Drift‑Detection Model
1. Resonance‑Phase Coherence (RPC)#
Resonance‑phase coherence measures the stability of phase progression relative to the count of resonance cycles. It is defined as:
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 R, I, or F.
RPC is sensitive to:
- interrogation errors
- cavity drift
- servo instability
- environmental perturbations
- frequency pulling
2. Environmental Susceptibility Index (ESI)#
The environmental susceptibility index quantifies how strongly the resonant frequency responds to external variables. It is defined as:
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.
ESI captures:
- thermal sensitivity
- magnetic field coupling
- blackbody radiation shifts
- gravitational potential differences
- local environmental drift
3. Structural Drift Condition#
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 + low ESI
The clock is structurally aligned. Resonance cycles accumulate coherently, and environmental coupling is suppressed. -
RPC deviation
Indicates loss of coherence in interrogation or feedback systems. -
High ESI
Indicates environmental sensitivity or insufficient compensation. -
Both conditions violated
Indicates systemic drift affecting multiple components of the triad.
5. Role in vST#
These invariants form the validation layer for vST‑aligned timekeeping. They provide a unified method for comparing architectures, diagnosing drift, and evaluating stability without relying on architecture‑specific corrections or empirical models.