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OMEGA NAUGHT

Specified objects. Explicit maps. Reconstructible results.

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Supplementary note · 24 October 2026

OMEGA as a reference language

A record names its template, calibration, Q, S, codec, step count, terminal, and ordered ranks. Syntax alone is not validity. Each rank has to land in the actual output fiber, and the initial integer has to satisfy the declared codec.

The grammar is ten lines: magic, template OMEGA-CANONICAL-DOWN/1, units calibrated-scale, Q 339949771344778, S 1000000000000000, one codec among scale, bytes-sentinel, and utf8-sentinel, then STEPS, TERMINAL, RANKS, and END. Exactly one space separates fields. The rank count equals STEPS. There is no reordering.

For output y, b(y) = ceil(S y / Q). A reverse step requires 0 ≤ w < b(y+1) − b(y) and sets d = b(y) + w. Scale 26 is terminal 0 and ranks 2 2 2, because 0 maps to 2, 2 maps to 8, and 8 maps to 26. Text A is UTF-8 byte 41 with marker 01, integer 321, six ranks 0 0 1 0 1 1, and history 321, 109, 37, 12, 4, 1, 0. Those scalar ranks are not the 120-coordinate residue witness on the 600-cell network. The two records have different domains, framing, and decoders. This parser does not accept a vector record.

utf8-sentinel uses Unicode scalar values. It rejects malformed UTF-8 and unpaired surrogates, preserves an initial U+FEFF, and does not normalize. bytes-sentinel returns the byte string and does not assign a text meaning. The empty message has integer code 1. ASCII here is a readable record, not an optimal packed wire protocol.

The mathematical grammar allows any finite length. The engine on this site accepts at most 256 transitions, 512 decimal digits, and 128 payload bytes, and rejects records longer than 20,000 characters. Those are interface budgets. They are not limits of the finite-history argument.

Changing a valid rank can produce another valid record with a different seed. Arithmetic validity is not sender authentication. This language is not a revision of frozen SRSD or of the canonical six-mark readout. It does not serialize an unrecorded position.

The engine module matches SHA-256 76f79d17064ca9bcbbbe73e8d3295a20739edc52630e4724d5740a329a9a89fa. On Node v22.23.2 this archive compared 32,768 canonical transitions with the audited Python source, round-tripped 65,793 byte messages of lengths 0 through 2, checked 10 Unicode texts, and rejected 21 malformed inputs. The conversation report used Node v24.22.1. The observed count line matched. That is a finite implementation check, not a review of the written language note.