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Scoped census: late-compensated R439 helper entrances; only #1179's kernel pair survives the carrier-checked class, one triple stays open (no new kappa) - #1932
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Tests the case CrocSwap#1128 and CrocSwap#1179 leave open: can a common-frame helper entrance (all 4,954 supports of CrocSwap#1253's closure, plus 5,212 source donors) be compensated after the scatter instead of by a frame-0 prefix? On the selected PR589 word and the four merged star words, the sound necessary test (LC-fav) admits only CrocSwap#1179's kernel pair 444+470 and the triple 444+470+578; the strict class A6 admits only the kernel pair; with storage relays (A6R) the triple stays open. Two engines with no shared code agree on K, the closure (= CrocSwap#1253's certificate), every dirt-only space and every verdict; a synthetic word's built witness replays; mutations flip verdicts.
- The synthetic witness is described exactly: its post-scatter reads undo W_syn's moved compensation, so after B it equals CrocSwap#1179's prefix entrance on PR589; it now also fails without its late reads (new control). - The open triple's obstacle is scoped to A6R (B++C fixed); LC-fav also allows a rewritten B/C. 'Settles/decides' becomes 'narrows to one open triple'. - PROOF.md: cone lemma is CrocSwap#1128 section 1 (Lemma 2 is the dual of section 2); Lemma 1 states only x-free, pivot-free D' contributions; Step 4 folds scatter-extension snapshot terms into u; frames at sigma equal raw frames; reads during C reduce to the end of B (asserted: C at FULL, no target). - Donors: 5,212 enumerated, 5,059 placeable. W_t are coordinate subspaces (recorded); the structural reason is restated accordingly. - Relaxation checked to contain every admission; census sanity checks are labelled as such; flipped-byte control recorded; engine-2 coverage stated precisely; credits for eumemic, DreamingOfClouds, CrocSwap#967, CrocSwap#915/CrocSwap#926, CrocSwap#1043, CrocSwap#1079, CrocSwap#1256.
thakrarsagar
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Batch review at Merged to Reviewed scope: Two independent exact engines reproduce fixed-word closure and late-entrance census across five pinned words. Written cone/span argument supports the stated single-common-frame LC-fav necessary test; A6 excludes late compensation, while storage-relay triple444/470/578 remains OPEN. Source-donor and relay relaxations retain their narrower execution coverage; full661-column synthetic positive and mutation controls pass. No universal entrance obstruction or supplier improvement follows. The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions. Batch review, attribution and evidence. Thank you for the contribution. |
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Scoped negative result with one open survivor. No construction, no new κ, and the selected record is unchanged.
bit-helper-contract, with the scope refined.0b1cccf8.research/r439-late-entrance-census-seed09/.The open case this narrows
The inherited H2/K interface requires every helper to start at frame 0, so that a frame-0 prefix D supplies all dirt compensation. An entrance would let a helper start at a nonzero frame instead: a pivot p, with the gauge q ^= p on a support c. That changes the response by ρ = Kc, so the targets in T = supp ρ need compensation from somewhere else.
Merged work decides only T = ∅:
Two cases were left open by name:
This PR narrows that case, for compensation after the scatter with A and the scatter fixed and one entrance at a time, to one open triple. It covers every one of #1253's 4,954 supports, plus 5,212 enumerated source-donor entrances (5,059 of them placeable), on the selected PR589 word and the four merged star words (#1062, #1122, #1188, #1208). The broader case of #1128 §4, compensation after A but before the scatter, is not covered.
The test
For each target t, W_t is the dirt-only space: the helper parts of all source-free F2 combinations of the values that t can legally read after the scatter. A support is admitted only if every t ∈ T has some u ∈ W_t with u·c = 1.
There are three classes:
PROOF.md: the cone lemma is #1128 §1's dependency-path argument; the monotone-span lemma is the dual of #1128 §2's erasure invariant). This is the necessary test.Results
They are identical on all five words.
The triple 444+470+578 is OPEN.
So, within A6R (B ++ C fixed, insertion-only target reads), covering all 8 needs storage relays outside T, which must later be restored. LC-fav also allows a rewritten B or C and fresh restored registers, which A6R does not model. It is handed on as open question 1.
Why so little survives. Every W_t is a coordinate subspace, spanned by at most 5 unit vectors (4 in A6). A target can compensate a support only where the support meets that set, and only 98 (47) of the 18,085 nonzero K incidences do.
Correctness
census.py) does the packed-int replay and the parity census.engine2.py, no shared code) uses set-valued replay, rational annihilators, a kernel-method LC-fav and per-pair change points for A6.CERTIFICATE.json), every W_t in both classes and every support verdict, on all five words. Engine 2 also checks that all 636 frames are closed, so label inclusion equals rational containment.W_synis PR589 with target 150's compensation of 470 moved after the scatter: three B reads into 150, and 470 dropped from D's row 150.wlib.replay, and fails at register 150 without its three late reads. The witness is: start[444] = 79, the shear and its inverse, three post-scatter reads into 150, and D′ = PR589's D without 444.W_syn's own moved compensation, so after B the witness carries the same values as Finite bit construction: sparse R439 kernel entrance gauge (no new kappa) #1179's prefix entrance on PR589. It shows that an admission can be realised; it is not a new construction.verify.pygivesPASS_R439_LATE_ENTRANCE_CENSUSin about 3 min, and RESULT.json is reproduced byte for byte.research_package.py --check-onlypasses.PASS_REGISTERED_RESEARCH_PACKAGEin 3 min 15 s.verify (…, tests)job is pre-existing on main (the stale spectrum-audit pin) and is not caused by this package. The repair is CI repair: refresh the single-intersection spectrum audit pin after #778 (tests job red on main) #1752.Scope
Covered. Single common-frame entrances, with fixed A and scatter and no pre-scatter wires, and with the endpoint required on all 661 columns.
Not covered:
PROOF.mdbut not run);No κ. The bit side does not bind, and an entrance's −H1 is cancelled by +H1 in width-8 hosting (#1179, #1253).
Reproduce
python3 -I -B research/r439-late-entrance-census-seed09/verify.py # about 3 min; PASS_R439_LATE_ENTRANCE_CENSUS python3 -I -B -m unittest discover -s research/r439-late-entrance-census-seed09 -p test_package.py python3.12 scripts/research_package.py --package research/r439-late-entrance-census-seed09Overlap and credit
xcheck_p.py: eumemic (Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543/Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555). The A-section transports andwlib.py: DreamingOfClouds (Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589).find_overlap.py --refreshfound no work on late compensation of R439 entrances.Disclosure
Prepared by Sagar Thakrar (thakrarsagar) with substantial AI assistance from Claude (Anthropic) via Claude Code.
Parallel read-only scout and judge subagents selected the question; both judges ranked it first.
Reader subagents and a synthesizer audited the scout's criterion. They found the triple the scout had missed and the missing carrier check in its strict class.
Both engines, the proof note and the controls were then written fresh.
A post-PR adversarial review corrected the witness description, the open triple's scope, the citations and the controls (second commit).
No claim was posted to Discussions. New material is Apache-2.0.