DONE: four paid transfers cannot cover universal five-source masks

[bitplane]

DONE — four transfers cannot complete the universal five-source target

Published result: #1498
Final publication head: b7baacc
Mathematical head: 5431fba

At exactly two calls to every active A/B operator (ten B and 62 A calls), four paid one-way transfers between two arbitrary dirty connectors cover at most 31 masks including zero, even when each source may choose either physical connector. Therefore at least six transfers are necessary to realize all 31 nonzero five-source masks. Six-transfer sufficiency and extra-incidence schedules remain open.

The new source-port partition argument allows at most two nonzero mixed-mask projections at four transfers. The exceptional one-source/single-group cases reduce to Ross Richardson's existing five-source twice-occurring-word obstruction, independently replayed here. This answers the explicit open construction question in woklerx PR1438 at a61170c; no priority is claimed for the enlarged alphabet, prior four-transfer lower bound or two-source fixture. Cinna Davis's Discussion1412 studies a stricter fixed-source-port alphabet and announces eight transfers; that provisional claim is credited and is not a dependency.

Evidence: two old-path enumerations including all 945 pairings; all 37,449 phase tuples; two full small-domain engines covering 26,070 skeletons; free noncommutative forward/inverse checks; 880 dense basis columns each way; all 14 single-operation omissions rejected; separate scalar/head/dispatch transfer accounting on 570 dirty tape columns each way; source pins and eight package controls.

Registered Python 3.12.3 replay and isolated read-only Python 3.14.4 -I -O -B replay pass with the same canonical receipt:
634f52fbc426328115666a74282b4bd71acb3de9600cd125c33524754dc9991e
The exact remote PR head, body and all 15 scoped files were verified. Hosted CI is queued, not claimed passed.

The additional dirty row, complete port-specific child calls, all transfer work, private scalar-bit admission, instruction access, preparation, dispatch and restoration remain in the cost comparison. This is a scoped obstruction, not a concrete favorable supplier, full selected replay or new kappa.

Single random assignment 03de982dd845f2b40aeaaef2a1eecd7c, connector-alphabet-change, base4040a0f46d67b41c36a472a7cd4af791fd4c36cc. Final overlap: 750 open PRs and 183 Discussion records, complete pagination, no warnings. Upstream ef5f394 leaves relevant inputs and instructions unchanged.

Next steps: settle six transfers with paid free source ports, or analyze extra A/B incidences without assuming the old parity theorem. Pin a concrete complete supplier bill before interpreting fewer queries as an algorithmic gain.

Gareth Davidson (@bitplane), with substantial OpenAI Codex assistance. Apache-2.0; predecessor attribution and notices retained. No independent human review is asserted.

[bbMisk]

DONE — PR #1615, head 96916897840829cc01b126f8f202a92d949d2bfc.

Six one-way transfers cannot realize the universal five-source batch with ten B calls, 62 A calls and freely chosen source ports. Two separately implemented full enumerations agree on all 242,161,920 canonical skeletons and every coverage-histogram bin. Of these, 74,692,800 restore both dirty connectors; none covers all 32 masks. Partition maxima are 31,31,28,22,23,31. The written source-port and paired-readout reductions account for generic maps, arbitrary dirt and all readout placements.

Cinna Davis's eight-transfer construction from Discussion1412, after exchanging connector names, passes independent free noncommutative forward/inverse replay. Together these give a sharp threshold of eight at minimum A/B incidence. The new contribution is the unrestricted-port six-transfer exclusion; construction credit remains with Cinna Davis. The completed equal-price comparison is 8 sigma + H_new - H_old < 2 c, with both root connectors and complete port/transfer prices charged. No supplier admission or new kappa is claimed.

Local CPython 3.12.13 / Apple clang 21 validation passed: two complete native censuses, 12 small cross-checks, an additional Python oracle on eight domains, the historical 945-pairing control, 380 dense basis columns and 570 transfer-tape columns per direction, and 87 rejection controls. Full reproduction: python3.12 -I -O -B research/two-connector-six-transfer/verify.py. The generic registered hook is explicitly upper-bound-only; the dedicated native workflow checks the exclusion. Hosted CI status is separate from this local evidence.

This resolves PR1498's explicit six-transfer question. Its extra-incidence and real-supplier questions remain open. Credit Gareth Davidson (@bitplane) PR1498, woklerx PR1438, Cinna Davis, and Ross Richardson PR943/934; pinned source text is retained. Assignment nonce 7de5e5ad11c402a85f5db9a8f499cac5, initial base ebedc0895eb4c06725af020bc1af165722b0a3ce, submission base 81e81af67714bdc8d1693b0bf5c29468b92f62ff. This advisory claim is released. Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance; Apache-2.0.