SSGF quantum-in-the-loop geometry gradient (BL-70)

scpn_quantum_control.ssgf_geometry_gradient_product governs the existing SSGF simulator path

\[ z \rightarrow W(z) \rightarrow H(W) \rightarrow |\psi(t)\rangle \rightarrow R \rightarrow C=1-R \rightarrow \nabla_z C. \]

The product is a bounded local-simulation evidence surface. It does not submit jobs, claim analytic automatic differentiation, or promote a short outer-cycle trace to convergence or advantage evidence.

Gradient-method policy

BL-52 route	Status	Reason
transform:ssgf.latent_finite_difference	supported	Central finite difference evaluates the complete nonlinear latent path.
transform:ssgf.latent_parameter_shift	permanent_boundary	Circuit parameter-shift does not directly compute dC/dz because z enters Hamiltonian coefficients through softplus(W(z)).

Unsupported latent dimensions fail before an ambient quantum evaluation. The product accepts exactly n_oscillators * (n_oscillators - 1) // 2 latent parameters and caps evidence probes at six oscillators.

Certificates

import numpy as np

from scpn_quantum_control.ssgf_geometry_gradient_product import (
    certify_geometry_gradient,
    certify_quantum_cost,
    materialise_outer_cycle_evidence,
)

z = np.array([0.2, -0.4, 0.7])
theta = np.array([0.1, 0.6, 1.4])

cost = certify_quantum_cost(z, 3, theta, trotter_reps=1)
assert cost.cost == cost.c_micro
assert cost.cost == 1.0 - cost.r_global

gradient = certify_geometry_gradient(z, 3, theta, trotter_reps=1)
assert gradient.route_id == "transform:ssgf.latent_finite_difference"
assert gradient.refinement_max_abs_delta <= 5e-3
assert gradient.periodic_gradient_max_abs_delta <= 1e-9

trace = materialise_outer_cycle_evidence(
    n_oscillators=3,
    z_init=z,
    theta_init=theta,
    max_iterations=3,
)
assert trace.evidence_label == "functional_non_isolated_local_simulation"

The cost certificate cross-checks the public quantum_cost result against compute_quantum_costs().c_micro and the complement law C + R = 1. The gradient certificate checks the expected evaluation count, step refinement from epsilon to epsilon / 2, and invariance under a global 2*pi phase shift. These are BL-46 metamorphic checks, not a proof of analytic AD.

Composition boundaries

• BL-50 consumes SsgfGeometryObserverRecord as geometry diagnostics.
• BL-33 may consume the same immutable record as optional evaluator telemetry; it is not an operational controller decision.
• BL-53 owns the negative space: wrong latent dimensions, latent parameter-shift, analytic-AD promotion, hardware promotion, and convergence promotion all remain explicit refusals.
• BL-47 remains authoritative for any future hardware execution policy. This BL-70 product performs no hardware submission.

Authored by Anulum Fortis & Arcane Sapience (protoscience@anulum.li)