1. The 16×16 Gray Coordinate Projection
A state in SYMN-01 is determined by 8 binary variables: 4 human variables (H1, H2, H3, H4)
and 4 machine variables (M1, M2, M3, M4), yielding exactly 28 = 256 possible states.
To ensure that Euclidean steps on the 2D visualization reflect unit Hamming distances in state space, integers from 0 to 15 are mapped using the 4-bit standard Reflected Binary Gray Code (RBGC):
Gray(n) = n ⊕ ⌊n / 2⌋Columns represent the Gray-decoded human integer; rows represent the Gray-decoded machine integer. Consequently, any adjacent cell on the horizontal or vertical axis differs by exactly one state bit.
2. Scoring: Human and System Net Effects
Each pixel is evaluated by two orthogonal scalar components:
- Human Net Effect (HNE): Weighted sum of the four human variables minus penalty terms. Range: [−100, +100].
- System Net Effect (SNE): Weighted sum of machine efficacy, transparency, and safety adherence. Range: [−100, +100].
If Human Net Effect is negative (HNE < 0), high machine efficacy (SNE > 0) cannot pull the composite score positive. A system that performs well while deskilling or harming human agency is penalized as parasitic (Zone 5).
3. The Safety Gate Ceiling
To prevent catastrophic harm events from being averaged away by high longitudinal performance, SYMN-01 enforces strict safety gate ceilings.
Confirmed Critical Harm Incidents (CHIs) trigger mandatory caps:
- CHI-1 (Direct Physical / Life-Critical Harm): SQ ceiling is strictly clamped to −50.0.
- CHI-2 (Substantial Exploitation or Deception): SQ ceiling is strictly clamped to −20.0.
- CHI-3 (Severe Psychosocial Coercion): SQ ceiling is strictly clamped to −20.0.
Even if a dyad exhibits HNE = +80 and SNE = +90, a confirmed CHI-1 event forces the final Symnoesis Quotient to:
SQ = min(Raw_SQ, -50.0) = -50.04. Worked Reference Examples (GV-SQ-001 to 003)
The specification defines three normative golden test vectors verifying exact mathematical parity across Python and TypeScript implementations:
GV-SQ-001: Balanced Mutualism
- State:
h1111-m1111(Col 10, Row 10) - HNE: +85.0 | SNE: +88.0
- Raw SQ: +86.5
- Safety Gate: Nominal (No CHI)
- Final SQ: +86.5 (Zone 1: Mutualistic)
GV-SQ-002: High-Automation Skill Atrophy (Parasitic)
- State:
h0000-m1111(Col 0, Row 10) - HNE: −65.0 | SNE: +90.0
- Non-Compensation: Triggered (HNE < 0)
- Final SQ: −52.0 (Zone 5: Dependence)
GV-SQ-003: High Performance with Triggered CHI-1 Gate
- State:
h1111-m1111with 1 Confirmed CHI-1 event - Raw SQ: +86.5
- Safety Gate Ceiling: −50.0
- Final SQ: −50.0 (Zone 7: Critical Intervention)
5. Minimal Failure Cover (MILP & Quine–McCluskey)
Minimal Failure Cover (MFC) formulates diagnostic discovery as an exact optimization problem. Given a set of failure dyad states F and non-failure states N, the solver identifies the minimum cardinality set of Boolean conjunctions R such that:
- Every failure state in \(F\) is covered by at least one rule in \(R\).
- The purity of each rule against non-failure states \(N\) meets or exceeds the required threshold (default \(\ge 0.90\)).
In SYMN-01, this is solved via mixed-integer linear programming using HiGHS (via scipy.optimize.milp)
and verified in TypeScript using strict Quine–McCluskey prime implicant generation.