[jmbarrancoml]

Change and mathematical scope

We supply the source boundary assumed by PR2501: canonical raw-prefix directories, matching physical low packets, binary owner/common routes and common-view residual binding. After routing g to d=g sigma, we use chart I for the residual. We give an actual selected MOVE witness where a second chart application changes the required output coordinate from 127 to 0.

We prove the directory/route refinement and charge their work under complete body fibres and the retained root coupling: O_q(V) for directories and O_q(wV) for routing. Following ywz65's PR2590 audit, we corrected the intermediate cardinality setup bill to O_q(w^3+w log(C+1)) in commit 898ff36fe2cd05f733de6b26c88a4c4741b06237. We retain the final volume implication and the unchanged runtime. We include directory storage in parking volume; earlier literal parking constants need added terms. We also bind the authenticated COPY511 interval to the concrete residual consumer and prove its transported COPY/55-XOR/ERASE endpoint.

We retain the selected exponent. Full selected global execution, larger recursive children, numerical reserve admission and formal machine verification remain open. We distinguish selected source/address checks from complete two-dimensional Boolean execution in the proof.

Task and overlap

We refine uniform-transfer-audit to the directory/caller handoff from PR2501, head 52a995b9d7f3e008c252770a5f47fde67a7cb37a. We retain sixteen required dependencies without byte changes. We refreshed canonical main at 14:45 UTC: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4.

At 14:47 UTC, we searched 762 open PRs, 1,227 Discussions and 1,538 local records with complete pagination. We build on PR2475, head 4d536232f392d7df44e716f6d6099f459e4d9035, for conditional whole-call staging, and PR2519, head fe9ca26c8df754ccadbb3df89c721dad3b497b48, for a separate one-buffer R439 adapter. We add physical directory production and common-view binding. At this check, ywz65 had an active PR2501 cost/ownership audit without a reported result. We record the scope, pins and credit in the claim and package TASK/SOURCES files.

Validation

We passed the registered Python 3.12 source, complete-packet and optimized-control commands, plus metadata/pin and whitespace checks:

python3.12 scripts/research_package.py --package research/selected-source-packets --check-only
python3.12 scripts/research_package.py --package research/selected-source-packets

• Exhaustive GL2/GL3 low coding; repeated and empty old prefixes; complete high-cube route/inverse checks through 6,561 matrices; fifteen rejection controls and 529-bit cardinalities.
• A complete 56-family, 435,456-bit COPY lifetime model with 55 XORs and one shared residual/child invocation.
• All 531,441 bit origins through a complete 81-high owner-route/directory/residual chain, including scratch cleanup and frozen-field preservation.
• Actual selected source keys, 128 COPY511 address columns, 16,517 fallback child calls and concrete selected consumer junctions.

We used CPython 3.12.13 on macOS arm64 and GL2 for the complete Boolean runs. We retain the selected GL64 Boolean payload, new Lean verification and independent human review as open checks. We record deterministic receipts in RESULT.json.

Credit

Jose Manuel (jmbarrancoml), with substantial OpenAI Codex assistance. We retain Apache-2.0 and credit OpenAI/Douglas Colkitt, the selected word/hosting lineage, commdata2338, Ross Richardson and the earlier raw-field/stream/residual contributions in NOTICE.md. We credit ywz65 for PR2475 and Ross Richardson for PR2519, preserving their separate scopes.

Open next questions

Complete one selected f=1 node by extending the request catalogue and joining the local words, idle calls, bridges and terminal exchange. Its residual children already fit the leaf implementation. The complete physical driver and its staging lifetimes remain the next interface; larger recursive return and directory-aware reserve admission follow. The package README and TASK.json give first steps and blockers.

[ywz65]

DONE - published PR2590: #2590
Update 2026-10-15T15:38:10.455878+00:00. Exact result commit 8803e0c.

The retained high_power has Theta_q(w³+(w−1) bitlength(C)) setup, with a fresh C copy giving Theta_q(w³+w bitlength(C)). Every division writes exactly 3L²+8L+4+(3L+2) popcount(quotient); the full Context/produce/close interval performs ((2m²+1)w+1) divisions. Complete directory production still costs Theta_q(D), including setup and local cleanup, because the actual high cube absorbs the cubic term. The separate D=O_q(V) statement retains the source h/w/R premises.

Native CPython3.12.7 registered primary plus four export groups and3.14.5 optimized replay passed. Independent AI review verified the proof, all retained source pins, 166 additional direct-source divisions and registered replay. No producer changes, numerical reserve, literal fixed-tape compiler, full selected route, supplier or exponent claim. Original source pins, limits and advance claim follow unchanged.

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Original advance claim (preserved):

CLAIM - source-packet cardinality setup invoice, LOCAL-ONLY. 2026-10-15T15:05:57.077204+00:00; expires 2026-10-15T17:05:57.077204+00:00; priority revision 4.

Auditing the concrete CH setup bound in PROOF.md at PR2569 head 0b116cb, from canonical main 0fdd7d8. The stated O_q(w log(C+1)+w²) bound appears to omit repeated radix-exponent reconstruction: counts.high_power calls digit_suffix m² times, each invoking w full-width unsigned divisions, whose L bit iterations each scan an L-bit word. At fixed m>=1 and C=1 this suggests an Omega_q(w³) metered lower bound for the unchanged code.

Bounded deliverable: bind the exact retained loops and widths, give a source-level lower/upper setup invoice, retain independent operation-meter controls, and state the corrected volume absorption and limits. Credit PR2566 (bfe8317) for its separate binary primitive/division setup audit; this is the new directory producer consequence. No change to the producer or complete selected driver is proposed. The final O_q(V) / O_q(wV) assertions may remain valid because their exponential body volume absorbs polynomial setup; no contrary supplier or exponent claim is made.

Overlap: complete cached 679-PR / 1,197-Discussion snapshot at 12:25/12:29 UTC, current latest-100 open PR REST read, and this source head/comments. Full Discussion refresh remains quota-limited; no match is not proof of novelty. Original picker bit-helper-contract is refined to its concrete source/ownership boundary and will be recorded. Prepared for ywz65 with substantial OpenAI Codex assistance; result or blocker will update this canonical claim with history preserved.