A reproducible check of your force model.
Model: SYNTHETIC / hidden_central_force_coupling
Recorded: 2026-09-10T20:53:25.421032+00:00
A consistency violation was detected
Local numerical tests of a static, deterministic, nonperiodic position-only force model in full 3N configuration space. No physical-accuracy, stability, chemical-validity, global-conservativity or safety certification.
Download complete evidence JSONClosed-loop work
Conservative forces should do zero net work around a closed path. Every path perturbs the complete atomic configuration. Smaller steps and fresh reverse traversal help separate a signal from integration error.
Work units: eV/angstrom × angstrom. Status: VIOLATION DETECTED.
| Loop | Result | Fine work | Refinement change | Detection threshold | Reversal residual |
|---|---|---|---|---|---|
| 1 | VIOLATION DETECTED | -8.208897e-06 | 3.041194e-08 | 2.628118e-06 | 4.336809e-19 |
| 2 | VIOLATION DETECTED | -0.001791555 | 3.825873e-08 | 9.644903e-06 | 1.301043e-18 |
| 3 | VIOLATION DETECTED | -0.001015405 | 4.779729e-08 | 7.494446e-06 | 2.168404e-19 |
Threshold = absolute tolerance + relative segment-work tolerance + four times the coarse-to-fine change. This refinement screen is not a rigorous error bound.
Force and energy agreement
The force projected along a direction is compared with the negative energy derivative at two finite-difference step sizes.
Status: NO VIOLATION DETECTED.
| Direction | Result | Projected force | −Energy derivative | Residual | Detection threshold |
|---|---|---|---|---|---|
| 1 | NO VIOLATION DETECTED | -0.1144035 | -0.1144035 | 7.379593e-10 | 0.0001244125 |
| 2 | NO VIOLATION DETECTED | -0.1754903 | -0.1754903 | 9.225637e-10 | 0.0001855014 |
| 3 | NO VIOLATION DETECTED | 0.02437585 | 0.02437585 | 3.255238e-10 | 3.437982e-05 |
Interpretation and limits
- No violation detected means only that these finite sampled tests did not detect one.
- Declared units must be compatible; the auditor performs no automatic unit conversion.
- Loop perturbations can encounter close contacts, discontinuities or extrapolation regions. Inspect each counterexample and the model's intended domain.
- Two quadrature resolutions cannot rule out aliasing or establish a rigorous integration-error bound. A flagged path merits finer independent replay before making a scientific claim.
The JSON evidence contains every completed loop frame, evaluated force, energy when supplied, seeded direction, threshold and configuration. A detected violation is a counterexample to a declared conservative-force or force–energy consistency claim under these assumptions. It does not by itself identify a software defect or establish accuracy against nature.
Reproducibility record
Show configuration, provenance and counterexample locations
{
"audit_spec_sha256": "f51d79ee3629972ec77e9e3ba98664674585b58dd8c7fde8c915c02a8502f81a",
"model": {
"label": "SYNTHETIC / hidden_central_force_coupling",
"callable": "__main__:Counted",
"declared_metadata": {
"synthetic_fixture": true,
"wrapped_callable": "examples.synthetic_models:hidden_central_corruption",
"fixture_source_path": "examples/synthetic_models.py",
"fixture_source_sha256": "f4c449a168bb2ce2c2935935f921f74f6858e1b4ade0c96940c1702704c1fc61"
},
"python_source_path": "benchmarks/run_benchmarks.py",
"python_source_sha256": "207efb13e8df2a00acfd3890350771d7d6de2974dfd66deedd6f4bc6f1eb0c87",
"provenance_limit": "A source-file hash does not identify external model weights, dependencies, hardware, or remote services. Supply those in model.audit_metadata."
},
"config": {
"loop_count": 3,
"loop_scale": 0.06,
"coarse_steps": 8,
"seed": 20260910,
"model_label": "SYNTHETIC / hidden_central_force_coupling",
"position_unit": "angstrom",
"energy_unit": "eV",
"force_unit": "eV/angstrom",
"work_abs_tol": 1e-06,
"work_rel_tol": 0.0001,
"energy_step": 0.0001,
"derivative_abs_tol": 1e-05,
"derivative_rel_tol": 0.001,
"determinism_abs_tol": 1e-09,
"determinism_rel_tol": 1e-07,
"energy_directions": 3,
"max_evaluations": 1000,
"pbc": false,
"driven": false
},
"input": {
"positions": [
[
0.0,
0.0,
0.0
],
[
1.2,
0.0,
0.0
],
[
1.9,
1.212435565298214,
0.0
]
],
"atom_count": 3,
"configuration_dimensions": 9
},
"determinism": {
"status": "NO_VIOLATION_DETECTED",
"repeat_count": 3,
"max_force_difference": 0.0,
"force_tolerance": 3.0999999999999986e-08,
"energy_difference": 0.0,
"energy_tolerance": 1e-06,
"limitation": "Three repeats at one configuration can detect some nondeterminism; they cannot establish determinism everywhere."
},
"counterexamples": [
{
"type": "closed_loop_work",
"loop_index": 0,
"fine_work": -8.208897053194422e-06,
"detection_threshold": 2.628118158516693e-06,
"trace_pointer": "/closed_loop/loops/0/fine/frames",
"replay": "Evaluate the same model at every stored frame in order; sum dot((F[i]+F[i+1])/2, q[i+1]-q[i]) over every atom and coordinate."
},
{
"type": "closed_loop_work",
"loop_index": 1,
"fine_work": -0.0017915548505565942,
"detection_threshold": 9.64490304823487e-06,
"trace_pointer": "/closed_loop/loops/1/fine/frames",
"replay": "Evaluate the same model at every stored frame in order; sum dot((F[i]+F[i+1])/2, q[i+1]-q[i]) over every atom and coordinate."
},
{
"type": "closed_loop_work",
"loop_index": 2,
"fine_work": -0.0010154046166957543,
"detection_threshold": 7.494446221267405e-06,
"trace_pointer": "/closed_loop/loops/2/fine/frames",
"replay": "Evaluate the same model at every stored frame in order; sum dot((F[i]+F[i+1])/2, q[i+1]-q[i]) over every atom and coordinate."
}
]
}