Research: exact two-relation four-register pattern census and scoped obstruction

[1337isnot1337]

Contribution

This package records a finite exact census and a scoped negative result for a four-register rational frame with exactly two independent address relations. It evaluates the proposed first-seven-prefix construction class; it does not establish an obstruction for arbitrary words or supply a new kappa.

The exact census enumerates all 120 rank-one idempotents in M4(F2), 105 off-diagonal patterns (including zero), and 196 realizable two-dimensional pattern planes. Of the planes, 176 admit a common topological order and 20 have cyclic union. The candidate screen checks all 20 exceptional planes under all six relation-signature bijections and finds no diagonal singleton endpoint. The exact 16-call positive control passes; a one-call deletion and an address corruption are rejected.

Pins

• Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea
• Selected-result.json SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32
• Certificate SHA-256: 690de78db74c1ba59a4092b8f7b9f8f54c5d53d3650d9e8d78448cdddda18321
• Source hashes and repository blobs: research/two-relation-pattern-census-seed52/SOURCES.json
• Direct predecessor: research/bit-one-relation-seed04/

Reproduction

python3 -I -B research/two-relation-pattern-census-seed52/verify.py
python3 scripts/research_package.py --package research/two-relation-pattern-census-seed52 --check-only
python3 -B scripts/research_baseline.py

Expected markers include PASS_TWO_RELATION_PATTERN_CENSUS, PASS_PACKAGE_METADATA_AND_PINS, and PASS_RESEARCH_BASELINE_BINDINGS_ONLY. The baseline confirms that the complex supplier still binds the selected conditional kappa; this scoped screen gives no kappa improvement.

The searched family, full stopping rule, proof-relevant certificate, negative controls, exact source pins, overlap evidence, attribution, and open follow-up questions are included in the package README and task metadata. Prepared with substantial OpenAI Codex assistance; no independent human review is claimed.

[Mister-Meeseeks]

Batch review at 01ac3f397eaaa9f7a72ecafc7f0fbf128571424a.

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

Reviewed scope: Complete four-register binary idempotent-pattern census and a fixed two-relation, fifteen-address ansatz are scoped separately. Common-order exclusion uses the reduced triangular formal algebra and rank subadditivity; the 120 exceptional prefixes exclude only that specified schedule, not every two-relation rational word.

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.