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Subsystem: ssgf — self-stabilising gauge-field closure

An optional closed-loop coupling synthesiser: a coupling matrix is decoded from a latent vector and driven by a cost. 8 files, ~1.6k LOC. Not part of the default step loop — opt-in.

Inputs

phases (N,) and a coupling matrix W (N, N) for the cost terms; a latent vector z (default dimension 8) for the decoder; cost weights.

Outputs

  • SSGFState(z, W, cost, grad_norm, step) — the decoded coupling and its cost.
  • SSGFCosts(c1_sync, c2_spectral_gap, c3_sparsity, c4_symmetry, u_total).
  • Observer snapshots from PGBO and topological-integration (diagnostic only).

Processing model

GeometryCarrier decodes z → W and updates z by finite-difference gradient descent on a four-term cost: c1 = 1 − R (synchrony deficit), c2 = −λ₂(L(W)) (maximise algebraic connectivity), c3 = ‖W‖₁/N² (sparsity), c4 = ‖W − Wᵀ‖_F/N (symmetry). CyberneticClosure runs the loop phases → costs → gradient → decode → feedback, tracking a non-increasing total cost. PGBO (phase-geometry observer) and the topological-integration observable (a persistent-homology topological-integration observer, ripser/PLV) produce diagnostics; the integration gate feeds the coupling plasticity update.

Backends

compute_ssgf_costs and the carrier decoder have Rust paths with NumPy fallback.

Wiring

The closure returns a coupling matrix the caller may feed back to upde. It is not invoked in the default simulation; integration is user-driven. The topological-integration observable is_conscious gate is consumed by coupling/plasticity.

Scope boundaries

EthicalCost is an early-stage module, exported but not part of the active cost objective. PGBO / topological-integration are observation-only — they do not fail a step or block actuation.