Scientific evidence matrix

Last reviewed:

25 July 2026

This matrix records why a numerical result is believed, not merely where its implementation is exercised. DIRECT means a test derives an expected value by hand or from a closed form. INDEPENDENT means a second algorithm or analytical physical model reaches the same result. REGRESSION means a frozen output is useful for detecting change but is not, by itself, evidence that the value is scientifically correct.

Table 64 Central numerical outputs and their independent evidence

Result	Implementation	Independent evidence	Status
Common means, block errors, MSD	analysis.analysis	Hand-computed running means, one- and two-point block standard errors, and the squared-lag MSD in test_analysis.py.	DIRECT
MD crossing flux	flux_analysis	Hand-counted crossings per physical time window in test_flux_analysis.py; end-to-end rates are also checked by the double-well campaign.	DIRECT + INDEPENDENT
TIS/RETIS crossing probability	path_analysis.analyse_path_ensemble and match_probabilities	Accepted-path integer ratios and their explicit product in test_path_analysis.py.	DIRECT
RETIS flux and rate	path_analysis.retis_flux and retis_rate	Direct inverse-path-time and product/error-propagation formula checks; the method campaign compares the final rate with Kramers–MM theory.	DIRECT + INDEPENDENT
WHAM crossing probability and rate	wham_analysis	Hand-built unweighted and weighted matrices with exact non-zero crossing probabilities; single-ensemble agreement with point matching; Kramers–MM campaign.	DIRECT + INDEPENDENT
REPPTIS local/global probability	repptis_analysis and _repptis_state	Raw-column occupancy counts feed both a closed-form recursion and a separately constructed Markov matrix in test_repptis_reference_oracle.py.	INDEPENDENT
REPPTIS MSM probability and MFPT	repptis_msm	Symmetric-random-walk closed form, a hand-computed three-state MFPT, stochastic-matrix invariants, and comparison with the upstream implementation.	DIRECT + INDEPENDENT
Path weights and transmission coefficient	path_weights	Equal-weight fixture and explicit 8 reactive / 10 crossings = 0.8 calculation in test_path_weights.py.	DIRECT
Interface placement	interface_placement and interface_estimation	Exact geometric placement on \(p(x)=0.5^x\), plus hand-counted binless crossing curves.	DIRECT
Permeability	path_analysis.perm_calculations	Hand-counted \(\xi\) and \(\tau\), explicit permeability product, and quadrature error propagation in test_path_analysis.py.	DIRECT
Energy/order descriptive reports	energy_analysis and order_analysis	Frozen fixture outputs, independently tested common statistics, and the shape-one kinetic gamma law checked against \(2\exp(-2E)\) in test_energy_analysis.py.	DIRECT
Cross-engine rate equivalence	examples/validation/engines/water_dimer	Shared-force-field energy gate, direct-MD timescale, and three-engine rate comparison documented in Cross-engine validation: water-dimer dissociation.	INDEPENDENT CAMPAIGN

Scope boundary

The matrix covers numerical results exposed by the analysis reports and interface tools. Plot layout, file formatting, and training-frame selection have deterministic functional tests, but are not themselves scientific estimators and are outside this oracle inventory.