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Certify exact finite-field H0 counts and the cap interior assumption - #219
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Root publishes the named nonauthor's exact review below. Reviewed bytes were compared to commit c1bac3be06b3ec8a921b67cd7882254bbec6a9d4; the source verdict is scoped and this shared-account COMMENT is not an independent GitHub approval.
C39 exact periodic H0 — nonauthor source review
Final disposition: SCOPED ACCEPT of the deterministic integer H0 engine, its separate connectivity verification, the exact bin-transfer argument, and the wrapper custody/replay interface at the identities below. No actionable finding remains in this reviewed scope. The production certificate and report pass source/result custody checks and independent exact rational recounting. Actual million-node generation/connectivity execution is author/root evidence, not an independently repeated execution by this reviewer. Required hosted checks and integration remain the root owner's responsibility. No Gaussian, infinite-field or lifetime-asymptotic acceptance follows.
Attribution. Dylan Roy — delegated AI review. Actual performer: OpenAI / Codex /root/c39_cap_constant_review. Fresh nonauthor of the C39 H0 engine, proof note and wrapper. The reviewer read the authors' current source and tests before constructing independent probes, and read the exact retained approximation interfaces. Same-provider review, zero organizational-independence credit. Dylan's personal reading PENDING. Root owns claim 4b399584 / WE368 and integration. Scientific effect NONE. This subagent made no candidate-source edits and no remote writes.
The base checkout is a4d4f8ccae932e71be77f8303a9575d07539d4d9. Candidate files are uncommitted as of initial exposure; an eventual commit must preserve the reviewed hashes or trigger review of its changed scope.
Exact mathematical object. The input is a finite list of strict integers on (Z/nZ)^2, n>=3, divided by one positive integer scale. At threshold t, vertices with value at least t and periodic axis edges whose endpoints both qualify form the graph. This is ordinary unreduced H0, with one essential class and every positive finite bar retained. Full cubical squares enter only after their complete connected boundary, so their attachment changes no component and respects all threshold inclusions. No fixed diagonal is silently introduced.
The retained approximation interface concerns a PL representative constructed with the minimum-corner diagonal in each square. That representative has the same cubical filtration module, unlike an arbitrary fixed-diagonal graph. C39 computes the specified cubical observable. It does not redo or strengthen the C38 interpolation/stability theorem.
Elder rule and equal-value blocks. The total priority (value,-vertex_id) determines the elder. After each complete equal-value block, every active edge has been considered and union-find components coincide with the threshold graph. The elder metadata is separate from the union-by-size root, so memory-balancing choices cannot change mathematical survival. Each successful union kills the younger generator, splitting off the standard H0 interval. Equal-level insertions produce zero pairs, which vanish when the refined insertion sequence is collapsed to its actual real parameters. Positive endpoints remain exact. The final elder is the smallest id among all highest vertices. Connectivity of the torus gives exactly N-1 unions and hence the stated positive/zero/essential conservation equation.
This argument works over any fixed field, including characteristic two, and does not assume distinct values. The endpoint convention (d/S,b/S] is correct for inclusive superlevel sets: at d/S the dying component is already merged. The corresponding sublevel interval of the negative function is [-b/S,-d/S).
Independent checker completeness. Equal-value plateau searches find exactly the regional maximum plateaus, one positive or essential birth each. Plateau representatives are their minimum ids. Every plateau with a higher neighbor attaches at its birth and contributes only zero pairs. Requiring all nonessential regional maxima to occur exactly once prevents an omitted positive interval from hiding between checked levels.
For each representative p, the true elder death is the maximum, over paths to an older maximum, of the minimum vertex value along the path. Testing whether BFS reaches any older vertex is equivalent: a reached vertex of larger value can follow a nondecreasing plateau ascent to an older maximum; an equal-valued lower-id vertex is outside p's plateau and either similarly ascends or belongs to a plateau with an older representative. The two inclusive tests at d and d+1 establish the exact integer death, since the graph at d+1 equals the graph strictly above d. The implementation's BFS uses explicit seam branches, separate from the sweep's modular-neighbor expressions, and does not call its union-find or replay its sweep.
Independent falsification. The reviewer added a third, structurally different oracle: all-pairs maximin path closure using the Floyd algorithm over max/min operations. Adjacency is constructed by pairwise coordinate-distance tests, without either production neighbor function. For every vertex, death is the maximum path capacity to any older vertex. Births dying at their own value are removed as zero pairs. This oracle uses neither union-find nor regional-plateau BFS.
It agrees exactly, including representatives and zero count, on all 19,683 ternary 3x3 grids, and 180 tied 4x4, 5x5 and 6x6 grids with offsets alternating between +2^96 and -2^96. These are exhaustive/seeded diagnostics of the general proof, not an assertion that finite tests prove arbitrary input correctness.
Six in-memory engine mutants were falsified by the maximin oracle and rejected by the production checker: missing periodic seams, an added fixed diagonal, youngest survival, reversed equal-birth elder, a downward-shifted death, and omission of the longest finite interval. Removing the d+1 BFS test lets the weakened checker accept an intentionally too-low death; the independent oracle still rejects it. This control confirms that the second threshold contributes substantive information rather than a redundant replay.
Bin transfer. With a supplied epsilon-matching and delta=2*epsilon, the lower contraction [a+delta,b-delta) guarantees a finite target partner in [a,b). The upper expansion [a-delta,b+delta) is valid only when a>delta, so a target point cannot disappear into the diagonal. Inclusion of each lower endpoint and exclusion of each upper endpoint are correct even at equality. A nonempty contraction requires b-a>2*delta; equality produces the empty interval. These rules agree with Fraction comparisons in the engine.
The reviewer checked 2,380 single-bar endpoint-shift/bin cases with exact endpoint displacements, including equalities. Changing the strict upper condition to a>=delta is falsified by an empty approximate diagram and a target bar of lifetime exactly delta: at distance delta/2, the latter can be diagonal matched yet contributes one point to [delta,2delta). The actual code returns None rather than the invalid zero upper count at this boundary.
Wrapper and frozen custody. The wrapper pins the exact C38 certificate SHA-256 c46cfc061465b951968f675270b649cd6b61c1dc4989635a1c3c7a3f7a564519 and original RUN SHA-256 3bea8119b5fc3b8aadf887b439d3032f7d88377771c338db44e320dfc60979e1. It validates the frozen receipt and each recorded dependency before consuming the bound. The wrapper's own nodal regeneration must match the original real-center digest, stage records and error; this binds the graph to the exact dyadic sample object. Endpoint integers are encoded as decimal strings, preserving values beyond JSON consumers' common 53-bit precision.
On temporary copies, changing nodal_core.py was rejected as a changed C38 dependency. Rewriting the upstream receipt and rebinding its digest was rejected because the fixed original RUN hash no longer matched. No Hessian computation, original C38 certificate generation or master experiment was run by this reviewer.
validate_directory explicitly checks custody only. verify_directory adds a full recomputation and canonical output comparison. Rebinding a synthetic receipt is not scientific evidence; the scoped source review does not confuse byte identities with mathematical proof or independently observed execution. The final production result was checked for exact bin arithmetic, source bindings and unchanged upstream objects. A fully rebound false Gaussian flag was deliberately admitted by custody-only validation, as that method documents, then rejected by the replay-comparison layer. That last control substituted the immutable expected certificate for the expensive certify function; it tests comparison plumbing and is not claimed as a million-node replay.
Execution exposure. The independent probes passed in ordinary and optimized standard-library Python; their outputs agree exactly after removing the mode flag. The candidate's 12 focused unit tests initially reported 11 passes and one explicit production-snapshot skip in each mode. After publication, the formerly skipped production test was run independently in both modes and passed. All 12 applicable focused cases have therefore executed successfully on unchanged source, without disguising the initial skip or repeating unchanged tests. The reviewer did not run any master/held-out experiment or repeat the C38 bound computations.
Final exact candidate source identities (unchanged from the reviewed initial bytes):
| File | SHA-256 |
|---|---|
exact_h0.py |
48ee16f2316cb1a233594ed10466340aa321d553c2b888198fe86b4bd9052970 |
test_exact_h0.py |
c22930ef4fd0007ab8fd78079f4560cdad3043b210f3b074f7b0220d99039610 |
EXACT_H0.md |
a788b46b1ea5640661e2692b84816bb3acfd1bae5a1fd3083dd18d5d8ba19fff |
exact_barcode_certificate.py |
986da88dd703b4598ebf7782f874854124272ef6dbf67d7deb130972a86a217b |
test_exact_barcode_certificate.py |
0f91e8e998a5c0b3c7b4c47e3a38d12f981369a00f1e7f57da23e75a47f28cd5 |
reviewer_probe.py, the normal/optimized probe JSON, initial unit logs, and final production-unit logs preserve the performed work. production_custody_probe.py and its normal/optimized outputs record the final byte and bin checks. FINAL_SOURCE_INVENTORY.json binds all candidate, result and consumed dependency bytes; final-sources/ preserves the exact new sources and four production artifacts. No candidate repair was requested because no actionable defect was found in the reviewed scope.
Production result readback. The frozen result has 69 positive finite bars, 1,048,506 zero pairs and one essential class, summing to the 1,048,576 vertices of the 1024-by-1024 grid. All finite endpoints are canonical integer strings, every finite birth exceeds its death, and the positive representatives and essential representative are distinct valid vertex ids. The sample digest is f549a5db7215213ff36b4704da4aef5b37472ae2dd3371d77ff38fe8a8d4d410. The retained finite-polynomial diagram bound is unchanged, with upward decimal display 0.001061264136756651120320.
The independent rational recount gives finite-field count intervals [0,1], [0,1], [0,2], [4,6], [3,3], [5,5] in the six bins beginning at 1/250, 1/125, 2/125, 4/125, 8/125, 16/125, respectively. The first two bins, beginning at 1/1000 and 1/500, have lower bound zero and no clean upper bound. Equality of lower and upper in the last two bins is a deterministic consequence for this one finite polynomial and these supplied matching premises; it is not an ensemble estimate.
| Production artifact | SHA-256 |
|---|---|
results/exact_h0_1/CERTIFICATE.json |
845dc940e1781e570d4a6614a00889f33b239274c00e367dc2af1e3b86906fb8 |
results/exact_h0_1/RESULTS.md |
4d11e5349b4713cadb13a11aa54a4962712a73d37f578cc855376ea2546dddab |
results/exact_h0_1/RUN.json |
e51fba013218e746c6845283312cd9ac1e688a8b960e9a2c577a097be5b54c45 |
results/exact_h0_1/RUN.sha256 |
3d51e65e03a26bd2017a00ee601e4844e604c30bfb1795573b0fd8eec7fa44d5 |
Dependency exposure and limits. EXACT_H0.md, the engine/wrapper and both new test files were read in full. APPROXIMATION.md and HESSIAN_GRID.md were read for the retained graph/PL/matching and exact-sample interfaces. Frozen NODAL/FINITE proofs, Fourier core and coefficient data were verified by their retained source identities and used as existing C38 dependencies; their numerical derivations were not independently rereviewed or rerun here. The independently supplied epsilon-matching remains a premise of the bin theorem. The actual field is the frozen rounded-coefficient finite polynomial, not the ideal Gaussian or infinite field. The review does not approve a master/held-out run, change any scientific gate, claim human reading, or establish organizational independence.
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Root publishes the named nonauthor's exact review below. Reviewed bytes were compared to commit c1bac3be06b3ec8a921b67cd7882254bbec6a9d4; the source verdict is scoped and this shared-account COMMENT is not an independent GitHub approval.
Nonauthor technical review of the interior-bump cap ablation
Dylan Roy — delegated AI review. Actual performer: OpenAI/Codex agent
/root/c39_exact_h0_design. Review principal: Dylan Roy. Dylan's personal
reading: PENDING. Organizational-independence credit: zero.
Verdict: ACCEPT at this narrow deterministic assumption-ablation scope.
No blocking mathematical or source-alignment defect was found in the candidate
PROOF.md, 12287 bytes, SHA256
c1a730d6f822f11f262e1af7d249cfc6d2e8b137e7302424b42d92769b45d075.
This verdict binds those bytes and the consumed source slices identified below.
The candidate was authored by /root/c39_elder_proof_review; I did not draft,
edit, or supply its bump construction, calculus, or completion argument.
This is a fresh nonauthor reconstruction, not a digest or execution-only audit.
I separately coauthored C39's exact discrete H0 engine and its proof note; that
is a different mathematical object. I read the ablation candidate, its controls,
source snapshots and the existing Claude review of PR196 before completing this
verdict. That source and reviewer exposure is disclosed, not treated as an
independence credit or inherited acceptance. I did not inspect the actual PR194
or PR175 candidates; their identities appear only in the author's context file.
The root owns claim 261de489-5594-464a-9542-719b9dfd8493, Work Event 370.
This review makes no candidate edit or remote mutation. It can accompany a
byte-identical publication, but does not itself authorize a scientific register,
Gaussian, coefficient, unrestricted-remainder or formal-scope transition.
1. What the source actually requires
I inspected AUDIT's first-exit statement and local good-event hypotheses and
CAP's deterministic statement/geometry. The consumed source identities are:
- AUDIT: Git blob
fdfccaf5356f4cc0cf8764bf323f94b6ff071768, SHA256
98356c5625aa07bcf62b9e6f1a3869ec1fea7dd789e8ea495a97b5c7abb473cf,
19468 bytes, at supplied PR196 head9706a2cb3ca4cc2df792b33ab440c92ee7c76dcc. - CAP: Git blob
0633aca3c2a2882b0de4399da0a75d64c2e6b2e1, SHA256
0bf922b9203c29088b12388807aa0e2ecd020485eb0f6e919679841b5b2636fc,
15160 bytes, at supplied source cut3e0a91b69892b9717564c592e7a966492a81566a.
Their first-exit implication uses the interior bound f<=b on C to force every
older endpoint outside C. The full boundary bound f<=s then bounds every
older-reaching path minimum above by s, and the explicit path bounded below
by s yields equality. These are three distinct obligations. Preserving only
the old boundary cannot exclude an older endpoint in the interior. The proposed
example attacks exactly this omitted premise, not the source implication.
The phrase "C1 cannot be dropped" is read in its stated sense: C2, C3, pin-jet
agreement and small uniform error do not suffice to replace it in this theorem.
It is not an assertion that C1 is a necessary condition for every possible
function whose elder pairing happens to be correct.
2. Local bump, all jets, boundary and uniform size
Direct evaluation of q gives q(-2)=-27/2, q(-1/2)=0, q(1/2)=-1 and
q(2)=25/2. Its derivative is 6x^2-3/2 and its second derivative is 12x.
Thus f0 has the stated pin heights and maximum/saddle Hessian signatures.
The bump eta is smooth and flat at the support endpoints: its derivatives are
the rapidly decaying exponential times rational functions of 1-t^2. The stated
closed support rectangle lies strictly inside C for 0<delta<1/16 and is
disjoint from both pins and the line y=0. Hence the perturbation is identically
zero in neighborhoods of those objects and of the entire old cap boundary.
Every pin derivative, of every finite order, is exactly unchanged. The pin
neighborhoods may shrink with delta; no common fixed neighborhood is claimed
or needed for the all-jets statement.
Both bump factors lie in [0,1] and equal one at their simultaneous center,
so the exact uniform difference is 256 delta^2, not merely an upper estimate.
Along the proposed vertical path, the nonnegative bump gives a height bound
-128 delta^2, and the endpoint height is +128 delta^2. Since delta<1/16,
-128 delta^2>-1/2>-1. This continuous path already excludes the old saddle
as the elder partner. The old axial path remains unchanged and has minimum
-1, so C2 and C3 literally persist while C1 fails at an interior older point.
3. Stationary equation, simplicity and full Hessians
I differentiated the bump independently:
eta'(z)=-2z eta(z)/(1-z^2)^2.
For u=2-2t in (0,1), this gives
v'(t)=-256t+1024u exp(-u^2/(1-u^2))/(1-u^2)^2.
Rearranging yields exactly (B4). Independently differentiating log A gives
-1/(2-u)-4u/(1-u^2)+2u/(1-u^2)^2-1/u.
Clearing the positive denominator u(2-u)(1-u^2)^2 gives
2(-1+u^3+3u^4-2u^5), as in (B5). Its inner polynomial has derivative
u^2(3+12u-10u^2)>0; the quadratic is positive on [0,1], including its
endpoint minima. Thus A has one minimum. Its endpoint limits are infinite,
and A(1/2)=54 exp(1/3)<81<256. The exponential inequality follows, for example,
from exp(x)<1/(1-x) at x=1/3 by comparing the positive power series.
There are exactly two simple crossings. The signs of v' at 1/2,3/4,1 locate
the minimum and maximum in the claimed disjoint intervals.
For t>=1 the derivative of the bump term is nonpositive; outside its support
v'=-256t. For t<0 the bump is absent and the only root is t=0. Thus there are
exactly the two additional positive roots. The bounds -128<m<0<128<h<=256
follow from nonnegativity of the bump, t_-<1, the initial negative derivative,
and the fact that v decreases from its strict maximum to v(1)=128.
On the x support, q' and xi' have the same strict sign away from -1/2.
Outside it the x derivative is q'. Thus there are no hidden off-axis critical
points. The mixed derivative vanishes at x=-1/2, and
f_xx=-6-8192 delta^2 eta(2t-2)<0 is correct. Since the two roots are simple,
f_yy=v'' is positive at T_delta and negative at O_delta. The stated saddle
and maximum are nondegenerate; M and S have unchanged Hessians.
4. Exact death by the smaller cap
On [-2,1/2], q<=0 and xi<=1. With a nonnegative second bump factor, this gives
f_delta(x,y)<=f_delta(-1/2,y). On the smaller cap the latter is at most zero:
for negative y this is immediate; for 0<=y<=delta t_- it decreases from zero
to delta^2 m. The smaller cap therefore excludes every older point.
Its top boundary has value at most delta^2 m. The left, right and bottom
boundaries are bounded respectively by -27/2, -1 and -512, each strictly
less than delta^2 m>-1/2. Every older-reaching path must exit this cap and
therefore has minimum at most delta^2 m. The same vertical path to y=delta
has minimum exactly delta^2 m and an older endpoint. Both inequalities hold
for arbitrary exterior extensions preserving D, proving (B7) exactly.
The numerical root brackets are unnecessary for this death-level argument.
On the eventual Morse/distinct-value completion, T_delta is the sole critical
point at that height, so it is the replacement ordinary superlevel elder saddle.
5. Fixed compact torus completion
The gluing argument is sufficient as a constructive smooth existence proof.
On each remaining circle arc, the assigned endpoint derivatives have the signs
required by the proposed monotone segments. Shortening fixed endpoint and
quadratic-extremum collars makes their integral contributions smaller than
the prescribed height difference. A strictly sign-preserving smooth connector
with small integral can then be enlarged by a nonnegative compactly supported
bump to match that difference exactly. Integration preserves all endpoint
jets and creates no extra zeros of the derivative. No bound on connector
derivatives is imposed, so the large specified height differences create no
obstruction on a circle of fixed length 16.
Q has four nondegenerate critical points, and V has two. Their product-sum
therefore has eight nondegenerate critical points with the eight listed distinct
critical values. The perturbation affects only the x=-1/2 line near positive
y=0; the x-sign argument excludes additional critical lines and the preceding
y analysis adds exactly T_delta and O_delta. Their heights lie in (-1/2,0)
and (0,1), disjoint from the eight old heights. Hence there are exactly ten
nondegenerate critical points with distinct critical values on the same torus.
The bump's exact uniform norm and the local death proof survive this completion.
6. Why this does not refute PR196 or CAP
With r=k=1, the original f0 has M3=12, M4=0 and lambda=256; the source depth
bound is 256>(4/3)*12^2=192. In dimension two these are precisely the stated
partial-block norms, with no tensor-norm substitution. The embedding condition
also holds on the length-16 torus: 1<16/(4 sqrt(2)).
Expanding eta at zero gives 1-t^2-t^4/2+O(t^6), hence eta''''(0)=-12.
The fourth y derivative of the perturbation at its center has absolute value
256 delta^2*(2/delta)^4*12=49152/delta^2. It is included in the source's
whole-cylinder M4, so the required rM4<=3/10 is violated. Preserved endpoint
jets do not preserve this supremum. The source theorem remains unrefuted;
this review does not claim a newly found defect in it or a re-audit of all
its quantitative and probabilistic dependencies.
7. Executed checks and limitations
independent_controls.py reconstructs the rational logarithmic-derivative
identity using six distinct rational evaluations after independently bounding
the cleared polynomial degree by five. It also rejects the wrong final sign.
For root brackets it uses a different enclosure method from the author's:
range reduction, alternating Taylor bounds for exp(-x), then exact interval
squaring. It verifies both root signs, the minimum/maximum ranges, source
good-event constants, the fourth-derivative scale and the separation of all
critical-value ranges. The actual result is in INDEPENDENT_RESULTS.json.
The author probe was also rerun and its output compared with RESULTS.json;
all supplied inventory members and both source Git blobs were checked exactly.
Those execution results support their stated finite identities. The smooth
gluing, continuum critical-point completeness, first-exit argument and exact
elder conclusion were reviewed above rather than inferred from test output.
No unresolved finding remains within this ablation scope. No independent-human
or institutional review, formal kernel proof, Gaussian/Kac–Rice audit, numerical
coefficient certification or larger theorem acceptance is supplied. The review
has zero organizational-independence credit, and Dylan's personal reading
remains PENDING. Exact identities and exposure are recorded in MANIFEST.json.
|
Integration check complete at c1bac3b: all 20 candidate paths and 37 inventoried source identities matched; 13 protected C38 paths unchanged; 83 local links resolve. The omitted ablation source-snapshot defect was repaired and its failure retained; normal/optimized exact output equals the frozen result. Integration review is by OpenAI/Codex /root/c39_elder_proof_review (ablation author, explicitly not its nonauthor mathematics reviewer), SHA256 f3fc67e116d150ea7be64fdd5206ef5d9701ea0ce5ec34862f105f975b04e848. Both separate mathematical reviews are posted above. All 7 hosted checks passed; original formal artifact11131462452 and its receipt/log/source bindings verified at actual merge test ad15a66. Automatic code review is still running, so integration waits for that result. Scientific/formal-alignment and human-review limits remain. |
|
Dylan Roy — delegated AI work; actual OpenAI/Codex C40 lane. Pickup at R17 claim |
Change and purpose
The C38 dyadic grid had a certified spatial error but no certified computed barcode. This adds integer-only periodic cubical H0, a separate plateau/BFS verification of every elder death, and exact rational bin transfer for the same frozen field. The 1024² grid has 69 positive finite bars and one essential class. The unchanged diagram bound is at most 0.001061264136756651120320; some wider bins now have exact smooth finite-field counts.
A separate smooth construction on a fixed torus preserves all pin jets, the complete old cap boundary and the older-reaching path under arbitrarily small uniform perturbations, while changing the elder saddle. It isolates why the cap interior-height condition is necessary, without contradicting the cap theorem. The public reading pages link both results.
Current disposition
3907754f19a14813b0c1e919ae3afbf0843569ae; reviewed headc1bac3be06b3ec8a921b67cd7882254bbec6a9d4; common tree96a037053413509da236ac8761de94e5d31f2a05.ad15a6696a86da943a34cf3541e405ef9c6387fc, run36790794615; artifact11131479652 binds landed commit, run36791303262. Original ZIP/log/source bindings verified; formal alignment remains separate.da21fb82a9c21c00599f7087fa46e1dcf770c885c210136e6ce16b38761039d5. Downloaded bytes matched; owner-only destination retained. Registered AI833 / EL555 / RQ70–72 / WE371–373; all three C39 claims released at WE374–376.Verification
One applicable 18-stage local master completed. The first run stopped at a missing ablation source-file dependency; after adding the two exact source files, only failed and unrun stages resumed. All command stages passed. The local test requiring an installed Lean toolchain was skipped; the subsequent required hosted formal execution passed with original receipts, rather than being inferred from local success.
Coverage: 72 experiment tests in normal/optimized modes; 293 repository tests in both modes (one local Lean skip), navigation/landing/formal-source checks, 98 JavaScript tests plus public-shop/museum checks, retained certificate replays, exact H0 replay, normal/optimized ablation controls, and the full fixed pilot. Independent H0 review additionally uses exhaustive maximin-path controls over 19,683 ternary landscapes and adversarial mutations. Exact endpoint integers are serialized as strings.
Evidence and limits
Frozen C36–C38 inputs and outputs are unchanged. New results live in
experiments/periodic_h0/results/exact_h0_1; the algorithm proof isEXACT_H0.md. The self-contained ablation isdocs/research-translation/20260930/cap-assumption-ablation/.Dylan Roy — delegated AI review; actual executors are the named OpenAI/Codex agents. Dylan's personal reading remains PENDING as an optional retrospective aid. Same-provider reviews have zero organizational-independence credit. No human-review, Gaussian-law, infinite-tail, asymptotic-window, numerical-remainder, full theorem or formal semantic-alignment claim is made.
The one immutable delivery and claim releases are complete. The final custody audit was kept outside the frozen ZIP and did not rerun the master or enlarge scientific scope.