[aliromman]

This construction closes the binary-alphabet handoff in PR #5188. It lowers the complete fixed 4,589-instruction interchange program and all five entries to 58,608 literal binary instructions on the same 20 tapes. A written opcode proof gives exact aligned-state simulation, at most eight times the source instruction count, and exactly three times its retained tape allocation at source boundaries. This removes one callee representation obligation. It does not improve the complete kappa calculation; selected kappa remains 60403/20000000.

Proof and scope, deterministic receipt, compiler and binary machine, and source pins are at reviewed head 3a153549bc704f4f25a7077a1be9153cffd7668d. Base and every consumed input pin are ff3cc58e370d0f678e529246f8c73e8094e18fcf.

The representation maps ZERO/ONE/LEFT/RIGHT/BLANK to 001/010/011/100/000 and head h to 3h. Actual test and write microprograms restore alignment; unit moves use three binary moves. Unallocated zero cells represent source blanks. Every bit write, move, test, jump and halt is counted. For a source entry with R reads, W writes, M moves, J jumps and one halt:

binary reads  = 3R
binary writes = 3W
binary moves  = 4R + 4W + 3M
binary jumps  = R + W + M + J
binary steps  = 8R + 8W + 4M + J + 1.

The written simulation holds for every valid source state and all valid widths, with no additional tape or runtime host callback. It inherits the source all-width proof. It yields a complete init/run/consume/close bound of 2^23 (H+1)(V+1)(L+1)^2 with the source's definitions. The exact per-entry factor also covers install; that optional caller action is outside the quoted four-entry session.

From the repository root, Python 3.12 with the standard library:

python3 -I -W error -B research/binary-elementary-interchange/verify.py
python3 -I -O -W error -B research/binary-elementary-interchange/verify.py
python3 -B scripts/research_package.py --package research/binary-elementary-interchange

Expected direct result: PASS_BINARY_ELEMENTARY_INTERCHANGE. Registered normal/optimized Python 3.12.13 and direct optimized 3.14.7 pass. The checks compare 68 full entry states over 16 sessions against a separate execution of the pinned source machine: tape bytes, retained lengths, heads, status and exact counters. They include eight independent payload columns, install, growing/shrinking history, 153 local instruction cases, all three unused codewords, and seven failure controls for origin crossing, alignment, bit writes, retained extent, callbacks, cycles and alphabet admission. The measured finite receipt is 654,512 binary instructions versus 122,805 source instructions. Committed-byte and official 12-file export checks pass; a Git-free optimized extraction passes and rejects source and receipt corruption. The source-history check requires full Git history and is not claimed from this shallow checkout.

The finite replay reaches H=3 and V=64. The predecessor's 196,608-cell fixture was not repeated. Encoded input and descriptors are boundary assumptions: the fixture encoder is not a free caller adapter. A complete caller must pay any codec, port conversion, storage and cleanup. The storage theorem is relative to source backing; it does not independently supply an absolute source-space grant. Unused codewords are rejected when read, not by a global validator. No whole raw/repair caller, ROM producer, native/selected admission, independent proof-kernel acceptance or full multiplication theorem is claimed. Hosted CI and external review remain separate.

The advance claim takes the explicit predecessor handoff. Final overlap covered 376 open PRs, 4,589 Discussion records and all 7,091 tracked README/TASK notes; only the source handoff and this claim matched the alignment scope. Canonical main still matched the base. Arbitrary diffs and unpublished work are outside that coverage.

Credit @JoyboyBrian for the source program, proof and handoff. The source retains Jose Manuel's wrapper, stream/cardinality predecessors, Cinna Davis, Hiroki KUMAZAKI and Douglas Colkitt. PR #5286 is related retained-backing work, not a consumed premise. Source notices are unchanged. Prepared by @aliromman with substantial OpenAI Codex assistance in proof, implementation, verification and review; Apache-2.0. No independent human review is claimed.