Research note: exact incident-safe parity frame dimensions (no new kappa)

[woklerx]

This research note completes the incident-residual analysis for the 692 completable radical-one nodes of the historical ParitySide(10) DAG. Among all 3,096 minimum separating frames, 2,538 pass every actual source/target line residual. Exactly 560 nodes work at minimum dimension, 12 require one extra dimension, 100 require two extra dimensions, and 20 admit no incident-safe frame at any dimension. A proof explains both the exhaustive domain and the dimension gap.

This extends ToikY's #972 pointwise completion census and ArnavSwiggy's #920 incident-residual rectangle analysis. The additional evidence is a full fixed-DAG census, explicit larger-frame witnesses, and 20 absolute local obstructions beyond the two already-known common-span obstructions. It does not supply simultaneous nested frames, a paid supplier, or a new kappa. It credits the historical work of Douglas Colkitt and DreamingOfClouds and discloses substantial OpenAI Codex assistance.

Base: 407d52ff15b2217b6e22bce44728b4c3907b6515. Structural decoder track, OS assignment seed 47. Predecessor heads: #920 913817423bbfaf241dec1d6b9edb1c7ded349508; #972 f39f92a085fc95fe4245b06d4a695739d79763bc. Open PR metadata and those heads were refreshed before submission. Only research/parity-incident-completions/ is added; source pins, exact certificate, proof, local claim, attribution and validation receipt are included.

Reproduce offline with Python 3.11+:

python -B research/parity-incident-completions/check.py

Expected status: PASS_PARITY_INCIDENT_COMPLETIONS, with the 560 / 12 / 100 / 20 node split. The checker uses explicit vector sets and actual residuals, independently of the producer's Gaussian/characteristic implementation; both reuse the pinned scalar DAG constructor.

Validation completed on Windows/CPython 3.14.5:

• All 14,400 signed kernel coefficients and all 3,096 minimum frames checked; 112 repair witnesses, dimension exclusions and 168 dimension-four frames checked.
• 22 corruption and geometric tests pass normally and with -O; isolated optimized checker passes.
• Fresh regeneration matches the actual Git certificate blob byte-for-byte, with explicit LF output.
• Four affected historical parity tests and selected-record consistency check pass.

make verify and the full selected supplier cold replay were not run for this additions-only finite geometry note. No Linux execution, Lean proof, full multiplication theorem verification, or change to inherited supplier assumptions is claimed.

[Mister-Meeseeks]

100-PR batch review at 76b71ff5bea1088fb5019dea25fe89698287e673.

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

Reviewed scope: Incident-safe frame dimension census for a fixed parity DAG; local frame feasibility does not imply a simultaneous circuit labelling.

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.