Every tool returns CONFIRMED, MISMATCH, ERROR, or NOT_APPLICABLE — never raises, never self-confirms. Grouped below into eight domain families across seven scaffold axes.
63 verify_* tools — 60 single-domain + 2 umbrella dispatchers + 1 cross-cutting phase classifier. Same shape every time: pass a spec, get back a verdict with derivation. Detailed code examples for the seven most-cited verifiers follow below.
Parses formulas with nested groups (Cu(OH)2) and charges (Fe^2+); verifies stated coefficients balance atoms and charge, or solves for the smallest balancing set.
Substitutes unit expressions for symbols; reduces both sides of an equation to base SI units (kg, m, s, A, K, mol, cd) and compares dimensional signatures.
Before/after balance arithmetic with named-law profiles for energy, momentum, charge, and mass-energy equivalence.
Umbrella. Dispatches to dimensional or conservation based on which spec key is present. Use when an answer needs both forms of physical sanity.
First/second-law relations, entropy, enthalpy, Gibbs free energy, Carnot efficiency bound, cycle work computations.
Half-life and decay constants, activity (Bq/Ci), mass defect, Q-values, binding energy per nucleon.
Snell's law, thin-lens and mirror equations, magnification, prism dispersion, fiber numerical aperture.
Sound speed in media, decibel arithmetic, wave equations, room modes, Doppler shift.
Ohm's law, AC impedance, RC/RL/RLC time constants, power factor, three-phase relations.
Conversion factors, efficiency bounds, capacity factor, LCOE arithmetic, storage round-trip.
Hardy-Weinberg consistency, primer Tm/GC, dose-response monotonicity, replicate adequacy via power calculation, Mendelian chi-squared.
Mendelian ratios, linkage maps, transcription/translation, mutation classification, pedigree consistency.
Macronutrient kcal arithmetic, RDA bounds, BMR/TDEE estimators, glycemic load consistency.
VO2 max from running speed, EPOC estimates, training-stress score, %1RM, HR zone targeting.
Drug dosing (mg/kg, BSA), GFR (Cockcroft-Gault, MDRD), ABG interpretation, MAP, anion gap.
Lotka-Volterra population dynamics, Shannon/Simpson diversity, trophic transfer efficiency, carrying capacity.
Radiometric dating, isostatic depth, stratigraphic ordering, mineral hardness comparisons.
Great-circle distance/bearing, map-projection sanity, polygon area from coordinates, UTC offsets.
Manning's open-channel flow, flood frequency (Gumbel / Log-Pearson III), runoff coefficients, Darcy's law.
Dry/moist adiabatic lapse, dew point, wind chill, density altitude, CAPE consistency.
Kepler orbits, distance ladder, magnitude conversions, parallax, redshift→velocity, transit timing.
Tide harmonics, salinity-temperature density, sound speed, hydrostatic pressure at depth.
Sympy across nine modes: equality, derivative, integral, limit, solve, matrix, inequality, series, ODE.
Recompute p from raw inputs across twelve test types — z, t (one/two/paired), chi², F, Fisher exact, Mann-Whitney, Wilcoxon, regression coefficient.
Bonferroni, Holm, Benjamini-Hochberg FDR; family-wise error verdicts on a vector of raw p-values.
Normal, t, and bootstrap CI bound recomputation; coverage and width sanity.
Umbrella. Dispatches to pvalue, multiple_comparisons, or confidence_interval based on spec keys.
Propositional and predicate validity via truth-table or Sympy SAT; modus ponens / tollens chain checks.
GCD/LCM, primality, modular inverse, Diophantine arithmetic, Euler totient, factor trees.
Permutations, combinations, Stirling, Catalan, partitions, derangements.
Euclidean lengths/angles/areas/volumes, vector and matrix transforms, coordinate-geometry sanity.
Shannon entropy, mutual information, channel capacity, prefix-code Kraft inequality.
LP/IP feasibility, queueing M/M/c, optimization gradient checks, game-theory equilibria.
Qubit-state arithmetic, gate matrix products, entanglement detection, Grover/Shor step counts.
Static termination scan, functional correctness in restricted namespace, complexity by log-log slope, run-twice determinism.
TCP throughput (BDP), DNS hierarchy, TLS handshake order, routing convergence, IP subnet math.
Hash output lengths, RSA/ECC key sizes, AES key/block bounds, modular arithmetic for primitives.
OWASP Top-10 categorization, CVSS scoring, common-control coverage, incident-response phase ordering.
GD&T tolerance stack-up, control-chart limits, lean takt time, MTBF/MTTR composition.
Crystal-structure density, phase-diagram ordering, mechanical-property regimes, fatigue S-N curves.
Beam deflection bounds, code minimums (IBC/IRC), foundation bearing capacity, project critical path.
Egress capacity, occupancy-load math, daylight factor, plenum and clear-height regulatory minimums.
Supply/demand equilibrium, elasticity, GDP-component identity, Phillips/Okun relations.
Time value of money, DCF, bond pricing, IRR/NPV, Sharpe ratio, options put-call parity.
Wage/hour FLSA arithmetic, productivity ratios, unemployment relations, union-density sanity.
Cap-rate / NOI / ROI, DSCR, LTV, IRR for waterfall, gross rent multiplier consistency.
Contract-element completeness, statutory citation sanity, deadline counting, jurisdictional ordering.
Structural completeness of decision packets across business / household / education / church / governance profiles.
Crop water use, yield-density curves, fertilizer NPK arithmetic, irrigation efficiency.
USDA texture-class triangle, CEC arithmetic, pH-buffer relations, horizon ordering.
IPA validity, syllable structure, morpheme decomposition, language-family branch ordering.
Interval / chord / scale construction, Roman-numeral analysis, voice-leading rule checks.
Exposure-triangle (EV) reciprocity, sensor crop math, depth-of-field, color-temperature consistency.
Aristotelian appeal coverage (ethos / pathos / logos), fallacy classification, argument-structure validity.
Syllogism validity, deontic and modal frame consistency, classical-tradition citation ordering.
Date arithmetic across calendar systems, anachronism detection, sequence ordering.
Win-probability arithmetic, Pythagorean expectation, rate-stat denominators, expected value.
UTC ↔ local conversion, ISO 8601 strictness, leap-year rules, Julian ↔ Gregorian.
Creedal continuity, doctrinal-position ordering, scripture-anchor consistency.
Eyewitness corroboration counts, attestation chain, two-or-three-witness threshold (Deut 19:15).
Provenance signatures, notarization, chain-of-custody hash linkage, attestation count.
Validates Bible references parse, exist, and resolve to canonical book/chapter/verse via the local concordance.
Cross-cutting. Classifies any packet by declared phase as setup / positioning / conversion per Prov 24:27 ("Prepare your work outside; get everything ready for yourself in the field, and after that build your house").
Seven verifiers with full input/output examples. The other 56 follow the same shape — pass a spec, receive a verdict.
Parses formulas with nested groups (Cu(OH)2) and charges (Fe^2+, MnO4^-). Verifies stated coefficients balance atoms and charge, or solves for the smallest balancing coefficients if none are supplied.
verify_chemistry(equation="C3H8 + 5 O2 -> 3 CO2 + 4 H2O", temperature_K=298.15)
→ {"equation": {"status": "CONFIRMED", "detail": "balanced (atoms + charge)"},
"temperature": {"status": "CONFIRMED", "detail": "298.15 K positive"}}
verify_chemistry(equation="H2 + O2 -> H2O")
→ {"equation": {"status": "MISMATCH",
"detail": "balances as: 2 H2 + O2 -> 2 H2O"},
"balanced_form": "2 H2 + O2 -> 2 H2O",
"balanced_coefficients": [2, 1, 2]}Substitutes unit expressions for symbols, converts both sides to base SI units (kg, m, s, A, K, mol, cd), compares unit signatures. Conservation arithmetic with named-law profiles.
verify_physics_dimensional(
equation="F = m * a",
symbols={"F": "newton", "m": "kilogram", "a": "meter/second**2"})
→ {"status": "CONFIRMED", "detail": "both sides reduce to kg·m/s²"}
verify_physics_conservation(
before={"KE": 5.0, "PE": 10.0},
after ={"KE": 8.0, "PE": 7.0},
law="energy")
→ {"status": "CONFIRMED",
"detail": "energy conserved: total 15.0 → 15.0 (rel 0.00e+00)"}
verify_physics({"dimensional": {...}, "conservation": {...}})
→ {"dimensional": {...}, "conservation": {...}} # umbrella runs bothSympy-based verification across nine modes: equality, derivative, integral, limit, solve, matrix, inequality, series, ODE.
verify_mathematics("matrix",
{"matrix": [[1, 2], [3, 4]],
"claim_type": "determinant",
"claimed_value": -2})
→ {"status": "CONFIRMED",
"detail": "determinant: actual=-2, claimed=-2"}
verify_mathematics("ode",
{"ode": "Derivative(y(x),x) - y(x)",
"claimed_solution": "exp(x)"})
→ {"status": "CONFIRMED",
"detail": "y(x)=exp(x) satisfies the ODE"}
verify_mathematics("series",
{"term": "1/2**k", "start": 0, "end": "oo", "claimed_sum": 2})
→ {"status": "CONFIRMED", "detail": "computed=2, claimed=2"}Recompute p-values from raw inputs across twelve test types. Multiple-comparisons correction. Confidence-interval bound recomputation. Use the verify_statistics umbrella to dispatch automatically.
| Test | Inputs |
|---|---|
| two_sample_t | n1, n2, mean1, mean2, sd1, sd2 |
| one_sample_t | n, mean, sd, mu0 |
| paired_t | n, mean_diff, sd_diff (or paired1/paired2) |
| z | z, tail |
| chi2 | statistic, df |
| f | statistic, df1, df2 |
| one_proportion_z | n, successes (or phat), p0 |
| two_proportion_z | n1, n2, successes1, successes2 |
| fisher_exact | 2×2 table |
| mannwhitney | x, y |
| wilcoxon_signed_rank | x, y (or d) |
| regression_coefficient_t | beta, se, n, k |
verify_statistics_pvalue({
"test": "paired_t", "n": 20,
"mean_diff": 0.5, "sd_diff": 1.0,
"tail": "two", "claimed_p": 0.0375
})
→ {"status": "CONFIRMED",
"detail": "claimed p=0.0375, recomputed p=0.0375 (diff 4e-05)"}
verify_statistics({"pvalue": {...}, "multiple_comparisons": {...}})
→ {"pvalue": {...}, "multiple_comparisons": {...}} # umbrellaStatic termination scan (catches while True: without break, unguarded recursion). Functional correctness via restricted-namespace execution. Runtime complexity via log-log slope fit. Space complexity via tracemalloc. Run-twice determinism check.
verify_computer_science(
code="def lsum(a):\n s = 0\n for x in a: s += x\n return s",
function_name="lsum",
test_cases=[{"args": [[1,2,3]], "expected": 6}],
determinism_trials=3)
→ {"static_termination": {"status": "CONFIRMED"},
"functional_correctness": {"status": "CONFIRMED"},
"determinism": {"status": "CONFIRMED",
"detail": "all cases identical across 3 trials"}}Replicate count, orthogonal assay diversity, dose-response monotonicity, sample-size adequacy via power calculation. Hardy-Weinberg consistency, primer Tm/GC sanity, molarity arithmetic, Mendelian-ratio chi-squared.
verify_biology(
hardy_weinberg={"counts": [490, 420, 90]})
→ {"checks": [{"status": "CONFIRMED",
"detail": "counts consistent with HWE (chi2=0.000, p=1)"}]}
verify_biology(
mendelian={"observed": [315, 108, 101, 32],
"expected_ratio": [9, 3, 3, 1]})
→ {"checks": [{"status": "CONFIRMED",
"detail": "consistent with 9:3:3:1 (chi2=0.470, p=0.926)"}]}Structural completeness of decision packets: title, scope, red_items, floor_items, way_path, execution_steps, witnesses. Per-domain profiles add domain-specific required fields.
| Domain | Required (in addition to base) | Recommended |
|---|---|---|
| governance | — | scripture_anchor |
| business | officers, fiduciary_basis | dollar_amount, risk_assessment |
| household | budget_category, affected_dependents | time_horizon, alternatives_considered |
| education | affected_cohort, learning_objective | accommodation_plan, policy_reference |
| church | elder_signoff, scripture_anchor | congregation_impact, prayer_record |
Sometimes you want only the structural check, not the full pipeline.
attest_red(packet) # RED gate only — domain validator output
attest_floor(packet) # FLOOR gate only — Scripture-anchor coverage