Interactive nonlinear benchmark · declared numerical model · Not peer reviewed

Watch an information geometry make testable claims.

Set a double pendulum in motion. OIG freezes its forecast first; then an independent solver reveals a held-out outcome. Compare what was promised with what actually appeared.

Evidence ladder

Three levels, kept visibly distinct

1 LiveFast numerical forecast Ready
2 RefinedSolver, response & energy gates Waiting
3 CertifiedFixed A+B artifact provenance Checking

Prepare the trial

Choose the declared state and instrument

Angles are measured from downward vertical. The held-out perturbation remains hidden until the forecast is frozen.

Initial state Angle θ₁ 0.800 rad Angle θ₂ −0.350 rad Velocity ω₁ 0.000 rad/s Velocity ω₂ 0.000 rad/s

Observation Sensor Horizon T 4.00 s Preparation radius 0.010 rad Sensor noise radius 0.015

Ready to prepare a forecast.

Ensemble calibration

One launch, or a finite cloud of declared alternatives

N = 1 preserves the detailed single-outcome wind tunnel. Larger N runs a deterministic seeded finite ensemble.

N = 1 uses the deterministic held-out boundary experiment; realism, distribution, seed, and structured-law controls activate only for N > 1.

Ensemble size N 1 Realism dial 20% Uncertainty declaration Seed Known design law Law amplitude α 0.25× Launch-angle direction Custom angle 0°

Disclose the actual uncertainty components

Angle radius: —
Velocity radius: —
Parameter radius: —
Sensor scale: —
Clock radius: —

Bounded mode: members are deterministic seeded points inside the displayed component bounds. Coverage is an empirical count over those points, not a probability guarantee.

Known design / hidden draws: f(s) = s with the resolved α shown above is disclosed before freezing. Individual microscopic draws remain hidden until the outcome and are revealed only in the audit/export. The forecast displays a tube or distribution summary, never member-specific realization predictions.

The wind tunnel

Declared world / frozen OIG forecast

Forecast sealOpen — controls editable

Independent outcome

Double-pendulum dynamics

t0.000 s

Idle

independent outcome forecast centre

Drag to orbit · scroll to zoom

First-order numerical forecast · sealed before observation

Sensor forecast vs outcome

Forecastunsealed

No forecast sealed yet Prepare a trial to draw the predicted sensor tube.

forecast centre declared tube / distribution band independent outcome

Finite-ensemble audit

Where did the forecast survive, exit, or remain unresolved?

Empirical numerical coverage over a finite seeded ensemble. A whole-horizon survival interval appears only for an eligible declared iid sample. This is not certified probability or physical truth.

Member-time tube coverage — fraction of all resolved member-time samples inside the frozen tube

Persistent exits — outside for ≥3 consecutive sampled times at the declared cadence

Survival at T — whole-horizon no-exit members; interval awaiting a declared iid ensemble

Outliers — declared robust-spread rule; member IDs appear after the outcome

Projected output reconvergence — exited and later returned to the output tube

Full-state separation at output re-entry — median declared scaled norm; not attraction or synchronization

Unresolved — invalid or incomplete member checks

Coverage and survivalPointwise output-tube coverage and never-exited survival over the declared horizon.

pointwise coveragenever-exited survival

Predicted vs observed spreadObserved percentile band against the frozen first-order predicted band.

predicted P05–P95predicted medianobserved P05–P95observed median

Predicted amplification: —
Observed median amplification: —
Observed P05 / P50 / P95 spread: —
Display policy: —

Reveal canonical member draws after the outcome

Seeded finite member results; these microscopic draws were hidden until the forecast was frozen.
Member	s	ξ	Base offset	Known-design offset	Total initial offset	Tube coverage	First persistent exit	Endpoint classification	Resolution
No ensemble outcome yet.

Prediction / result

Did the promised information appear?

Run a trial to compare a frozen local forecast with a held-out outcome.

Tube coverage — samples inside the frozen first-order numerical tube

Predicted amplification — RMS local response per radian

Observed amplification — held-out RMS response per radian

Endpoint verdict — at the declared sensor-noise radius

Local response geometry

Observable and quiet directions

θ₁, θ₂

Weakest gain—

least visible launch-angle direction

Strongest gain—

most amplified launch-angle direction

Quiet direction—

Observable direction—

Held-out perturbationhidden until run

Strong / weak gain ratio—

Independent numerical check

Refinement diagnostics

Forecast / refined baseline: —
Response h / h⁄2 relative discrepancy: —
Weakest-gain relative shift: —
Strongest-gain relative shift: —
Relative energy drift: —
Outcome solver: Dormand–Prince 5(4)
Forecast solver: Fixed-step RK4

Initial-condition atlas

A torus of possible launches

The seams meet: +π and −π are the same angle. The selected launch is marked on a committed 13 × 13 evidence field.

Toroidal angle slice

Weakest local gain

Drag to orbit · select a torus cell to prepare that launch

low high unresolved

Active experimental design

What should we measure next?

Live recommendation for resolving the current launch-angle geometry—not a certified global optimum.

Recommended next reading Awaiting a forecast

at —, with projected squared information floor —.

Background laboratoryScale a live trial into a queued calibration study N 50–1000 · T 1–30

Runs remain synthetic, finite, seeded, and numerical. They can expose failure patterns; they do not establish physical adequacy or certified probability laws.

Idle0% 0%

N-by-T calibration surfaceCoverage or survival summary appears after a queued study.

Compact completed-cell aggregates across repeated seeds
N	T	Law	α	Repeats	Member-time coverage	Whole-horizon survival	Status
No completed jobs yet.

Committed Tier-3 result

A narrow theorem, not a blanket badge

The certified result belongs to the fixed five-output A+B physical-parameter protocol with exact preparation and one shared clock direction. Slider-selected launch-angle trials remain live or refined evidence.

Inspect the certificate artifact

Certified response floor: Unavailable until verified
Exact rational floor: Unavailable until verified
Outputs: Awaiting verified data
Nuisance profiled: Awaiting verified data
Artifact integrity: Checking…
Two-row floor (no nuisance): Unavailable until verified

Certificate unavailable until all source verifiers pass.

Waiting for committed evidence data…

Auditable record

Prediction-versus-result ledger

Chronological record of forecast, outcome, and evidence events for the current experiment
Test	Frozen claim	Observed	Verdict
No trial recorded. The ledger begins when a forecast is frozen.

A mismatch can be falsified or unresolved; the interface does not silently convert either into agreement.

What is being benchmarked?

The pendulum is the wind tunnel. OIG is the aircraft.

The equations are deterministic, yet finite knowledge of the launch can make the future practically unpredictable. The animation shows that complex world.

OIG is tested on a harder question: which changes a sensor can see, which remain quiet, how uncertainty amplifies, and whether those claims survive an independent outcome.

A physical pendulum would add the next layer: calibration error, sensor behavior, preparation uncertainty, and the possibility that the declared model itself is inadequate.

Formal research and reproduction

Read the atlas, audits, and committed artifacts

The browser chamber is a public numerical interface. The formal scope, theorem/Tier boundaries, adversarial audits, and exact artifact records remain available as immutable reproduction material. This research is not peer reviewed, and the repository has no third-party reuse license; TGN is displaying the package under the owner's publication authorization.