KO42 — Metric Tensioner

The mandatory operator in every Zeq computation. KO42 overlays a HulyaPulse-synchronised modulation on the metric tensor, ensuring all results are temporally aligned to the 1.287 Hz / 0.777 s Zeqond clock cycle.

caution

KO42 is always included automatically by the 7-step wizard protocol (Step 1: PRIME DIRECTIVE). You cannot opt out.

KO42.1 — Automatic Mode

ds² = g_μν dx^μ dx^ν + α sin(2π · 1.287 t) dt²

Default mode. The coupling constant α ≈ 1.29 × 10⊃−³ is tuned so that averaging over one Zeqond recovers the unmodulated metric exactly. This ensures ≤0.1% error on any single-tick measurement.

KO42.2 — Manual Mode

ds² = g_μν dx^μ dx^ν + β sin(2π · 1.287 t) dt²

Manual mode allows specifying β directly for specialised applications (e.g., strong-field corrections, custom damping).

Zeq Equation (Proper-Time Modulation)

R(t) = S(t) [1 + α sin(2π f t + φ&sub0;)]
α ≈ 1.29 × 10⊃−³
f = 1.287 Hz

The universal proper-time modulation. S(t) is the unmodulated signal; R(t) is the Zeq-modulated output. Average over one Zeqond (0.777 s) to recover S(t) exactly.

Zeq Timebase Bridge (ZTB1)

ZTB1(t, from_base, to_base) = (t × conv_factor) + phase_offset
conv_factor = 0.777 (Unix → Zeq) or 1/0.777 (Zeq → Unix)

Lossless bidirectional mapping between Unix time and Zeqond time. Auto-injected whenever mixed timebases are detected in a computation.

HulyaPulse Frequency Derivation

f = c / λ_φ
λ_φ = 2π r_φ
→ f ≈ 1.287 Hz

The fundamental frequency derived from the field radius. All Zeq timing is phase-locked to this frequency.

API Usage

Call any operator via the Compute API:

curl -X POST https://zeq.dev/api/zeq/compute \
  -H "Content-Type: application/json" \
  -H "Authorization: Bearer zk_live_..." \
  -d '{"query": "Apply KO42 tensioner to flat Minkowski metric", "operators": ["KO42"]}'

The 7-step wizard protocol selects the right operators automatically when you omit the operators field. KO42 is always included.