681040000054054, "build": 0.4507714169449173, "emit": 0.2863587500178255, "teardown": 0.03476704197237268}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.7718972089351155, "live_fraction": 1.0, "peak_rss_bytes": 342704128, "threads": 8, "record": "timing", "repeat": 1}
-{"case": "nodal", "size": "d100", "arm": "duckdb@1GB", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": "1GB", "lp_bytes": 94886786, "phases": {"import": 0.06803066696738824, "build": 0.4493851659935899, "emit": 0.3109667500248179, "teardown": 0.05269654199946672}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.8130484580178745, "live_fraction": 1.0, "peak_rss_bytes": 328220672, "threads": 8, "record": "timing", "repeat": 1}
-{"case": "nodal", "size": "d100", "arm": "duckdb", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": "-1", "lp_bytes": 94886786, "phases": {"import": 0.06891670799814165, "build": 0.4503028329927474, "emit": 0.357798749988433, "teardown": 0.0574842500500381}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.8655858330312185, "live_fraction": 1.0, "peak_rss_bytes": 348258304, "threads": 8, "record": "timing", "repeat": 2}
-{"case": "nodal", "size": "d100", "arm": "duckdb@1GB", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "lp", "memory_limit": "1GB", "lp_bytes": 94886786, "phases": {"import": 0.06789241702063009, "build": 0.44841537496540695, "emit": 0.15533137501915917, "teardown": 0.04759400000330061}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.6513407499878667, "live_fraction": 1.0, "peak_rss_bytes": 325943296, "threads": 8, "record": "timing", "repeat": 2}
-{"case": "nodal", "size": "d100", "arm": "lpspec", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": null, "lp_bytes": null, "phases": {"import": 0.10402041597990319, "build": 0.04497175000142306, "emit": 0.09187225002096966, "teardown": 4.9124995712190866e-05}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": 1200000}, "wall_seconds": 0.1368931250181049, "live_fraction": 1.0, "peak_rss_bytes": 631324672, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d100", "arm": "lpspec", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": null, "lp_bytes": null, "phases": {"import": 0.1042594580212608, "build": 0.04513991699786857, "emit": 0.06861062499228865, "teardown": 4.97090513817966e-05}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": 1200000}, "wall_seconds": 0.11380025104153901, "live_fraction": 1.0, "peak_rss_bytes": 635977728, "threads": 8, "record": "timing", "repeat": 1}
-{"case": "nodal", "size": "d100", "arm": "lpspec", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": null, "lp_bytes": null, "phases": {"import": 0.10504966595908627, "build": 0.04778654203983024, "emit": 0.06920587498461828, "teardown": 5.079095717519522e-05}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": 1200000}, "wall_seconds": 0.11704320798162371, "live_fraction": 1.0, "peak_rss_bytes": 629391360, "threads": 8, "record": "timing", "repeat": 2}
-{"case": "nodal", "size": "d100", "arm": "linopy", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": null, "lp_bytes": null, "phases": {"import": 0.18620324996300042, "build": 0.2187065840116702, "emit": 0.20887112501077354}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.42757770902244374, "live_fraction": 1.0, "peak_rss_bytes": 568623104, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d100", "arm": "linopy", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": null, "lp_bytes": null, "phases": {"import": 0.1874740410130471, "build": 0.22144233400467783, "emit": 0.2041846250067465}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.42562695901142433, "live_fraction": 1.0, "peak_rss_bytes": 568131584, "threads": 8, "record": "timing", "repeat": 1}
-{"case": "nodal", "size": "d100", "arm": "linopy", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": null, "lp_bytes": null, "phases": {"import": 0.1922065420076251, "build": 0.22029625001596287, "emit": 0.20309320802334696}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.42338945803930983, "live_fraction": 1.0, "peak_rss_bytes": 568328192, "threads": 8, "record": "timing", "repeat": 2}
-{"case": "nodal", "size": "d100", "arm": "duckdb", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": "-1", "lp_bytes": null, "phases": {"import": 0.06819208402885124, "build": 0.4508345830254257, "emit": 0.1802363329916261, "teardown": 0.049729084013961256}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.680800000031013, "live_fraction": 1.0, "peak_rss_bytes": 554369024, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d100", "arm": "duckdb@1GB", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": "1GB", "lp_bytes": null, "phases": {"import": 0.06915716599905863, "build": 0.45030783402035013, "emit": 0.14518524997401983, "teardown": 0.049870124959852546}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.6453632089542225, "live_fraction": 1.0, "peak_rss_bytes": 556548096, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d100", "arm": "duckdb", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": "-1", "lp_bytes": null, "phases": {"import": 0.0676761670038104, "build": 0.4614201249787584, "emit": 0.15064804098801687, "teardown": 0.04891320801107213}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.6609813739778474, "live_fraction": 1.0, "peak_rss_bytes": 554614784, "threads": 8, "record": "timing", "repeat": 1}
-{"case": "nodal", "size": "d100", "arm": "duckdb@1GB", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": "1GB", "lp_bytes": null, "phases": {"import": 0.0684986250125803, "build": 0.453210833016783, "emit": 0.14619645901257172, "teardown": 0.05074991600122303}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.6501572080305777, "live_fraction": 1.0, "peak_rss_bytes": 554909696, "threads": 8, "record": "timing", "repeat": 1}
-{"case": "nodal", "size": "d100", "arm": "duckdb", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": "-1", "lp_bytes": null, "phases": {"import": 0.06955324998125434, "build": 0.45521854201797396, "emit": 0.1493602079572156, "teardown": 0.05017179198330268}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.6547505419584922, "live_fraction": 1.0, "peak_rss_bytes": 558481408, "threads": 8, "record": "timing", "repeat": 2}
-{"case": "nodal", "size": "d100", "arm": "duckdb@1GB", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 1.0, "io_api": null, "sink": "highs", "memory_limit": "1GB", "lp_bytes": null, "phases": {"import": 0.06798524997429922, "build": 0.4468745409976691, "emit": 0.14863429201068357, "teardown": 0.05185375001747161}, "counts": {"columns": 1200000, "rows": 100000, "nonzeros": null}, "wall_seconds": 0.6473625830258243, "live_fraction": 1.0, "peak_rss_bytes": 556875776, "threads": 8, "record": "timing", "repeat": 2}
-{"case": "nodal", "size": "d50", "arm": "lpspec", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 0.5, "io_api": null, "sink": "lp", "memory_limit": null, "lp_bytes": 48393178, "phases": {"import": 0.12018079200061038, "build": 0.035985083028208464, "emit": 0.09715962497284636, "teardown": 2.2292020730674267e-05}, "counts": {"columns": 600000, "rows": 100000, "nonzeros": 600000}, "wall_seconds": 0.1331670000217855, "live_fraction": 0.5, "peak_rss_bytes": 419659776, "threads": 8, "record": "timing", "repeat": 0}
-{"case": "nodal", "size": "d50", "arm": "lpspec", "dimensions": {"node": 50, "tech": 12, "snapshot": 2000}, "nominal_variables": 1200000, "density": 0.5, "io_api": null, "sink": "lp", "memory_limit": null, "lp_bytes": 48393178, "phases": {"import": 0.10173370799748227, "build": 0.03498729201965034, "emit": 0.09651291702175513, "teardown": 3.08750313706696e-05}, "counts": {"columns": 600000, "rows": 100000, "nonzeros": 600000}, "wall_seconds": 0.13153108407277614, "live_fraction": 0.5, "peak_rss_bytes": 425689088, "threads": 8, "record": "timing", "repeat": 1}
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diff --git a/bench/results/latest.jsonl b/bench/results/latest.jsonl
index 923cd7272..39c36840d 100644
--- a/bench/results/latest.jsonl
+++ b/bench/results/latest.jsonl
@@ -1,655 +1,343 @@
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diff --git a/bench/results/scaling.jsonl b/bench/results/scaling.jsonl
index 374e8451e..fc6245268 100644
--- a/bench/results/scaling.jsonl
+++ b/bench/results/scaling.jsonl
@@ -1,49 +1,25 @@
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+{"record": "run", "platform": "macOS-26.2-arm64-arm-64bit-Mach-O", "machine": "arm64", "processor": "arm", "python": "3.13.2", "versions": {"lpspec": "0.0.1a55", "linopy": "0.8.0.post1.dev140+g346943317", "highspy": "1.15.1", "polars": "1.43.0", "pandas": "3.0.5", "numpy": "2.5.1", "xarray": "2026.7.0", "pyarrow": "25.0.0"}, "commits": {"lpspec": "98f382d-dirty"}}
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+{"case": "dispatch", "size": "xs", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 100}, "nominal_variables": 10000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 703382, "phases": {"import": 0.10079945903271437, "build": 0.010420999955385923, "emit": 0.003870041109621525, "teardown": 7.292022928595543e-06}, "counts": {"columns": 10000, "rows": 100, "nonzeros": 10000}, "wall_seconds": 0.014298333087936044, "live_fraction": 1.0, "peak_rss_bytes": 169426944, "threads": 8, "record": "timing", "repeat": 1}
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+{"case": "dispatch", "size": "xs", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 100}, "nominal_variables": 10000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 733385, "phases": {"import": 0.2010126250097528, "build": 0.19639499997720122, "emit": 0.007736791973002255}, "counts": {"columns": 10000, "rows": 100, "nonzeros": null}, "wall_seconds": 0.20413179195020348, "live_fraction": 1.0, "peak_rss_bytes": 222248960, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "s", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 1000}, "nominal_variables": 100000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 7346570, "phases": {"import": 0.1001628750236705, "build": 0.012432708987034857, "emit": 0.012304708012379706, "teardown": 4.832982085645199e-06}, "counts": {"columns": 100000, "rows": 1000, "nonzeros": 100000}, "wall_seconds": 0.02474224998150021, "live_fraction": 1.0, "peak_rss_bytes": 209059840, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "s", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 1000}, "nominal_variables": 100000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 7346570, "phases": {"import": 0.10085087490733713, "build": 0.012654791004024446, "emit": 0.012110667070373893, "teardown": 5.375011824071407e-06}, "counts": {"columns": 100000, "rows": 1000, "nonzeros": 100000}, "wall_seconds": 0.02477083308622241, "live_fraction": 1.0, "peak_rss_bytes": 208535552, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "s", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 1000}, "nominal_variables": 100000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 7646573, "phases": {"import": 0.20123999996576458, "build": 0.1973310000030324, "emit": 0.018429124960675836}, "counts": {"columns": 100000, "rows": 1000, "nonzeros": null}, "wall_seconds": 0.21576012496370822, "live_fraction": 1.0, "peak_rss_bytes": 268615680, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "s", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 1000}, "nominal_variables": 100000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 7646573, "phases": {"import": 0.20049604191444814, "build": 0.19732170808129013, "emit": 0.018359208945184946}, "counts": {"columns": 100000, "rows": 1000, "nonzeros": null}, "wall_seconds": 0.21568091702647507, "live_fraction": 1.0, "peak_rss_bytes": 270843904, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "m", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 10000}, "nominal_variables": 1000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 76375489, "phases": {"import": 0.10043600003700703, "build": 0.027504042023792863, "emit": 0.08950300002470613, "teardown": 3.358302637934685e-05}, "counts": {"columns": 1000000, "rows": 10000, "nonzeros": 1000000}, "wall_seconds": 0.11704062507487833, "live_fraction": 1.0, "peak_rss_bytes": 428163072, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "m", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 10000}, "nominal_variables": 1000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 76375489, "phases": {"import": 0.10061787499580532, "build": 0.028076916933059692, "emit": 0.09308454208076, "teardown": 5.249981768429279e-06}, "counts": {"columns": 1000000, "rows": 10000, "nonzeros": 1000000}, "wall_seconds": 0.12116670899558812, "live_fraction": 1.0, "peak_rss_bytes": 427311104, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "m", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 10000}, "nominal_variables": 1000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 79375492, "phases": {"import": 0.2050370000069961, "build": 0.20152137498371303, "emit": 0.13215770793613046}, "counts": {"columns": 1000000, "rows": 10000, "nonzeros": null}, "wall_seconds": 0.3336790829198435, "live_fraction": 1.0, "peak_rss_bytes": 591347712, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "m", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 10000}, "nominal_variables": 1000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 79375492, "phases": {"import": 0.20073054207023233, "build": 0.1990429579745978, "emit": 0.14141216699499637}, "counts": {"columns": 1000000, "rows": 10000, "nonzeros": null}, "wall_seconds": 0.3404551249695942, "live_fraction": 1.0, "peak_rss_bytes": 575930368, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "l", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 100000}, "nominal_variables": 10000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 796454817, "phases": {"import": 0.1003951660823077, "build": 0.16768337495159358, "emit": 0.9585582920117304, "teardown": 1.1792057193815708e-05}, "counts": {"columns": 10000000, "rows": 100000, "nonzeros": 10000000}, "wall_seconds": 1.1262534590205178, "live_fraction": 1.0, "peak_rss_bytes": 1586364416, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "l", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 100000}, "nominal_variables": 10000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 796454817, "phases": {"import": 0.10278425004798919, "build": 0.17832833295688033, "emit": 1.049989458057098, "teardown": 1.2333039194345474e-05}, "counts": {"columns": 10000000, "rows": 100000, "nonzeros": 10000000}, "wall_seconds": 1.2283301240531728, "live_fraction": 1.0, "peak_rss_bytes": 1582497792, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "l", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 100000}, "nominal_variables": 10000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 826454820, "phases": {"import": 0.2026642500422895, "build": 0.262890417012386, "emit": 1.6655128749553114}, "counts": {"columns": 10000000, "rows": 100000, "nonzeros": null}, "wall_seconds": 1.9284032919676974, "live_fraction": 1.0, "peak_rss_bytes": 2199322624, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "l", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 100000}, "nominal_variables": 10000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 826454820, "phases": {"import": 0.2028417920228094, "build": 0.26644049992319196, "emit": 1.4170047920197248}, "counts": {"columns": 10000000, "rows": 100000, "nonzeros": null}, "wall_seconds": 1.6834452919429168, "live_fraction": 1.0, "peak_rss_bytes": 2151055360, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "xl", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 400000}, "nominal_variables": 40000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 3285751292, "phases": {"import": 0.10171762492973357, "build": 0.631205709069036, "emit": 4.765833540936001, "teardown": 1.595797948539257e-05}, "counts": {"columns": 40000000, "rows": 400000, "nonzeros": 40000000}, "wall_seconds": 5.397055207984522, "live_fraction": 1.0, "peak_rss_bytes": 5414993920, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "xl", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 400000}, "nominal_variables": 40000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 3285751292, "phases": {"import": 0.10217316693160683, "build": 0.6078623330686241, "emit": 5.906316332984716, "teardown": 9.625102393329144e-06}, "counts": {"columns": 40000000, "rows": 400000, "nonzeros": 40000000}, "wall_seconds": 6.514188291155733, "live_fraction": 1.0, "peak_rss_bytes": 5418418176, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "xl", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 400000}, "nominal_variables": 40000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 3405751295, "phases": {"import": 0.19971650000661612, "build": 0.47652833303436637, "emit": 7.368872457998805}, "counts": {"columns": 40000000, "rows": 400000, "nonzeros": null}, "wall_seconds": 7.845400791033171, "live_fraction": 1.0, "peak_rss_bytes": 8220262400, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "xl", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 400000}, "nominal_variables": 40000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 3405751295, "phases": {"import": 0.20392770797479898, "build": 0.47727829206269234, "emit": 6.031111041898839}, "counts": {"columns": 40000000, "rows": 400000, "nonzeros": null}, "wall_seconds": 6.5083893339615315, "live_fraction": 1.0, "peak_rss_bytes": 7984791552, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "2xl", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 1200000}, "nominal_variables": 120000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 9971142786, "phases": {"import": 0.09995954192709178, "build": 2.0692317920038477, "emit": 18.36785433301702, "teardown": 4.012498538941145e-05}, "counts": {"columns": 120000000, "rows": 1200000, "nonzeros": 120000000}, "wall_seconds": 20.43712625000626, "live_fraction": 1.0, "peak_rss_bytes": 9242738688, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "2xl", "arm": "lpspec", "dimensions": {"generator": 100, "snapshot": 1200000}, "nominal_variables": 120000000, "density": 1.0, "io_api": null, "sink": "lp", "lp_bytes": 9971142786, "phases": {"import": 0.10296466597355902, "build": 2.025357750011608, "emit": 18.87203483399935, "teardown": 2.5499961338937283e-05}, "counts": {"columns": 120000000, "rows": 1200000, "nonzeros": 120000000}, "wall_seconds": 20.897418083972298, "live_fraction": 1.0, "peak_rss_bytes": 12437913600, "threads": 8, "record": "timing", "repeat": 1}
+{"case": "dispatch", "size": "2xl", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 1200000}, "nominal_variables": 120000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 10331142789, "phases": {"import": 0.2733117920579389, "build": 1.0531431660056114, "emit": 38.30962029204238}, "counts": {"columns": 120000000, "rows": 1200000, "nonzeros": null}, "wall_seconds": 39.36276345804799, "live_fraction": 1.0, "peak_rss_bytes": 12581044224, "threads": 8, "record": "timing", "repeat": 0}
+{"case": "dispatch", "size": "2xl", "arm": "linopy", "dimensions": {"generator": 100, "snapshot": 1200000}, "nominal_variables": 120000000, "density": 1.0, "io_api": "lp-polars", "sink": "lp", "lp_bytes": 10331142789, "phases": {"import": 0.29569591698236763, "build": 1.0038105410058051, "emit": 36.87760879192501}, "counts": {"columns": 120000000, "rows": 1200000, "nonzeros": null}, "wall_seconds": 37.88141933293082, "live_fraction": 1.0, "peak_rss_bytes": 13624246272, "threads": 8, "record": "timing", "repeat": 1}
diff --git a/docs/benchmarks-scaling.html b/docs/benchmarks-scaling.html
index 2e50f895f..3c846360c 100644
--- a/docs/benchmarks-scaling.html
+++ b/docs/benchmarks-scaling.html
@@ -197,7 +197,7 @@ <h2>The numbers</h2>
 </style>
 
 <script>
-const DATA = {"scaling": {"vars": [10000, 100000, 1000000, 10000000, 40000000, 120000000], "wall": {"polars": [0.015, 0.027, 0.128, 1.123, 5.989, 35.358], "linopy": [0.21, 0.218, 0.34, 1.538, 8.805, 106.226]}, "peak": {"polars": [0.17, 0.212, 0.468, 2.04, 5.978, 8.301], "linopy": [0.214, 0.261, 0.564, 2.134, 7.922, 7.775]}}, "cases": {"dispatch": {"vars": [10000, 100000, 1000000, 10000000], "wall": {"polars": [0.017, 0.022, 0.084, 0.687], "linopy": [0.207, 0.219, 0.374, 1.93]}, "peak": {"polars": [0.168, 0.208, 0.52, 3.127], "linopy": [0.201, 0.229, 0.495, 3.304]}}, "fleet": {"vars": [12000, 120000, 1200000, 12000000], "wall": {"polars": [0.044, 0.057, 0.177, 1.481], "linopy": [0.288, 0.322, 0.578, 3.404]}, "peak": {"polars": [0.174, 0.231, 0.653, 3.764], "linopy": [0.203, 0.246, 0.703, 4.871]}}, "nodal": {"vars": [3000, 30000, 300000, 3000000], "wall": {"polars": [0.017, 0.02, 0.048, 0.491], "linopy": [0.213, 0.232, 0.298, 1.339]}, "peak": {"polars": [0.167, 0.186, 0.333, 1.42], "linopy": [0.202, 0.213, 0.352, 1.709]}}, "profiled": {"vars": [12000, 120000, 1200000, 12000000], "wall": {"polars": [0.022, 0.044, 0.228, 2.843], "linopy": [0.286, 0.281, 0.459, 2.613]}, "peak": {"polars": [0.174, 0.261, 0.836, 4.114], "linopy": [0.205, 0.247, 0.642, 4.73]}}, "sector": {"vars": [1000, 10000, 100000, 1000000], "wall": {"polars": [0.02, 0.025, 0.049, 0.38], "linopy": [0.225, 0.232, 0.333, 1.248]}, "peak": {"polars": [0.168, 0.19, 0.342, 0.946], "linopy": [0.203, 0.22, 0.493, 2.978]}}, "transport": {"vars": [9800, 98000, 980000, 9800000], "wall": {"polars": [0.024, 0.035, 0.142, 1.552], "linopy": [0.243, 0.26, 0.469, 2.61]}, "peak": {"polars": [0.174, 0.221, 0.596, 3.089], "linopy": [0.204, 0.234, 0.565, 3.952]}}}, "caseNames": ["dispatch", "fleet", "nodal", "profiled", "sector", "transport"], "rungs": ["xs", "s", "m", "l"]};
+const DATA = {"scaling": {"vars": [10000, 100000, 1000000, 10000000, 40000000, 120000000], "wall": {"polars": [0.014, 0.025, 0.117, 1.126, 5.397, 20.437], "linopy": [0.201, 0.216, 0.334, 1.683, 6.508, 37.881]}, "peak": {"polars": [0.169, 0.209, 0.427, 1.582, 5.415, 9.243], "linopy": [0.222, 0.269, 0.576, 2.151, 7.985, 12.581]}}, "cases": {"dispatch": {"vars": [10000, 100000, 1000000, 10000000], "wall": {"polars": [0.017, 0.022, 0.076, 0.573], "linopy": [0.199, 0.207, 0.275, 1.029]}, "peak": {"polars": [0.17, 0.204, 0.494, 2.88], "linopy": [0.197, 0.211, 0.372, 1.968]}}, "fleet": {"vars": [12000, 120000, 1200000, 12000000], "wall": {"polars": [0.041, 0.051, 0.142, 1.083], "linopy": [0.281, 0.285, 0.399, 1.62]}, "peak": {"polars": [0.174, 0.223, 0.611, 4.067], "linopy": [0.199, 0.223, 0.538, 3.71]}}, "nodal": {"vars": [3000, 30000, 300000, 3000000], "wall": {"polars": [0.017, 0.02, 0.044, 0.295], "linopy": [0.206, 0.213, 0.259, 0.745]}, "peak": {"polars": [0.169, 0.187, 0.331, 1.323], "linopy": [0.199, 0.205, 0.319, 1.485]}}, "profiled": {"vars": [12000, 120000, 1200000, 12000000], "wall": {"polars": [0.018, 0.033, 0.173, 1.692], "linopy": [0.206, 0.213, 0.309, 1.331]}, "peak": {"polars": [0.176, 0.263, 0.806, 3.926], "linopy": [0.201, 0.227, 0.489, 3.098]}}, "sector": {"vars": [1000, 10000, 100000, 1000000], "wall": {"polars": [0.02, 0.023, 0.043, 0.263], "linopy": [0.212, 0.221, 0.311, 1.169]}, "peak": {"polars": [0.17, 0.186, 0.309, 0.941], "linopy": [0.2, 0.218, 0.48, 2.837]}}, "transport": {"vars": [9800, 98000, 980000, 9800000], "wall": {"polars": [0.023, 0.032, 0.114, 0.978], "linopy": [0.223, 0.235, 0.329, 1.477]}, "peak": {"polars": [0.175, 0.223, 0.565, 2.881], "linopy": [0.2, 0.217, 0.438, 2.612]}}}, "caseNames": ["dispatch", "fleet", "nodal", "profiled", "sector", "transport"], "rungs": ["xs", "s", "m", "l"]};
 
 /* Two categorical slots, validated all-pairs in both modes (worst CVD dE 24.7
    light / 26.8 dark, worst normal-vision 33.6 / 31.8, both clear of the surface
diff --git a/docs/benchmarks.md b/docs/benchmarks.md
index 86f70beed..d6b2415e6 100644
--- a/docs/benchmarks.md
+++ b/docs/benchmarks.md
@@ -43,10 +43,17 @@ while the laptop was doing other work and it inflated `profiled` by 55% —
 enough to turn "level" into "the one case we lose". Best of three, nothing else
 running.
 
-macOS-26.2-arm64-arm-64bit-Mach-O, python 3.13.2, 26 GB · polars 1.43.0 ·
-linopy 0.8.0.post1.dev140+g346943317 (the v1-semantics build, PyPSA/linopy#717)
-· highspy 1.15.1 · numpy 2.5.1. Parity gate: all six cases agree to 0.0e+00
-relative (`fleet` to 4.6e-16) before anything is timed.
+**Measured at `98f382d`, on a clean tree.** Each results file's fingerprint
+carries that hash, so a number on this page can be traced to the code that
+produced it — which is the whole point of committing the files. (`density` and
+`scaling` record it as `98f382d-dirty`: they ran after `latest.jsonl` had been
+rewritten, and that file is tracked. The only modified paths were the earlier
+runs' own output.)
+
+macOS-26.2-arm64-arm-64bit-Mach-O, python 3.13.2, 26 GB · lpspec 0.0.1a55 ·
+polars 1.43.0 · linopy 0.8.0.post1.dev140+g346943317 (the v1-semantics build,
+PyPSA/linopy#717) · highspy 1.15.1 · numpy 2.5.1. Parity gate: all six cases
+agree to 0.0e+00 relative (`fleet` to 4.6e-16) before anything is timed.
 
 *This lane replaced a duckdb engine, and the three-way comparison that decided
 it — speed against a settable memory ceiling — is in
@@ -58,14 +65,14 @@ re-run is a claim with a shelf life.*
 
 ### dispatch — highs sink
 
-Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy()`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
+Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy(set_names=False)`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 10k | 100% | 100 | 0.02 s | 0.21 s | 0.08x | 0.17 GB | 0.20 GB | 0.83x | — |
-| 100k | 100% | 1k | 0.02 s | 0.22 s | 0.10x | 0.21 GB | 0.23 GB | 0.91x | — |
-| 1M | 100% | 10k | 0.08 s | 0.37 s | 0.23x | 0.52 GB | 0.50 GB | 1.06x | — |
-| 10M | 100% | 100k | 0.69 s | 1.93 s | 0.36x | 3.14 GB | 3.30 GB | 0.95x | — |
+| 10k | 100% | 100 | 0.02 s | 0.20 s | 0.08x | 0.17 GB | 0.20 GB | 0.86x | — |
+| 100k | 100% | 1k | 0.02 s | 0.21 s | 0.10x | 0.20 GB | 0.21 GB | 0.97x | — |
+| 1M | 100% | 10k | 0.08 s | 0.28 s | 0.28x | 0.50 GB | 0.37 GB | 1.34x | — |
+| 10M | 100% | 100k | 0.57 s | 1.03 s | 0.56x | 2.88 GB | 1.97 GB | 1.46x | — |
 
 ### dispatch — lp sink
 
@@ -73,21 +80,21 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 10k | 100% | 100 | 0.01 s | 0.21 s | 0.07x | 0.17 GB | 0.21 GB | 0.79x | 1 MB |
-| 100k | 100% | 1k | 0.03 s | 0.22 s | 0.13x | 0.21 GB | 0.26 GB | 0.81x | 7 MB |
-| 1M | 100% | 10k | 0.13 s | 0.35 s | 0.37x | 0.47 GB | 0.59 GB | 0.80x | 76 MB |
-| 10M | 100% | 100k | 1.11 s | 1.55 s | 0.72x | 2.02 GB | 2.25 GB | 0.90x | 796 MB |
+| 10k | 100% | 100 | 0.01 s | 0.20 s | 0.07x | 0.17 GB | 0.22 GB | 0.77x | 1 MB |
+| 100k | 100% | 1k | 0.02 s | 0.22 s | 0.11x | 0.21 GB | 0.27 GB | 0.77x | 7 MB |
+| 1M | 100% | 10k | 0.12 s | 0.34 s | 0.35x | 0.42 GB | 0.58 GB | 0.73x | 76 MB |
+| 10M | 100% | 100k | 1.07 s | 1.69 s | 0.63x | 1.59 GB | 2.11 GB | 0.75x | 796 MB |
 
 ### fleet — highs sink
 
-Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy()`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
+Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy(set_names=False)`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 12k | 100% | 6.02k | 0.04 s | 0.29 s | 0.15x | 0.17 GB | 0.20 GB | 0.86x | — |
-| 120k | 100% | 60.2k | 0.06 s | 0.32 s | 0.18x | 0.23 GB | 0.25 GB | 0.94x | — |
-| 1.2M | 100% | 602k | 0.18 s | 0.58 s | 0.31x | 0.65 GB | 0.70 GB | 0.93x | — |
-| 12M | 100% | 6.02M | 1.48 s | 3.40 s | 0.44x | 4.38 GB | 5.24 GB | 0.84x | — |
+| 12k | 100% | 6.02k | 0.04 s | 0.28 s | 0.15x | 0.17 GB | 0.20 GB | 0.88x | — |
+| 120k | 100% | 60.2k | 0.05 s | 0.29 s | 0.18x | 0.22 GB | 0.22 GB | 1.00x | — |
+| 1.2M | 100% | 602k | 0.14 s | 0.40 s | 0.36x | 0.61 GB | 0.54 GB | 1.14x | — |
+| 12M | 100% | 6.02M | 1.08 s | 1.62 s | 0.67x | 4.07 GB | 3.71 GB | 1.10x | — |
 
 ### fleet — lp sink
 
@@ -95,21 +102,21 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 12k | 100% | 6.02k | 0.04 s | 0.30 s | 0.14x | 0.18 GB | 0.22 GB | 0.82x | 1 MB |
-| 120k | 100% | 60.2k | 0.06 s | 0.32 s | 0.19x | 0.24 GB | 0.25 GB | 0.98x | 9 MB |
-| 1.2M | 100% | 602k | 0.24 s | 0.47 s | 0.51x | 0.67 GB | 0.45 GB | 1.49x | 89 MB |
-| 12M | 100% | 6.02M | 1.99 s | 1.93 s | 1.03x | 2.78 GB | 1.66 GB | 1.68x | 920 MB |
+| 12k | 100% | 6.02k | 0.04 s | 0.30 s | 0.13x | 0.18 GB | 0.22 GB | 0.79x | 1 MB |
+| 120k | 100% | 60.2k | 0.06 s | 0.31 s | 0.18x | 0.24 GB | 0.26 GB | 0.95x | 9 MB |
+| 1.2M | 100% | 602k | 0.20 s | 0.45 s | 0.43x | 0.64 GB | 0.45 GB | 1.41x | 89 MB |
+| 12M | 100% | 6.02M | 1.75 s | 1.98 s | 0.88x | 2.34 GB | 1.61 GB | 1.46x | 920 MB |
 
 ### nodal — highs sink
 
-Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy()`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
+Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy(set_names=False)`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 3k | 25% | 1k | 0.02 s | 0.21 s | 0.08x | 0.17 GB | 0.20 GB | 0.83x | — |
-| 30k | 25% | 10k | 0.02 s | 0.23 s | 0.09x | 0.19 GB | 0.21 GB | 0.87x | — |
-| 300k | 25% | 100k | 0.05 s | 0.30 s | 0.16x | 0.34 GB | 0.35 GB | 0.95x | — |
-| 3M | 25% | 1M | 0.49 s | 1.34 s | 0.37x | 1.42 GB | 1.71 GB | 0.83x | — |
+| 3k | 25% | 1k | 0.02 s | 0.21 s | 0.08x | 0.17 GB | 0.20 GB | 0.85x | — |
+| 30k | 25% | 10k | 0.02 s | 0.21 s | 0.10x | 0.19 GB | 0.21 GB | 0.91x | — |
+| 300k | 25% | 100k | 0.04 s | 0.26 s | 0.17x | 0.33 GB | 0.32 GB | 1.04x | — |
+| 3M | 25% | 1M | 0.29 s | 0.74 s | 0.40x | 1.34 GB | 1.49 GB | 0.90x | — |
 
 ### nodal — lp sink
 
@@ -117,21 +124,21 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 3k | 25% | 1k | 0.02 s | 0.21 s | 0.07x | 0.17 GB | 0.21 GB | 0.79x | 0 MB |
-| 30k | 25% | 10k | 0.02 s | 0.23 s | 0.09x | 0.19 GB | 0.24 GB | 0.81x | 2 MB |
-| 300k | 25% | 100k | 0.07 s | 0.28 s | 0.25x | 0.32 GB | 0.45 GB | 0.71x | 25 MB |
-| 3M | 25% | 1M | 0.63 s | 0.84 s | 0.74x | 1.19 GB | 1.46 GB | 0.82x | 264 MB |
+| 3k | 25% | 1k | 0.01 s | 0.21 s | 0.07x | 0.17 GB | 0.22 GB | 0.76x | 0 MB |
+| 30k | 25% | 10k | 0.02 s | 0.21 s | 0.09x | 0.19 GB | 0.25 GB | 0.77x | 2 MB |
+| 300k | 25% | 100k | 0.06 s | 0.27 s | 0.23x | 0.32 GB | 0.46 GB | 0.70x | 25 MB |
+| 3M | 25% | 1M | 0.49 s | 0.83 s | 0.59x | 1.07 GB | 1.55 GB | 0.69x | 264 MB |
 
 ### profiled — highs sink
 
-Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy()`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
+Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy(set_names=False)`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 12k | 100% | 1k | 0.02 s | 0.29 s | 0.08x | 0.17 GB | 0.21 GB | 0.85x | — |
-| 120k | 100% | 10k | 0.04 s | 0.28 s | 0.16x | 0.26 GB | 0.25 GB | 1.06x | — |
-| 1.2M | 100% | 100k | 0.23 s | 0.46 s | 0.50x | 0.84 GB | 0.64 GB | 1.30x | — |
-| 12M | 100% | 1M | 2.84 s | 2.61 s | 1.09x | 4.15 GB | 4.73 GB | 0.88x | — |
+| 12k | 100% | 1k | 0.02 s | 0.21 s | 0.09x | 0.18 GB | 0.20 GB | 0.88x | — |
+| 120k | 100% | 10k | 0.03 s | 0.21 s | 0.15x | 0.26 GB | 0.23 GB | 1.16x | — |
+| 1.2M | 100% | 100k | 0.17 s | 0.31 s | 0.56x | 0.83 GB | 0.49 GB | 1.70x | — |
+| 12M | 100% | 1M | 1.69 s | 1.33 s | 1.27x | 3.93 GB | 3.10 GB | 1.27x | — |
 
 ### profiled — lp sink
 
@@ -139,21 +146,21 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 12k | 100% | 1k | 0.02 s | 0.22 s | 0.09x | 0.18 GB | 0.22 GB | 0.81x | 1 MB |
-| 120k | 100% | 10k | 0.04 s | 0.25 s | 0.17x | 0.26 GB | 0.30 GB | 0.88x | 9 MB |
-| 1.2M | 100% | 100k | 0.33 s | 0.51 s | 0.64x | 0.71 GB | 0.72 GB | 0.99x | 95 MB |
-| 12M | 100% | 1M | 4.48 s | 3.06 s | 1.46x | 3.19 GB | 3.14 GB | 1.02x | 986 MB |
+| 12k | 100% | 1k | 0.02 s | 0.21 s | 0.08x | 0.18 GB | 0.23 GB | 0.78x | 1 MB |
+| 120k | 100% | 10k | 0.04 s | 0.22 s | 0.16x | 0.26 GB | 0.30 GB | 0.87x | 9 MB |
+| 1.2M | 100% | 100k | 0.24 s | 0.38 s | 0.61x | 0.71 GB | 0.69 GB | 1.03x | 95 MB |
+| 12M | 100% | 1M | 2.36 s | 2.20 s | 1.07x | 2.46 GB | 3.12 GB | 0.79x | 986 MB |
 
 ### sector — highs sink
 
-Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy()`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
+Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy(set_names=False)`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 1k | 6% | 1k | 0.02 s | 0.23 s | 0.09x | 0.17 GB | 0.20 GB | 0.83x | — |
-| 10k | 6% | 10k | 0.02 s | 0.23 s | 0.11x | 0.19 GB | 0.22 GB | 0.86x | — |
-| 100k | 6% | 100k | 0.05 s | 0.33 s | 0.15x | 0.34 GB | 0.49 GB | 0.69x | — |
-| 1M | 6% | 1M | 0.38 s | 1.25 s | 0.30x | 0.95 GB | 2.98 GB | 0.32x | — |
+| 1k | 6% | 1k | 0.02 s | 0.21 s | 0.09x | 0.17 GB | 0.20 GB | 0.85x | — |
+| 10k | 6% | 10k | 0.02 s | 0.22 s | 0.10x | 0.19 GB | 0.22 GB | 0.86x | — |
+| 100k | 6% | 100k | 0.04 s | 0.31 s | 0.14x | 0.31 GB | 0.48 GB | 0.64x | — |
+| 1M | 6% | 1M | 0.26 s | 1.17 s | 0.23x | 0.95 GB | 2.84 GB | 0.34x | — |
 
 ### sector — lp sink
 
@@ -161,21 +168,21 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 1k | 6% | 1k | 0.02 s | 0.23 s | 0.07x | 0.17 GB | 0.21 GB | 0.79x | 0 MB |
-| 10k | 6% | 10k | 0.02 s | 0.24 s | 0.09x | 0.19 GB | 0.24 GB | 0.79x | 1 MB |
-| 100k | 6% | 100k | 0.07 s | 0.31 s | 0.24x | 0.34 GB | 0.52 GB | 0.65x | 12 MB |
-| 1M | 6% | 1M | 0.62 s | 1.14 s | 0.55x | 0.93 GB | 2.91 GB | 0.32x | 120 MB |
+| 1k | 6% | 1k | 0.02 s | 0.21 s | 0.08x | 0.17 GB | 0.22 GB | 0.77x | 0 MB |
+| 10k | 6% | 10k | 0.02 s | 0.22 s | 0.09x | 0.19 GB | 0.25 GB | 0.75x | 1 MB |
+| 100k | 6% | 100k | 0.05 s | 0.31 s | 0.16x | 0.31 GB | 0.53 GB | 0.59x | 12 MB |
+| 1M | 6% | 1M | 0.35 s | 1.17 s | 0.30x | 0.95 GB | 2.91 GB | 0.33x | 120 MB |
 
 ### transport — highs sink
 
-Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy()`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
+Both arms end holding a populated `highspy.Highs` with `run()` never called: lpspec through `build_highs`, linopy through `to_highspy(set_names=False)`. The simplex is the same work whoever filled the model, so timing it would say nothing about the lane that filled it.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 9.8k | 100% | 1.4k | 0.02 s | 0.24 s | 0.10x | 0.17 GB | 0.20 GB | 0.85x | — |
-| 98k | 100% | 14k | 0.03 s | 0.26 s | 0.13x | 0.22 GB | 0.23 GB | 0.95x | — |
-| 980k | 100% | 140k | 0.14 s | 0.47 s | 0.30x | 0.60 GB | 0.57 GB | 1.05x | — |
-| 9.8M | 100% | 1.4M | 1.55 s | 2.61 s | 0.59x | 3.14 GB | 3.95 GB | 0.80x | — |
+| 9.8k | 100% | 1.4k | 0.02 s | 0.22 s | 0.10x | 0.18 GB | 0.20 GB | 0.88x | — |
+| 98k | 100% | 14k | 0.03 s | 0.23 s | 0.13x | 0.22 GB | 0.22 GB | 1.03x | — |
+| 980k | 100% | 140k | 0.11 s | 0.33 s | 0.35x | 0.57 GB | 0.44 GB | 1.30x | — |
+| 9.8M | 100% | 1.4M | 0.98 s | 1.48 s | 0.66x | 2.96 GB | 2.63 GB | 1.13x | — |
 
 ### transport — lp sink
 
@@ -183,40 +190,49 @@ lpspec writes the LP file, linopy through its `lp-polars` writer.
 
 | variables | live | rows | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak | LP |
 |---|---|---|---|---|---|---|---|---|---|
-| 9.8k | 100% | 1.4k | 0.02 s | 0.23 s | 0.10x | 0.18 GB | 0.22 GB | 0.81x | 1 MB |
-| 98k | 100% | 14k | 0.04 s | 0.25 s | 0.15x | 0.23 GB | 0.29 GB | 0.81x | 8 MB |
-| 980k | 100% | 140k | 0.27 s | 0.50 s | 0.55x | 0.55 GB | 0.66 GB | 0.84x | 79 MB |
-| 9.8M | 100% | 1.4M | 2.37 s | 2.49 s | 0.95x | 2.20 GB | 1.85 GB | 1.19x | 820 MB |
+| 9.8k | 100% | 1.4k | 0.02 s | 0.23 s | 0.09x | 0.18 GB | 0.23 GB | 0.78x | 1 MB |
+| 98k | 100% | 14k | 0.04 s | 0.24 s | 0.15x | 0.23 GB | 0.29 GB | 0.79x | 8 MB |
+| 980k | 100% | 140k | 0.18 s | 0.39 s | 0.45x | 0.53 GB | 0.66 GB | 0.81x | 79 MB |
+| 9.8M | 100% | 1.4M | 1.66 s | 2.09 s | 0.79x | 1.92 GB | 1.78 GB | 1.08x | 820 MB |
 
 ## What this says
 
-**Ahead on peak on all six models and on wall on five**, at the `l` rung through
-the sink most callers use:
+**Ahead on wall on five of six, on both sinks. Peak depends on which sink you
+use, and through `highs` we are mostly behind.** At the `l` rung:
 
 | | dispatch | fleet | nodal | profiled | sector | transport |
 |---|---|---|---|---|---|---|
-| wall | **0.36x** | **0.44x** | **0.37x** | 1.09x | **0.30x** | **0.59x** |
-| peak | **0.95x** | **0.77x** | **0.83x** | **0.87x** | **0.32x** | **0.78x** |
-
-**`profiled` is the case in the ladder to be lost.** It is level here — 2.84 s
-against 2.61, from a case whose own repeats span 2.33–2.84 s at ~4 GB resident —
-and an unambiguous 1.46x through the LP sink, where no HiGHS copy dilutes it. A
-parameter dense over the whole variable product is the array xarray already
-wants and a full-size join for us. It is in the set on purpose.
-
-**The LP file is the weaker route.** Three numbers are against us there:
-`profiled` 1.46x and `fleet` 1.03x on wall, `fleet` 1.64x and `transport` 1.19x
-on peak. What is left is structural in two ways — most of an LP write is turning
-doubles into text, work neither lane avoids, so the wall ratio compresses toward
-1.00 however fast the build gets; and COO carries a `(row, col, coeff)` triple
-per nonzero where a dense array carries one float, which is `fleet`'s 1.64x.
-The many-declaration shape is the one that shows it, which is why that case
-exists.
+| wall — `highs` | **0.56x** | **0.67x** | **0.40x** | 1.27x | **0.23x** | **0.66x** |
+| peak — `highs` | 1.46x | 1.10x | **0.89x** | 1.27x | **0.33x** | 1.10x |
+| wall — `lp` | **0.63x** | **0.88x** | **0.59x** | 1.07x | **0.30x** | **0.79x** |
+| peak — `lp` | **0.75x** | 1.47x | **0.68x** | **0.80x** | **0.31x** | 1.08x |
+
+**Read the `highs` peak row before quoting anything from this page.** An earlier
+version of these tables had us ahead on peak on all six through that sink. That
+was not a real result: linopy's `to_highspy()` was being timed *with* variable
+naming, which neither of our solver sinks does, and the names are memory as well
+as time — 82% of its hand-off
+([#438](https://github.com/FBumann/lpspec/pull/438)). Both arms now pass
+`set_names=False` and end holding the same artifact, which is what
+`bench/README.md` always claimed was the only reason the two are comparable.
+Corrected, HiGHS's own dense model dominates both arms and our COO triples show
+up as the difference.
+
+**`profiled` is the case in the ladder we lose**, on both sinks — 1.27x and
+1.07x. A parameter dense over the whole variable product is the array xarray
+already wants and a full-size join for us. It is in the set on purpose.
+
+**The LP file is where the representation pays off**, which is the opposite of
+what this page used to say. Ahead on peak on four of six there, including 0.75x
+on `dispatch` and 0.31x on `sector`. Two go against us: `fleet` **1.47x** and
+`transport` 1.08x, and both are structural — COO carries a `(row, col, coeff)`
+triple per nonzero where a dense array carries one float, and the
+many-declaration shape is the one that shows it.
 
 **Sparsity is what separates the peak numbers**, not size. At the same rung
-`sector` is 0.32x of linopy's peak and `dispatch` 0.95x: a coordinate that does
-not exist is an absent row here and a NaN in a dense array there, so the gap
-tracks how much of the coordinate product a model actually uses.
+`sector` is 0.31x of linopy's peak through the LP sink and `dispatch` 0.75x: a
+coordinate that does not exist is an absent row here and a NaN in a dense array
+there, so the gap tracks how much of the coordinate product a model uses.
 
 ### Two costs, and both are real
 
@@ -231,30 +247,30 @@ Build only, repeated in one process. **first** is what a caller pays who builds
 
 | case | vars | lpspec: first | lpspec: steady | linopy: first | linopy: steady | steady vs linopy |
 |---|---|---|---|---|---|
-| transport | 9.8k | 28.8 ms | **13.7 ms** | 289.9 ms | 34.7 ms | 0.39x |
-| dispatch | 10k | 166.1 ms | **5.7 ms** | 449.0 ms | 13.8 ms | 0.41x |
-| profiled | 12k | 14.9 ms | **7.8 ms** | 205.7 ms | 19.4 ms | 0.40x |
-| nodal | 12k | 14.3 ms | **7.1 ms** | 224.0 ms | 19.1 ms | 0.37x |
-| fleet | 12k | 43.8 ms | **32.1 ms** | 293.4 ms | 95.5 ms | 0.34x |
-| sector | 17k | 108.6 ms | **9.4 ms** | 455.4 ms | 23.9 ms | 0.39x |
-| transport | 98k | 24.3 ms | **18.0 ms** | 228.8 ms | 37.7 ms | 0.48x |
-| dispatch | 100k | 15.3 ms | **7.9 ms** | 199.9 ms | 14.3 ms | 0.56x |
-| profiled | 120k | 26.3 ms | **18.0 ms** | 217.5 ms | 21.2 ms | 0.85x |
-| nodal | 120k | 15.1 ms | **8.6 ms** | 211.0 ms | 20.8 ms | 0.41x |
-| fleet | 120k | 44.6 ms | **37.5 ms** | 283.8 ms | 98.1 ms | 0.38x |
-| sector | 170k | 19.7 ms | **12.6 ms** | 221.4 ms | 28.4 ms | 0.44x |
-| transport | 980k | 78.6 ms | **69.4 ms** | 251.6 ms | 62.4 ms | 1.11x |
-| dispatch | 1M | 28.2 ms | **18.3 ms** | 209.0 ms | 21.0 ms | 0.87x |
-| profiled | 1.2M | 150.8 ms | **130.6 ms** | 238.5 ms | 39.1 ms | 3.34x |
-| fleet | 1.2M | 90.4 ms | **78.5 ms** | 294.2 ms | 105.7 ms | 0.74x |
-| nodal | 1.2M | 27.9 ms | **20.5 ms** | 220.5 ms | 30.2 ms | 0.68x |
-| sector | 1.7M | 38.3 ms | **31.7 ms** | 267.1 ms | 62.5 ms | 0.51x |
-| transport | 9.8M | 783.1 ms | **933.5 ms** | 654.9 ms | 406.4 ms | 2.30x |
-| dispatch | 10M | 157.9 ms | **137.0 ms** | 280.1 ms | 85.9 ms | 1.60x |
-| profiled | 12M | 1868.8 ms | **2059.1 ms** | 581.3 ms | 269.3 ms | 7.65x |
-| fleet | 12M | 651.4 ms | **668.9 ms** | 507.5 ms | 206.2 ms | 3.24x |
-| nodal | 12M | 178.0 ms | **182.8 ms** | 410.7 ms | 140.5 ms | 1.30x |
-| sector | 17M | 265.9 ms | **287.9 ms** | 878.9 ms | 573.9 ms | 0.50x |
+| transport | 9.8k | 17.1 ms | **12.6 ms** | 218.0 ms | 33.8 ms | 0.37x |
+| dispatch | 10k | 10.3 ms | **5.9 ms** | 195.6 ms | 12.8 ms | 0.46x |
+| profiled | 12k | 12.3 ms | **7.6 ms** | 197.3 ms | 17.9 ms | 0.42x |
+| fleet | 12k | 35.1 ms | **29.2 ms** | 265.2 ms | 87.2 ms | 0.34x |
+| nodal | 12k | 11.7 ms | **7.0 ms** | 199.0 ms | 18.2 ms | 0.38x |
+| sector | 17k | 13.6 ms | **9.0 ms** | 204.6 ms | 23.3 ms | 0.39x |
+| transport | 98k | 23.3 ms | **18.1 ms** | 219.8 ms | 35.2 ms | 0.51x |
+| dispatch | 100k | 12.7 ms | **7.9 ms** | 196.2 ms | 13.2 ms | 0.60x |
+| fleet | 120k | 39.3 ms | **33.6 ms** | 266.1 ms | 89.5 ms | 0.37x |
+| nodal | 120k | 13.5 ms | **8.6 ms** | 202.0 ms | 19.8 ms | 0.43x |
+| profiled | 120k | 22.4 ms | **17.5 ms** | 200.0 ms | 19.9 ms | 0.88x |
+| sector | 170k | 16.0 ms | **11.3 ms** | 211.2 ms | 27.4 ms | 0.41x |
+| transport | 980k | 78.3 ms | **67.0 ms** | 242.8 ms | 57.8 ms | 1.16x |
+| dispatch | 1M | 29.7 ms | **22.2 ms** | 198.4 ms | 19.0 ms | 1.17x |
+| fleet | 1.2M | 71.8 ms | **61.0 ms** | 279.8 ms | 98.4 ms | 0.62x |
+| nodal | 1.2M | 25.5 ms | **19.3 ms** | 221.2 ms | 30.2 ms | 0.64x |
+| profiled | 1.2M | 121.3 ms | **112.8 ms** | 215.5 ms | 34.3 ms | 3.29x |
+| sector | 1.7M | 32.0 ms | **26.2 ms** | 263.0 ms | 74.2 ms | 0.35x |
+| transport | 9.8M | 644.3 ms | **628.9 ms** | 618.1 ms | 387.0 ms | 1.62x |
+| dispatch | 10M | 167.8 ms | **148.0 ms** | 264.3 ms | 57.5 ms | 2.57x |
+| profiled | 12M | 1186.4 ms | **1134.4 ms** | 379.2 ms | 161.0 ms | 7.05x |
+| fleet | 12M | 423.9 ms | **379.2 ms** | 366.7 ms | 161.6 ms | 2.35x |
+| nodal | 12M | 151.7 ms | **135.0 ms** | 346.6 ms | 127.9 ms | 1.06x |
+| sector | 17M | 200.2 ms | **181.3 ms** | 782.8 ms | 479.5 ms | 0.38x |
 
 ## Absurd sizes
 
@@ -264,28 +280,35 @@ plotted in [benchmarks-scaling.html](benchmarks-scaling.html):
 
 | variables | lpspec | linopy | wall | peak |
 |---|---|---|---|---|
-| 10k | **0.02 s** / 0.17 GB | 0.21 s / 0.21 GB | **0.07x** | **0.79x** |
-| 100k | **0.03 s** / 0.21 GB | 0.22 s / 0.26 GB | **0.12x** | **0.81x** |
-| 1M | **0.13 s** / 0.47 GB | 0.34 s / 0.56 GB | **0.38x** | **0.83x** |
-| 10M | **1.12 s** / 2.04 GB | 1.54 s / 2.13 GB | **0.73x** | **0.96x** |
-| 40M | **5.99 s** / 5.98 GB | 8.80 s / 7.92 GB | **0.68x** | **0.75x** |
-| 120M | **35.36 s** / 8.30 GB | 106.23 s / 7.77 GB | **0.33x** | 1.07x |
+| 10k | **0.01 s** / 0.17 GB | 0.20 s / 0.22 GB | **0.07x** | **0.76x** |
+| 100k | **0.02 s** / 0.21 GB | 0.22 s / 0.27 GB | **0.11x** | **0.78x** |
+| 1M | **0.12 s** / 0.43 GB | 0.33 s / 0.58 GB | **0.35x** | **0.74x** |
+| 10M | **1.13 s** / 1.58 GB | 1.68 s / 2.15 GB | **0.67x** | **0.74x** |
+| 40M | **5.40 s** / 5.41 GB | 6.51 s / 7.98 GB | **0.83x** | **0.68x** |
+| 120M | **20.44 s** / 9.24 GB | 37.88 s / 12.58 GB | **0.54x** | **0.73x** |
 
 **Nothing falls over**, on either lane, at a 9.97 GB LP file. The wall ratio
-does not decay with size — it is 0.33x at 120M against 0.73x at 10M, because
-linopy's curve steepens above 10M and this one does not.
+does not decay with size — 0.54x at 120M against 0.67x at 10M, because linopy's
+curve steepens above 10M and this one does not.
 
-**Peak is where the advantage runs out.** 1.07x at 120M: past a certain size
-both lanes are holding the same model, and the representation stops deciding
-anything. Whatever memory headroom this lane has over the eager one is a
-small-and-sparse-model property, not a scaling one — which is the honest
-reading of the `sector`-against-`dispatch` spread above, at a size where it can
-no longer hide.
+**Peak does not run out, and this page used to say it did.** An earlier version
+of this section read 1.07x at 120M and concluded that "whatever memory headroom
+this lane has over the eager one is a small-and-sparse-model property, not a
+scaling one". That does not survive re-measurement: peak is **0.68-0.78x across
+four orders of magnitude**, 0.73x at the top rung.
 
-*The `2xl` rung is noisy between runs* — this lane read 20.6 s once and 35.4 s
-another time, linopy 38.5 s and 106.2 s — because 8-10 GB of peak on a 26 GB
-machine is where other things start to matter. Read the ordering, not the
-seconds.
+Two things moved it and only one is us. `cols` became positional
+([#433](https://github.com/FBumann/lpspec/pull/433)) and took ~20% off this
+case. The rest is that the earlier reading came from a run *this section itself
+flagged as noisy* — it recorded linopy at 38.5 s and 106.2 s for the same rung.
+The old number was a conclusion drawn across the noise floor.
+
+**This is the LP sink, and it is the sink where the representation wins.** It is
+not evidence for the `highs` peak row above, which goes the other way.
+
+*The `2xl` rung is still the noisiest* — 9-13 GB of peak on a 26 GB machine is
+where other things start to matter, and it is best-of-two rather than
+best-of-three. Read the ordering, not the seconds.
 
 ## The density sweep, and the claim it used to refuse
 
@@ -297,10 +320,10 @@ the 12 technologies each node has installed.
 
 | case | live | variables | wall: lpspec | wall: linopy | wall | peak: lpspec | peak: linopy | peak |
 |---|---|---|---|---|---|---|---|---|
-| nodal | 100% | 1.2M | 0.22 s | 0.44 s | 0.50x | 0.58 GB | 0.64 GB | 0.91x |
-| nodal | 50% | 600k | 0.12 s | 0.31 s | 0.38x | 0.43 GB | 0.59 GB | 0.72x |
-| nodal | 25% | 300k | 0.07 s | 0.29 s | 0.23x | 0.32 GB | 0.45 GB | 0.72x |
-| nodal | 8% | 100k | 0.04 s | 0.25 s | 0.17x | 0.26 GB | 0.34 GB | 0.78x |
+| nodal | 100% | 1.2M | 0.16 s | 0.38 s | 0.41x | 0.54 GB | 0.62 GB | 0.88x |
+| nodal | 50% | 600k | 0.10 s | 0.31 s | 0.32x | 0.41 GB | 0.60 GB | 0.68x |
+| nodal | 25% | 300k | 0.06 s | 0.27 s | 0.23x | 0.32 GB | 0.46 GB | 0.68x |
+| nodal | 8% | 100k | 0.04 s | 0.24 s | 0.16x | 0.26 GB | 0.35 GB | 0.72x |
 
 **It now does, and it did not before.** Wall time falls from 0.50x to 0.17x as
 density drops, and peak improves at every rung — 0.91x, 0.72x, 0.72x, 0.78x.