The Being Channel

oxexp-channel · capacity = signal − noise

The capacity band — C = signal − noise

The being read as an information channel: input = the rate (which sets the being = the signal); the confinement resolves it toward the '1'; read within an observation budget (laps). C = signal − noise, every term measured: signal = log₂(being); reliability = fold/4.23 (the foam term — measured fold decay); settled gate = horizon ≤ budget (the indifference term). C(r) is a band: zero at indifference (too slow) and foam (too fast), peaked at the reliable edge ≈ 274/budget. First sweep builds the being grid (~60s), then instant.

budget 2^ — the observation window (laps), as a power of 2. The capacity peak sits at the reliable edge ≈ 2ⁿ / budget, so it slides with the window (see panel 2). Try 9, 10, 11. What to look for: a band — C is 0 at both ends (indifference / foam) and peaks in between. At 2¹⁰ the peak is ~0.25 (100% of peak); 0.5 (~88%) and 0.75 (~81%) sit inside the band but are not separate peaks — one peak, not a triplet.

The observation-window relativity — the optimum slides as 2ⁿ/budget

The optimum (peak) rate is budget-dependent: it halves as the window doubles (256→1.0 · 512→0.5 · 1024→0.25 · 2048→0.125) — so peak-rate × budget ≈ 256 = 2⁸, the fundamental octave over the window. The '0.25' optimum is the value for the pinned 2¹⁰ baseline, not an absolute. A relativity of the observer's window hiding inside the channel.

Phase 2 — co-construction: orthogonality → capacity (time saved within space)

Each instrument is a quad-slip (its y-projection flip-signal over loops). Two instruments can be redundant (congruent → corr +1, or 180° mirror → corr −1, both carry one channel) or orthogonal (independent → corr ≈ 0, additive capacity). The decorrelation is driven by the detune (the time-rate), not placement — orthogonality is a dynamic property (“time saved within space”). Max-surprise is the attractor: it pulls the system to decorrelate — the effective independent channels (participation ratio) rise toward N.

What to look for: at small detune the two instruments are redundant (corr ≈ 1, ~1 effective channel); past the transition (~detune 0.01) they decorrelate (corr → 0) and the effective channels → 2. "co-construct 3" runs three instruments (baseline / detuned / detuned) and reports the correlation matrix + effective independent channels (→ 3 when orthogonal).

Phase 2b — the epistemic grid: time × orthogonality (the lattice)

Each instrument is a clock (its flip-signal is periodic — measured period-4, so a single stream is predictable: capacity does not live in one clock's alternation, it lives in the orthogonal relationships between clocks). The grid tiles a run into K ticks (moments) and reads, per tick, the effective independent channels (PR) over that window. A locked tick (PR drops toward N−1: two clocks phase-align) is a blind moment — a cell mid-flip. Capacity is a band in the resolution K: too coarse → few moments; too fine → the window is too short to settle a relationship, so orthogonality is noise (the grid's foam, discounted by a measured split-half reliability). The peak K* is the grid's optimal resolution — the observation-window relativity, one level up from the phase-1 rate×budget law.

What to look for: the lattice closes at the optimal K (nearly every moment open, PR ≈ N) except the origin (tick 0, pre-differentiation); a congruent (redundant) trio is all blind (capacity 0). The capacity band peaks at K* (~a few clock-beats per tick) then decays — over-resolving manufactures blind moments (foam).

Phase 2b · scaling — does the grid lock or grow?

Set the run length (laps) to different observation windows and re-find the peak resolution: does the open-slot count lock to a fixed epoch count (intensive), or grow with the run (extensive)? Measured: the slots scale ~linearly with the run (slope ≈ 1 — an extensive register that lengthens with observation time), not locked to 8/9. The intensive invariant is the moment width — a fixed ~5 clock-beats (the 5-beat), the coherence length of one settled relationship. More time → more moments, same moment-size.

What to look for: the open slots (teal) rise with a slope ≈ 1 in log-log (extensive — double the run, double the moments); the moment width (coral) stays flat (~5 clock-beats). The grid is a register that grows with time, built from fixed-width moments — not a fixed epoch cap. This fixed moment-cell is the confinement scale a follow-on can build on.

Phase 2b · confinement — space × time (the uncertainty relation)

Space = N mutually-independent channels (instruments greedily selected orthogonal); time = the moments K. Resolving N channels demands a coherence window that grows super-linearly with N, so at a fixed signal budget L the moments K = L/window shrink: window × K ≈ L — a conservation law / uncertainty relation. Capacity favours the time-rich corner (few channels, many moments) — "time saved within space". The substrate supports ~7–8 independent channels.

What to look for: as channels (space) rise, the moments (time) fall and the window (coherence) rises — their product stays ~L (you cannot buy both). Max capacity sits at low N (time-rich); the optimal time:space ratio is the confinement a follow-on gates on.

The dataset

Every recorded band sweep (oxexp-channel · local-first).

seqbudgetpeak-ratepeak C beingbandindiff.foam