OMEGA NAUGHT
Reference language prototype 0.1

Construct · retain · decipher

Read a recoverable scale history

A record names its reference, calibration, arithmetic, content convention, terminal state, and ordered witnesses. The decoder reconstructs the initial scale and every intermediate state. All integer calculations below are exact.

Construct a record

Use a nonnegative integer, up to 512 decimal digits.

Choose 0–256. The terminal state is retained even when it is nonzero.

Decipher a record

The fields and witness order are part of the meaning. Paste a complete record to decode it.

Recovered content

Initial scale
Terminal scale
Witness steps

The history reconstructed from the terminal and ordered ranks
StageState dNext stateRankRemainder ρ

The rule behind the language

Qd = Sd′ + ρ
q(dp) = d′p + (ρ/S)p
d = ceil(Sd′/Q) + rank

The same scalar remainder corrects every corresponding point of the fixed template. The rank identifies which predecessor produced the output. It needs a three-symbol alphabet, stored in two bits when the output is already known.

This text format stores readable decimal symbols; it is not a packed two-bit wire format. Record validity checks arithmetic consistency. Another valid record can describe another state. Text meaning uses the declared UTF-8 convention.