verification_cases.csv

project_id,id,case,expected,method,evidence,execution_status
A01,A01-V1,Interior and conjugation,c=0 and c=-1 are bounded; conjugates share escape behavior.,Check predicates and reflected direct trajectories.,Quadratic fixed and period-two orbits.,specified; not executed here
A01,A01-V2,Julia escape inequality,Modulus increases after the justified radius crossing.,Evaluate exact rational or interval fixtures.,Triangle inequality derivation.,specified; not executed here
A01,A01-V3,Precision stress,Contradictory certificates fail R4; cap-sensitive nonescape remains unresolved.,Double precision and cap separately; compare direct and perturbation kernels.,Proposed benchmark gate; outcomes TBD.,specified; not executed here
A02,A02-V1,Pure-species vertices,Entropy/excess mixing terms vanish.,Approach each pure endpoint analytically and numerically.,x ln x limit.,specified; not executed here
A02,A02-V2,Lever-rule section,Reconstructed bulk equals input within R1.,Compare tangent and constrained binary solutions.,Independent mass balance; execution pending.,specified; not executed here
A02,A02-V3,Closed thermal box,Zero boundary flux leaves temperature/inventory constant.,Disable forcing and refine integration step.,Species and energy conservation.,specified; not executed here
A03,A03-V1,Zero-torque rotation,Total angular momentum stays constant and lag decays exponentially.,Compare unequal-inertia integration to derived solution.,Conservation and sign checks.,specified; not executed here
A03,A03-V2,Power-off thermal limit,"With all heating/luminosity terms zero, T stays constant.",Check reduced solver and production adapter with refined steps.,Energy conservation.,specified; not executed here
A03,A03-V3,Withheld observable,Unsupported gap information widens intervals or produces explicit predictive failure.,Withhold cooling epoch or timing stream and examine predictions.,Proposed identifiability test; result pending.,specified; not executed here
A04,A04-V1,No-information limit,p1=p0 yields zero evidence increment.,Evaluate guarded analytic likelihood fixtures.,Bernoulli identity.,specified; not executed here
A04,A04-V2,Consensus conservation,Doubly stochastic connected fixed W preserves mean.,Compare matrix reference and bounded transition outputs.,Linear identity; quantization differences explicit.,specified; not executed here
A04,A04-V3,Duplicate and partition replay,Oracle evidence unchanged by duplicate; illegal partition raises fault.,Script message cycles and node losses.,R3/R4; results pending.,specified; not executed here
A05,A05-V1,Static beam limit,Uniform q produces qL^4/(8EI) tip deflection.,Compare discretized mechanics to analytic cantilever.,Beam boundary conditions.,specified; not executed here
A05,A05-V2,Zero input,"U=0, drive=0 and Delta T=0 yield baseline b.",Evaluate complete forward/readout chain.,Defined signal model.,specified; not executed here
A05,A05-V3,Inverse degeneracy,Static-only data with unknown mu and U show a flat product ridge.,"Profile synthetic noiseless likelihood, then add dynamic responses.",Structural identifiability; response improvement TBD.,specified; not executed here
A06,A06-V1,Mixture endpoint,One component with a=1 reproduces its template; coefficients remain nonnegative.,Synthetic mixture and normalization fixtures.,Defined response model.,specified; not executed here
A06,A06-V2,Ohmic units/sign,Fixed G gives linear I–V slope with units S.,Check archived summaries and synthetic sign-reversed voltages.,Dimensional identity; no new channel experiment.,specified; not executed here
A06,A06-V3,Evidence removal,"Without raw state traces, kinetic outputs are unavailable rather than populated.",Exercise missing-data pipeline and leave-type-out state ranking.,Data-contract requirement.,specified; not executed here
A07,A07-V1,Mass ledger,Input equals recovered plus explicitly unmeasured/lost remainder.,Check synthetic complete and incomplete recovery records.,Conservation bookkeeping; unknown loss retained.,specified; not executed here
A07,A07-V2,Closure invariance,Multiplying every recovered mass by the same positive factor leaves log ratios unchanged.,Analytic and numeric fixture across K fractions.,Definition of f and CLR.,specified; not executed here
A07,A07-V3,Confounded pair,Design checker reports aliased line/status effects for a single fixed pair.,Generate known-rank matrices and withhold a line pair.,Linear-model rank; no causal cancer estimate claimed.,specified; not executed here
A08,A08-V1,Zero nonlinearity/loss,Linear spectral phase preserves energy and bandwidth magnitude.,Set n2=alpha=0 and compare analytic dispersion.,Fourier unitary propagation.,specified; not executed here
A08,A08-V2,Pure Kerr step,Temporal intensity unchanged; phase increment equals gamma P dz.,Compare one-step analytic solution.,Local nonlinear ODE.,specified; not executed here
A08,A08-V3,Compression reversal,Known quadratic chirp removed by equal/opposite phase returns synthetic transform-limited pulse.,Round-trip retrieval and compressor pipeline.,Analytic synthetic fixture; real results pending.,specified; not executed here
A09,A09-V1,Low-redshift limit,"At z=0, luminosity reduces to 4 pi D_L^2 S.",Unit and sign fixture with fixed nonzero test distance.,K-correction identity.,specified; not executed here
A09,A09-V2,Complete equal-probability sample,"If C=1 and all p=p0, fraction equals p0.",Analytic synthetic catalog.,Weighted-estimator algebra.,specified; not executed here
A09,A09-V3,Injection/holdout selection,Recovered synthetic population lies within declared uncertainty; held-out regional residuals expose mismatch.,Generate known counts through size/flux selection and refit.,Proposed coverage check; no survey outcome invented.,specified; not executed here
A10,A10-V1,Circular orbit,"For e=0, velocity is a sinusoid with mean gamma.",Compare Kepler solver against analytic phase.,Keplerian limit.,specified; not executed here
A10,A10-V2,Instantaneous kernel,A unit impulse at zero delay reproduces orbital velocity.,Refine discrete convolution and compare.,Normalization/causality identity.,specified; not executed here
A10,A10-V3,Symmetric translated profile,Centroid and symmetric bisector recover the injected wavelength shift.,Replay analytic emission profiles with known contamination variants.,Synthetic measurement fixture; observed performance pending.,specified; not executed here
A11,A11-V1,Single-standard endpoint,Weight one reconstructs the exact standard; other weights zero.,Synthetic constrained-fit fixture.,Mixture definition.,specified; not executed here
A11,A11-V2,DBE/adduct sanity,Known neutral formulas give expected DBE; impossible negative values flag convention errors.,Use documented formula examples after ion correction.,Hydrogen-deficiency algebra.,specified; not executed here
A11,A11-V3,Indistinguishable standards,Identical standards yield nonunique weights and an ambiguity flag.,Duplicate one basis spectrum and profile fits.,Identifiability check; no invented specimen result.,specified; not executed here
A12,A12-V1,Pure source/endmember,f_s=1 reproduces that source's corrected ratios.,Count-space endpoint fixture.,Mixture algebra.,specified; not executed here
A12,A12-V2,Zero grain contribution,a=0 reproduces background; a=1 reproduces grain.,Beam-model synthetic extremes.,Count mixing identity.,specified; not executed here
A12,A12-V3,Equal denominator approximation,Linear ratio interpolation agrees only when denominator counts match.,Compare equal and unequal denominator fixtures.,Derived condition; known-source coverage check pending.,specified; not executed here
B01,B01-V1,Identical endmembers,Algebraic singularity is flagged; no finite mixing estimate.,Condition/fixture: Inversion reports nonidentifiable f when C_T=C_M. Verification procedure: Synthetic equal-endmember input..,Synthetic equal-endmember input.,specified; not executed here
B01,B01-V2,Conservative midpoint,Recover 0.5 within floating-point tolerance.,"Condition/fixture: With C_T=100 and C_M=20 mg/L, C=60 gives f=0.5. Verification procedure: Unit-tested synthetic mixture..",Unit-tested synthetic mixture.,specified; not executed here
B01,B01-V3,No incremental signal,Augmented skill should not be presented as validated without held-out improvement.,Condition/fixture: Chemistry randomized within training-compatible blocks. Verification procedure: Negative-control forecast comparison..,Negative-control forecast comparison.,specified; not executed here
B01,B01-V4,Station offset,Offset metadata recovers the original trend; omission changes residual flags.,Condition/fixture: Inject a known 10 mm discontinuity into a synthetic series. Verification procedure: Adapter integration test..,Adapter integration test.,specified; not executed here
B02,B02-V1,Graph limits,Recover both limits with no negative edges.,"Condition/fixture: As d=0, w=h; as d tends to infinity, w tends to zero. Verification procedure: Analytic distance sweep..",Analytic distance sweep.,specified; not executed here
B02,B02-V2,Known nondetection,All-zero history probability equals 0.125.,Condition/fixture: Synthetic psi=1 and p=0.5 over three visits. Verification procedure: Exact likelihood comparison..,Exact likelihood comparison.,specified; not executed here
B02,B02-V3,Budget boundary,Only portfolios with summed cost at most 100 are feasible.,"Condition/fixture: Synthetic costs 40,60,80 USD with B=100. Verification procedure: Exhaustive small-graph enumeration..",Exhaustive small-graph enumeration.,specified; not executed here
B02,B02-V4,Neighborhood holdout,Report calibration and rank stability separately by taxon.,Condition/fixture: Reserve complete neighborhoods and survey seasons. Verification procedure: Spatial-temporal holdout evaluation..,Spatial-temporal holdout evaluation.,specified; not executed here
B03,B03-V1,Symmetric choices,Each probability is 0.5.,Condition/fixture: Two available steps have equal covariates. Verification procedure: Exact conditional-likelihood check..,Exact conditional-likelihood check.,specified; not executed here
B03,B03-V2,Zero hazard,S(T)=1 and no modeled road-attributable loss.,Condition/fixture: Set h_0=0 for a synthetic individual. Verification procedure: Analytic survival fixture..,Analytic survival fixture.,specified; not executed here
B03,B03-V3,Uncertain road intersection,Output plausible/unresolved probability; never a guaranteed crossing.,Condition/fixture: Two fixes straddle a road with broad covariance. Verification procedure: Monte Carlo path integration..,Monte Carlo path integration.,specified; not executed here
B03,B03-V4,Animal holdout,Report step calibration and fate predictions without shared-individual leakage.,Condition/fixture: Reserve all fixes from selected individuals. Verification procedure: Blocked evaluation..,Blocked evaluation.,specified; not executed here
B04,B04-V1,No attenuation,A=0 dB.,Condition/fixture: P_obs=P_quiet with common units. Verification procedure: Exact ratio fixture..,Exact ratio fixture.,specified; not executed here
B04,B04-V2,Known power ratio,A=10 dB; 100 gives 20 dB.,Condition/fixture: P_quiet/P_obs=10. Verification procedure: Analytic conversion check..,Analytic conversion check.,specified; not executed here
B04,B04-V3,High-frequency limit,Modeled absorption approaches one quarter.,Condition/fixture: Double f with identical path and nu much smaller than 2pi f. Verification procedure: Dimensionless regime sweep..,Dimensionless regime sweep.,specified; not executed here
B04,B04-V4,Missing spacecraft metadata,"Spacecraft/link product is blocked, ground product remains labeled ground.",Condition/fixture: Input lacks orbit or antenna weighting. Verification procedure: Integration gate test..,Integration gate test.,specified; not executed here
B05,B05-V1,Thermal threshold,GDD=0 °C day; 2°C above base gives 20 °C day.,Condition/fixture: Ten days at T_mean=T_base. Verification procedure: Exact accumulation fixture..,Exact accumulation fixture.,specified; not executed here
B05,B05-V2,Interval probability,Interval probability is 4/10=0.4.,Condition/fixture: Uniform onset over days 1–11; observed bracket 3–7. Verification procedure: Known distribution likelihood check..,Known distribution likelihood check.,specified; not executed here
B05,B05-V3,Zero establishment,Realized resources are zero regardless of bloom probability.,Condition/fixture: Set e_s=0 for every species. Verification procedure: Portfolio boundary test..,Portfolio boundary test.,specified; not executed here
B05,B05-V4,Year holdout,Report onset interval coverage and weekly shortfall calibration.,Condition/fixture: Reserve complete hot/dry observation years. Verification procedure: Chronological evaluation..,Chronological evaluation.,specified; not executed here
B06,B06-V1,Ideal-gas conversion,c=10^-9 P/(RT); changing T scales inversely.,Condition/fixture: 1 ppb at declared P and T. Verification procedure: Unit-aware analytic fixture..,Unit-aware analytic fixture.,specified; not executed here
B06,B06-V2,Deposition-only box,c(t)=c0 exp(-v_d t/h).,"Condition/fixture: Set production, other loss and exchange to zero. Verification procedure: Compare integrator against exact solution..",Compare integrator against exact solution.,specified; not executed here
B06,B06-V3,Zero source perturbation,Delta MDA8=0 within numerical tolerance.,Condition/fixture: Identical baseline and scenario inputs. Verification procedure: Scenario-manifest integration test..,Scenario-manifest integration test.,specified; not executed here
B06,B06-V4,Episode holdout,"Report metric bias, interval coverage and regime-dependent error.",Condition/fixture: Withhold complete ozone episodes and years. Verification procedure: Blocked observational/model evaluation..,Blocked observational/model evaluation.,specified; not executed here
B07,B07-V1,Closed conservative network,Total tracked element inventory remains constant.,Condition/fixture: Synthetic reaction has elemental balance a^T N=0 and no transport. Verification procedure: Integrator conservation check..,Integrator conservation check.,specified; not executed here
B07,B07-V2,Pure sorption,Parent total and carbon inventory stay unchanged.,Condition/fixture: Move one mol from water to solids without reaction. Verification procedure: Compartment-transfer fixture..,Compartment-transfer fixture.,specified; not executed here
B07,B07-V3,Censored measurement,Likelihood integrates below L and does not use C=0.,Condition/fixture: Observed record states C<L. Verification procedure: Compare exact CDF fixture..,Compare exact CDF fixture.,specified; not executed here
B07,B07-V4,Incomplete product coverage,Output flags incomplete closure and avoids mineralization claim.,Condition/fixture: Remove a known synthetic product channel from observations. Verification procedure: Integration evidence gate..,Integration evidence gate.,specified; not executed here
B08,B08-V1,Identical trends,BACI effect equals zero.,Condition/fixture: Synthetic treated/control cover changes are both +5 points. Verification procedure: Exact difference calculation..,Exact difference calculation.,specified; not executed here
B08,B08-V2,Known intervention contrast,Estimated contrast is +8 percentage points.,"Condition/fixture: Treated change +12 points, control +4 points. Verification procedure: Unit-aware fixture..",Unit-aware fixture.,specified; not executed here
B08,B08-V3,Closed water ledger,Storage change is +5 mm/day.,"Condition/fixture: P=10, ET=2, outflow=3, other terms zero mm/day. Verification procedure: Independent balance arithmetic..",Independent balance arithmetic.,specified; not executed here
B08,B08-V4,Control spillover holdout,Report effect movement and prediction calibration.,Condition/fixture: Exclude nearby controls and reserve catchments. Verification procedure: Spatial blocked sensitivity..,Spatial blocked sensitivity.,specified; not executed here
B09,B09-V1,Balanced simple water,CBE=0%; replacing Cl with 0.5 gives +33.333%.,Condition/fixture: Na+=1 meq/L and Cl-=1 meq/L. Verification procedure: Exact equivalents fixture..,Exact equivalents fixture.,specified; not executed here
B09,B09-V2,Unit conversion,1 meq/L within rounding of declared constants.,Condition/fixture: 23 mg/L Na with illustrative MW=23 g/mol and charge +1. Verification procedure: Unit adapter check..,Unit adapter check.,specified; not executed here
B09,B09-V3,Unsupported basin,Return unsupported/null with support flag.,Condition/fixture: Request map cell in a basin with no eligible sample. Verification procedure: Domain-mask integration test..,Domain-mask integration test.,specified; not executed here
B09,B09-V4,Feature holdout,Report predictive coverage and residuals in physical/log units.,Condition/fixture: Remove all samples from selected features and years. Verification procedure: Blocked interpolation evaluation..,Blocked interpolation evaluation.,specified; not executed here
B10,B10-V1,NDVI limits,NDVI=0 and 1 respectively.,Condition/fixture: Equal positive red/NIR reflectance; red=0 with positive NIR. Verification procedure: Exact ratio checks..,Exact ratio checks.,specified; not executed here
B10,B10-V2,Uniform thermal field,Every valid weighted neighborhood exposure equals 3 K.,Condition/fixture: Every populated pixel has anomaly 3 K. Verification procedure: Aggregation unit test..,Aggregation unit test.,specified; not executed here
B10,B10-V3,No population support,Output null with unsupported-population flag.,Condition/fixture: Neighborhood denominator is zero. Verification procedure: Integration boundary fixture..,Integration boundary fixture.,specified; not executed here
B10,B10-V4,Neighborhood/year holdout,Report canopy calibration and thermal residuals separately.,Condition/fixture: Reserve complete areas and acquisition years. Verification procedure: Spatial-temporal evaluation..,Spatial-temporal evaluation.,specified; not executed here
B11,B11-V1,Superseded requirement,Both persist; current view selects B and exposes A lineage.,Condition/fixture: Synthetic revision B replaces A with later effective date. Verification procedure: Revision replay test..,Revision replay test.,specified; not executed here
B11,B11-V2,Missing deadline,Deadline stays null and status unresolved.,Condition/fixture: Candidate clause lacks due-date evidence. Verification procedure: Extraction/review integration check..,Extraction/review integration check.,specified; not executed here
B11,B11-V3,Coverage boundary,Coverage=0.75; empty corpus yields undefined.,Condition/fixture: Reference corpus has 20 reviewed obligations; 15 evidenced. Verification procedure: Exact ledger calculation..,Exact ledger calculation.,specified; not executed here
B11,B11-V4,Retrieval holdout,Measure answer-span retrieval and unsupported-answer rate.,Condition/fixture: Reviewer authors unseen site/authority questions. Verification procedure: Frozen-task evaluation..,Frozen-task evaluation.,specified; not executed here
B12,B12-V1,No supply,Volume remains constant.,Condition/fixture: Q_in=Q_out=0 in a closed synthetic domain. Verification procedure: Conservation integration check..,Conservation integration check.,specified; not executed here
B12,B12-V2,Constant supply,Added volume=200 m³.,"Condition/fixture: Q_in=2 m³/s for 100 s, no outflow. Verification procedure: Independent flux-volume calculation..",Independent flux-volume calculation.,specified; not executed here
B12,B12-V3,Yield limit,No yielded flow; regularized leakage is quantified separately.,Condition/fixture: Driving shear remains below tau_y in the ideal constitutive case. Verification procedure: Constitutive benchmark..,Constitutive benchmark.,specified; not executed here
B12,B12-V4,Reserved contacts,"Report distance residuals and compatibility intervals, not only training fit.",Condition/fixture: Withhold mapped boundary segments and transects. Verification procedure: Spatial reconstruction holdout..,Spatial reconstruction holdout.,specified; not executed here
B13,B13-V1,Identical/disjoint masks,IoU=1 and 0 respectively.,Condition/fixture: Compare equal masks and nonoverlapping masks. Verification procedure: Exact geometry fixtures..,Exact geometry fixtures.,specified; not executed here
B13,B13-V2,Half-overlap masks,IoU=5/15=1/3.,Condition/fixture: Two equal-area masks of area 10 have intersection 5. Verification procedure: Analytic mask-area calculation..,Analytic mask-area calculation.,specified; not executed here
B13,B13-V3,Perfect commission calibration,Corrected estimate is 20 instances under declared calibration.,Condition/fixture: Ten retained detections have q=1 and p=0.5. Verification procedure: Estimator unit check..,Estimator unit check.,specified; not executed here
B13,B13-V4,Site holdout,"Report calibration, omission and ecological bias by stratum.","Condition/fixture: Reserve complete sites, acquisitions and shared-crown blocks. Verification procedure: Spatial evaluation..",Spatial evaluation.,specified; not executed here
B14,B14-V1,Volume conversion,I=10 mm.,Condition/fixture: 1000 mm³ over 100 mm² contact area. Verification procedure: Exact adapter calculation..,Exact adapter calculation.,specified; not executed here
B14,B14-V2,Known infiltration curve,I=8 mm and instantaneous rate=1.5 mm/hour.,"Condition/fixture: S=2 mm/hour^0.5, A_t=1 mm/hour, t=4 hours. Verification procedure: Compare fitter/derivative with analytic values..",Compare fitter/derivative with analytic values.,specified; not executed here
B14,B14-V3,Green–Ampt wet limit,f approaches K_s.,Condition/fixture: Delta_theta=0 or F grows much larger than psi_f Delta_theta. Verification procedure: Analytic parameter sweep..,Analytic parameter sweep.,specified; not executed here
B14,B14-V4,Plot holdout,Report hydraulic predictive coverage and burn-effect sensitivity.,Condition/fixture: Reserve whole plots rather than individual readings. Verification procedure: Hierarchical blocked evaluation..,Hierarchical blocked evaluation.,specified; not executed here
B15,B15-V1,Hydrostatic rest,u=0 with grad p=rho g.,"Condition/fixture: Uniform density, zero imposed velocity and isothermal boundaries. Verification procedure: Compare solver to analytic equilibrium..",Compare solver to analytic equilibrium.,specified; not executed here
B15,B15-V2,Pure thermal diffusion,Recover documented one-dimensional diffusion solution and energy balance.,Condition/fixture: No velocity/heating; fixed boundary temperatures. Verification procedure: Independent analytic benchmark..,Independent analytic benchmark.,specified; not executed here
B15,B15-V3,Mesh/time refinement,Metrics converge within declared target; otherwise inference is withheld.,Condition/fixture: Repeat a synthetic scenario with finer mesh and steps. Verification procedure: Richardson/residual analysis..,Richardson/residual analysis.,specified; not executed here
B15,B15-V4,Withheld observation group,Report predictive residuals and mechanism rank reversals.,Condition/fixture: Fit geometry while reserving upper-plate/thermal evidence. Verification procedure: Group holdout comparison..,Group holdout comparison.,specified; not executed here
B16,B16-V1,Null contrast,Effect centers on zero with nominal uncertainty; no resistance conclusion.,Condition/fixture: Synthetic matched data have identical group distributions. Verification procedure: Known-null statistical fixture..,Known-null statistical fixture.,specified; not executed here
B16,B16-V2,Perfect batch confounding,Design is rank deficient and adjusted effect is blocked.,Condition/fixture: Exposure column equals batch column. Verification procedure: Linear-algebra rank check..,Linear-algebra rank check.,specified; not executed here
B16,B16-V3,Duplicate technical replicate,Independent sample count remains unchanged.,Condition/fixture: Add a duplicate measurement of one biological sample. Verification procedure: Metadata/pipeline integration test..,Metadata/pipeline integration test.,specified; not executed here
B16,B16-V4,Study holdout,Report prediction/contrast consistency and unresolved metadata limits.,Condition/fixture: Reserve a complete archived study. Verification procedure: Leave-study-out synthesis..,Leave-study-out synthesis.,specified; not executed here
B17,B17-V1,Zero effort,Expected modeled harvest is zero.,Condition/fixture: Set E=0 with finite B and q. Verification procedure: Analytic observation fixture..,Analytic observation fixture.,specified; not executed here
B17,B17-V2,Closed stock balance,Next biomass is 105 kg.,"Condition/fixture: B=100, R=20, M=5, H=10 kg/interval. Verification procedure: Independent mass-ledger test..",Independent mass-ledger test.,specified; not executed here
B17,B17-V3,Catchability ambiguity,"Expected catch is identical, exposing nonidentifiability.",Condition/fixture: Two scenarios double B and halve q. Verification procedure: Likelihood/sensitivity fixture..,Likelihood/sensitivity fixture.,specified; not executed here
B17,B17-V4,Permission revoked,Export is blocked while governed internal provenance is retained per policy.,Condition/fixture: Synthetic partner policy withdraws public linkage. Verification procedure: Access-control integration test..,Access-control integration test.,specified; not executed here
B18,B18-V1,Zero gradient,F=0.,Condition/fixture: p_w=p_a at arbitrary valid k and K0. Verification procedure: Exact flux identity..,Exact flux identity.,specified; not executed here
B18,B18-V2,Signed flux fixture,F=3x10^-8 mol/m²/s outward.,"Condition/fixture: k=10^-5 m/s, K0=30 mol/m³/atm, gradient=100 microatm. Verification procedure: Independent unit calculation..",Independent unit calculation.,specified; not executed here
B18,B18-V3,Decomposition closure,"Delta F=15, matching (3*7)-(2*3).","Condition/fixture: Choose k0=2, G0=3, Delta k=1, Delta G=4 in consistent abstract units. Verification procedure: Exact factorial arithmetic..",Exact factorial arithmetic.,specified; not executed here
B18,B18-V4,Float/event holdout,Report flux and chemistry prediction coverage plus supported area-time fraction.,Condition/fixture: Withhold entire storms and floats. Verification procedure: Blocked validation..,Blocked validation.,specified; not executed here
B19,B19-V1,Density conversion,n=1 cm^-3=10^6 m^-3.,Condition/fixture: f_pe=8980 Hz in the declared approximate relation. Verification procedure: Independent SI/approximation comparison..,Independent SI/approximation comparison.,specified; not executed here
B19,B19-V2,Frequency doubling,Density increases by factor four.,Condition/fixture: Double f_pe with all constants fixed. Verification procedure: Analytic scaling test..,Analytic scaling test.,specified; not executed here
B19,B19-V3,Temperature units,"T=e/k_B K, approximately 11604.5 K.",Condition/fixture: Use a declared 1 eV electron temperature. Verification procedure: Constant-version unit check..,Constant-version unit check.,specified; not executed here
B19,B19-V4,Encounter holdout,Report density/temperature residuals and conditional contrast stability.,Condition/fixture: Reserve entire encounters and independent structures. Verification procedure: Blocked analysis..,Blocked analysis.,specified; not executed here
B20,B20-V1,Zero apparent removal,q=0 mg/g.,Condition/fixture: C0=Ce for any valid V and m. Verification procedure: Exact capacity identity..,Exact capacity identity.,specified; not executed here
B20,B20-V2,Capacity fixture,q=4 mg/g.,"Condition/fixture: C0=10, Ce=4 mg/L, V=2 L, m=3 g. Verification procedure: Independent unit arithmetic..",Independent unit arithmetic.,specified; not executed here
B20,B20-V3,Recovery versus removal,Removal can be 0.8 while recovery is 0.2.,"Condition/fixture: Synthetic feed 100 mg, sorbed 80 mg, product 20 mg. Verification procedure: Element-ledger integration test..",Element-ledger integration test.,specified; not executed here
B20,B20-V4,Al-only input,Y removal/recovery outputs remain unresolved.,Condition/fixture: Record contains Al measurements and no Y assay. Verification procedure: Element-provenance gate test..,Element-provenance gate test.,specified; not executed here
B21,B21-V1,Identical codon distributions,Conceptual KL divergence equals zero.,Condition/fixture: p=q with valid positive support. Verification procedure: Exact frequency-table test..,Exact frequency-table test.,specified; not executed here
B21,B21-V2,Fraction fixture,D=0.25.,Condition/fixture: Five disordered valid residues out of twenty. Verification procedure: Independent summary arithmetic..,Independent summary arithmetic.,specified; not executed here
B21,B21-V3,Zero phylogenetic covariance,Model reduces to the corresponding nonphylogenetic working model.,Condition/fixture: Set sigma_phylo=0 in synthetic data. Verification procedure: Likelihood comparison..,Likelihood comparison.,specified; not executed here
B21,B21-V4,Clade holdout,Report calibrated predictions and coefficient stability across predictors.,Condition/fixture: Reserve complete clades and homologous domain groups. Verification procedure: Blocked comparative evaluation..,Blocked comparative evaluation.,specified; not executed here
B22,B22-V1,Zero-flux feasibility,v=0 satisfies S v=0.,Condition/fixture: All bounds include zero and no compulsory demand. Verification procedure: Independent linear-constraint check..,Independent linear-constraint check.,specified; not executed here
B22,B22-V2,Canonical reaction ledger,Consumes 16 mol ATP and 8 mol electrons; forms 2 mol NH3 and 1 mol H2.,Condition/fixture: One mol N2 reduced under the stated idealized reaction. Verification procedure: Reaction accounting fixture..,Reaction accounting fixture.,specified; not executed here
B22,B22-V3,Element imbalance,Atom/charge checker rejects the model.,Condition/fixture: Inject one deliberately unbalanced synthetic reaction. Verification procedure: Network integration test..,Network integration test.,specified; not executed here
B22,B22-V4,Existing phenotype holdout,Report feasible-range compatibility and unresolved discrepancies.,Condition/fixture: Reserve published conditions from fitting bounds. Verification procedure: Retrospective holdout comparison..,Retrospective holdout comparison.,specified; not executed here
B23,B23-V1,Depth-volume conversion,Q_depth=86.4 mm/day.,Condition/fixture: A=1 km² and Q=1 m³/s. Verification procedure: Independent unit calculation..,Independent unit calculation.,specified; not executed here
B23,B23-V2,Closed storage step,Storage increases 4 mm.,"Condition/fixture: P=10, ET=2, Q=3, D=1 mm/day for one day. Verification procedure: Conservation arithmetic..",Conservation arithmetic.,specified; not executed here
B23,B23-V3,Decision threshold,Alert threshold p>0.1.,Condition/fixture: False-alert cost 1 and missed-event cost 9. Verification procedure: Exact expected-loss comparison..,Exact expected-loss comparison.,specified; not executed here
B23,B23-V4,Operational replay,"Report skill, coverage, latency failures and regret.",Condition/fixture: Withhold full drought/flood events and enforce historical issue-time availability. Verification procedure: Chronological event replay..,Chronological event replay.,specified; not executed here
B24,B24-V1,Step displacement,L=5 m and displacement speed=5 m/hour.,"Condition/fixture: Synthetic positions (0,0) and (3,4) m over one hour. Verification procedure: Exact geometry/unit check..",Exact geometry/unit check.,specified; not executed here
B24,B24-V2,Equal choice covariates,Each probability is 0.25.,Condition/fixture: Four alternatives have identical X. Verification procedure: Conditional-likelihood symmetry test..,Conditional-likelihood symmetry test.,specified; not executed here
B24,B24-V3,Normalized utilization,Integral equals one; full support area is 1 km².,Condition/fixture: Synthetic uniform UD over 1 km². Verification procedure: Independent density integration..,Independent density integration.,specified; not executed here
B24,B24-V4,Animal/date holdout,Report movement prediction and range-cadence sensitivity.,Condition/fixture: Reserve individuals and dated cover transitions. Verification procedure: Blocked evaluation..,Blocked evaluation.,specified; not executed here
B25,B25-V1,Chain probability,p_established=0.1.,Condition/fixture: p_v=0.8 and each later stage probability=0.5. Verification procedure: Exact conditional-product calculation..,Exact conditional-product calculation.,specified; not executed here
B25,B25-V2,Hydrotime sign,H=1 MPa day; psi below base contributes zero.,"Condition/fixture: psi=-0.5, psi_base=-1 MPa for two days. Verification procedure: Independent integration fixture..",Independent integration fixture.,specified; not executed here
B25,B25-V3,Zero survival,Establishment is zero and cost ratio flagged undefined.,Condition/fixture: p_s|e=0 with finite earlier probabilities. Verification procedure: Boundary integration test..,Boundary integration test.,specified; not executed here
B25,B25-V4,Species/lot holdout,Report stage calibration and final establishment interval coverage.,Condition/fixture: Reserve complete lots and species. Verification procedure: Blocked transfer evaluation..,Blocked transfer evaluation.,specified; not executed here
B26,B26-V1,PV conversion,P=2 kW.,"Condition/fixture: G=1000 W/m², area=10 m², efficiency=0.2, no other loss. Verification procedure: Independent unit calculation..",Independent unit calculation.,specified; not executed here
B26,B26-V2,Faraday charge,Produces one mol H2 before system losses.,"Condition/fixture: One ideal cell, eta_F=1, charge=2F C. Verification procedure: Exact electrochemical accounting..",Exact electrochemical accounting.,specified; not executed here
B26,B26-V3,Battery round trip,Delivered energy=0.81 kWh.,Condition/fixture: Charge 1 kWh at eta_c=eta_d=0.9 then discharge stored increment. Verification procedure: Independent state-ledger test..,Independent state-ledger test.,specified; not executed here
B26,B26-V4,Weather holdout,"Report balance, unserved energy, cycling and cost distributions.",Condition/fixture: Reserve complete weather/load periods and inject forecast error. Verification procedure: Rolling-policy replay..,Rolling-policy replay.,specified; not executed here
B27,B27-V1,Constant water field,y remains x regardless of tau or route.,Condition/fixture: x is constant and sensor starts at x. Verification procedure: Exact response-model test..,Exact response-model test.,specified; not executed here
B27,B27-V2,Step response,"y=x+(y0-x)exp(-t/tau); at tau, 63.2% of change is complete.",Condition/fixture: Sensor starts y0; constant new input x after t=0. Verification procedure: Integrator analytic comparison..,Integrator analytic comparison.,specified; not executed here
B27,B27-V3,Clock/lag geometry,Clock-induced location shift is 1 m; tau=4 s implies characteristic lag 2 m.,Condition/fixture: v=0.5 m/s and Delta t=2 s. Verification procedure: Independent unit calculation..,Independent unit calculation.,specified; not executed here
B27,B27-V4,Transect/reference holdout,"Report parameter-specific bias, coverage and unsupported-depth fraction.",Condition/fixture: Reserve complete transects and independent samples. Verification procedure: Blocked map validation..,Blocked map validation.,specified; not executed here
B28,B28-V1,Gompertz limits,M approaches M_inf; early-time M tends to zero.,"Condition/fixture: For positive parameters, t tends to infinity. Verification procedure: Analytic asymptotic check..",Analytic asymptotic check.,specified; not executed here
B28,B28-V2,Maximum-rate point,M=M_inf/e and dM/dt=R_max.,Condition/fixture: t=lambda+M_inf/(R_max e). Verification procedure: Differentiate and compare numerical slope..,Differentiate and compare numerical slope.,specified; not executed here
B28,B28-V3,Heating ledger,Q=40 kJ=0.011111 kWh.,"Condition/fixture: m=1 kg, c_p=4 kJ/kg/K and Delta T=10 K, no recovery. Verification procedure: Independent dimensional calculation..",Independent dimensional calculation.,specified; not executed here
B28,B28-V4,No combined evidence,Combined output stays scenario-only with unresolved synergy.,Condition/fixture: Sources contain only separate heating/freezing records. Verification procedure: Provenance integration test..,Provenance integration test.,specified; not executed here
C01,C01-V1,Uniform Doppler shift,All synthetic line centroids move by the imposed shift while equivalent widths remain unchanged apart from discretization.,Translate profiles and refine wavelength sampling.,Doppler coordinate and equivalent-width conservation.,specified; not executed here
C01,C01-V2,Coherence-free null,A nonperiodic injected series must not systematically favor a narrow period.,Generate through actual timestamp gaps and compare seasonal predictions.,Declared false-period baseline; no measured outcome claimed.,specified; not executed here
C01,C01-V3,Exposure-smearing check,Integrated predictions converge to the instantaneous model as duration tends to zero.,Analytic constant and sinusoidal exposure integrals.,Exposure observation operator.,specified; not executed here
C01,C01-V4,Held-out wind season,Intervals and residual correlations are reported without retuning line windows.,"Freeze preprocessing, then predict a withheld season.",Proposed independent validation.,specified; not executed here
C02,C02-V1,Uniform noiseless scene,Recovered sky equals B0 within floating-point/resampling error.,Pass a constant map through every pipeline stage.,Constant-preserving operator.,specified; not executed here
C02,C02-V2,Poisson/read-noise scene,Sample mean and variance approach mu and mu+sigma_R squared.,Independent replicated detector draws with convergence intervals.,Analytic count moments.,specified; not executed here
C02,C02-V3,Linear gradient,Reference and spatial-mean truths differ by the analytic coordinate average.,Inject a known slope and compare named estimands.,"Specified B(x,y).",specified; not executed here
C02,C02-V4,Unknown galaxy wings,Bias and coverage are reported for a withheld profile generator.,Freeze tuning and evaluate independent scenes.,Proposed holdout requirement.,specified; not executed here
C03,C03-V1,Thin-limit expansion,Brightness approaches eta_f(Jex-Jbg)tau for tau tending to zero.,Compare exact and first-order expressions over decreasing tau.,Taylor expansion of radiative transfer.,specified; not executed here
C03,C03-V2,Thick-limit saturation,"Brightness approaches eta_f(Jex-Jbg), independent of larger tau.",Synthetic high-tau channel evaluation.,Analytic transfer limit.,specified; not executed here
C03,C03-V3,Two-component blend,Posterior includes ambiguity rather than a falsely precise single flow.,Inject separated and overlapping hyperfine spectra through measured channel response.,Proposed identifiability test.,specified; not executed here
C03,C03-V4,Withheld map positions,Gradient prediction is assessed away from fit positions.,Spatial block holdout with matched beams.,Proposed spatial validation.,specified; not executed here
C04,C04-V1,Blackbody integral,Integrated spectral luminosity equals 4 pi Rph squared sigma T to the fourth.,Numerical frequency integration over expanding bounds.,Planck/Stefan-Boltzmann identity.,specified; not executed here
C04,C04-V2,Zero-delay limit,A narrowing normalized kernel reproduces fallback away from discontinuities.,Compare quadrature with direct fallback function.,Causal convolution limit.,specified; not executed here
C04,C04-V3,Host-only observation,No flare amplitude is required when synthetic data contain only host and noise.,Count/flux-domain null fit.,Proposed false-flare check.,specified; not executed here
C04,C04-V4,Withheld UV or late epochs,Predictive intervals and residuals are reported with fixed model choices.,Waveband or time-block holdout.,Proposed independent validation.,specified; not executed here
C05,C05-V1,Unit consistency,Earth-unit and cgs implementations give the same physical density.,Evaluate matched synthetic mass-radius pairs.,Density dimensional identity.,specified; not executed here
C05,C05-V2,Radius perturbation,A factor-two radius change at fixed mass yields one-eighth density.,Analytic fixture through full feature sampler.,Cubic density relation.,specified; not executed here
C05,C05-V3,Minimum-mass record,True density remains unavailable unless inclination information is supplied.,Type-contract integration test.,Declared physical typing rule.,specified; not executed here
C05,C05-V4,Host/survey holdout,Reliability and abstention coverage are measured without refitting on test hosts.,Grouped nested split and independent survey evaluation.,Proposed transferability check.,specified; not executed here
C06,C06-V1,Zero acceleration,Corrected timing recovers an injected intrinsic period derivative.,Synthetic arrivals through known orbit.,Timing-decomposition identity.,specified; not executed here
C06,C06-V2,Localization offset,Association probability decreases for a source moved away from target under a fixed uncertainty model.,Integrate synthetic localization maps and competing-source hypotheses.,Normalized spatial likelihood.,specified; not executed here
C06,C06-V3,Radius limits,r_m grows as mass flow decreases and r_lc scales linearly with P.,Parameter-sweep analytic checks.,Displayed characteristic-radius equations.,specified; not executed here
C06,C06-V4,Unseen orbit,Phase-resolved detection/count predictions are evaluated without updated state thresholds.,Temporal holdout with recorded exposure.,Proposed independent prediction.,specified; not executed here
C07,C07-V1,Zero slope,Exponential continuation remains at endpoint offset.,Set a=0 and compare time/frequency operators.,Integrated-tail identity.,specified; not executed here
C07,C07-V2,Integrated exponential,Added memory equals a times tau.,Numerical quadrature versus analytic value.,Exact tail integral.,specified; not executed here
C07,C07-V3,Distance rescaling,Strain and offset scale as inverse distance; normalized shape overlap is unchanged.,Rescale both polarizations and repeat comparison.,Declared far-field amplitude convention.,specified; not executed here
C07,C07-V4,Artificial truncation,Continuation uncertainty is compared to hidden longer waveform without retraining on it.,Truncate several physical simulations at preregistered endpoints.,Proposed extrapolation holdout.,specified; not executed here
C08,C08-V1,Pure-endmember limits,At fraction zero/one the areal prediction equals the corresponding measured endmember.,Boundary fraction fixtures.,Linear mixture identity.,specified; not executed here
C08,C08-V2,Flat-spectrum convolution,A constant input remains constant across channels.,Apply every response kernel.,Normalized spectral-response identity.,specified; not executed here
C08,C08-V3,Zero-carbonate challenge,False detection rate is measured with dust and atmosphere-like residuals.,Blind zero-carbonate and synthetic residual cases.,Proposed specificity test.,specified; not executed here
C08,C08-V4,Blind mixture recovery,Coverage and bias are reported against weighed labels with fraction-type distinctions.,Fit preregistered blind replicates.,Proposed independent material validation.,specified; not executed here
C09,C09-V1,Known collected charge,A synthetic sum q maps to epsilon_pair times q for unit efficiency.,Noiseless unit/gain fixture.,Charge-energy dimensional identity.,specified; not executed here
C09,C09-V2,Charge diffusion conservation,Redistributing charge across pixels preserves total deposit before thresholding.,Inject normalized diffusion kernels.,Charge conservation.,specified; not executed here
C09,C09-V3,Penetrating track,Incident energy can exceed inferred deposit without contract violation.,Transport fixture with finite silicon thickness.,Finite-path stopping-power integral.,specified; not executed here
C09,C09-V4,Qualified reference holdout,Deposited/incident interval coverage and abstention are reported by species and angle.,Freeze response fit before laboratory holdout.,Proposed calibration validation.,specified; not executed here
C10,C10-V1,Isotropic power-law tracer in flat circular-speed potential,"For nu proportional to r^-alpha, sigma_r squared equals v_c squared/alpha under the stated boundary.",Evaluate Jeans quadrature against analytic integral.,Analytic Jeans limit.,specified; not executed here
C10,C10-V2,Projection dimensional check,Projected density has kpc^-2 and normalized moment has velocity squared.,Unit-aware integration fixture.,Projection equation.,specified; not executed here
C10,C10-V3,Contaminating stream,Recovered uncertainty responds to injected non-equilibrium component.,Forward observe mock catalogs with stream mixture.,Proposed model-stress test.,specified; not executed here
C10,C10-V4,Tracer/DM separation,Changing beta_DM changes secondary predictions while leaving stellar likelihood unchanged.,Hold potential posterior fixed and rerun DM solver.,Distinct population contracts.,specified; not executed here
C11,C11-V1,Distance scaling,Halving distance doubles strain and SNR under fixed noise.,Project matched synthetic polarization.,Inverse-distance and inner-product relation.,specified; not executed here
C11,C11-V2,Arrival-delay consistency,Injected network timing matches the trial sky within sampling/interpolation tolerance.,Known sky fixture and fractional-delay refinement.,Geometric projector.,specified; not executed here
C11,C11-V3,Zero-signal baseline,Posterior does not claim precise track or physics without a signal.,Noise-only inference with detection gate.,Proposed hallucinated-parameter check.,specified; not executed here
C11,C11-V4,Unseen simulation code,"Coverage, domain flags and morphology errors are reported without retraining.",Hold out an entire code/family.,Proposed physical generalization.,specified; not executed here
C12,C12-V1,Component reconstruction,Sum of fitted terms reproduces total predicted sky in common units.,Round-trip likelihood/export fixture.,Additive light budget.,specified; not executed here
C12,C12-V2,Shared gain error,Increasing visit count does not remove imposed common calibration uncertainty.,Synthetic correlated-gain ensemble.,Covariance propagation.,specified; not executed here
C12,C12-V3,Zero diffuse injection,Pipeline reports coverage and false positive behavior for foreground-only skies.,Geometry-preserving simulated visit sample.,Proposed null-residual check.,specified; not executed here
C12,C12-V4,Withheld geometry,Predictions are assessed on visits at excluded solar/dust geometry.,Visit-block holdout with fixed screening.,Proposed foreground transfer test.,specified; not executed here
C13,C13-V1,Zero baseline,Visibility equals total source flux.,Evaluate Fourier operator at u=v=0.,Fourier normalization identity.,specified; not executed here
C13,C13-V2,Point-source translation,Visibility phase gains minus 2 pi u dot displacement while amplitude stays fixed.,Translate an analytic point source.,Fourier shift theorem.,specified; not executed here
C13,C13-V3,Thin ring,Numerical visibilities match F J0(2 pi a q).,Compare radial quadrature with analytic Bessel values.,Analytic source transform.,specified; not executed here
C13,C13-V4,Blind nonring source,False ring recovery and metric uncertainty are reported.,Replay withheld synthetic source through real uv/station patterns.,Proposed feature-specificity check.,specified; not executed here
C14,C14-V1,No-aberration propagation,Reference PSF matches the analytic aperture transform under the selected approximation.,Pupil-to-focal transform fixture.,Fourier optics identity.,specified; not executed here
C14,C14-V2,Opposite probes,Intensity difference matches four times the field/probe real product in the small-probe limit.,Refine probe magnitude and compare analytic expression.,Pairwise-probing derivation.,specified; not executed here
C14,C14-V3,Unavailable actuator,Faulted mode is removed or bounded without unstable commands.,Synthetic stuck-actuator replay.,Declared bounded-control interface.,specified; not executed here
C14,C14-V4,Withheld off-axis source,Suppression and throughput meet declared pilot targets or document failure.,Independent source offset and drift episode.,Proposed control/throughput validation.,specified; not executed here
C15,C15-V1,Area scaling,"Doubling collecting area doubles expected photons for fixed F, T and t.",Noiseless expectation and Poisson mean fixture.,Dimensional photon equation.,specified; not executed here
C15,C15-V2,Zero OPD,PSF reduces to the declared pupil diffraction model.,Analytic aperture comparison.,Fourier propagation limit.,specified; not executed here
C15,C15-V3,Flux conservation,Captured plus lost/undetected photons matches incident expectation statistically.,Count ledger and repeated seeds.,Photon accounting.,specified; not executed here
C15,C15-V4,Flight star/epoch holdout,Metric residuals and covariance are reported without fitting that observation.,Freeze optical/detector correction on training stars.,Proposed flight validation.,specified; not executed here
C16,C16-V1,Zero calibration error,All paired branches recover identical likelihoods up to numerical sampling.,Set deltaA=deltaPhi=0.,Transfer identity.,specified; not executed here
C16,C16-V2,Constant amplitude error,Signal amplitude scales by 1+deltaA without changing normalized waveform shape.,Noise-free amplitude fixture.,Multiplicative response relation.,specified; not executed here
C16,C16-V3,Pure time delay,Phase slope equals minus 2 pi f delay and can be absorbed by fitted time within bounds.,Analytic delayed waveform.,Fourier shift theorem.,specified; not executed here
C16,C16-V4,Held-out epoch/family,Bias and interval coverage are measured under frozen calibration prior choices.,Independent noise and CCSN-family holdout.,Proposed calibration inference validation.,specified; not executed here
C17,C17-V1,No subtraction baseline,A normalized injected source preserves flux through basic calibration.,Known PSF source with subtraction disabled.,Flux conservation.,specified; not executed here
C17,C17-V2,Zero-flux controls,False-positive frequency is measured at the frozen threshold.,Independent background locations/exposures.,Proposed null search calibration.,specified; not executed here
C17,C17-V3,Sparse injection,Single-source throughput stays within the proposed 5% multi-source tolerance.,Paired sparse/multiple replay.,Declared injection-interference target.,specified; not executed here
C17,C17-V4,Withheld disk/epoch,Completeness and false-positive behavior are assessed without retuning settings.,Hold out a host or independent epoch.,Proposed disk-domain transfer test.,specified; not executed here
C18,C18-V1,Unit transmission and full escape,"Observed LyC equals intrinsic LyC for f=1, T_IGM=T_MW=1.",Noiseless attenuation-chain fixture.,Flux-factorization identity.,specified; not executed here
C18,C18-V2,No escape,Source LyC counts reduce to background expectation.,Set f=0 and evaluate Poisson likelihood.,Null photon model.,specified; not executed here
C18,C18-V3,OII doublet conversion,Summed OII preserves ratio under identical repartition of its two components.,Line-integral fixture.,Declared O32 convention.,specified; not executed here
C18,C18-V4,Galaxy/domain holdout,Probability calibration and fraction coverage are reported without retuning.,Hold out galaxies and an excitation-selection subset.,Proposed proxy transfer validation.,specified; not executed here
C19,C19-V1,Gravity units,SI and cgs calculations produce identical physical g after conversion.,Known mass/radius fixture.,Dimensional gravity identity.,specified; not executed here
C19,C19-V2,Kernel normalization,Convolving constant flux preserves it.,Wavelength-dependent response fixture.,Normalized line-spread operator.,specified; not executed here
C19,C19-V3,Binary alternative,A combined spectrum is not automatically assigned single-star gravity with narrow intervals.,Inject two template spectra before convolution.,Proposed multiplicity robustness test.,specified; not executed here
C19,C19-V4,Independent benchmark,Empirical and physical gravity errors are measured without refitting benchmark-specific calibration.,Mass/radius benchmark holdout with pedigree audit.,Proposed physical validation.,specified; not executed here
C20,C20-V1,OU stationary variance,Long simulated series approaches sigma squared tau/2 within Monte Carlo uncertainty.,Exact OU transition sampler.,Stationary stochastic-process identity.,specified; not executed here
C20,C20-V2,Zero lag and long lag,Normalized correlation equals one at zero and approaches zero at lags much larger than tau.,Analytic covariance fixture.,OU kernel limits.,specified; not executed here
C20,C20-V3,Redshift dilation,An observed timescale is multiplied by 1+z for the same rest process.,Matched redshifted cadence simulations.,Time-dilation transformation.,specified; not executed here
C20,C20-V4,Different-survey holdout,Autocorrelation and selected flux distributions are predicted with frozen extension parameters.,Independent cadence/noise/selection replay.,Proposed temporal-domain validation.,specified; not executed here
C21,C21-V1,Vector-angle identities,"Aligned/perpendicular/antiparallel fields yield z=0, 0.5, 1.",Exact vector fixtures in a common frame.,Dot-product geometry.,specified; not executed here
C21,C21-V2,Coordinate rotation,Common orthogonal rotation leaves deflection unchanged.,Rotate B and B0 with the same matrix.,Rotational invariance.,specified; not executed here
C21,C21-V3,Injected gap,One continuous-looking reversal is split and exposure excludes the gap.,Mask a known synthetic interval.,Declared gap contract.,specified; not executed here
C21,C21-V4,Held-out encounter,Boundary errors and quiet/current-sheet false positives are measured with frozen settings.,Blinded labels on excluded encounter.,Proposed independent catalog validation.,specified; not executed here
C22,C22-V1,No-wind rotating disk,False wind evidence is measured under beam smearing.,Forward PSF/LSF cube simulation.,Proposed specificity control.,specified; not executed here
C22,C22-V2,Instrument-limited line,Inference returns unresolved intrinsic width rather than negative variance.,Inject sigma_gas tending to zero.,Quadrature-resolution limit.,specified; not executed here
C22,C22-V3,Rate dimensions,Column-radius-speed formula converts consistently to solar masses per year.,SI/cgs rate fixture.,Mass-flux dimensional identity.,specified; not executed here
C22,C22-V4,Held-out environment/sample,Incidence/strength predictions are checked without redefining wind thresholds.,Group or survey-block holdout.,Proposed association validation.,specified; not executed here
C23,C23-V1,Perfect survey,"With selection factors one, expected detections equal integrated occurrence times target count.",Analytic constant-rate fixture.,Poisson exposure identity.,specified; not executed here
C23,C23-V2,Zero metallicity effect,Injected b=0 is assessed for coverage without hard metallicity bins.,Forward survey with noisy abundance and selection.,Proposed slope-null test.,specified; not executed here
C23,C23-V3,Selection scaling,Halving detection probability halves expected detections at fixed occurrence.,Intensity integration fixture.,Multiplicative selection relation.,specified; not executed here
C23,C23-V4,DR25 recovery/host holdout,Observed selection recovery and candidate distributions are checked on unused injections/hosts.,Freeze cuts and calibration before holdout.,Primary simulated-data products and proposed validation.,specified; not executed here
C24,C24-V1,Circular orbit,"For e=0, separation is constant and velocity is a sinusoid under fixed orientation.",Analytic orbital fixture.,Kepler limit.,specified; not executed here
C24,C24-V2,Kepler equation closure,Computed E satisfies E-e sin E=M within proposed tolerance.,Eccentricity/phase grid and solver residual.,Declared numerical target.,specified; not executed here
C24,C24-V3,Dust scaling,"At fixed T and opacity, doubling mass doubles excess flux and doubling distance quarters it.",Noise-free SED fixture.,Optically thin flux equation.,specified; not executed here
C24,C24-V4,Independent era,Velocity and multiband dust predictions are compared with withheld campaign data.,Freeze orbit/dust choices before era holdout.,Proposed temporal validation.,specified; not executed here
C25,C25-V1,Projector identities,P squared equals P and coherent plus null energy equals total energy.,Analytic full-rank/rank-deficient matrices.,Orthogonal projection identities.,specified; not executed here
C25,C25-V2,No background events,Upper FAR bound is finite and scales inversely with exposure.,Poisson k=0 fixture.,Declared 95% count limit.,specified; not executed here
C25,C25-V3,Detector dropout,Pipeline uses recalibrated rank/threshold or emits unsupported configuration.,Synthetic missing detector stream.,Declared availability contract.,specified; not executed here
C25,C25-V4,Unseen family/noise,Efficiency at frozen FAR and latency are reported without retuning.,Independent physical and noise holdouts.,Proposed detection validation.,specified; not executed here
C26,C26-V1,Static force,"At frequency tending to zero, displacement per force approaches 1/k.",Analytic/measured low-drive comparator.,Susceptibility limit.,specified; not executed here
C26,C26-V2,High-frequency stiffness isolation,Magnitude approaches omega0 squared/omega squared for the declared stiffness-input model.,Frequency sweep and alternate damping-input check.,Transfer asymptote.,specified; not executed here
C26,C26-V3,Thermal equilibrium,Integrated passive displacement PSD approaches kBT/k for a single viscous mode.,Numerical PSD integration over converged bounds.,Equipartition/fluctuation-dissipation consistency.,specified; not executed here
C26,C26-V4,Unseen drive/amplitude,Transfer/noise predictions are checked without reidentifying the model.,Held-out low-amplitude sweep and sensor-noise injection.,Proposed bench validation.,specified; not executed here
C27,C27-V1,Isolated constant SED,Extracted amplitude reproduces inserted spectrum within numerical target.,Noiseless response-level source injection.,Flux/response closure.,specified; not executed here
C27,C27-V2,Two coincident identical sources,Individual amplitudes are nonidentifiable while summed flux may be constrained.,Degenerate design-matrix fixture.,Linear inverse-problem rank.,specified; not executed here
C27,C27-V3,Missing wavelength coverage,No measured point is emitted for unavailable bands.,Mask injection and spectrum assembly audit.,Declared missing-data contract.,specified; not executed here
C27,C27-V4,Spectroscopic holdout,Redshift interval coverage and alternate modes are evaluated with frozen templates/extraction.,Independent benchmark source/field.,Proposed redshift validation.,specified; not executed here
C28,C28-V1,No atmosphere,With tau=0 count rate is independent of airmass.,Synthetic standard fixture.,Separated throughput identity.,specified; not executed here
C28,C28-V2,Collecting-area scaling,Rate scales linearly with area under fixed throughput convention.,Dimensional count fixture.,Photon rate equation.,specified; not executed here
C28,C28-V3,Delta-line response,Count prediction follows transmission at the line wavelength.,Narrow-line limit against full integral.,Spectral-response limit.,specified; not executed here
C28,C28-V4,Withheld star/night,Flux residual and interval coverage are measured without retuning coefficients.,Independent standard and night holdouts.,Proposed instrument calibration validation.,specified; not executed here
C29,C29-V1,Zero energetic intensity,Partial pressure and energy density are zero.,Set j(E)=0 through all response conversions.,Integral zero identity.,specified; not executed here
C29,C29-V2,Analytic power-law spectrum,Numerical finite-band pressure/energy match quadrature references.,Known j(E) with declared relativistic relation.,Integration/convergence target.,specified; not executed here
C29,C29-V3,Normal/frame consistency,All signed normal fluxes transform consistently under reversed normal convention.,Reverse normal and update sign ledger.,Vector projection convention.,specified; not executed here
C29,C29-V4,Window/spacecraft holdout,Budgets are compared on alternate windows or a related encounter without forcing equality.,Freeze integration and geometry settings.,Proposed observational robustness.,specified; not executed here
C30,C30-V1,No accretion/mergers,Mass stays at seed value.,Set lambda or duty to zero.,Growth equation limit.,specified; not executed here
C30,C30-V2,Constant growth,Numerical history matches exponential within proposed target.,"Fixed lambda, efficiency and duty fixture.",Analytic integration.,specified; not executed here
C30,C30-V3,Radiative bookkeeping,Retained mass and radiated energy obey the chosen efficiency relation.,Integrate supplied mass and luminosity.,Mass-energy accounting.,specified; not executed here
C30,C30-V4,Synthetic survey holdout,Seed/growth degeneracy and selection recovery are measured without retuning scenario priors.,Held-out host trees/observation fields.,Proposed population validation.,specified; not executed here
D01,D01-V1,Actuation-off limit,C_mu=0 and zero auxiliary input reproduce baseline configuration.,Disable actuator and compare repeated blocked runs.,Boundary-condition identity.,specified; not executed here
D01,D01-V2,Constant jet fixture,Constant flow/speed gives analytic C_mu; pulsed product averaging matches quadrature.,Synthetic pulse trace test.,Momentum units and integration.,specified; not executed here
D01,D01-V3,Net-power ledger,Equal drag with positive actuator power gives negative net benefit.,Analytic fixture plus paired uncertainty calculation.,Power accounting; actual sign TBD.,specified; not executed here
D02,D02-V1,Fixed-angle relaxation,s(t)=s_eq+(s0-s_eq)exp(-t/tau).,Compare ODE integration to exact solution.,Analytic state response.,specified; not executed here
D02,D02-V2,Zero-rate unique equilibrium,Up/down curves coincide as rate tends to zero under identical initialization.,Rate refinement and long-dwell synthetic tests.,Reduced-model limit.,specified; not executed here
D02,D02-V3,Time reversal/orientation,Reversing integration orientation changes signed area but not branch-angle difference definition.,Known closed-loop numeric fixture.,Loop algebra and immutable thresholds.,specified; not executed here
D03,D03-V1,D03a zero aerodynamic load,"With F_z=0, descent acceleration is g; zero net torque holds Omega.",Analytic ODE fixture.,Sign and dimensional check.,specified; not executed here
D03,D03-V2,D03a stable linear equilibrium,Small perturbations follow exp(Jt) and decay for negative-real eigenvalues.,Compare integration with matrix exponential.,Local stability derivation.,specified; not executed here
D03,D03-V3,D03b PSD normalization,Integrated one-sided PSD equals variance within window correction.,Synthetic known-frequency signal and Parseval check.,Spectral conservation; records pending.,specified; not executed here
D03,D03-V4,D03 package isolation,Missing transfer approval leaves D03a aerodynamic envelope unchanged.,Integration fixture with incompatible D03b geometry.,Transfer contract.,specified; not executed here
D04,D04-V1,Creeping-flow force,C_D tends to 24/Re as inertia and boundary effects vanish.,Re/domain sequence plus analytic force integration.,Stokes derivation.,specified; not executed here
D04,D04-V2,Manufactured field,Solver residual/source recovers prescribed solution at claimed order.,Independent forcing and refined grids.,Discretization verification; outcome TBD.,specified; not executed here
D04,D04-V3,Uniform inflow conservation,Boundary mass ledger satisfies R3; time averages stabilize for unsteady case.,Flux integration and sampling-window extension.,Conservation and proposed tolerance.,specified; not executed here
D05,D05-V1,Audience restriction,A report allowed only for role A never appears in role B's simulated view.,Policy matrix fixtures and log audit.,Data-contract constraint.,specified; not executed here
D05,D05-V2,Censored exercise,Incomplete recovery remains censored; no fabricated duration.,Stop replay mid-case and recompute metrics.,Missing-data rule.,specified; not executed here
D05,D05-V3,Scorer endpoints,Perfect synthetic labels give precision/recall one; no positives yields undefined relevant metric.,Confusion-matrix fixtures.,Metric algebra; live efficacy not claimed.,specified; not executed here
D06,D06-V1,Sonic shock limit,"At M1=1, M2=1 and p02/p01=1.",Evaluate analytic formulas approaching one.,Normal-shock continuity.,specified; not executed here
D06,D06-V2,Isentropic throat,"At M=1, A/A*=1.",Direct formula and inverse-branch fixtures.,Area-Mach identity.,specified; not executed here
D06,D06-V3,Shared pressure scale,Multiplying p02 and p01 by one scale leaves ratio-based Mach unchanged.,Correlated calibration perturbation fixture.,Dimensionless inversion; absolute-state changes separate.,specified; not executed here
D07,D07-V1,Level-flight scaling,"At fixed mass/area/C_L, required speed scales rho^-1/2.",Compare analytic Earth/Mars scenario ratios.,Lift-balance identity.,specified; not executed here
D07,D07-V2,Zero mission duration,Integrated variable energy is zero; fixed deployment cost remains separately recorded.,Ledger endpoint fixture.,Energy-boundary definition.,specified; not executed here
D07,D07-V3,Certain/failed return,Conditional return probability one preserves acquired usable data; zero returns none.,Event-tree synthetic extremes.,Probability accounting; real probabilities TBD.,specified; not executed here
E01,E01-V1,Damage endpoints,H=0 gives p=0; H tending infinity gives p=1 and count bounded by N.,Analytic likelihood fixture with separate background/control term.,Binomial definition.,specified; not executed here
E01,E01-V2,Rare-event approximation,Poisson and Binomial means approach one another as kH tends zero.,Compare exact probabilities over declared small-probability grid.,Taylor limit; approximation gate.,specified; not executed here
E01,E01-V3,No service/zero load,No channel service delivers no frames; zero net energy flux keeps storage constant.,Replay and energy integration fixtures.,Boundary conservation; measured results pending.,specified; not executed here
E02,E02-V1,Zero angular rate,Identity attitude remains fixed; covariance still evolves under noise.,Nominal/filter fixture.,Quaternion kinematics.,specified; not executed here
E02,E02-V2,Constant axis rotation,Quaternion matches analytic sine/cosine half-angle solution.,Compare integration and sign conventions.,Solà-supported rotation model.,specified; not executed here
E02,E02-V3,Invalid echo/dose calibration,Missing echo yields no speed; count-only record yields no Gy.,Integration fixtures with absent calibration.,Information-sufficiency contract.,specified; not executed here
E03,E03-V1,No dead time,"As tau tends zero, corrected rate equals observed rate.",Analytic inversion fixture.,Detector model limit.,specified; not executed here
E03,E03-V2,Zero flux/background,Expected count lambda zero; positive observed count is incompatible with that exact model.,Likelihood endpoint fixture.,Poisson definition.,specified; not executed here
E03,E03-V3,Missing dose sensitivity,Count profile remains available while dose output is null.,Integration test with R present and S_D absent.,Information boundary; measured results pending.,specified; not executed here
E04,E04-V1,Constant mole fraction,Pressure decline changes number density while x remains constant.,Ideal-gas synthetic altitude fixture.,Density versus composition distinction.,specified; not executed here
E04,E04-V2,Humidity conversion,"At zero water, dry equals wet; positive water raises dry value for fixed wet.",Analytic endpoint fixture.,Denominator algebra.,specified; not executed here
E04,E04-V3,Step/flight lag,First-order response matches exponential and produces speed-times-lag displacement.,Simulated ascent/descent known-profile replay.,Response model; observed gradient pending.,specified; not executed here
E05,E05-V1,Cantilever stiffness,Tip deflection approaches FL^3/(3EI) for matching simple beam assumptions.,Surrogate and FE common fixture.,Analytic elasticity.,specified; not executed here
E05,E05-V2,Rigid-body free model,Unconstrained 3D body has six zero-frequency rigid modes.,Modal fixture before applying deployment constraints.,Mechanical invariance.,specified; not executed here
E05,E05-V3,Missing ICD/load,Pipeline returns pending margins and no qualification label.,Integration fixture with absent controlling inputs.,Requirements R1/R2; actual flight results unavailable.,specified; not executed here
E06,E06-V1,Two isolated nodes,Temperatures approach energy-weighted equilibrium; total heat conserved.,Compare symmetric-edge ODE with analytic decay.,Conduction conservation.,specified; not executed here
E06,E06-V2,Equal environment temperature,"With T=T_air=T_rad and zero solar/internal heat, net flux is zero.",Full model endpoint fixture.,Radiation/convection identities.,specified; not executed here
E06,E06-V3,Radiation unit fault,Celsius input rejected or converted before fourth power.,Typed temperature integration test.,Kelvin requirement; actual flight fit pending.,specified; not executed here
E07,E07-V1,Independent endpoints,Ai=1 gives A>=2=1; exactly one Ai=1 and others zero gives zero.,Enumerate eight survival states.,Two-of-three algebra.,specified; not executed here
E07,E07-V2,Common all-module failure,p_c=1 gives zero science availability despite ai=1.,Conditional fault-tree fixture.,Dependency example.,specified; not executed here
E07,E07-V3,Clock/bias known trace,"Injected offsets/bias recover within declared uncertainty, while constant x cannot separate timing.",Synthetic varying/constant environment cases.,Identifiability; original data unavailable.,specified; not executed here
E08,E08-V1,Resistive surrogate,V_DUT=Vs-IRh and harness loss I^2Rh.,Analytic low-energy/software fixture.,Circuit law.,specified; not executed here
E08,E08-V2,No current,Ideal power and resistance loss zero; meter offsets remain uncertainty.,Signed-current endpoint fixture.,Power identity.,specified; not executed here
E08,E08-V3,Missing limits/interlock,Stimulus-enabled transition rejected and logged.,State-machine integration fixture.,R1; no high-energy fault test.,specified; not executed here
E08,E08-V4,Known energy flow,Analytic constant-power duration closes ledger within propagated interval.,Replay source/storage/loss model.,Accounting conservation; measured closure TBD.,specified; not executed here
F01,F01-V1,Simulator delay,Delivered timestamp minus send timestamp equals imposed delay before jitter.,Deterministic queue fixture.,Communication interface.,specified; not executed here
F01,F01-V2,Coder endpoints,Identical nondegenerate labels yield kappa one; all-one marginals produce undefined denominator.,Synthetic codebook fixtures.,Agreement algebra.,specified; not executed here
F01,F01-V3,Crossover confounding,Protocol perfectly aligned with order triggers aliasing; balanced design permits separate effects.,Known design-matrix fixtures.,Identifiability; study outcomes pending.,specified; not executed here
F02,F02-V1,Matched-claim graph,Variants contain identical required claim IDs; omitted uncertainty fails content gate.,Set-equality and expert-review fixture.,Requirement R1/R2.,specified; not executed here
F02,F02-V2,Brier endpoints,p=y gives zero; opposite certainty gives one; p=0.5 gives 0.25.,Analytic item-scoring fixtures.,Probability algebra.,specified; not executed here
F02,F02-V3,Attrition/holdout,Missing delayed score remains missing; topic holdout does not reuse its outcomes for format choice.,Analysis integration fixture.,Data separation; reader results pending.,specified; not executed here
G01,G01-V1,Uniaxial projection,"For strain diag(e,0,0), a sensor at angle theta reads e cos^2 theta.",Analytic orientation fixture.,Tensor projection.,specified; not executed here
G01,G01-V2,Temperature-only FBG,"With mechanical strain zero, wavelength shift equals thermal coefficient times Delta T.",Forward-model synthetic fixture.,Readout identity.,specified; not executed here
G01,G01-V3,Rank-deficient array,Repeated collinear channels cannot identify transverse strain; output flags/nulls persist despite regularization.,Duplicate-channel inversion fixture.,Linear algebra; measured accuracy pending.,specified; not executed here
G02,G02-V1,No interference/reference,"With r=0 and initialized w=0, corrected stream equals d.",Zero-reference fixture with regularizer.,Cancellation identity.,specified; not executed here
G02,G02-V2,Known linear path,"For v=a r and independent s, a correctly set weight removes v without changing s.",Analytic synthetic mixture before adaptation tests.,Linear model endpoint.,specified; not executed here
G02,G02-V3,Reference science leakage,Increasing leakage can reduce desired tone despite lower residual power; preservation gate detects failure.,Inject known s into r and replay adaptation/bypass.,Model warning; quantitative outcomes pending.,specified; not executed here
G03,G03-V1,Free-space scaling,Doubling R reduces received power by factor four at fixed calibrated gains.,Synthetic Friis ledger and range check.,Inverse-square relation.,specified; not executed here
G03,G03-V2,Uniform rectangular aperture,Transform gives separable sinc field with known first nulls.,Complex-scan synthetic fixture with extent refinement.,Fourier aperture analytic pattern.,specified; not executed here
G03,G03-V3,Missing phase/system temperature,Power-only scan cannot enter full near-field transform; absent T forbids G/T output.,Data-contract integration fixture.,"Information sufficiency, not measured pattern success.",specified; not executed here
G04,G04-V1,Uniform pressure gradient,One-dimensional q=-k Delta p/(mu L) with declared sign.,Analytic Darcy fixture.,Unit/sign conservation.,specified; not executed here
G04,G04-V2,Closed undrained limit,No boundary flux implies conserved mixture volume under stated incompressibility.,Boundary-ledger integration.,Mass balance.,specified; not executed here
G04,G04-V3,Relaxation endpoints,E(0)=E_inf+sum E_j and E(infinity)=E_inf for positive tau.,Analytic and fitted-function checks.,Relaxation identity; measured fitting pending.,specified; not executed here
G05,G05-V1,Ideal oxygen stoichiometry,Two mol processed CO2 yield at most one mol O2 before losses.,Molar-to-mass conversion fixture.,Atom conservation.,specified; not executed here
G05,G05-V2,Qualification rejection,f_q=0 increases no qualified inventory despite production.,Batch-routing integration fixture.,Quality gate.,specified; not executed here
G05,G05-V3,Constant outage demand,Reserve depletion equals demand times outage plus losses.,Analytic inventory trajectory.,Mass ledger; reliability results pending.,specified; not executed here
G06,G06-V1,LDF fixed state,Loading approaches q* exponentially without overshoot for positive k.,Exact-solution comparison.,Kinetic ODE.,specified; not executed here
G06,G06-V2,Zero working capacity,Delta q=0 gives zero captured mass even with utility emissions.,Cycle endpoint fixture.,Mass conversion.,specified; not executed here
G06,G06-V3,Zero retention/high emissions,No permanent stored mass or excess emissions prevents positive net removal.,Carbon-fate integration extremes.,Accounting identity; real net result pending.,specified; not executed here
G07,G07-V1,Grating differential,Finite small-angle perturbations converge to analytic delta lambda.,Compare exact relation and Jacobian.,First-order derivation.,specified; not executed here
G07,G07-V2,Uniform free expansion,Unconstrained homogeneous length changes alpha L Delta T.,Thermal FE analytic fixture.,Expansion identity.,specified; not executed here
G07,G07-V3,Assembly return,Repeated calibrated line centroids stay within R2-derived budget or expose hysteresis.,Return-to-setting sequence with independent centroid fitting.,Proposed verification; no built-mount performance claimed.,specified; not executed here
G08,G08-V1,No signals/division/loss,"With transition rates disabled, populations and volume remain constant.",Exact ODE/observation fixture.,Bookkeeping limit.,specified; not executed here
G08,G08-V2,Single replicating cohort,"With only division active, R decays and Q gains twice lost R; N gains one per event.",Compare R0 exp(-k_div t) and Q0+2R0(1-exp(-kt)).,Analytic division solution.,specified; not executed here
G08,G08-V3,Volume-only confounding,Equal volumes can arise from different N and cell size; fitter flags the ridge.,Synthetic alternate observation mapping.,Identifiability algebra; clinical outcomes unclaimed.,specified; not executed here
H01,H01-V1,Provenance break,Item is marked unsupported and cannot enter confirmed release.,Condition/fixture: Remove the source edge for one scientific claim. Verification procedure: Graph integrity fixture..,Graph integrity fixture.,specified; not executed here
H01,H01-V2,Learning arithmetic,"Delta=0.2, or 20 percentage points.",Condition/fixture: Synthetic correct-response rates are 0.8 and 0.6. Verification procedure: Exact effect calculation..,Exact effect calculation.,specified; not executed here
H01,H01-V3,Cluster planning,DE=1.6 and n_eff=n/1.6.,Condition/fixture: m=4 and rho=0.2 in the planning approximation. Verification procedure: Independent formula check..,Independent formula check.,specified; not executed here
H01,H01-V4,Accessible delivery,Every required caption/source path remains usable; failures are recorded for repair.,Condition/fixture: Review representative print/mobile tasks with keyboard and screen reader plus low bandwidth. Verification procedure: Task-based integration review..,Task-based integration review.,specified; not executed here
H02,H02-V1,Zero transfer timing,S=0 and x=F^-1(y-b-dt)/g where supported.,Condition/fixture: tau=0 with valid flat/gain and offsets. Verification procedure: Exact operator limit..,Exact operator limit.,specified; not executed here
H02,H02-V2,Zero scene,"y=b+d t, with no scene smear.",Condition/fixture: x=0 in noiseless synthetic acquisition. Verification procedure: Offset-only matrix fixture..,Offset-only matrix fixture.,specified; not executed here
H02,H02-V3,Known sharp-limb scene,Recover supported unsaturated signal within proposed residual target and report edge bias.,"Condition/fixture: Forward project a declared synthetic x through verified K, then invert. Verification procedure: Independent forward/inverse benchmark..",Independent forward/inverse benchmark.,specified; not executed here
H02,H02-V4,Calibration holdout,"Report radiance bias, covariance coverage and narrow-feature retention.",Condition/fixture: Reserve complete calibration scenes/campaigns. Verification procedure: Blocked flight/synthetic comparison..,Blocked flight/synthetic comparison.,specified; not executed here
H03,H03-V1,Single dipole axis/equator,Axial magnitude is twice equatorial magnitude; direction follows vector formula.,Condition/fixture: Equal distance R from a dipole aligned with z. Verification procedure: Exact field fixture..,Exact field fixture.,specified; not executed here
H03,H03-V2,Nuisance projection,H^T W_perp=0 within scaled numerical tolerance.,Condition/fixture: Use full-rank synthetic H and positive-definite C. Verification procedure: Independent matrix calculation..,Independent matrix calculation.,specified; not executed here
H03,H03-V3,Shared source/nuisance mode,Projected data sensitivity for that mode is zero; it cannot be called resolved.,Condition/fixture: A column of G lies entirely in span(H). Verification procedure: Nullspace fixture..,Nullspace fixture.,specified; not executed here
H03,H03-V4,Independent polar passes,"Report vector residuals, coverage and resolution support.",Condition/fixture: Reserve full passes and matched-altitude Prospector observations. Verification procedure: Pass-level holdout comparison..,Pass-level holdout comparison.,specified; not executed here
H04,H04-V1,Reference ratio,delta13C=0 per mil; R=1.01 R_ref gives +10 per mil.,Condition/fixture: Set R=R_ref. Verification procedure: Exact isotope conversion check..,Exact isotope conversion check.,specified; not executed here
H04,H04-V2,Atom-weighted mixture,R_mix=(R1+R2)/2; unequal inventories use explicit weights.,Condition/fixture: Equal n12 with ratios R1 and R2. Verification procedure: Independent mixture calculation..,Independent mixture calculation.,specified; not executed here
H04,H04-V3,Pure background,Counts contain no identifiable specimen ratio; output unresolved.,Condition/fixture: Synthetic Lambda=0 with known backgrounds. Verification procedure: Count-likelihood boundary fixture..,Count-likelihood boundary fixture.,specified; not executed here
H04,H04-V4,Registration shift,Recovered transform and phase-attribution intervals reflect that uncertainty.,Condition/fixture: Inject a known synthetic map translation with uncertain landmarks. Verification procedure: Correlative integration test..,Correlative integration test.,specified; not executed here
H05,H05-V1,Temperature conversion,35°C.,Condition/fixture: Scenario temperature 308.15 K. Verification procedure: Exact unit-adapter fixture..,Exact unit-adapter fixture.,specified; not executed here
H05,H05-V2,Heat sequence,H=2 days and C=2 consecutive days.,"Condition/fixture: Tmax=[35,36,37,34]°C with threshold 35°C. Verification procedure: Exact indicator calculation..",Exact indicator calculation.,specified; not executed here
H05,H05-V3,Regret identity,Regret=0; all other regrets are nonnegative.,Condition/fixture: Action is the least-loss feasible choice in a scenario. Verification procedure: Independent action-ledger calculation..,Independent action-ledger calculation.,specified; not executed here
H05,H05-V4,Protected knowledge export,Public export is blocked or approved aggregate substituted.,Condition/fixture: Synthetic sensitive-site layer lacks public permission. Verification procedure: Policy integration test..,Policy integration test.,specified; not executed here
H06,H06-V1,Flat terrain,Height and slope are zero after consistent detrending.,Condition/fixture: z is constant with no ridge signal. Verification procedure: Analytic profile fixture..,Analytic profile fixture.,specified; not executed here
H06,H06-V2,Profile-normal geometry,Extracted cross profiles run along y and are perpendicular.,Condition/fixture: Straight centerline parallel to x axis. Verification procedure: Vector dot-product check..,Vector dot-product check.,specified; not executed here
H06,H06-V3,Along-strike covariance limits,Covariance approaches zero at large separation.,Condition/fixture: s=s' gives covariance sigma²; large separation relative to ell. Verification procedure: Analytic kernel sweep..,Analytic kernel sweep.,specified; not executed here
H06,H06-V4,Ridge holdout,Report shape prediction coverage and family-rank sensitivity.,Condition/fixture: Reserve full ridges or long contiguous segments. Verification procedure: Spatial model comparison..,Spatial model comparison.,specified; not executed here
H07,H07-V1,Face-on rotation,v_los=v_sys at all resolved radii.,Condition/fixture: Set i=0 in the thin-disk model. Verification procedure: Analytic alignment fixture..,Analytic alignment fixture.,specified; not executed here
H07,H07-V2,Fixed-template null,SNR null mean 0 and variance 1 in the ideal model.,"Condition/fixture: Synthetic d~Normal(0,C) with fixed supported t. Verification procedure: Monte Carlo/analytic covariance check..",Monte Carlo/analytic covariance check.,specified; not executed here
H07,H07-V3,Beam flux conversion,Aperture flux equals F in Jy km/s.,Condition/fixture: One beam-equivalent aperture with constant channel-integrated intensity F. Verification procedure: Independent area-ledger calculation..,Independent area-ledger calculation.,specified; not executed here
H07,H07-V4,Search/injection holdout,Report global false alarms and recovery completeness with uncertainty.,Condition/fixture: Reserve targets and replay every trial on null and injected cubes. Verification procedure: Full-pipeline benchmark..,Full-pipeline benchmark.,specified; not executed here
H08,H08-V1,Zero dust supply,dm/dt=0 in the reduced accretion model.,Condition/fixture: rho_d=0 or Delta v=0 or epsilon=0. Verification procedure: Analytic growth boundary test..,Analytic growth boundary test.,specified; not executed here
H08,H08-V2,Thin-shell limit,m approaches 4pi a_c² t_r rho_s(1-phi).,Condition/fixture: t_r much smaller than a_c. Verification procedure: Series-expansion/numerical convergence check..,Series-expansion/numerical convergence check.,specified; not executed here
H08,H08-V3,Compaction ratio,"Shell volume halves, since 0.4/0.8=0.5.",Condition/fixture: phi changes from 0.6 to 0.2 at conserved mass. Verification procedure: Independent mass/porosity ledger..,Independent mass/porosity ledger.,specified; not executed here
H08,H08-V4,Specimen/section holdout,Report censored thickness coverage and mechanism prediction stability.,Condition/fixture: Reserve meteorites and complete sections with simulated cut offsets. Verification procedure: Hierarchical stereology benchmark..,Hierarchical stereology benchmark.,specified; not executed here
H09,H09-V1,No absorption feature,BD=0; r=0.8 r_cont gives BD=0.2.,"Condition/fixture: r_lambda=r_cont,lambda with valid continuum. Verification procedure: Exact feature-ratio test..",Exact feature-ratio test.,specified; not executed here
H09,H09-V2,Thermal scaling,"I_th increases by sqrt(2), not factor two.",Condition/fixture: Double k with rho and c fixed. Verification procedure: Analytic thermophysical check..,Analytic thermophysical check.,specified; not executed here
H09,H09-V3,Model prior odds,"Posterior odds=1:2, yielding probabilities 1/3 and 2/3.",Condition/fixture: Two models have prior odds 1:4 and likelihood ratio 2. Verification procedure: Exact Bayes odds calculation..,Exact Bayes odds calculation.,specified; not executed here
H09,H09-V4,Mixture/basin holdout,"Report fraction/size coverage, degeneracy and unsupported-trend flags.",Condition/fixture: Reserve known laboratory mixtures and entire comparison basins/units. Verification procedure: Instrument-degraded and spatial validation..,Instrument-degraded and spatial validation.,specified; not executed here
I01,I01-V1,Adiabatic known input,Stored thermal energy increase equals integrated supplied power.,Uniform-property insulated fixture.,Energy conservation.,specified; not executed here
I01,I01-V2,Zero heat and equal boundaries,Uniform initial temperature remains unchanged.,Exact equilibrium fixture.,Conduction equilibrium.,specified; not executed here
I01,I01-V3,Free expansion alternative,Removing restraint eliminates the screened thermal stress despite nonzero temperature rise.,Constraint-toggle analytic case.,Elastic restraint distinction.,specified; not executed here
I01,I01-V4,Withheld inert heat shape,Temperature/strain interval coverage is assessed without changing contact/lag fits.,Noncombusting known-power surrogate holdout.,Proposed thermal validation gate.,specified; not executed here
I02,I02-V1,Steady insulated limit,Input equals coolant enthalpy rise after storage tends to zero.,Known single-node steady fixture.,Energy conservation.,specified; not executed here
I02,I02-V2,Heater-off cooling,Stored energy falls through independently modeled ambient/coolant paths.,Analytic linear cooling comparator.,Thermal-network decay.,specified; not executed here
I02,I02-V3,Internal conductance cancellation,Summed network energy excludes internal pairwise exchanges.,Two-node unequal-temperature fixture.,Conservative graph identity.,specified; not executed here
I02,I02-V4,Withheld inert transient,Outlet and hotspot coverage plus energy residual are reported with frozen parameters.,Known-power single-phase surrogate holdout.,Proposed noncombusting validation.,specified; not executed here
I03,I03-V1,No heat input,Wall/fluid temperatures remain at common inlet/ambient equilibrium.,Zero-load thermal fixture.,Energy equilibrium.,specified; not executed here
I03,I03-V2,Pressure-work identity,Pump work equals pressure drop times volume rate divided by efficiency.,Unit-aware hydraulic fixture.,Hydraulic power relation.,specified; not executed here
I03,I03-V3,Friction convention,Equivalent Darcy/Fanning inputs yield identical pressure drop after factor-four conversion.,Typed coefficient fixture.,Friction-factor convention.,specified; not executed here
I03,I03-V4,Withheld inert family,Pressure and hotspot predictions are checked before calibration on that coupon.,Known-power noncombusting coupon holdout.,Proposed transport/thermal validation.,specified; not executed here
I04,I04-V1,No higher-priority tasks,Response bound reduces to C+B.,Analytic scheduler fixture.,Response-time equation.,specified; not executed here
I04,I04-V2,Perfect independent lanes,TMR failure tends to zero as p tends to zero and equals one at p=1.,Polynomial boundary/Monte Carlo fixture.,Voting combinatorics.,specified; not executed here
I04,I04-V3,Reset with duplicate packets,Committed unique scientific record set is unchanged by duplicate replay.,Journal checkpoint/reset integration.,Idempotent integrity requirement.,specified; not executed here
I04,I04-V4,Shared-clock fault,Fault is reported as common mode rather than masked by three lanes.,Deterministic emulator scenario.,Declared redundancy boundary.,specified; not executed here
I05,I05-V1,Constant atmosphere,A lagged sensor approaches X+b exponentially with timescale tau.,Analytic step-response fixture.,First-order sensor solution.,specified; not executed here
I05,I05-V2,Uniform wind/zero slip,Position follows x0+ut.,Coordinate-aware trajectory fixture.,Advection limit.,specified; not executed here
I05,I05-V3,Zero net power,"Stored energy remains constant, with consumption/harvest ledgers still populated.",Balanced-power replay.,Energy conservation.,specified; not executed here
I05,I05-V4,Delayed/missing packets,Recovered path keeps original times and explicitly missing samples.,Synthetic track through packet-loss/reorder patterns.,Proposed transport integrity.,specified; not executed here
I06,I06-V1,Cantilever static limit,Tip deflection equals FL cubed/(3EI) for the declared slender uniform beam.,Mesh-refined beam fixture.,Euler-Bernoulli analytic limit.,specified; not executed here
I06,I06-V2,Mass scaling,Multiplying all masses by factor s divides modal frequencies by sqrt(s) at fixed stiffness.,Generalized eigenvalue fixture.,Modal scaling identity.,specified; not executed here
I06,I06-V3,Rigid-body freedom,Unconstrained model retains expected zero-frequency rigid modes.,Free/free modal model.,Boundary-condition consistency.,specified; not executed here
I06,I06-V4,Withheld inert load case,Static/modal response is predicted without re-fitting that fixture/load.,Independent nonpropulsive test case.,Proposed structural validation.,specified; not executed here
I07,I07-V1,Duplicate replay,State and unique-image completeness remain unchanged.,Replay every valid event/chunk twice.,Idempotence/set-count identity.,specified; not executed here
I07,I07-V2,Delayed fresh-looking packet,Age follows source time and field becomes stale/unknown as appropriate.,Late receive-time injection.,Declared freshness equation.,specified; not executed here
I07,I07-V3,Restart equivalence,Checkpoint plus replay yields the same authoritative state as uninterrupted run.,Deterministic reset at varied event positions.,Event-ledger integration.,specified; not executed here
I07,I07-V4,Missing/corrupt image chunk,Completeness stays below one and assembler reports exact missing/conflicting IDs.,Synthetic inert image manifest replay.,Integrity contract.,specified; not executed here
I08,I08-V1,Monopole,Zero higher coefficients reproduces mu/r and inward inverse-square acceleration.,Analytic harmonic/point-mass comparison.,Potential-gradient identity.,specified; not executed here
I08,I08-V2,Frame round trip,Forward/inverse position-velocity transformation reproduces original state within numerical target.,Time-dependent transform fixture.,Declared frame interface.,specified; not executed here
I08,I08-V3,Matched Horizons/SPICE geometry,Residuals are computed only with identical center/epoch/correction conventions.,Frozen query/kernel comparison.,Primary convention documentation.,specified; not executed here
I08,I08-V4,Exterior Laplace/mesh check,Potential Laplacian approaches zero outside mass; mesh mass matches density times volume.,Derivative refinement and topology fixture.,Newtonian exterior field and mass accounting.,specified; not executed here
I09,I09-V1,Zero body spin,Rotating-frame inertial terms vanish.,Omega=0 fixture.,Dynamics limit.,specified; not executed here
I09,I09-V2,Passive collision limits,e=1 preserves normal kinetic energy and e=0 removes it.,Analytic impulse fixture.,Restitution energy identity.,specified; not executed here
I09,I09-V3,No external torque,Body-plus-wheel angular momentum is conserved in inertial coordinates.,Internal exchange simulation.,Angular-momentum conservation.,specified; not executed here
I09,I09-V4,Withheld terrain/contact family,Useful-hop coverage and failure categories are evaluated without retuning actions.,Independent seeded surfaces and contact-law holdout.,Proposed reliability-domain validation.,specified; not executed here
I10,I10-V1,Angular wrap,Targets around plus/minus pi yield the short signed error.,Exact trigonometric fixture.,Wrapped-angle identity.,specified; not executed here
I10,I10-V2,Torque sign/conservation,Positive u accelerates body negatively; body-plus-wheel momentum stays constant without external torque/friction.,No-disturbance synthetic plant.,Internal angular-momentum exchange.,specified; not executed here
I10,I10-V3,Electrical/mechanical separation,Driver loss can increase cumulative draw without the same wheel-energy increase.,Synthetic power/loss and speed ledger.,Energy accounting distinction.,specified; not executed here
I10,I10-V4,Withheld maneuver/reset,Pointing/settling and bounded momentum are assessed with frozen plant/controller.,Independent angle/disturbance plus dropout/reset cases.,Proposed bench-domain acceptance.,specified; not executed here
I11,I11-V1,Identical variants,Paired difference is zero and shared-noise cancellation is represented.,Run identical references/operators twice.,Paired algebra identity.,specified; not executed here
I11,I11-V2,Known dark shift,Difference follows inserted electron offset divided by exposure/area/flat with sign.,Synthetic dark perturbation.,Detector calibration equation.,specified; not executed here
I11,I11-V3,Known flat shift,Difference scales with scene counts according to reciprocal flat factors.,Uniform scenes at different sky levels.,Multiplicative calibration relation.,specified; not executed here
I11,I11-V4,Withheld exposure strata,Context-dependent differences are predicted without retuning masks/references.,Filter/epoch/position group holdout.,Proposed calibration transfer validation.,specified; not executed here
I12,I12-V1,Scaling round trip,Dimensional-to-scaled-to-dimensional states/costs reproduce inputs.,"Known a,n state fixture.",Nondimensionalization identity.,specified; not executed here
I12,I12-V2,Coast Jacobi invariant,Unforced integrations meet the proposed drift target.,Refine step/tolerances over representative coasts.,CR3BP conservation.,specified; not executed here
I12,I12-V3,DRO periodic return,Target state returns to its family boundary within declared acceptance.,Independent integration of target period.,Periodic-orbit contract.,specified; not executed here
I12,I12-V4,Budget/model holdout,Optimization comparison includes all failures and promotion residuals without selecting only best seeds.,Independent runs/checker and ephemeris promotion.,Proposed fair-validation design.,specified; not executed here
I13,I13-V1,Zero normalized offset,Synthetic propagation equals passive baseline.,Identical-state integration fixture.,Deterministic propagation identity.,specified; not executed here
I13,I13-V2,STM identity at initial epoch,Phi is identity and propagated covariance starts at P0.,Initial-condition fixture.,Variational boundary condition.,specified; not executed here
I13,I13-V3,Linear constant dynamics,STM covariance matches nonlinear ensemble moments within Monte Carlo uncertainty.,Analytic linear-state benchmark.,Covariance propagation identity.,specified; not executed here
I13,I13-V4,Correlated duplicate observation,A perfectly redundant modeled observation does not double independent information.,Shared-bias/correlation fixture with deduplication or rank-revealing whitening before any inverse update; compare with the single independent observation.,Observation covariance contract.,specified; not executed here
I13,I13-V5,Encounter nonlinearity holdout,Linear approximation error is reported for unused offset scales/directions.,Independent seeded ensemble comparison.,Proposed sensitivity-domain validation.,specified; not executed here