{"schema":"scorecompute.engine-examples.v1","recorded_on":"2026-11-02","endpoint":"https://scorecompute.com/mcp","service_release":"0.17.1","note":"Each published example called once through the public MCP endpoint. response_sha256 covers the response serialized as sorted-key compact UTF-8 JSON. Elapsed times vary between runs. A recorded response shows what the tool returned for these inputs; it does not certify the model or other inputs.","engines":{"analyze_chess_game":{"arguments":{"positions":[{"fen":"rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1","played":"e4"},{"fen":"rnbqkbnr/pppppppp/8/8/4P3/8/PPPP1PPP/RNBQKBNR b KQkq - 0 1","played":"e5"},{"fen":"rnbqkbnr/pppp1ppp/8/4p3/4P3/8/PPPP1PPP/RNBQKBNR w KQkq - 0 2","played":"Nf3"},{"fen":"rnbqkbnr/pppp1ppp/8/4p3/4P3/5N2/PPPP1PPP/RNBQKB1R b KQkq - 1 2","played":"Nc6"},{"fen":"r1bqkbnr/pppp1ppp/2n5/4p3/4P3/5N2/PPPP1PPP/RNBQKB1R w KQkq - 2 3","played":"Bb5"},{"fen":"r1bqkbnr/pppp1ppp/2n5/1B2p3/4P3/5N2/PPPP1PPP/RNBQK2R b KQkq - 3 3","played":"a6"}],"depth":8},"response_sha256":"09e573a8a3e6fdea8f6d012fb1f1accb593258e599aa041f9363b0a223752d71","response":{"positions":6,"depth":8,"engine_name":"Stockfish (stockfish)","match_rate":0.6666666666666666,"average_loss_cp":3.3333333333333335,"big_losses":0,"verdict":"zone_grise","reasons":["Correspondance avec le premier choix du moteur : 67 % (profondeur 8). Perte moyenne : 3 centipions, dont 0 coup(s) au-delà de 300.","Un signal statistique n’est pas une preuve : profondeur limitée, petit échantillon et choix humains excellents se ressemblent."],"rows":[{"fen":"rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1","played_uci":"e2e4","engine_best":"e2e4","matches":true,"best_score_cp":25,"played_score_cp":26,"loss_cp":0},{"fen":"rnbqkbnr/pppppppp/8/8/4P3/8/PPPP1PPP/RNBQKBNR b KQkq - 0 1","played_uci":"e7e5","engine_best":"c7c5","matches":false,"best_score_cp":-30,"played_score_cp":-24,"loss_cp":0},{"fen":"rnbqkbnr/pppp1ppp/8/4p3/4P3/8/PPPP1PPP/RNBQKBNR w KQkq - 0 2","played_uci":"g1f3","engine_best":"g1f3","matches":true,"best_score_cp":34,"played_score_cp":26,"loss_cp":8},{"fen":"rnbqkbnr/pppp1ppp/8/4p3/4P3/5N2/PPPP1PPP/RNBQKB1R b KQkq - 1 2","played_uci":"b8c6","engine_best":"b8c6","matches":true,"best_score_cp":-37,"played_score_cp":-39,"loss_cp":2},{"fen":"r1bqkbnr/pppp1ppp/2n5/4p3/4P3/5N2/PPPP1PPP/RNBQKB1R w KQkq - 2 3","played_uci":"f1b5","engine_best":"b1c3","matches":false,"best_score_cp":39,"played_score_cp":29,"loss_cp":10},{"fen":"r1bqkbnr/pppp1ppp/2n5/1B2p3/4P3/5N2/PPPP1PPP/RNBQK2R b KQkq - 3 3","played_uci":"a7a6","engine_best":"a7a6","matches":true,"best_score_cp":-29,"played_score_cp":-29,"loss_cp":0}],"elapsed_ms":943.781058,"method":"Chaque position est évaluée par Stockfish (UCI, profondeur demandée) : meilleur coup et évaluation. Le coup joué est comparé au premier choix et sa perte en centipions est mesurée. Les seuils v0.1 (correspondance ≥ 80 % et perte ≤ 40) restent des conventions à calibrer — aucun verdict de triche, seulement un profil statistique.","engine":"rust-cpu+stockfish","provenance":{"tool":"analyze_chess_game","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"analyze_kinematics":{"arguments":{"angular_speed_deg_per_s":1,"claimed_distance_km":10,"claimed_speed_kmh":600},"response_sha256":"c0862dc571d6214831e2537aeca943fdc3730b574e1e1d660b610b30f0cf6d4a","response":{"angular_speed_deg_per_s":1,"angular_speed_arcmin_per_s":60,"distance_min_km":0.01,"distance_max_km":400000,"minimum_speed_kmh_at_min_distance":0.6283185307179587,"maximum_speed_kmh_at_max_distance":25132741.228718344,"hypotheses":[{"name":"ballon stratosphérique","max_speed_kmh":150,"max_distance_km":2.38732414637843},{"name":"drone civil","max_speed_kmh":250,"max_distance_km":3.9788735772973833},{"name":"avion de ligne","max_speed_kmh":950,"max_distance_km":15.119719593730055},{"name":"avion de chasse","max_speed_kmh":2500,"max_distance_km":39.78873577297384},{"name":"Lune (vitesse orbitale)","max_speed_kmh":3680,"max_distance_km":58.56901905781748},{"name":"station spatiale (ISS)","max_speed_kmh":27600,"max_distance_km":439.26764293363107},{"name":"satellite en orbite basse","max_speed_kmh":28000,"max_distance_km":445.63384065730696}],"claim":{"distance_km":10,"claimed_speed_kmh":600,"minimum_speed_kmh":628.3185307179587,"verdict":"contredit","reasons":["À 10 km, cette vitesse angulaire impose au moins 628 km/h en déplacement transversal ; la vitesse revendiquée (600 km/h) est inférieure.","Hypothèse d’un déplacement transversal : toute composante dans l’axe de visée ne ferait qu’augmenter la vitesse nécessaire."]},"elapsed_ms":0.270461,"method":"Vitesse transversale minimale v = ω × d (ω en rad/s) ; aucun jugement d’origine. Les profils (ballon, drone, avion, satellite) sont des bornes de vitesse documentées : si la vitesse angulaire observée est réelle, elle plafonne la distance à laquelle chaque type d’objet peut se trouver. Un déplacement non transversal exige davantage de vitesse.","engine":"rust-cpu","provenance":{"tool":"analyze_kinematics","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"audit_statistics":{"arguments":{"n":10,"mean":3.48,"decimals":2,"min_value":1,"max_value":5},"response_sha256":"182bc60b036a11d9b1552fdebfeeca4a5ad5db3bfd24fbcdf856768f261b03e1","response":{"n":10,"min_value":1,"max_value":5,"decimals":2,"sum_needed":34.8,"sum_round":35,"mean_reported":3.48,"mean_nearest_attainable":3.5,"mean_consistent":false,"sd_reported":null,"sd_attainable_min":null,"sd_attainable_max":null,"sd_nearest_attainable":null,"sd_consistent":null,"verdict":"inconsistant","issues":["Aucune somme entière ne donne la moyenne 3.48 : la plus proche atteignable est 3.50 (écart 0.0200)."],"elapsed_ms":0.008365000000000001,"method":"Contrôles nécessaires GRIM (moyenne) et GRIMMER (écart-type d’échantillon, diviseur n−1) pour des valeurs entières bornées. Toutes les sommes compatibles avec les intervalles de demi-arrondi sont examinées ; les sommes des carrés sont filtrées par leurs bornes exactes et leur parité. Consistant signifie que ces filtres ne détectent pas d’incohérence : ce n’est pas une preuve d’existence d’un jeu de données. sd_nearest_attainable désigne le candidat le plus proche passant ces filtres. Les arrondis aux frontières sont acceptés dans les deux sens. Une incohérence ne prouve jamais une fraude.","engine":"rust-cpu","provenance":{"tool":"audit_statistics","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"check_arithmetic":{"arguments":{"expression":"a+b","values":[{"name":"a","value":0.1},{"name":"b","value":0.2}],"claimed_value":0.3},"response_sha256":"34b3582ea97946f4f1df490115441f177f372eefba3246ba2c204c2862d5a3fe","response":{"contract_version":"0.2.0","engine":"rust-cpu","method":"Checked reduced i128 rational arithmetic and exact comparison against a rational absolute/relative tolerance. Unsupported or overflowing exact evaluation is reported as an unvalidated float64 estimate with an undetermined verdict. SHA-256 binds the versioned calculation payload; it is not a signature.","expression":"a+b","claimed_value":0.3,"computed_value":0.3,"exact_value":"3/10","exact_supported":true,"comparison":"exact_rational","absolute_error":0,"relative_error":0,"tolerance_absolute":0,"tolerance_relative":1e-09,"effective_tolerance":3e-10,"verdict":"consistent","scope":{"decimal_source":"Numeric JSON fields are decoded to binary64, then interpreted through the decoded value's shortest round-trip decimal text; the original JSON token is not retained. Their magnitude is limited to 9007199254740991. Expression literals retain their written decimal value when representable as an i128 rational.","exact_range_bits":127,"functions":["sqrt","abs","exp","ln","log10","sin","cos","tan","asin","acos","atan","floor"],"tolerance_rule":"Consistent when absolute_error <= tolerance_absolute + tolerance_relative * |computed_value|.","limits":["Exact arithmetic can be unavailable when an intermediate i128 operation overflows, an input decimal is not representable, or an integer power exceeds 64. The verdict is then undetermined.","Float64 fallback is an estimate, not a certified enclosure. Cancellation, libm error and lost precision are not bounded here; no consistent or inconsistent verdict is issued on that path.","The checker validates arithmetic, not units, the model's meaning or the claimant's intent."]},"digest":{"payload_version":"scorecompute.check_arithmetic.result.v2","sha256":"8c77785639975e82c7981d63cff6118bb0cd83fd7e592dabb75840232f6116df"},"assumptions":["Operators + - * /, negation, abs, perfect-square sqrt and integer powers are exact only while all checked rational operations succeed.","floor and transcendental functions produce estimates only and an undetermined verdict. Non-perfect-square sqrt also uses this estimate-only path.","x^y with a non-integer exponent and 0^0 follow float64 powf semantics."],"notes":["The digest is an integrity aid for a signing layer; it is not a signature and does not prove that the expression matches the claimant's intent.","Relative error is measured against the displayed computed value; it is null when that value is zero or the ratio is outside the finite output range. It is descriptive, not an error bound.","An exact expression result does not ensure an exact comparison: claim and tolerances must also fit the checked rational path. The displayed numeric value may be rounded; exact_value is authoritative when present."],"statement":"Claim 0.3 against computed 0.3: consistent. Comparison exact_rational, effective tolerance 3e-10.","elapsed_ms":1.548638,"provenance":{"tool":"check_arithmetic","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"check_ephemeris":{"arguments":{"date_utc":"2026-09-30T23:00:00Z","latitude":48.85,"longitude":2.35,"object":"lune","claimed_azimuth_deg":81,"claimed_elevation_deg":27.1,"tolerance_deg":2},"response_sha256":"13aeab2240604a0832efe5bb1b418bba9b87ada8dba716e5359d3066cdbe732e","response":{"date_utc":"2026-09-30T23:00:00Z","latitude":48.85,"longitude":2.35,"object":"lune","sun":{"azimuth_deg":346.0296136146129,"elevation_deg":-43.426662859964594},"moon":{"azimuth_deg":91.36845516917907,"elevation_deg":35.82586596164553,"illumination":0.7820815808469797,"phase":"gibbeuse décroissante","distance_km":369785.5308439496,"waxing":false},"check":{"claimed_azimuth_deg":81,"claimed_elevation_deg":27.1,"separation_deg":12.408802949370415,"allowed_deg":2.3,"verdict":"contredit","reasons":["Écart angulaire de 12.4° entre la position revendiquée et l’éphéméride."]},"elapsed_ms":0.20094599999999999,"method":"Éphéméride : Soleil (NOAA) et Lune (Meeus ch. 47 abrégé, parallaxe topocentrique pour un observateur WGS84 au niveau de la mer), réfraction standard incluse. Distance lunaire géocentrique. Séparation angulaire sphérique ; tolérance = tolérance revendiquée + marge conventionnelle de 0,3°, qui n’est pas une borne d’erreur certifiée. Relief, altitude et météo réels non modélisés ; positions près de l’horizon à traiter avec prudence. Le moteur compare des positions, il ne conclut jamais à la nature de l’objet observé.","engine":"rust-cpu","provenance":{"tool":"check_ephemeris","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"check_shadow_track":{"arguments":{"date_utc":"2026-06-21T08:00:00Z","latitude":48.85,"longitude":2.35,"samples":[{"minutes":0,"azimuth_deg":277.56},{"minutes":30,"azimuth_deg":284},{"minutes":60,"azimuth_deg":291.16},{"minutes":90,"azimuth_deg":299.32},{"minutes":120,"azimuth_deg":308.82},{"minutes":150,"azimuth_deg":320.01}],"tolerance_deg":5},"response_sha256":"59508009a1a1e6565278775795c52165d096a8df7c79edfbe0cd00faf7e08cd7","response":{"date_utc":"2026-06-21T08:00:00Z","latitude":48.85,"longitude":2.35,"samples":6,"window_minutes":150,"sun_elevation_min_deg":38.23248413696972,"expected_slope_deg_per_hour":16.84962443650897,"measured_slope_deg_per_hour":16.849714285714278,"speed_ratio":1.000005332415903,"mean_offset_deg":-0.0014160272668372424,"max_abs_residual_deg":0.004564658247659281,"residuals":[{"minutes":0,"measured_deg":277.56,"expected_deg":277.5597010438408,"residual_deg":0.0002989561592130485},{"minutes":30,"measured_deg":284,"expected_deg":284.0020273975808,"residual_deg":-0.002027397580775414},{"minutes":60,"measured_deg":291.16,"expected_deg":291.1645646582477,"residual_deg":-0.004564658247659281},{"minutes":90,"measured_deg":299.32,"expected_deg":299.3225735165607,"residual_deg":-0.0025735165606874943},{"minutes":120,"measured_deg":308.82,"expected_deg":308.8165707721576,"residual_deg":0.003429227842389082},{"minutes":150,"measured_deg":320.01,"expected_deg":320.0130587752135,"residual_deg":-0.003058775213503395}],"verdict":"compatible","reasons":["Rotation cohérente (16.85°/h contre 16.85°/h, écart moyen -0.00°)."],"elapsed_ms":0.30106099999999997,"method":"L’azimut d’ombre attendu (soleil + 180°) est calculé à chaque instant par l’éphéméride, puis comparé à l’azimut mesuré : pente horaire, rapport de vitesse (révèle un time-lapse), décalage moyen (révèle un lieu ou une date différents). 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141.42 Hz (C#3 +35 cents); overtone ratios 1.000, 1.581, 1.581.","assumptions":["Ideal membrane: −Δu = λu on the polygon. fixed: u = 0 on the edge (a drumhead, a TM waveguide). free: zero normal derivative (a TE waveguide, a 2-D acoustic cavity).","Uniform tension and density; stiffness, air loading, damping and nonlinearity are not modelled, so a real drum differs, often by several percent.","eigenvalue_upper_bound is the finest P1 finite-element value: an upper bound of the exact eigenvalue of this idealized problem, up to rounding and the 1e-12 solver tolerance.","eigenvalue is a Richardson extrapolation over three nested meshes with the observed order; its error estimate is not a rigorous bound.","Nodal domains are counted exactly for the piecewise-linear mode on the finest mesh; a nodal-line crossing can merge two domains there, and for repeated eigenvalues the count depends on the basis chosen inside the eigenspace.","frequency_hz = wave_speed × √eigenvalue / 2π; notes use equal temperament with A4 = 440 Hz."],"method":"Ear-clipping triangulation with Delaunay edge flips; three nested uniform refinements; P1 finite elements with consistent mass; reverse Cuthill–McKee ordering and profile Cholesky; block subspace iteration with Rayleigh–Ritz and warm starts prolongated between levels; Richardson extrapolation with the observed convergence order.","engine":"rust-cpu","elapsed_ms":281.961241,"provenance":{"tool":"hear_the_shape","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"kepler_stability":{"arguments":{"a_min_au":2.6,"a_max_au":2.8,"e_min":0,"e_max":0.05,"n_a":4,"n_e":2,"duration_yr":150,"steps_per_year":32,"initial_phase_deg":0,"max_work_units":200000},"response_sha256":"ace09f733ad533209954acb7e6e88543156a8d39f4b7eeb641c7004d23050ea1","response":{"contract_version":"0.2.0","engine":"rust-cpu","method":"Yoshida fourth-order composition of a Wisdom-Holman kick-drift-kick step with universal-variable Kepler drift; two-particle finite-time Lyapunov exponent with Benettin renormalization; Jacobi-constant drift diagnostic.","system":{"mass_ratio":0.0009537,"jupiter_semi_major_au":5.2044,"jupiter_period_yr":11.872877919914108,"sun_gm_au3_yr2":39.44076703748816,"jupiter_gm_au3_yr2":0.03765056686927568,"total_work_units":38400,"executed_work_units":38400,"jacobi_warning_threshold":0.001,"work_unit_cap":200000},"grid":{"n_a":4,"n_e":2,"points_total":8,"points_evaluated":8,"low_sensitivity":8,"moderate_sensitivity":0,"high_sensitivity":0,"jupiter_crossing":0,"escaped":0,"close_encounter":0,"kepler_failed":0,"numerical_warning":0,"not_evaluated":0,"a_min_au":2.6,"a_max_au":2.8,"e_min":0,"e_max":0.05},"points":[{"a_au":2.6,"e_init":0.05,"status":"low_sensitivity","steps":4800,"integrated_years":150,"stop_reason":"window_complete","e_max":0.05,"lyapunov_per_yr":0.046454185904533304,"stretch_log":6.968127885679996,"jacobi_drift":2.8167086254961025e-10,"crossing_year":null},{"a_au":2.6666666666666665,"e_init":0.05,"status":"low_sensitivity","steps":4800,"integrated_years":150,"stop_reason":"window_complete","e_max":0.05,"lyapunov_per_yr":0.04571462830517979,"stretch_log":6.857194245776968,"jacobi_drift":2.674518623093432e-10,"crossing_year":null},{"a_au":2.7333333333333334,"e_init":0.05,"status":"low_sensitivity","steps":4800,"integrated_years":150,"stop_reason":"window_complete","e_max":0.05,"lyapunov_per_yr":0.046077588221558906,"stretch_log":6.911638233233836,"jacobi_drift":2.5421227013011905e-10,"crossing_year":null},{"a_au":2.8,"e_init":0.05,"status":"low_sensitivity","steps":4800,"integrated_years":150,"stop_reason":"window_complete","e_max":0.05,"lyapunov_per_yr":0.04621842474656874,"stretch_log":6.93276371198531,"jacobi_drift":2.4223025346648024e-10,"crossing_year":null},{"a_au":2.6,"e_init":0,"status":"low_sensitivity","steps":4800,"integrated_years":150,"stop_reason":"window_complete","e_max":0.0023541092432106977,"lyapunov_per_yr":0.045727715800346846,"stretch_log":6.859157370052027,"jacobi_drift":2.316470639144647e-10,"crossing_year":null},{"a_au":2.6666666666666665,"e_init":0,"status":"low_sensitivity","steps":4800,"integrated_years":150,"stop_reason":"window_complete","e_max":0.0028616029329161102,"lyapunov_per_yr":0.0454749902999167,"stretch_log":6.8212485449875055,"jacobi_drift":2.201047804993801e-10,"crossing_year":null},{"a_au":2.7333333333333334,"e_init":0,"status":"low_sensitivity","steps":4800,"integrated_years":150,"stop_reason":"window_complete","e_max":0.0035093881927695763,"lyapunov_per_yr":0.04522392662868697,"stretch_log":6.783588994303045,"jacobi_drift":2.0971270650898842e-10,"crossing_year":null},{"a_au":2.8,"e_init":0,"status":"low_sensitivity","steps":4800,"integrated_years":150,"stop_reason":"window_complete","e_max":0.004357133912864774,"lyapunov_per_yr":0.04498154397442146,"stretch_log":6.7472315961632185,"jacobi_drift":2.003986822835424e-10,"crossing_year":null}],"map_text":["....","...."],"assumptions":["Motion is confined to Jupiter's orbital plane (2D).","Only the Sun and Jupiter are modelled; other planets, tides and collisions are absent.","The fixed-Sun heliocentric reduction is used: Jupiter follows a circular orbit and the perturbation includes the indirect term.","The particle starts at perihelion, prograde, at initial_phase_deg relative to Jupiter phase zero.","Units: astronomical unit and year, with GM_total = 4*pi^2 AU^3/yr^2 (Kepler's third law).","Sensitivity: two-particle finite-time logarithmic growth rate; phase-space Benettin renormalization, initial 1e-8 AU position offset. Positive finite-time rates occur even for integrable Kepler orbits."],"notes":["Fixed-step approximation. Both trajectories are guarded at every Yoshida substep at distance <=0.01 AU; these guards are not event-localized physical encounters and can miss approaches between samples.","Bands use stretch_log - ln(integrated_years / 1 yr): <2.5 low, [2.5,4.5) moderate, >=4.5 high. They depend on initial geometry, perturbation direction and elapsed time, and do not diagnose chaos.","crossing_year is first sampled radial overlap of the current bound osculating ellipse with Jupiter's +/-2% orbital-radius annulus, including t=0. It is not a collision or encounter time; unbound conics are excluded.","Jacobi drift is the maximum relative change over initial and every completed outer step, including final/last valid state. Drift >1e-3 or unavailable diagnostics stops as numerical_warning; a smaller value is not certification.","total_work_units reserves full requested per-cell step budgets, including cells stopped early. executed_work_units counts completed outer steps; split stages and failed attempts are not separate work units.","integrated_years covers completed outer steps only; rejected partial steps are rolled back. stop_reason distinguishes completion, work budget, stretch limit, encounter guards, escape and numerical failure. Fractional durations round down to a whole step.","Nonfinite or unrepresentable (>1e300 absolute) optional diagnostics are null, never clamped. The per-cell eccentricity maximum includes the initial state. Narrow resonances and unresolved encounters require a different investigation."],"statement":"Planar circular restricted Sun-Jupiter model over 150 yr: 8 of 8 cells evaluated, 0 high-sensitivity, 0 moderate-sensitivity, 0 radial-overlap, 0 escaped. 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Affine temperature units (°C, °F) are refused; use K.","The Monte Carlo interval is probabilistically symmetric; the shortest interval is reported separately."],"coverage":0.95,"samples":200000,"seed":7,"method":"First-order GUM propagation (JCGM 100:2008) with exact forward-mode derivatives; Monte Carlo propagation (JCGM 101:2008) with SplitMix64, Box–Muller and 10 independently seeded blocks; JCGM 101 §8 validation of the first-order interval; block spread checked against the 2-significant-digit numerical tolerance.","engine":"rust-cpu","elapsed_ms":12.419601,"provenance":{"tool":"propagate_uncertainty","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"route_optimizer":{"arguments":{"metric":"euclidean_km","points":[{"x":0,"y":0},{"x":1,"y":0},{"x":1,"y":1},{"x":0,"y":1},{"x":0.5,"y":0.5}],"return_to_start":true,"time_budget_ms":1000},"response_sha256":"a6496001f48981809f17b5d143c7d914782c7aef8024a12ad12868bca064f312","response":{"contract_version":"0.1.0","metric":"euclidean_km","unit":"km","points":5,"return_to_start":true,"order":[0,4,3,2,1],"tour_legs":[{"from_index":0,"to_index":4,"distance_km":0.7071067811865476},{"from_index":4,"to_index":3,"distance_km":0.7071067811865476},{"from_index":3,"to_index":2,"distance_km":1},{"from_index":2,"to_index":1,"distance_km":1},{"from_index":1,"to_index":0,"distance_km":1}],"total_distance_km":4.414213562373095,"upper_bound_km":4.414213562373095,"exact":true,"method":"held_karp_exact","stop_reason":"exact_search_completed","greedy_reference_km":4.414213562373095,"improvement_vs_greedy_pct":0,"work_units":72,"work_limit":4000000,"elapsed_ms":0.007344000000000001,"limitations":["Ni trafic, ni routes, ni fenêtres horaires, ni capacité de véhicule.","Aucune durée de trajet n'est estimée : seules des distances sont calculées.","La borne de temps est coopérative et dépend de la charge de la machine.","exact=true uniquement si la recherche exhaustive est allée au bout dans les bornes.","L'exactitude concerne la recherche combinatoire sur des distances calculées en f64, pas une preuve en arithmétique réelle.","La convergence 2-opt utilise une tolérance absolue de 1e-12 km ; aucune garantie globale pour n > 13.","upper_bound_km est le coût de la tournée produite ; aucun écart à l'optimum n'est revendiqué."],"provenance":{"tool":"route_optimizer","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"scan_counterexample":{"arguments":{"expression":"x ^ 2","relation":"le","bound":4,"variables":[{"name":"x","min":-3,"max":3,"steps":7}]},"response_sha256":"d8f587005e7d998e8e1e4eec46bfe245ba9d1198b358be2ba84da9dc2ec5f1c3","response":{"contract_version":"0.2.0","engine":"rust-cpu","method":"Deterministic lexicographic grid scan (last variable fastest), bounded local expression parser, float64 evaluation and a propagated numerical screening guard. Undefined intermediates remain undefined. The guard is not a certified interval or formal proof.","expression":"x ^ 2","relation":"le","bound":4,"tolerance":0,"grid_total":7,"evaluated":1,"finite_evaluations":1,"undefined_evaluations":0,"uncertain_evaluations":0,"complete":false,"stopped_early":true,"stop_reason":"counterexample_limit","counterexamples":[{"values":[{"name":"x","value":-3}],"expression_value":9,"margin":5,"comparison_guard":1.5987211554602254e-14}],"first_counterexample":{"values":[{"name":"x","value":-3}],"expression_value":9,"margin":5,"comparison_guard":1.5987211554602254e-14},"verdict":"counterexamples_found","work_units":1,"limits":["Returned counterexamples are numerical witnesses requiring independent verification, not formal mathematical proofs. Margin is measured against the declared bound; comparison_guard applies at bound +/- tolerance.","Absence of a counterexample covers only the evaluated grid cells, at the declared steps; it is not a proof over the continuous box or elsewhere.","Cells whose guarded result overlaps the tolerance boundary are uncertain. The float64/libm guard is a screening heuristic, not a certified rounding-error bound; unmodelled numerical error remains possible.","This scan does not replace domain-specific stress tests (observation, stability, shadow tracks)."],"assumptions":["Variables use min + (max-min) * i/(steps-1), with endpoints pinned to the supplied bounds. Interior roundoff is screened; input bounds are the supplied float64 numbers.","The claim is a single scalar comparison with one bound and one tolerance; no chains or multi-claims.","Non-finite intermediate or final evaluations are counted as undefined. Finite evaluations include uncertain cells. A complete scan means every grid cell was visited, not that every value was defined or the continuous domain was checked."],"notes":["Grid order is fixed and documented so any verifier can reproduce the first counterexample.","Raise max_evaluations to scan more cells; the budget bounds total work, never the claim.","work_units counts visited cells, not CPU operations. Expressions have at most 256 nodes and 64 nesting levels; no dynamic code, recursion or external calls are accepted."],"statement":"Claim x ^ 2 <= 4 with tolerance 0e0: scanned 1 of 7 grid cells, found 1 numerical witnesses; 0 undefined and 0 numerically uncertain evaluations. First: x=-3 gives 9 (margin 5e0 beyond the bound).","elapsed_ms":0.478834,"provenance":{"tool":"scan_counterexample","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"screen_wash_trading":{"arguments":{"trades":[{"ts_s":1000,"price":100,"volume":10},{"ts_s":1010,"price":100.04,"volume":10},{"ts_s":1020,"price":100,"volume":10},{"ts_s":1030,"price":100.04,"volume":10},{"ts_s":1040,"price":100,"volume":10},{"ts_s":1050,"price":100.04,"volume":10},{"ts_s":1060,"price":100,"volume":10},{"ts_s":1070,"price":100.04,"volume":10},{"ts_s":1080,"price":100,"volume":10},{"ts_s":1090,"price":100.04,"volume":10},{"ts_s":1100,"price":100,"volume":10},{"ts_s":1110,"price":100.04,"volume":10},{"ts_s":1120,"price":100,"volume":10},{"ts_s":1130,"price":100.04,"volume":10},{"ts_s":1140,"price":100,"volume":10},{"ts_s":1150,"price":100.04,"volume":10},{"ts_s":1160,"price":100,"volume":10},{"ts_s":1170,"price":100.04,"volume":10},{"ts_s":1180,"price":100,"volume":10},{"ts_s":1190,"price":100.04,"volume":10},{"ts_s":1200,"price":100,"volume":10},{"ts_s":1210,"price":100.04,"volume":10},{"ts_s":1220,"price":100,"volume":10},{"ts_s":1230,"price":100.04,"volume":10},{"ts_s":1240,"price":100,"volume":10},{"ts_s":1250,"price":100.04,"volume":10},{"ts_s":1260,"price":100,"volume":10},{"ts_s":1270,"price":100.04,"volume":10},{"ts_s":1280,"price":100,"volume":10},{"ts_s":1290,"price":100.04,"volume":10}],"window_s":3600,"price_band_pct":0.25},"response_sha256":"d1080e759fa6f6aa010ed6ff952e2a0877cdcaa4e58f73acb2afc7850b78cc1c","response":{"trades":30,"window_s":3600,"price_band_pct":0.25,"price_min":100,"price_max":100.04,"price_span_pct":0.039992001599686314,"round_trips":15,"recycled_volume":150,"total_volume":300,"recycled_ratio":0.5,"mean_interval_s":10,"verdict":"a_examiner","reasons":["15 aller-retours de prix dans la bande de 0.25 % sur la fenêtre de 3600 s, soit 50 % du volume total recyclé (30 échanges, 10 s en moyenne entre deux).","Des volume(s) ré-échangés à des prix quasi identiques en boucle sont un motif à examiner — pas une preuve : market makers, bots de arbitrage et marchés calmes produisent des profils proches."],"elapsed_ms":0.255695,"method":"Appariement glissant : deux échanges de sens supposé opposé (prix de retour dans une bande serrée, dans une fenêtre courte) forment un aller-retour ; chaque échange n’est compté qu’une fois. L’outil mesure un profil statistique de recyclage, jamais une intention ni une identité.","engine":"rust-cpu","provenance":{"tool":"screen_wash_trading","server":"scorecompute","client":{"name":"scorecompute-docs-recording","version":"1.0"},"identity_source":"MCP clientInfo (self-reported)","model":null}}},"shape_the_sound":{"arguments":{"target_ratios":[1.25,1.5],"vertices":10,"tolerance_cents":5,"max_evaluations":300,"seed":1,"fundamental_hz":196,"wave_speed":120,"include_mode_shapes":true},"response_sha256":"012ff0d64aa5a68c5e25f09f45fe8da3bf99c05d8e4453aee3d80757e4092e49","response":{"contract_version":"0.3.0","verdict":"achieved","feasibility":{"verdict":"not_excluded","domain":"Connected planar membrane with uniform tension and density and a fixed (Dirichlet) edge. These exclusions do not cover free edges, disconnected drums or nonuniform membranes.","tolerance_cents":5,"windows":[[1.2463950666682364,1.2536153598367088],[1.4956740800018837,1.5043384318040507]],"exact_target_excluded":false,"checks":[{"theorem":"simple_fundamental","reference":"The first Dirichlet eigenvalue of a connected domain is simple, so λ2 > λ1 (M. S. Ashbaugh, Isoperimetric and universal inequalities for eigenvalues, arXiv:math/0008087, §1.1).","statement":"f2/f1 must exceed 1. Exact target 1.25; window [1.246395, 1.253615].","exact_target_excluded":false,"request_excluded":false},{"theorem":"ashbaugh_benguria","reference":"M. S. Ashbaugh and R. D. Benguria, Annals of Mathematics 135 (1992) 601–628: λ2/λ1 ≤ (j11/j01)², with equality for the disk (see arXiv:math/0008087, §2.3, eq. 2.16).","statement":"f2/f1 ≤ j11/j01 = 1.5933405057 for every such drum, the disk attaining it. Exact target 1.25; window [1.246395, 1.253615].","exact_target_excluded":false,"request_excluded":false},{"theorem":"yang_first_inequality","reference":"H. C. Yang (1991): Σ_{i≤k}(λ_{k+1}−λ_i)² ≤ (4/n) Σ_{i≤k} λ_i(λ_{k+1}−λ_i), n = 2 (S. Ilias and O. Makhoul, arXiv:1001.5102, eq. 1.4; M. S. Ashbaugh, arXiv:math/0008087).","statement":"k = 1: dimensionless violation margin Σ(Λ2−Λi)² − 2ΣΛi(Λ2−Λi), with Λ = λ/λ1 (the original residual divided by λ1²), is -0.808594 at the exact targets and at least -0.816432 over the whole tolerance box (positive means the inequality fails).","exact_target_excluded":false,"request_excluded":false},{"theorem":"yang_first_inequality","reference":"H. C. Yang (1991): Σ_{i≤k}(λ_{k+1}−λ_i)² ≤ (4/n) Σ_{i≤k} λ_i(λ_{k+1}−λ_i), n = 2 (S. Ilias and O. Makhoul, arXiv:1001.5102, eq. 1.4; M. S. 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10-vertex drum plays the ratios 1 : 1.25 : 1.5 within 5 cents according to a reanalysis on three refined meshes with the shared solver (worst estimated error 1.07 ± 0.66 cents; estimates, not rigorous bounds); fundamental estimated at 196.00 Hz (G3 +0 cents).","notes":[],"assumptions":["Ideal drumhead: −Δu = λu with a fixed edge, uniform tension and density; stiffness, air loading and damping are not modelled.","target_ratios are frequency ratios f_k/f_1 of the lowest modes counted with multiplicity, in ascending order; each is accepted within ±tolerance_cents.","proven_impossible is reported only when published theorems exclude every ratio combination inside the tolerance windows, for a connected planar membrane of uniform tension and density with a fixed edge; it does not depend on the search.","not_achieved reports the best polygon found by a bounded search; it is never a proof that no drum exists.","Achieved ratios come from Richardson-extrapolated eigenvalues of the shared hear_the_shape solver on three refined meshes, the same finite-element method as the search; uncertainty_cents propagates estimated discretization errors, which are not rigorous bounds.","With fundamental_hz, the drum is rescaled from the numerical estimate of its fundamental; the reported frequency is an estimate with the same numerical uncertainty.","The drum is a simple polygon; curved edges, holes and nonuniform membranes would allow other spectra."],"method":"Feasibility over the whole tolerance window from proven universal eigenvalue inequalities (simplicity of the fundamental, Ashbaugh–Benguria 1992, Yang 1991; exact box minimum for Yang). 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