[jmbarrancoml]

I give a written recursive construction for ordinary binary chunk interchange in O(V E^(1-a)) time, with a=169711/100000000=0.00169711, in the stated complete-stream, fixed-tape model. I close the completed weighted-child premise by strong induction on width, starting with elementary digit interchanges. This is a proposed scoped theorem for review; I leave the selected frontier and multiplication claim unchanged.

The selected BIT components previously required completed weighted children and coverage of the remaining local-frame labels. This package binds 541 actual residual bases and 1,235 owner charts, gives causal symbolic ancestor expressions across whole high packets, and completes the weighted leaf and header ordinary bases. PROOF.md specifies the chronological caller, low-packet endpoint factorization, fresh row reserve, unequal-buffer parking and uniform control costs. It then derives the stopped recurrence and internal borrowing. I use c=17/10000 from the existing moment certificate, giving a=c(1-c).

Reviewers should focus on PROOF.md sections 5–7: whole-low-packet execution, frozen-field access and the locality/time induction. The Python macroplan is an interface checker; I have not compiled or run the full GL64 recursive payload machine, produced transition tables, or formalized the proof. Constants may be enormous, and I claim no practical cutoff. The complex and analytic interfaces remain separate.

Validation: registered Python 3.12 normal and optimized replays, source authentication before imports, and the retained PR1627 literal/chronological replay. New checks cover 1,082 split-basis cases, 120 full 128-coordinate operators, completed physical leaf/header cases, temporal and coefficient controls, recursive plans and two outward-rational coarse moment calculations. The completed leaf/header paths reject opaque child calls. Reproduce with:

python3.12 scripts/research_package.py --package research/selected-bit-recursive-closure

I retain DreamingOfClouds' PR589 tuning, eumemic's base-word and GL work, alephnan's PR1627 proof, RossRichardson's PR2159 fallback and commdata2338's PR2160/2188/1379 contributions. NOTICE.md and SOURCES.json distinguish inherited work, eight unchanged vendored files and this composition. I also credit 1337isnot1337's adjacent PR2212 route census without repeating it.

Coordination: Discussion2209. I started from canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. The final overlap refresh covered 467 open PRs, 927 Discussions and 1,538 local records, with complete remote pagination and no warnings. I found no competing closure claim; the search does not cover arbitrary code diffs. The relevant predecessor heads remain unchanged.

Contribution by Jose Manuel (jmbarrancoml), with substantial OpenAI Codex assistance in mathematics, implementation, verification and writing. I claim no independent human or proof-assistant verification.