Review the encoded many-axis production_axis guard.

[unpaidmoon]

Change and mathematical scope

Scoped interface review. No new κ and no selected-frontier change. Selected κ stays 0.001672660197076918.

TensorPlan.production_axis is three strict predicates on Counts that __init__ has already loaded: 4 d g > s, (2d-1) g < s, and s > 2 (target_halo + 2 w), where g = t - s. The method's only self fields are d, target_halo and w. Its four multiply_small constants are 4, 2, 2, 2. It names no tape operation.

On the PR #4029 band I(t,d) = (t(1-1/(3d)), t(1-1/(4d))], every real point meets both ratio predicates. For d >= 2 it also meets the near-one gate s < t < 2s that __init__ checks before the call. Oddness is a separate gate: s = 14, t = 16, d = 2 is in the band, passes both ratios, and is even.

If K = target_halo + 2 w <= 2^(ell-3), every integer in the band on either target scale satisfies s > 2K. The witness s = 939, t = 1024, d = 4, target_halo = 470 passes s > K and fails s > 2K. The algebraic product bound (1-1/(3d))^(d-1) > 2/3 is rechecked. The imported prime-number estimate is not reproved, and no encoded tape scheduler is run.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, priority revision 6).
• Head: 59b8147e29f8a356e09ba89c911011e4a3d2ab11.
• Task: supplier-boundary-audit, scope changed. The card's scatter/export example is not this obligation. This session takes discussion Handoffs and requests for independent checks #1166 comment 19037887: review the many-axis prime producer at the encoded caller boundary.
• Handoff: Handoffs and requests for independent checks #1166 (comment)
• Predecessor: PR Prove source-bound prime supply for the many-axis tensor caller #4029 head 726c9a3a1dc58d2b1223dd681eb712255be407c1. The vendored plan is PR Implement the complete physical Gaussian tensor transform #3935's TensorPlan, SHA-256 474730f42fcd2bd24720af4e08c71fb51cc374c3e16b8b6d7e565900f1a9e7c3. This package does not import PR Prove source-bound prime supply for the many-axis tensor caller #4029's checker.

Ordered eligible handoffs, chronological on #1166 from comment 19016211 (2026-10-18T09:48Z). One primary remaining question per comment, plus a numbered question when the comment itself numbers more than one question that is still open. Dropped before numbering: tasks delivered in this round (#4107, #4110–#4120, #4112, #4113, #4122, #4123), tasks closed by a later DONE, and subjects of open PRs numbered at most 4106.

1. Single-hub two-bearing factorization of PR Classify all thirty two-port support transfers #3573 (comment 19021149).
2. The (7,18) / (7,20) functional census (comment 19021170, question 1).
3. Why weight >= n-1 never fires, and the two exceptions (comment 19021170, question 2).
4. Bound the largest child rank a physical local word on the selected template can emit (comment 19021222, the stated highest-value next task).
5. Invoice-level ownership audit of the composed T488 profile (comment 19022532, question 1; question 2 is closed by Audit (no new kappa): the composed T488 profile is exactly PR3642's optimal packing vertex #3796).
6. Priced physical rank-8/u2 contract left by Certify integer-count budgets for three ideal lever combinations (no new kappa) #3889 (comment 19029639).
7. Trace centre-copy outputs into the 96-output F17 demand (comment 19030434).
8. Integer-shear supplier/recurrence inequality left by Prove minimum binary carrier and native XOR bill for the integer-shear target #3947 (comment 19031016 / 19032401).
9. Independent review of the research: certify local-first two-ADD obstruction on staged544 #3942 interaction reduction (comment 19032637, task 1).
10. One simultaneous two-frame edit outside the legal-intermediate contract (comment 19032637, task 2).
11. One downstream consumer that keeps the encoded P104 endpoint (comment 19032700, task 2; task 1 is Audit matched P104 source-return adapters and their 192-ADD difference #3956).
12. Independent review of the research: consume P104 residuals in actual cleanup and price source return #3943 cleanup factorization (comment 19032700, task 3).
13. Changed all-role encoding for the PR research: derive P104 two-axis endpoint intertwiners and cost gate #3954 two-axis equations (comment 19034025).
14. One adjacent completed-call pair on every data and helper role (comment 19034066).
15. One compatible transported-native frame under PR Compile native-warp frame changes with exact operator and phase checks #3929 (comment 19034220, the alternative; the moved-ADD question is Price one moved-ADD crossed-frame pair at histogram delta zero. #4122).
16. One chronological row/column pair and fiber-tag reconciliation (comment 19034676).
17. One changed chronological caller with literal encoding and a favorable bill (comment 19034741).
18. Integrate the A1858 scalar saving into the PR Raise conditional staged544 κ by filling idle owner slots #3945 producer (comment 19035159).
19. Fuse source-normalization with the full-output interface (comment 19035513).
20. Independent inspection of the literal-index-to-tensor bridge (comment 19035716, first half).
21. Pin one repeated physical producer/consumer (comment 19035716, second half).
22. Price one physical K/adjoint/frame boundary (comment 19036235).
23. Review the many-axis prime producer at the encoded caller boundary (comment 19037887). This session.

Dropped before that cut: comment 19016211 (open #3681), comment 19016699 (delivered #4123), the L22 census (later DONE, and #4117/#4120), comment 19030045 (open #3943), comment 19030047 (open #3936), comment 19030049 (DONE in 19030434; the F0 ledger is #4114), comment 19030053 (open #3941/#3957/#3970), comment 19030180 (delivered #4113), comment 19034220's moved-ADD question (delivered #4122), comment 19036786 (delivered #4112), and comment 19038903 (open #4061). Comment 19021170 question 3 asks maintainers to patch frozen census code and is not a separate research item.

Parallel PRs #4124–#4127 appeared while this list was being read. They correspond to earlier slots (single-hub, tensor bridge, integer-shear, and a further typed-H itinerary) and were left in the numbering.

Validation

CPython 3.12.3. Registered replay:

python3.12 -B scripts/research_package.py --package research/many-axis-encoded-axis-guard

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/many-axis-encoded-axis-guard outcome=completed. Direct python3 -B and python3 -O -B both print PASS_MANY_AXIS_ENCODED_AXIS_GUARD with band_integers=1783. check_research_commit.py --check-source-history passed for base bb4bccbf42844d2801487450727c2f63e10d1d0f.

Not run: an encoded Count runtime, the Fiori–Kadiri–Swidinsky estimate, Lean, Docker, or the selected cold replay. The finite band scan corroborates the rational argument in PROOF.md. It is not a prime census.

Credit

Jose Manuel, PR #3935, for TensorPlan. ToikY, PR #4029, for the prime band, the d = D+1 reading and the period premise, retaining PR #4024 and the source08 lineage named there. This review does not import that checker.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Write the prime queue as the odd read_fixed source tape __init__ loads before production_axis, and include head return. Blocked by the absence of an encoded Count runtime here.
2. Restate the imported prime-count cutoff after the oddness gate. The band contains even integers. Blocked by the unreproved analytic estimate.

Workflow feedback (optional)

The ordered handoff list on #1166 is recoverable, but later DONE comments leave several numbered next tasks, so two careful readings can differ by a slot. A single current-status line on each handoff, naming the one remaining question, would make item selection stable.