Inverse-PINN modeled fixture

Historical configuration; runtime unavailable

The migrated recipe recorded an illustrative Duffing-oscillator result near 0.989 and a set of gate thresholds. No pinned current inverse engine, input trajectory, route response, receipt, or signature is established here. The recorded value remains HISTORICAL_MODELED_FIXTURE.

For the Duffing oscillator

[ m x'' + c x' + \delta x + \alpha x^3 = F\cos(\omega t), ]

an inverse method may fit parameters such as (\alpha) from trajectory data. A credible result requires the exact trajectory, preprocessing, solver revision, hyperparameters, residuals, identifiability diagnostics, and uncertainty method. None of those is replaced by the local gate fixture below.

Executable historical gate fixture

This standard-library code evaluates only the threshold shape retained in the migrated recipe. It does not train a PINN, recover a parameter, or reproduce the historical value.

import json

HISTORICAL_THRESHOLDS = {
    "min_causal_weight": 0.99,
    "max_grad_norm": 1e-5,
    "max_kappa_fim": 1e6,
    "min_fisher": 1e-8,
}


def historical_gate(metrics: dict[str, float]) -> str:
    checks = [
        metrics["min_causal_weight"] > HISTORICAL_THRESHOLDS["min_causal_weight"],
        metrics["grad_norm"] < HISTORICAL_THRESHOLDS["max_grad_norm"],
        metrics["kappa_fim"] < HISTORICAL_THRESHOLDS["max_kappa_fim"],
        metrics["min_fisher"] > HISTORICAL_THRESHOLDS["min_fisher"],
    ]
    return "MODELED_FIXTURE_PASS" if all(checks) else "MODELED_FIXTURE_FAIL_CLOSED"


fixture_metrics = {
    "min_causal_weight": 0.995,
    "grad_norm": 2e-16,
    "kappa_fim": 1.0,
    "min_fisher": 0.1,
}
report = {
    "gate_result": historical_gate(fixture_metrics),
    "historical_reported_alpha": 0.9894,
    "evidence_state": "HISTORICAL_MODELED_FIXTURE",
    "runtime_state": "UNAVAILABLE",
    "receipt_state": "UNAVAILABLE",
}
assert report["gate_result"] == "MODELED_FIXTURE_PASS"
print(json.dumps(report, indent=2, sort_keys=True))

A fixture pass means only that the displayed numbers satisfy the displayed inequalities. It is not evidence of convergence, identifiability, parameter recovery, physical plausibility, or live execution.

Promotion contract

A current inverse-discovery claim requires:

1. immutable trajectory bytes and provenance;
2. exact solver source, environment, configuration, and random-state controls;
3. independently reproduced residual, gradient, Fisher, and uncertainty calculations;
4. negative and non-identifiable cases that fail closed;
5. an artifact-specific receipt and signature result, if claimed; and
6. exact runtime request/response evidence, if an endpoint is claimed.

Evidence state

Surface	Current status
Duffing equation and PINN literature	CITED_PRIOR_ART
Threshold evaluator above	HISTORICAL_MODELED_FIXTURE
Reported alpha near 0.989	HISTORICAL_MODELED_FIXTURE_NOT_REPRODUCED
Current solver and input trajectory	SOURCE_ARTIFACT_UNAVAILABLE
Route, receipt, and signature	UNAVAILABLE

References: M. Raissi, P. Perdikaris, and G. E. Karniadakis, Journal of Computational Physics 378 (2019), 686-707; G. Duffing (1918).

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A threshold fixture is not a reproduced inverse-physics result or an operational service.