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Main: scope the imported dilation result to a per-time unitary family (#924 M1+M2) - #1034
Conversation
Barandes' stochastic-quantum theorem (arXiv:2309.03085v2 §5.7-§5.9;
arXiv:2302.10778v3 §3.4) gives one unitary for each target time on a
common space of dimension <= n^3. It has no composition law, no
time-homogeneity hypothesis and no fixed generator; its only Hamiltonian
is H(t) = i hbar dU/dt U^dagger, defined where U is differentiable.
M1:
- The definition of unitarily evolving QM (condition (i)) becomes that
per-time family. Removed from it: the fixed Hermitian H and
U(t) = e^{-iHt}.
- Five sites that imported a fixed-H form are restated: the
characterization proof, the time-homogeneity remark, the §3.4
consequence, and two status rows. The fixed-H form remains in-house,
as (Q2) via the fixed-H lemma, for realized processes at integer
horizon times.
- §3.2 credits (Q2) to the fixed-H lemma.
M2:
- The "n^2 at a single step, within the source's <= n^3 bound for the
full process family" contrast is removed.
- In its place, §3.1 states the per-time form that follows from the
one-step Lemma. Extending |i>(x)|a0> -> W|i> for a fixed ancilla
configuration gives the §3.4 definition at every time on dimension
n^2. This is a derivation on paper over the kernel-checked isometry
and marginal clauses; no statement or status changes.
- Hence §3.2's dependency scope and (v) of §3.4 no longer list the
compressed form among what a failure of the correspondence would cost.
The <= n^3 bound stays attributed to the source.
No theorem or lemma statement is changed, and no physical assumption
is added. The time-homogeneity and (T) hypotheses at Main:538/:498 are
left as unneeded but true conditions.
Mechanical:
- LEDGER: MAIN:D-unitarily-evolving-qm fingerprint
c1bc7b35a7c12e99 -> 139a68c2f2c5c3d1, taken from proof_census.py.
No other row moves.
- SC-42: Main:216 anchor re-cut. Result and controls regenerated with
check_sc42_integration.py; they differ only in site_table_sha256.
- tdilate_probes.py: dropped the "<= n^3 not needed at one step"
remark from the printed line.
- Main.tex and Main.pdf rebuilt with build.sh: 99 pages, no dropped
glyphs.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
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Serialized unit 3 checkpoint (2026-11-02): head Independent exact-head review: READY-WITH-NITS (no blocker).
Non-blocking nits, outside the authorized scope and left untouched:
CI: run 41395967646 ( The five holds and every other backlog item are untouched. Generated by Claude Code |
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Merge record. Merged at the owner-approved exact SHA
The four non-blocking nits are recorded as follow-up obligations on #924 and #1028 (GR:20 is assigned to #1028). None of them was changed by this merge. Generated by Claude Code |
Draft. Serialized unit 3, authorized by the owner on 2026-11-02 (#924 Option A). Not for merge without the owner's exact-SHA approval.
This PR implements the reviewed M1+M2 correction proposal recorded on #924 (summary comment 6567820151; proposal sha256 prefix
5aef407b3ede43e2; review and confirmation1fee6d45ca99dc56) as one indivisible unit. It is based on main7a4321c5. Since the proposal's base02009693, main has changed only by #1017's audit files. All 15 Main spans and the probe span were re-verified to occur exactly once before editing.What changes
papers/Main.md: 15 spans.Ũ(t←0)for each target time, on one space of dimension ≤ n³, with no fixed generator.Ĥappears only as OI's in-house form (Q2), at integer horizon times.tdilate_probes.py:73: print-line wording only.verification/coverage/LEDGER.json:MAIN:D-unitarily-evolving-qmchangesc1bc7b35a7c12e99→139a68c2f2c5c3d1, the value computed byproof_census.py. This is the only row that moves.Main.tex/Main.pdf: rebuilt withsh ./build.sh Mainon the native toolchain. The PDF is 99 pages before and after, with no dropped glyphs, and is not provisional.What does not change
Local checks (writer):
coverage_check: OK, 134 statements;check_sc42_integration.py: 618 checks pass;py_compileand the touched probe: pass;Still to do before the owner's decision: independent exact-head review, and CI including the Lean checks. The five holds (#1009, #1023, #1011, #1003, #918) are unchanged.
Generated by Claude Code