Replace repeated child-program admission seeks with linear record cursors

[Clear1nsight]

The physical caller's actual SelectedBinding.child_program repeatedly seeks from the left through every earlier Program and raw-field record during Callback admission. This package derives its exact source-bound tape invoice and supplies a package-local monotone-cursor adapter that removes those repeated scans while preserving successful admission, returned bytes, numerical predicates, ownership and the original random-access Program after admission.

For history h, index/residue widths I/L and code width Q, let n=h+1, r=2I+L+5, c=Q+2I+90, F=Q+2+4096(L+1), and P=r+hc. The adapted complete producer uses Program (5P+2hI+1,0,4P+8) and Fields (n(3F-Q-2)+3,0,2nF+4) reads/writes/unit-moves. Returned-output construction and empty continuation checks are charged separately and unchanged. Original Fields work is quadratic in history. Complete record backing remains exactly P+D+nF+14, including LEFT, adjacent blanks and four empty continuation tapes; the adapter adds no tape or numerical word.

In the admitted h=6 fixture, complete record actions fall 4,633,704→1,166,975 (74.8155%), with identical returned bytes. Numerical actions separately fall 805,059→684,070; they are not treated as zero. The proof derives a conservative numerical action envelope from encoded loops and actual root/history coupling h<2(I−1), tightened to h<2(I−7) for successful extension. The claim is a tape/word-action ledger and candidate optimization, not a primitive finite-state realization or complete Pi/stock theorem.

Validation covers six original/adapted child-program pairs (good/pair/unit/half), three leaf-only pairs, exact record invoices, decoded chronology, residue counts, preserved bytes/heads, cleanup and visited backing. Seven malformed admissions and an altered-AST guard reject. Normal and optimized replay plus actual Git-free optimized positive, all 9 source-corruption controls and receipt mutation are registered.

An additional projected-definition pair uses exact current Q=6507 codes for rank-26 IDLE27776 and rank-7 COPY1603, verifies request/view tags and low hashes with canonical LowCodes, and executes actual child_program at modulus9 with nonzero high fields: 2048→832→91. The metadata projection came from the concurrent residual lane; source-plan/good-class reconstruction is an explicit fixture premise, not independently recertified here. This pair's Fields actions fall 518,355→297,839 with equal output bytes. No full GL64 payload, selected cold replay, Lean, Docker, new κ, or independent human/formal review is claimed.

Same-session independent AI review authenticated all 9 source pins, examined cursor semantics/cost/root-history proof, checked mixed q3 history and leaf/random-access restoration, and reran the projected pair without blockers. The frozen baseline and candidate remain separately replayable. Shared and predecessor files are unchanged.

Canonical base 20ecf28, priority revision 6. Explicit assigned scope refines selected-stock-envelope and PR3983's producer gap. Canonical claim: #3967 (comment). Adjacent PR3999 concerns interruptions/abort; PR3995 pools IR; this package addresses normal unpooled source admission. Source history consists only of canonical inputs; the projected fixture is self-contained derived evidence.

Credit Jose Manuel/jmbarrancoml's physical caller and SelectedBinding; David Arias/PR2753 and retained Nick Petalas/encoded controller/record/continuation lineage; PR3983; R437/OQ4 ai-nanachi/3647, zxv/3690, Ali Romman/1043, Sagar Thakrar/3700 and selected/native authors; immediate 3936/3950/3967. New work by Chris R/Clear1nsight with substantial OpenAI Codex and same-session cross-agent assistance. Apache-2.0.

Reproduce: python3 -B scripts/research_package.py --package research/r437-source-preparation-bound.

Next obligations: actual source/directory generation, child_extents/read_prefix, geometry/context and coefficient work, full lifetime role maxima, dispatch/slot/primitive tariffs, and admitted original-width stock. The new cursors are a research candidate awaiting shared-caller integration; unknown costs remain explicit.

Published head: fc1426353de3389409a27e5b9bc146a95edf811c, branch Clear1nsight:audit/r437-forward-admission-20261019. Exact 23-file package/input byte comparison and source-history preflight pass; base-to-head and staged whitespace checks pass. All three registered commands passed in 226.109 seconds on Python 3.12.3 with frozen files unchanged. Canonical main refreshed unchanged at 08:50 UTC; live overlap checked through #4003. Hosted CI is pending separately.

Publication head fc1426353de3389409a27e5b9bc146a95edf811c passes exact23-file package/input byte and source-history validation plus whitespace checks. The three registered commands pass on frozen bytes; hosted CI is reported separately.

[ToikY]

CLAIM — source-bound directory.produce / old_prefix / Odometer component invoice, complementary to PR4011 at fc1426353de3389409a27e5b9bc146a95edf811c.

Pin canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority6, actual retained producer research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/directory.py (Gitblob c74cacf5ce809c0561d374f137a52df0992b4226). Starting with an already-live valid Context, derive the producer's complete source Tape/Word-action invoice, including count/counter bookkeeping, old-prefix validation, output construction/rewinds and temporary-state lifetime. Preserve physical duplicate-prefix multiplicity. Context preparation remains an explicit caller charge.

First test: meter the unchanged producer on an actual dimension64,cap1 fixture and bounded smaller dimensions/caps, with exact output/order/head-return comparisons. For cap>1 at dimension64, use the proved formula rather than enumerate the enormous lift set. For M=d²,c=modulus/q,H=c^M, candidate output size is B H(h+1)[Q+2+M(L+1)]; all count/ripple work must still be charged. Stop at this component; do not call an admission-only +64 bound a directory bound or infer full Pi/selected stock, source-code admission, all-size supplier or κ.

Handoff-first changed selected-stock-envelope scope. Main/selected/catalogue unchanged; all724 open PR bodies paginated at09:31:03UTC, repository overlap helper and bounded live1166/start-here/active boards checked. Broader Discussion/closed/code coverage partial. PR4011 explicitly leaves directory generation open; PR4008's coefficient preparation does not price it. Source/card baseline command attempted in sparse checkout but omitted selected-package ASSEMBLY prevents its full inventory check; no unrelated historical closure repair. Exact source exports and checks will be self-contained.

Science cutoff10:14:56UTC; claim expires10:29:56UTC on2026-10-19. Expected artifact: source-bound proof/invoice checker, actual instrumented fixtures, independent formulas and semantic controls, or a precise remaining-lemma handoff if the complete component cannot be bounded. Credit Jose Manuel/jmbarrancoml's physical caller and David Arias/PR2753, Nick Petalas and retained compiler/record/stock lineage; Chris R/Clear1nsight PR4011/3983 for the admission bill and named producer gap. ToikY with substantial OpenAI Codex assistance and separate AI math/test contexts. No merge, closure, maintainer edits or frontier change.

[ToikY]

UPDATE — narrowed scope after checking retained predecessors.

PR2590 / ywz65 (research/source-directory-setup-cost) already proves the cubic repeated-radix setup and complete Theta_q(D) producer cost. selected-directory-storage-reserve already prices serialized storage, and Ross Richardson's selected-stream-directory-numerical-audit already proves max(d²,6) additional residue Words. These facts and duplicate-prefix semantics are credited prior work, not new findings here.

The useful next question is PR2590's explicit open question: share one charged encoded radix traversal across matrix coordinates. Test a package-local high_power_shared that traverses radix_power once, skips its first yield and makes d² multiply_small(q) calls on each later yield. Original and candidate perform the same ordered d²(w−1) q-multiplications; the candidate should remove exactly (d²−1) complete radix traversals, with no decoded exponent or new numerical Word. Frozen runtime bytes remain unchanged. The unchanged full produce is tested with original or candidate high_power; every counter, output, rewind and retained validation charge remains in the invoice.

Canonical main refreshed unchanged at09:42UTC before this narrowing; original724-body open-PR cache and latest100-body delta through4022, retained main packages, live1166/source thread checked. No competing shared-radix result found in that bounded coverage; broader Discussion/closed/code coverage remains partial. Successful valid-input execution only, not exception rollback or full physical Pi/stock/supplier admission. Existing science cutoff10:14:56UTC / expiry10:29:56UTC remains.

[ToikY]

DONE / claim released — focused PR4025, head 84bd28ef6da3a3473d14a48088f30ba82d414450, answers PR2590's explicit shared-radix traversal question. Original/candidate complete producer outputs, counters, record/index bills, protected state and successful cleanup agree; exact residue-Word saving is (d²−1)rho. Dimension64/cap1 saves2,141,685 reads /389,025 writes /2,276,820 moves, with the credited4096 peak unchanged. Seven pairedfixtures, separate no-import invoice/byte oracle,24 rejections+3 positives, normal/-O read-only coldexport and exact18-file publication/history checks pass. Hosted CI39233311002 passes at that exact head.

Discussion handoff gives remaining obligations and credit. Prior Theta_q(D), cubic correction, storage and max(d²,6) facts remain credited to ywz65/#2590 and Ross Richardson. Full caller/physical Pi/stock/source admission remain open; successful restoration is not exception rollback. This is opt-in local research; shared/frozen sources and frontier unchanged. No continuing reservation.