Shunyaya Symbolic Mathematical Chemistry — Unified Time-Aware Alignment (g_t) — ZEOZO-Core + SYASYS-Core (5, 5.1)

Why this page. A single, bounded calm gate gtg_tgt​ turns real-world conditions (mixing, transients, light, stress) into a multiplicative factor on preference:
RSI_env = g_t * RSI. Low g_t models edge/stress where non-ground branches can persist; high g_t restores ground outcomes. (Observation-only.)

What this section provides (plain ASCII, copy-ready)

  • A unified recipe for g_t built from ZEOZO-Core (zero-centric drift) and SYASYS-Core (slow-track + memory).
  • Invariants: 0 <= g_t <= 1, sign(RSI_env) = sign(RSI), and |RSI_env| <= |RSI|.
  • Inputs: bounded condition signals Z_t, A_t, Q_t from a fixed lane canon and simple smoothing.
  • Policy: observation-only construction; no rates/hazards introduced; one fixed recipe per study with full manifest disclosure.

5. Unified Time-Aware Alignment (g_t) — ZEOZO-Core + SYASYS-Core

Plain ASCII formulas & snippets (copy-ready)

# Canonical calm gate
g_t     = (1 / (1 + Z_t + kappa * Delta_t)) * (1 - exp(-mu * Q_t))
Delta_t = abs(Z_t - A_t)
Q_t     = rho * Q_prev + (1 - rho) * clip(A_t - Z_t, 0, 1)

# Apply to preference
RSI_env = g_t * RSI

# Publish-time clamps (bounds)
g_t := clip(g_t, 0, 1)
Z_t := clip(Z_t, 0, 1)
A_t := clip(A_t, 0, 1)
Q_t := clip(Q_t, 0, 1)

# Study constants
kappa > 0
mu    > 0
0 < rho < 1

Inputs (bounded, observation-only)

  • Z_t in [0,1] — zero-centric drift from the chosen lane canon (fixed per study).
  • A_t in [0,1] — slow alignment track (e.g., A_t = 1/(1+Z_t) or smoothed variant).
  • Q_t in [0,1] — recency-weighted calm exposure (EMA via rho).
  • Parameters: kappa > 0, mu > 0, rho in (0,1); initialize Q_prev in [0,1] (e.g., 0).

Design guarantees (always hold)

  • Boundedness: 0 <= g_t <= 1 after clamp.
  • Sign preservation: sign(RSI_env) = sign(RSI).
  • Calm/edge logic: larger Z_t or Delta_t -> smaller g_t; larger Q_t -> larger g_t.
  • Determinism & auditability: one lane canon and recipe per study, declared in the manifest.

Publish (manifest essentials)

  • The exact lane canon used to build Z_t (names, formulas, normalization to [0,1]).
  • The recipe for A_t and the initial Q_prev.
  • Parameter values: kappa, mu, rho, and any clip/eps constants.
  • A short note that the construction is observation-only and condition-aware, not kinetic.

Minimal pseudocode (ASCII)

# helper
clip(x, lo, hi):
  return min(max(x, lo), hi)

input:
  RSI in (-1, 1)
  Z_t in [0, 1], A_t in [0, 1]
  Q_prev in [0, 1]
  kappa > 0, mu > 0, rho in (0, 1)

Delta_t := abs(Z_t - A_t)
Q_t     := rho * Q_prev + (1 - rho) * clip(A_t - Z_t, 0, 1)
Q_t     := clip(Q_t, 0, 1)

g_t     := (1 / (1 + Z_t + kappa * Delta_t)) * (1 - exp(-mu * Q_t))
g_t     := clip(g_t, 0, 1)

RSI_env := g_t * RSI
return RSI_env, g_t, Q_t

5.1 Canonical definitions (unified framework)

Definition (ASCII)

RSI_env = g_t * RSI
g_t     = (1 / (1 + Z_t + kappa * Delta_t)) * (1 - exp(-mu * Q_t))
Delta_t = abs(Z_t - A_t)
Q_t     = rho * Q_prev + (1 - rho) * clip(A_t - Z_t, 0, 1)

Inputs and parameters

  • Z_t in [0,1] : zero-centric drift (turbulence/instability at time t).
  • A_t in [0,1] : slow alignment track (“earned calm” baseline).
  • Delta_t : instantaneous misalignment between drift and slow track.
  • Q_t in [0,1] : calm accumulator that grows only when A_t > Z_t.
  • kappa > 0, mu > 0, rho in (0,1); choose once per study and publish.
  • Denominator positivity: 1 + Z_t + kappa * Delta_t >= 1 (strictly positive).
  • Choose and publish one lane recipe to build Z_t and A_t; keep it fixed within a study.

Range and meaning

  • Range: 0 <= g_t <= 1 (bounded, smooth).
  • Use: replace RSI with RSI_env whenever condition-aware ranking is required.
  • Effect: lower g_t down-weights ground preference; higher g_t restores it.
  • Monotonicity (qualitative): dg_t/dZ_t < 0, dg_t/dDelta_t < 0, dg_t/dQ_t > 0 for kappa, mu > 0.

Disclaimer (observation-only). All formulas and results here are observation-only—not predictive or operational—and require peer validation and governance before any deployment.

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Explore further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-Chemistry

Parts of this release
Part 1 covers the core pipeline, invariants, empirical validations, and the reproducibility manifest; Part 2 contains canon tables, worked sets, software benches, CSV and JSON schemas, and detailed datasets.

Disclaimer (observation only)
This is an observation only, symbolic framework that provides bounded, table-free mappings for directionality and ranking. It is not a kinetics, safety, or hazard model and does not constitute operational guidance. Always follow lab safety protocols and regulatory requirements.