Bit construction (no κ; conditional on #1043): R438 + one transport + optimal window-respecting re-hosting → c = 0.0017348463 (+0.082% vs #589); fixes two #1345 atlas crashes

[thakrarsagar]

Finite conditional bit-supplier construction plus a tool fix. No new κ. The bit supplier does not bind: complex is 0.0016754627 and κ is 0.0016726602. Everything here is conditional on #1043 (Ali Romman's R438 word, helper 470 deleted), which is still open.

bit endpoint c (exact; accepted at c, rejected at c + 1e-24)	value	vs #1043
#589, selected (control)	0.001733427039589844234749
#1043 R438, its own in-place hosting (control)	0.001734176288479865766692
R438 + one transport, #1043 hosting	0.001734220472884893243548	+0.0025%
R438, optimal window-respecting re-hosting	0.001734802047828389852783	+0.0361%
R438 + transport + optimal re-hosting	0.001734846264120199151475	+0.0386% (+0.0819% vs #589)

1. One improving transport (verify_transport.py).

• The move. A op 2027 (444 += 77) moves from frame 186 to slot 154 at frame 79, next to the existing frame-79 reads of source 77. Slots 155 and 425 are equivalent.
• Effect. The profile changes by +e1 − 2e2 + e3 at equal mass 5,121. ADDs stay at 24,248, and the 18 multi-source A gates are kept.
• Checks.
  • The R438 word rebuilt from Finite BIT construction: R438 source boundary with full hosted invoice #1043's stdlib builder matches Finite BIT construction: R438 source boundary with full hosted invoice #1043's CERTIFICATE and FRAME-PATHS.
  • The new word passes Finite BIT construction: R438 source boundary with full hosted invoice #1043's replay (arbitrary dirty endpoint, precision bounds unchanged) and xcheck_p.py (H1–H5, K = D, C = U⁻¹, F2 replay on 660 columns).
• Local optimality afterwards. Frameopt finds 0 improving components. The patched atlas finds 0 improving singles and 0 among 442,817 pairs.

2. Optimal re-hosting of R438's slack (verify_rehost.py).

• What changes. Deleting helper 470 leaves 54 width-8 slack units per replica. Finite BIT construction: R438 source boundary with full hosted invoice #1043 folds them back into their own hosts and runs no hosting search.
• Optimum. Under Research note: PR589 bit hosting is width-8 optimal; width-7 residuals worth up to +17-23% bit headroom (no new kappa) #1023's slot model, an exact top-3 interval DP, cross-checked by branch-and-bound over all 10,556,685 layouts, gives a unique optimum: 10 fully idle rank-42 slots plus one 42-slot holding a single helper. The runner-up is worse by Σg 0.0079 per replica, and S = 45 reproduces Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589.
• Windows and placement.
  • All 22 slack splits are stage-window feasible (maxflow plus a separate Hall test).
  • An explicit placement of 126,144 owner roles passes two audits.
  • There are 29 controls in all.

3. Two crash bugs in #1345's transport atlas (atlas.patch, 3 lines; atlas_bugs.py reproduces them).

• A dict(..., improving=...) duplicate-keyword TypeError at line 282, whenever any move improves.
• A Fraction < tuple comparison at line 416 (best[0] should be best[0][0]); line 375 has the same pattern.
• Effect: the improving branch was never exercised. On Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589's word, the patched and the pristine atlas both reproduce Scoped negative result: PR589's bit word is exactly transport-locally optimal (no new kappa) #1345's result.json, so its conclusion stands. On R438 the pristine atlas crashes, and the patched one finds the move above.

Verification.

• Both deliverables were rebuilt and challenged by adversarial AI verifiers. Their checks covered an independent word rebuild and replay, Decimal endpoint roots, layout counts, the DP optimum and their own mutations; their hygiene findings are fixed.
• Run on CPython 3.14.4. The registered 3.12 replay was not run locally.
• --check-only passes, and the research tests pass (65, 2 skipped).

python3 -I -B research/bit-r438-transport-rehost/verify_transport.py   # PASS_R438_T154_TRANSPORT ... c=...->0.001734220472884893243548 ...
python3 -I -B research/bit-r438-transport-rehost/verify_rehost.py --check research/bit-r438-transport-rehost/verify_rehost.receipt.json   # PASS_R438_WINDOW_REHOST S=54 ...
python3 -I -B research/bit-r438-transport-rehost/atlas_bugs.py         # PASS_PR1345_ATLAS_BUGS ...

Scope.

• These are local and slot-model certificates, not a supplier admission.
• Not run: Finite BIT construction: R438 source boundary with full hosted invoice #1043's native C++/Boost/NumPy lane (hosted emission, full hosted audit, assemble9, outer). Hosted profiles are assembled as 288·local + 32·remainders.
• Not checked: projector compatibility (Audit: selected PR589 bit-hosting pending projectors across all hosted helpers (no new kappa) #1307) and cross-replica owner maps.
• Not searched: transport triples.
• Base: main 0fdd7d82. Card selected-packing; scope changed to the pending R438 supplier, with the reason in TASK.json.

Credits.

• Finite BIT construction: R438 source boundary with full hosted invoice #1043 Ali Romman: R438 word, builder, replay and hosting (vendored).
• Scoped negative result: PR589's bit word is exactly transport-locally optimal (no new kappa) #1345 hipotures: transport atlas (vendored, with the fix as a patch).
• Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589/Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555 lineage.
• Research note: PR589 bit hosting is width-8 optimal; width-7 residuals worth up to +17-23% bit headroom (no new kappa) #1023: slot model.
• seed72 and seed14 packages: windows, allocation and placement audit.
• Scoped negative result: PR589's bit word is exactly frame-optimal (no new kappa) #886: frameopt.
• e8-bit-p111-tuned: xcheck.

Prepared with substantial AI assistance (Claude Code, Anthropic, Claude Opus 5.5): an AI scouting pass, two builders and two adversarial verifiers. No independent human review is claimed. Apache-2.0.

🤖 Generated with Claude Code

[thakrarsagar]

Status of open question 1 (native lane): the parent #1043 native C++17/Boost lane now passes on Linux x86_64 (g++ 15.2, Boost 1.90), reproducing its certificate canonically: #1043 (comment). This package's transported word (words/r438-t154.json.gz) and its re-hosted layout have still not been through that lane. #1043's verify.py hard-codes its own candidate and boundary check, so the t154 word needs a separate driver around pipeline.run, and the optimal re-hosting needs a selection-plan input for emit_k.py.