Research note: 30 all-dimension parity edge obstructions beyond local frames

[thakrarsagar]

This scoped negative result identifies 30 internal edges of the historical ParitySide(10) DAG whose endpoints each admit legal frames but admit no legal nested pair at any dimension. It also supplies exact one-dimension local repairs for 50 other edges. No new kappa or supplier is claimed.

The initial census exhausts all minimum separating frames at 2,271 nodes and all 9,832 endpoint pairs on 3,518 locally feasible edges. It finds 200 failed edges: 120 corroborate the historical source-span diagnosis; 80 involve newly completed radical-one targets. For those 80, an all-dimension follow-up checks 1,155 endpoint subspaces with two different exhaustive algorithms and distinguishes the 30 absolute pair obstructions from the 50 local repairs. The certificate includes all failed edges, all extended endpoint frames and explicit repair witnesses. A small obstruction at edge 736 → 737 is worked out in the note.

This extends the pointwise analyses of ArnavSwiggy's #920, ToikY's #972 and woklerx's #993. Their pinned heads, the historical parity work and DreamingOfClouds' format-limit analysis are credited. No open-PR implementation is imported. Substantial OpenAI Codex assistance is disclosed.

Base: 8bddbee377e2f3ce1f1247196c4b290d55767d20. Structural decoder track, OS seed 46. Only research/parity-edge-compatibility-seed46/ is added. Before submission, PR metadata was refreshed through #1012; the three predecessor heads and all runtime inputs on refreshed main 2921874911956718fcaaaf9396fe8267b3cfa9f0 were unchanged. No overlapping edge census was found.

Reproduce with Python 3.11+ and the standard library:

python3.11 -I -O -B research/parity-edge-compatibility-seed46/verify.py

Expected status: PASS_PARITY_EDGE_COMPATIBILITY, with 200 minimum-frame failures and the 30 impossible / 50 repairable all-dimension split.

Validation: normal and isolated optimized replay; exact parsed regeneration equality; all 14,400 signed coefficients; complete source pins; characteristic/literal residual agreement; ten built-in geometric controls; four rejected artifact/source corruptions; four existing parity tests; selected-record consistency; staged whitespace check. Exact scope and commands are in VALIDATION.md.

The 50 repair witnesses are individual edges, not a globally compatible labelling or a paid cost recurrence. The selected construction and upstream/ are unchanged. Repository-wide make verify, the selected supplier's cold replay, Linux execution and a proof-assistant formalization were not run for this isolated finite geometry contribution.

[Mister-Meeseeks]

100-PR batch review at 830842d08c48d7b7f6847882d065157b3e978b3c.

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

Reviewed scope: Thirty fixed parity-DAG edge obstructions beyond pointwise legality, plus fifty local larger-frame repairs; no global repair claimed.

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.