Two causal actors each instantiate the pinned quad-slip baseline (the shared 'is'). A
relational time-rate difference (rate-eps) separates them — actor B's bus-detune is
A's × (1+rate-eps), so B's 'is' drifts relative to A's. Each reads an address on the shared
'is'; a claim is effectual while the two agree to within one Pi-quantum
(10⁻dp), and slips once the residual exceeds it — the
effectual horizon. With rate-eps = 0 the 'is' is identical → effectual forever (a pure
offset is absorbed; the address is frame-independent). The horizon ≈ quantum / (drift × rate-eps)
— the cross-actor coherence law. Phase B (space): a space-offset (actor B's
placement) is a pure constant — the 'is' is footprint-blind — so it is a known transform,
fully absorbed: the effectual residual and the horizon are independent of it. Space is free;
only the time-rate costs.
Each run computes both actors on the shared baseline 'is' and records the residual at every catch, the effectual fraction, and the horizon. rate-eps is the relational difference; Pi (dp) the readout precision (the quantum = the agreement tolerance); laps how far to reach.
Sweep laps over the octaves 2ⁿ and read the residual-max at each (summary-only, so it scales
past 2¹⁹). The residual grows ~linearly with laps, so on log-residual vs octave it is a straight
line: it emerges (first resolves at the readout) at one octave and crosses the
Pi-quantum (the effectual horizon) at another. At rate-eps 1.0 / Pi 1:
0.0001 emerges at 2⁸, the horizon at 2¹⁸.
Every recorded run (oxexp-hinge · local-first).
| seq | rate-eps | space-off | Pi | laps | horizon | effectual | eff-frac | residual-max |
|---|