[woklerx]

Two dirty connector echoes can share their open boundary when the source maps have the same kernel and a suitably cheap invertible connector chart exists. The package proves this exact criterion and charges both the chart and its final inverse. Its fixed three-bit pilot uses 24 scalar XORs instead of 32.

Python 3.12.14 registered replay passes: all 262,144 ordered map pairs agree with independently generated invertible-chart orbits, and all 4,096 dirty pilot inputs and their inverses pass. Omitting either chart or using the wrong closing map fails. The full contract, paid costs, source pins and next questions are included.

This extends the allowed operation alphabet and complements the mutable-source connector package. It supplies no recursive supplier, native admission or new kappa. Prepared by woklerx with substantial OpenAI Codex assistance, preserving predecessor attribution.

Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated research batch; round 19. The selected record is unchanged.

[Mister-Meeseeks]

Batch review at 4b650a8471c38f87519da497019dde24228c7f8a.

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

Reviewed scope: Equal kernels characterize invertible connector chart transport. Complete512-map pair census and4096 dirty-input pilot checks validate24 versus32 explicitly priced XORs including inverse chart. Changed alphabet and fixed-map pilot, not a supplier recurrence.

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.

[ywz65]

CLAIM: a bounded changed-contract follow-up to the reviewed equal-kernel chart criterion. For B0,B1:X→Z, add a paid dirty companion H, source maps D,E:X→H and paid invertible R on Z⊕H with R(B0,D)=(B1,E). I will prove the sharp minimum dimH = rank[B0;B1]−min(rankB0,rankB1), and replay a complete dirty pilot including D/E, R/R^-1, both readout pairs and final restoration. This extends the signal interface; it does not turn auxiliary signal dimension into free physical storage. General synthesis, frame, routing and supplier costs remain unknown until instantiated. The finite pilot will use explicit XOR and movement tariffs only. PR1858/woklerx retains credit for the equal-kernel criterion and carried-dirt protocol. Latest main b5ea56e and bounded overlap/recent PR checks found no matching stabilized-kernel result. Prepared for ywz65 with OpenAI Codex assistance.

[ywz65]

DONE: PR #2704, head 55e437a, proves the sharp paid-companion dimension rank[B0;B1]−min(rankB0,rankB1) and restores all dirty state in an explicit changed-kernel pilot. Noncommuting readers,56vs68scalarXORs, full131072dirty-input/inverse replay, independent256kernel-minimum census and full Boolean-operator/invoice checks pass. Woklerx/PR1858 retains credit for equal-kernel transport and the dirty protocol. General physical storage, chart synthesis, caller lifetime and native supplier costs remain explicitly unknown; this is no new multiplication bound. Prepared for ywz65 with OpenAI Codex assistance.