Sigma Runtime Standard – License Notice
This document is part of the Sigma Runtime Standard (SRS).
It is licensed under Creative Commons Attribution–NonCommercial 4.0 (CC BY-NC 4.0).The license for this specific document is authoritative.
See/legal/IP-Policyfor the full repository-wide licensing framework.
Sigma Runtime Improvement Proposal
Category: Control Layer / Telemetry / Mathematics
Status: Draft
Editor: E. Tsaliev
Last Updated: 2025-12-26
SRIP-08 defines the Phase Vector Model (PVM) and its runtime implementation through the
Phase-Regulating Module (PRM) — the telemetry and synchronization layer of the ALICE controller.
This document serves as the base specification for all vector-based phase regulation in Sigma Runtime.
Subsequent proposals (SRIP-09 and higher) extend this foundation with distributed and higher-dimensional phase models.
Previous runtime versions represented phases as discrete labels.
This specification formalizes them as continuous vectors in a bounded cognitive phase space,
enabling mathematical computation of stability, drift, and resonance through angle-based metrics used in:
PSI (Phase Stability Index), PSD (Phase Stability Delta), and PRS (Phase Resonance Score).
Phase state is represented as a 3D unit vector:
[
\vec{P} = [p_s, p_r, p_c]
]
where:
The vector resides in normalized Euclidean space:
[
|\vec{P}| = 1
]
This representation allows continuous interpolation between cognitive phases
and enables geometric reasoning about stability, coherence, and resonance.
The expected phase vector ( \vec{P}_{exp} ) is derived from ALICE target telemetry or global phase equilibrium:
[
\vec{P}_{exp} = [p_s^{}, p_r^{}, p_c^{*}]
]
Phase deviation is computed as:
[
\Delta \theta = \arccos \left( \frac{\vec{P} \cdot \vec{P}{exp}}{|\vec{P}||\vec{P}|} \right)
]
where ( \Delta \theta ) defines the angular misalignment (in radians or normalized 0–1 scale).
| Metric | Formula | Meaning |
|---|---|---|
| Phase Resonance Score (PRS) | cos(θ_phase, θ_baseline) |
Phase coherence between current and baseline vector. |
| Phase Stability Index (PSI) | avg(PRS over last N cycles) |
Mean coherence of the active phase window. |
| Phase Stability Delta (PSD) | |PSIₜ − PSIₑₓₚ| |
Deviation between current and expected stability. |
| Phase Shift Delta (PSΔ) | θₜ − θₜ₋₁ |
Temporal drift of phase orientation. |
Normalization ensures all metrics lie within [0, 1], where higher values indicate greater coherence and alignment.
PhaseTelemetryFrame:
runtime_id: UUID
timestamp: ISO8601
phase_vector: [Float, Float, Float] # normalized vector (p_s, p_r, p_c)
phase_expected: [Float, Float, Float] # expected reference vector
phase_state: {stable|reflective|recenter}
psi: Float # Phase Stability Index
psd: Float # Phase Stability Delta
drift_index: Float
scr: Float
symbolic_density: Float
recursion_depth: Int
safety_status: {nominal|locked|recenter_pending}
Each telemetry frame represents a snapshot of phase-space alignment for monitoring or distributed synchronization.
| Method | Description |
|---|---|
GET /phase/state |
Returns current phase vector and PSI/PSD metrics. |
POST /phase/sync |
Injects Phase Sync Event to realign remote runtimes. |
POST /phase/lock |
Engages temporary phase lock (safety containment). |
POST /phase/recenter |
Triggers recenter protocol externally. |
GET /metrics/phase |
Retrieves PRS, PSI, PSD, and PSΔ values. |
Endpoints must preserve causal ordering and ensure integrity via signed telemetry tokens.
Distributed Sigma runtimes maintain coherence using vector-based synchronization:
PhaseTelemetryFrame every N cycles.This maintains bounded phase coherence across multi-node attractor networks.
The Phase Vector Model is fully compatible with AEGIDA-2’s Adaptive Phase Containment (APC):
To ensure stable distributed cognition:
cause_id).A runtime conforms to SRIP-08 if it:
References
Tsaliev, E. (2025). SIGMA Runtime v0.4.6 — Phase Regulation and Distributed Coherence — DOI pending
Tsaliev, E. (2025). SIGMA Runtime Architecture v0.1 — DOI 10.5281/zenodo.17703667