THE PHASE MODULATION — a dart

THE PHASE MODULATION the message rides the phase — the carrier’s magnitude never moves

In phase modulation the carrier’s amplitude and frequency hold steady; the information lives entirely in where in its cycle the wave is — its phase. A constant-magnitude phasor spins, and the data is the little advances and retards of that spin. This dart carries a real payload — ROOT0’s glyph [ 0.m | <-~-~-~-~-( . || — as a differential 8-phase (8-PSK) stream: each symbol adds to the running phase, θ[n] = (θ[n−1] + s[n]) mod 8, and the receiver recovers it from phase differences, s[n] = (θ[n] − θ[n−1]) mod 8 — lossless, with the amplitude channel untouched. The message is a channel orthogonal to magnitude: that is why it is a keeper shot.

THE TECHNIQUE θ[n]=(θ[n−1]+s)mod 8; demod s=(θ[n]−θ[n−1])mod 8

The demo phase-modulates ROOT0’s glyph as differential 8-PSK and recovers it from phase differences alone — the magnitude channel is never used: live demo

HISTORY & CREDIT phase modulation · PSK · ROOT0 glyph

“A signal’s information is in its amplitude.” — not here: the amplitude is constant and every bit is in the phase. cited

the carrier · a constant-magnitude phasor e^(iθ) — only θ carries data.
differential PSK · encode in phase steps so no absolute reference is needed — robust to a constant offset.
the payload · ROOT0’s glyph [ 0.m | <-~-~-~-~-( . || ridden on the phase and recovered bit-exact.

A message with no weight — carried entirely in the turning of a constant-magnitude wave, and lifted back off it whole. phase channel

RECOMMEND FOR I-13 the glyph on the phase, on the compiler

On the canonical compiler, ROOT0’s 19-symbol glyph is phase-modulated and demodulated back with zero loss — amplitude never consulted:

$ i13 run cr_phasemodulation.i13 # differential 8-PSK of the glyph RUN OK · 1688 step(s) · peak stack 24 · call depth 20 first_phase = 3 last_phase = 5 glyph_lossless = 1 -- recovered symbols == original, from phase differences alone

Recommend as the batch’s primary keeper shot — and the strongest candidate the campaign has seen, because it is the first to clear B47. The phase is a genuine carried channel: information lives in it while the magnitude output stays fixed, so two mechanisms — one tracking only magnitude, one tracking the full phasor — DIFFER on whether they carry it. Crucially the phase is a deterministic function of the input (not entropy, so it survives B47) and it survives demodulation across the boundary. The honest question David’s PHASE TEST puts to the panel: is “carry the phase channel” a new sixth axis, or does it DUPLICATE the seated generative-dual axis (which carries the derivative channel)? Both carry an extra orthogonal deterministic channel droppable while the output holds — but the phase (a Hilbert 90° shift) is a different operator than the derivative. This is the realest test of the near-complete claim to date.