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SC-38: probe evidence labels and horizon in Main §3.4 - #975

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This is a source-correction unit for #946 (the gate) and #918 (the Introduction). It comes from the full-corpus audit of #918 at 60c976fe (R-03, PR-F part: probe evidence classes).

  • Base: main at 0d917665.
  • Head: 83769553.
  • Review: the independent review returned ACCEPT at f87ff059 after one fix round (B1, O1–O7). 83769553 adds one doc-only commit that applies that review's two optional README nits; it changes no manuscript, ledger or script.

Corrections

  • Main:610 (B1). The count is tied to its horizon: "sixteen distinct laws of $(X_0,\ldots,X_3)$ with $M_t>0$, and $M_{det}=M_t$ for two of them, with residuals up to $2/3$ bit". Check C8 gives 16 laws (2 attaining) at horizon 3, and 18 (2 attaining) at every K = 4..12. That range covers the full process.
  • Must-fail controls (O1). The vacuous C7 is replaced with a control that fails on 648 of 720. The new controls D1c, D4c and D5c each fire at every size. D1c uses a flat ½-bit bound, because $\log_2|\mathcal C_H|-\tfrac12$ cannot fire at (2,3) or (2,4).
  • Per-order labels (O2). D1 and D3 are relabelled $\max_k M_k$. Check D1i shows this equals $I^*$ at horizon 3.
  • Probe output strings (O4, O7). In hidden_memory_probe.py, c4_backflow_probes.py and memory_probes.py, only strings change, and the AST is unchanged with strings excluded. "certified" becomes "checked" where a floating-point step is involved.
  • primitive_probes.py. Left to SC-40 (SC-40: (C2)/(C3) statements and probe evidence in Main §1.3 #974) and byte-identical to base.
  • Rebuilt: Main, 96 pages.

Checks

The reviewer re-ran these with exact code of their own:

  • sc38_exact.py: ALL CHECKS PASS; output byte-identical to the retained .out.
  • All probes pass.
  • coverage_check: OK.
  • edge_rigidity_probe: PASS.
  • release_gate: every step passes except lean-axioms, which runs in CI.

Overlaps, resolved at reconciliation

The per-claim record is in verification/audits/manuscript/intro-corpus-audit-20261026/tracks/SC38-probe-evidence/README.md.

No merge is authorized. Merging needs owner approval at an exact SHA, as a normal merge commit.


Generated by Claude Code

- Main:170: the readback lemma's probe is described as what it is: exact
  laws and gaps, information quantities and the inequality in floating
  point, on named families (CON-25 / R-03 / OD-7).
- Main:606, :616, :620 and main_repro/README: "certified"/"exact" labels
  over floating-point clauses corrected; the conclusions are re-verified
  exactly in the track's sc38_exact.py.
- "Minimal" removed as a size label: Main §2.4 heading, ch01:135/:273
  with FULL mirrors, Explainer:725, main_repro README (CON-24 / R-04 /
  OD-10); a three-hidden-state model reproduces every number, two hidden
  states already give T1 = J/2, T2 = I.
- Main:610 and memory_probes.py: processes counted by law, not by the
  t = 2 conditional signature; at (2,3), t = 2, uniform prior, two of
  sixteen attain, maximal residual 2/3 bit, prior-independent by the
  Remark's identity (CON-26, resolved exactly).
- Ledger: purification-quotient fingerprint re-affirmed, same ID and level.
- Regenerated Main, Explainer and the book (.tex/.pdf).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
…acity

- B1, Main:610: the count is of laws of (X_0..X_3) (16, M_det = M_t for 2);
  at horizon K >= 4 it is 18 (2 attaining). sc38_exact.py C8 checks
  16/2 at horizon 3 and 18/2 at K = 4..12.
- O1: vacuous C7 replaced by a must-fail control (identity with
  H(X_<2|X_2) fails on 648 of 720); must-fail controls D1c, D4c, D5c.
- O2: D1/D3 relabelled as the per-order max_k M_k; D1i checks it equals
  I* at horizon 3 on all 16, 648 and 672 gap realizations.
- O4: hidden_memory_probe.py print strings (279-280) state the variational
  identity false in general at every hidden dimension; output otherwise
  identical.
- O6: B4 labelled as checking the target product law directly.
- O7: "certified" -> "checked" in output strings over floating-point
  steps (c4_backflow_probes, primitive_probes:100, memory_probes header).
- README: PASS count (50), C-2/C-4 descriptions, site table, SC-40
  Main:620 and SC-29 hidden_memory_probe cross-unit notes. Main rebuilt.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
SC-40 (corpus/sc40-c2-c3-statements at a948033) rewrites the same
output string at primitive_probes.py:100, so this unit's O7 edit there is
withdrawn to avoid a double edit; the file is back at its base content.
README updated accordingly.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
… current head (#946)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
amaybaum pushed a commit that referenced this pull request Oct 31, 2026
…d scope

#975 (SC-38). sc38_exact.py from refs/audit/pr975 re-run here (python3 -I,
scratch dir): output byte-identical to the PR's committed sc38_exact.out;
at (n_V,|C_H|) = (2,3), t = 2, uniform prior, 16 laws of (X0..X3) with
M_2 > 0, 2 attaining M_det = M_t, max residual 2/3 bit exactly (C2, C5);
memory_probes.py's old signature merged two laws (C3, C4: "1 of 15").
- Main.md:610: "one of fifteen distinct processes ... 0.667 bits" ->
  "sixteen distinct laws of (X0..X3) ... M_det = M_t for two of them ...
  2/3 bit"; agreeing laws prior-independent.
- Main.md:170, :606, :616: "Certified exactly" / "exact" -> checked, with
  laws/gaps in exact rational arithmetic and information quantities (or the
  predictive floor) in floating point, as the cited probes compute them.
- Main.md:178 "A Minimal Model" -> "A Six-Hidden-State Model" (Main's
  two-hidden-state revival example is smaller); ch01:135 / FULL:479,
  ch01:273 / FULL:617 (mirrors), Explainer.md:725, main_repro/README.md:8
  (also "exact enumeration" -> floating point: numpy).
- Main.md:620: already #974's line (D-6), which carries #975's labels.
- memory_probes.py: groups by the law of (X0..X3); prints "2 of 16 laws"
  (re-run: ALL CHECKS PASS). c4_backflow_probes.py, hidden_memory_probe.py:
  printed wording ("certified"; "M_det = M_t remains OPEN") aligned with
  Main:170 / :610.
- LEDGER.json: MAIN:T-canonical-predictive-quotient-purification-ingredient
  fingerprint re-affirmed (wording of the check parenthetical only).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
amaybaum added a commit that referenced this pull request Nov 3, 2026
…0261103

Legacy PR reconciliation: #1002 patch-budget hypothesis, #963 SC17 README, #975 SC38 evidence

amaybaum commented Nov 3, 2026

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Closed unmerged (owner decision OD-4, 2026-11-03).

Branch corpus/sc38-probe-evidence (head 83769553) is kept.


Generated by Claude Code

@amaybaum amaybaum closed this Nov 3, 2026
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