d0re / research

04 / The instrument

Theory 2.42 / reviewed 15 OCT 2026

Repetition cannot erase a shared calibration error.

A prediction must reach a detector with its uncertainty intact. The new discipline makes response, calibration, chronology and data reuse part of the claim.

σ(mean), normalized1128 repeats
32
0.30
Shared calibration retained Incorrectly treated as independent:
Blue: √(1/n+c²). Dashed gray: √((1+c²)/n). Statistical standard deviation s=1; zero statistical/calibration cross-covariance is assumed. These normalized curves are conditional arithmetic, not fitted instrument data.

01 / 05

Move the detector inside the model

A simulated field is not yet the quantity recorded by a camera. Propagation, finite apertures, point-spread blur, pixel integration, efficiency and counting statistics change what reaches the observation record. The project’s AB response fixture makes those operations explicit under supplied standard-physics assumptions.

For a sinusoidal response, Gaussian blur and a finite top-hat pixel attenuate contrast; a position offset also shifts the apparent phase. A phase/origin ambiguity can make two descriptions observationally equivalent. A fit cannot decide which description is physical without an independently justified reference.

02 / 05

Keep the covariance shared

For a locally linear response with statistical noise uncorrelated with calibration error, uncertainty propagates as Cᵧ=Cstat+J Cθ Jᵀ. The Jacobian maps calibration uncertainty into the observation. That second term can correlate every exposure: repeating a measurement does not redraw the common calibration independently.

For n repeats with individual statistical variance s² and one common calibration variance c², the mean has variance s²/n+c². If statistical noise and calibration error have a nonzero cross-covariance B, the linearized result also contains B Jᵀ+J Bᵀ. A valid joint covariance model is then required; the implemented helper covers the zero-cross-covariance case. Nonlinear responses require more than local linearization.

Cᵧ = Cstat + J Cθ Jᵀ Var(mean) = s²/n + c² If B ≠ 0, add B Jᵀ + J Bᵀ.

03 / 05

A confidence interval can become falsely precise

The saved synthetic coverage study used 2,000 apparatus realizations across 36 conditions. Its nominal 95% phase coverage was 94.55–96.20%. In the 32-repeat control, retaining shared calibration gave 95.55% coverage; incorrectly treating it as independent gave 35.80%. Those are results of the declared synthetic noise model, not a discovered calibration fault in a real instrument.

The small interactive figure uses normalized statistical standard deviation s=1 and a user-chosen common calibration standard deviation c. Its two curves compare the stated correct mean uncertainty with the incorrect independent-calibration calculation. It does not estimate errors for an actual device.

04 / 05

Evidence labels now bind to actual bytes

The earlier admission path could accept a complete set of declarations without reading the referenced evidence. The strengthened path checks file hashes, model/prediction agreement, timezone-aware freeze and access chronology, separation of recording and sample-group identities, calibration references, units and covariance. Claim lineage must match the evidence actually named by the record.

The checking fixtures use synthetic data. Their positive cases certify a software acceptance path; they do not authenticate a laboratory, the honesty of supplied timestamps or unreported data reuse. All 57 current engine records still require physical inputs before a new measured-prediction claim can enter.

05 / 05

What a complete next submission contains

A useful submission names one forward model and one prospective target, fixes every fitted choice and nuisance bound, supplies independently obtained calibration, and freezes its prediction before the validation measurements are accessed. The comparison must score the predicted distribution or calibrated error envelope, including shared uncertainties.

This is how the programme can begin to predict measurement error rather than absorbing every discrepancy into a new parameter. Whether it succeeds is a future empirical question. The site keeps the distinction between a functioning gate, historical reanalysis, and a newly validated physical prediction visible.

Evidence & sources

Source-bound editorial synthesis of the cited record. The claim classes above separate imported physics, conditional mathematics, finite simulations, historical measurements and prospective tests.

  1. Measurement claim ledger — Measurement_Discipline_Claim_Ledger.md
    Reviewed source record · full text outside this preview
  2. Current execution and covariance limits — Engine_Spec_Execution_Report.md
    Reviewed source record · full text outside this preview
  3. Theory 2.42, Appendices EK–EM — Theory_of_Reality.md
    Reviewed source record · full text outside this preview

Continue the investigation / Finite modes

Positive modes. A finite difference. An attractive force.

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