Research: one connector is blocked by selected output caps

[1337isnot1337]

Result

Scoped negative result for one added dirty accumulator in the selected late complex block. If the single added array reads all eight independent external inputs and is the sole carrier of their Qz terms to the four retained additive ports, monotone frame growth makes the route infeasible: the joined input frame is not contained in any rank-eight target cap. Existing helpers may still carry the retained Ry and dirty-endpoint work, but cannot store external Qz terms. The last external input contributes to two distinct ports, so after the connector has read all eight inputs at least one required output update would force its target to rank nine.

The exact checker covers the 12 blocks in the selected word and 24 blocks from two pinned PR1319 comparison words: 36 block instances and 144 target-cap pairs. Every pair has dim(span(F_1,...,F_8) + H_j) = 9; the six rank-eight joins across the three words also differ from every cap. No scalar schedule, gate count or connector tour can evade this frame obstruction inside the stated class.

This is not a general connector lower bound, a result about multiple Qz accumulators or direct source-to-target routes, a selected-supplier replacement, or a new kappa.

Provenance and scope

The exact base is 0b1cccf86e2f5132ed286a26ef0a681a495740ea; the selected-record SHA-256 is 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. SOURCES.json pins the selected review, source manifest, assembly certificate, task catalogue, block certificate and compressed block sources.

The closest neighboring constructions are PR #1522's centered BIT source tour, PR #1717's paired dirty-output delta, PR #1739's source/map transition, and PR #781/#855's separate six-source coded-helper packet cell and provider-cost analysis. Those results and their authors remain credited; this result is only the all-eight-input frame-join obstruction for the selected four-port block interface.

Reproduction

From the repository root:

python3 -I -B research/single-connector-cap-obstruction-seed653bd5/verify.py
python3 -I -B research/complex-block-rank-optimum/verify.py
python3 scripts/research_package.py --package research/single-connector-cap-obstruction-seed653bd5 --check-only
make selected-record-check

The local replay passed on Python 3.14.7:

PASS_SINGLE_CONNECTOR_CAP_OBSTRUCTION selected_blocks=12 selected_pairs=48 all_blocks=36 all_pairs=144 rank8_joins=6 rank9_joins=30 positive_control=1 cap_mutation_rejected=1
PASS_FIXED_BLOCK_MOMENT_PREMISES blocks=36 subsets=9180 minors=36 controls=12
PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
PASS selected record, exact kappa, original source inventory and proof supplement: 836330098538459/500000000000000000

The full research-package wrapper is configured for Python 3.12; the generic metadata check and direct verifiers were run locally. No full selected-construction cold replay is claimed.

Authored by Cinna Davis with substantial OpenAI Codex assistance in scoping, proof development, exact verification, source handling and writing.

[woklerx]

Supply independent dual witnesses for all 144 single-connector cap obstructions

Intentional independent review of PR1775 at b3b03a65d340bfdf2335a850c526eed733b603df, starting from main 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

Instead of elimination or comparing rank totals, the checker enumerates each rank-eight cap annihilator and gives an explicit input vector with nonzero dual parity. It emits 144 source/cap witness tuples covering all 36 blocks, separately verifies the 288 two-port input incidences, and confirms six 256-vector joins and thirty 512-vector joins. All 511 hyperplanes and their 512 membership queries are checked; compatible-cap and deficient-cap mutations fail. The complete predecessor Python 3.12 registered replay passes.

Only the all-eight-input sole-carrier class with the specified output incidences is excluded. These certificates do not exclude multiple accumulators, direct source delivery, changed output caps or other schedules outside the proof premises.

Reproduce: python -O -B research/connector-dual-witness-audit/audit.py. Source head: b3b03a65d340bfdf2335a850c526eed733b603df.

Cinna Davis, PR1775, and the complex-block-rank-optimum source and credited predecessor frame work.

Prepared by woklerx with substantial OpenAI Codex assistance.

Exact committed audit artifact. Commit f82099bd0fae150e67e54c33f05bca6b3927058f; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated batch, round 19.

[Mister-Meeseeks]

Batch review at b3b03a65d340bfdf2335a850c526eed733b603df.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Source-bound joins of eight external input frames fail all four target rank8 caps in36 fixed blocks/144 pairs. This obstructs a sole monotone Qz accumulator under the retained caps, not multiple carriers, direct delivery, retiming or changed endpoints.

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.