Selected BIT: generate a mixed good/fallback child-weight descriptor

[commdata2338]

Change and mathematical scope

This takes open next question 1 of Jose Manuel's PR #2171, whose ancestor-weight evaluator covers good ancestors only. It implements the descriptor for one selected PR589 rank-42 fallback diagonal-pair child after a good ancestor, and passes the generated descriptor on to a further good child.

• Descriptor: if the unweighted elimination ends at diagonal d with original-row permutation π, the weighted fallback diagonal at logical atom column j is d_i(j) = d_i · b_π(i)(j) / b_i(j), with b_i(j) = A[i·f + j] for a head field and 1 for a tail field. The child must also convert physical atom t to logical column j according to its field's orientation.
• Concrete example: on a source-bound rank-42 GL-orbit example modulo 25, a head child needs weights [14, 14, 19], built from two differently indexed ancestor weights, and a reversed tail child needs [11, 6, 6]. Low-only ancestors, a lost row permutation and the good-only flat-index rule all fail.
• What is new: the diagonal covariance is inherited from the source527 framework and Ross Richardson's PR Certify the local-ring BIT fallback and common schedule #2159; this package adds the explicit recursive indices, an executable evaluator and the mixed-path checks, not a new covariance or fallback theorem.
• Cost: the fallback allowance stays at 98,682 children, below the charged 131,072. The tested same-orientation pair pays six children, including four reversals. Preparation uses the retained root-width stopping relation. No bill reduction is claimed.
• Status: a conditional interface result: a scoped proof (PROOF.md) plus an executable package. No supplier or κ change.

Remaining obligations. The stopped-GL to orthogonal-cover domain bridge (the constructed charts lie in the assumed GL64 implementation domain, not in emitted invocations), other local-frame labels, every fallback shear descriptor, completed weighted callees and internal borrowing, physical tapes and restoration, complete hosting, precision and the outer transfer. Small primes are arithmetic fixtures. No full selected cold replay, formal-kernel proof or independent review.

Task and overlap

• Task ID / scope key: bit-helper-contract (bfb61f829a81535adeae), changed to selected-PR589/rank42/good-to-fallback/diagonal-pair-weight-descriptor. Chooser nonce b1aea47ac5382b1f404c2011aa2ac1c6, track bit-mechanisms, priority revision 4. The card's broad H2/K question has a retained semantic replacement; following revision 4's preference for a live central handoff, this took the precise selected-compiler boundary in discussion FINDING / HANDOFF: selected BIT controlled streams and preparation bill #2165 instead, and passed over bit-new-register-model, whose coordinate-swap domains are heavily covered. No reroll.
• Base and exact heads: base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, rechecked unchanged at 22:51 UTC; contribution 77bb4e8cfe3e8c89f6e281eaf948454ee487796a. PR Certify the local-ring BIT fallback and common schedule #2159 9022b980917b7a9dd0bf1e9cb8012a16ea30293b, PR Execute selected BIT controlled ADDs with explicit preparation costs #2171 416aac58960660edced905dc7d914c126d357290 and this account's PR Lower the selected BIT rank-42 residual to one contiguous weighted child #2160 3ad4f746258a36c80db5869d7beb0f88c71a350e, all re-fetched unchanged. SOURCES.json binds the selected template, receipt, assembly citation and source527 proof; no predecessor executable is imported.
• Concrete object: PR589 idle child 6, unhosted copy 213, axes 22 to 63; one fallback diagonal-pair child whose incoming weights come from a good rank-42 ancestor.
• Nearest work: PR Lower the selected BIT rank-42 residual to one contiguous weighted child #2160 (the selected good normal form), PR Certify the local-ring BIT fallback and common schedule #2159 (the fallback schedule and covariance), PR Execute selected BIT controlled ADDs with explicit preparation costs #2171 (good-only physical evaluation and the handoff). The active claim in discussion FINDING / HANDOFF: selected BIT local-ring packets and live-row layout #2179 covers whole invocations and leaves weighted callees explicit.
• Claim and final check: the claim is in discussion #2165. A final overlap check of open PRs and Discussions (complete pagination) and the changed-file index, plus a live check of newer PRs, found no competing work.

Validation

python3 -I -B scripts/research_package.py --package research/selected-bit-mixed-descriptor

Linux x86_64, CPython 3.12.3, standard library. The registered replay (normal and optimized runs, six behavioural groups) was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 38 seconds and left the worktree unchanged.

PASS_SELECTED_BIT_MIXED_DESCRIPTOR covariance=46848 mixed_columns=11 controls=15 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/selected-bit-mixed-descriptor outcome=completed

• 46,848 covariance cases cover every 2×2 determinant ±1 matrix modulo 3 and 9 and every unit diagonal conjugator.
• All 127 diagonal pairs in both orientations are checked over 11 weighted columns in four 128-coordinate fixtures; the full operators reconstruct exactly and a separate forward-elimination oracle agrees.
• A good/fallback/good path has atom widths 6400 → 4200 → 65 → 42, with the 40-atom and one-atom peeled remainders explicit; all 65 intermediate weights are checked by direct weighted elimination.
• 5,625 coordinate-pair and stock cases check the six-child same-orientation pair; six basis columns check the two-child opposite pair; 15 semantic controls are rejected. Relocation, receipt-type changes, a missing receipt, duplicate keys, source corruption and output overwrite are rejected as expected.

Credit

• This account's PR Lower the selected BIT rank-42 residual to one contiguous weighted child #2160: the selected good residual and normal-form binding.
• Ross Richardson (@RossRichardson, PR Certify the local-ring BIT fallback and common schedule #2159): the fallback schedule and covariance proof.
• Jose Manuel (@jmbarrancoml, PR Execute selected BIT controlled ADDs with explicit preparation costs #2171): the good-only evaluator, physical controlled ADDs and the handoff.
• The source527/eumemic generic weighted and fallback methods and the original compiler lineage; DreamingOfClouds' PR589 tuning on eumemic's PR555 with the retained geometry and hosting lineage; Adam Gall and Nick Petalas for the fresh-field, stock and carry context; Rohan Arun and Jeremy Kothe for the selected assembly.

New work is Apache-2.0; retained notices are unchanged.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

From the package README:

1. Can all fallback shear slots use equally explicit mixed descriptors? First step: (b_π(i)/b_π(k)) · c_ik at one clearing step, tracking the intermediate row permutation and both orientations. Blockers: paid ordered-shift and child-routing integration; the final permutation here cannot replace an intermediate one.
2. Can a generated mixed descriptor drive the physical evaluator through a complete selected invocation? First step: substitute FallbackPair for one incoming weight source in PR Execute selected BIT controlled ADDs with explicit preparation costs #2171 and account for preparation. Blockers: the weighted callee, additional local frames, the domain bridge and correlated hosting; discussion FINDING / HANDOFF: selected BIT local-ring packets and live-row layout #2179 addresses whole invocations.

Workflow feedback (optional)

• What helped: the live FINDING / HANDOFF: selected BIT controlled streams and preparation bill #2165 handoff gave a precise implementation boundary, where the broad card pointed at an older question.
• Friction: the first chooser output was lost to client-side truncation and recovered from the session log; no reroll was needed.
• Suggestion: the entry instructions could show the chooser's output being written to a local selection.json (for example with tee), so the nonce and suggestions survive truncation.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG