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QQ16: add an F0-B1 selected-state shear - #2216
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This was referenced Oct 15, 2026
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Review update: I reproduced and checked the native frame counterexamples in #2252. At the retained F0/B1 boundary, The payload-constant rank-eight result is not refuted: C_q acts as identity on that restricted subspace. Please separate that local result from the sixteen-addition native invoice, and either supply a typed adaptation/fusion with its complete bill or explicitly leave that implementation open. I am retaining this PR for that revision; successful constant-payload replay alone cannot resolve the mismatch. |
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Prices the initial-prefix part of PR #2252's typed-fusion handoff. After factoring the common completed frame, PR #2216's paired A-to-T shear followed by B1's eight initial X_T inverse-line normalizations has, for each selected pair, the endpoint a' = a, t' = C_q^-1 (t + a), v' = v - C_q^-1 a. At payload characters 0 and 256 every actual q_T has bit 8 set, so each inverse line changes from 1 to -i; the difference of the two transfer matrices contains a 16-by-16 minor of determinant (-1-i)^16 = 256. Free payload-independent scalar gates have zero character difference and each single-field native line has difference rank at most one, so rank telescoping gives at least sixteen lines for any circuit in the model, even with scratch, copies and clears. A typed one-C0 prefix attains sixteen (eight more than inherited), restoring every borrowed helper and clearing C0. Fusion with later B1 operations or cover maps is outside the model; no supplier or kappa change. Adds research/qq16-shear-prefix-cost/ only. Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
Mister-Meeseeks
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Takes PR #2268's full-injectivity handoff. With PR #2216's F0-to-B1 A-to-T shear and a paired tap from any one ordinary source port into a selected T field, some original selected inputs stay invisible through the complete retained QQ16 schedule. A new three-port witness on ports 1, 16 and 88 (r_1 = r_16 + r_88, zero at the tapped port 2) defeats PR #2268's U2-to-T21 tap; its support is disjoint from PR #2093's witness, so all 768 single taps fail. For each source port, two nonsingular 8-by-8 parity minors (192 in all) give eight hidden A dimensions at the identity owner, so reading any fixed set of k <= 8 source ports leaves at least 9 - k dimensions invisible: at least nine source ports are necessary in this coordinate-access model, not proved sufficient. Negative result; no supplier or kappa change. Adds research/qq16-coordinate-tap-kernel/ only, with PR #2093's pinned source helper under references/ (credited to Adam Gall). Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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New mechanism
This package tests the reversible selected-state shear
between the fixed QQ16 F0 and B1 calls. It preserves each selected
X_T+Y_Tsum and uses existing fields. The exact source-pinned group-algebra replay propagates all eight directions of the retained selected-input erasure witness through B1. Without the shear the T output has rank 0; with it the T output has rank 8. The package includes a nonsingular exact 8-row minor with determinant-1/4096and its owner-map keys and rational coefficients.This establishes a local interface mechanism for the fixed witness family. It does not establish that later events preserve these values, a complete controller, a supplier, or a new κ.
Cost and validation
The shear adds 16 scalar additions per owner at the common
completed(0)data frame. It uses no new helper, owner map, precision, temporary storage, or recursive child. It preserves selected sums and leaves the inherited helper-restoration contract unchanged.Reproduce from the repository root:
Observed locally on CPython 3.14.7:
PASS_QQ16_F0_B1_IDENTITY_SHEAR_WITNESS, rank 8 / zero-control rank 0, minor determinant-1/4096; package metadata and all 14 source pins pass. This machine has no local Python 3.12 executable; the registered package specifies normal and optimized 3.12 replays for hosted CI.Provenance
Base:
0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; selected record SHA-256:10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.Ali Romman and the retained joint-query lineage (PR #1969) supply the maps, routes, local words and erased-input witness. PR #2086 treats changed A logging while leaving the T output fixed; this contribution inserts an A-to-T shear between F0 and B1 without adding an ordinary query. Cinna Davis (PR #2079) and Adam Gall (PR #2093) supply adjacent observation analyses. Substantial OpenAI Codex assistance; no independent human review is claimed.
Claim and status: #2205