Resonance Invariants for Drift Detection

1. Resonance‑Phase Coherence (RPC)#

RPC measures the stability of phase progression relative to the count of resonance cycles.

RPC = Δφ / ΔN

Where:

Δφ = phase deviation between successive measurements
ΔN = number of resonance cycles elapsed

A stable clock maintains a constant RPC under substrate‑aligned conditions. Deviations indicate loss of coherence in one or more components of the triad.

2. Environmental Susceptibility Index (ESI)#

ESI quantifies how sensitive the resonant frequency is to environmental perturbations.

ESI = ∂f / ∂E

Where:

f = measured resonance frequency
E = environmental variable (temperature, magnetic field, gravitational potential, etc.)

High ESI values indicate that the resonant system or interrogation apparatus is not adequately isolated or compensated.

3. Drift Detection Rule#

A clock is structurally drifting when either condition holds:

d(RPC)/dt ≠ 0
ESI exceeds its validated threshold

These conditions identify drift at the structural level, independent of architecture, implementation, or calibration strategy.

4. Interpretation#

Stable RPC → coherent resonance progression
Low ESI → environmental robustness
Deviations in either metric → drift in (R, I, or F)

These invariants form the validation layer for vST‑aligned timekeeping.