{"query":"colony.optimize@v1","category":null,"matches":[{"product_id":"prod-colony","capability_id":"colony.optimize@v1","source_hub":"https://oracles.modelmarket.dev/family","source_hub_name":"AIMarket Oracle Family","name":"colony.optimize","evidence":{"kind":"signed_catalogue","scope":"catalogue","signer":"https://oracles.modelmarket.dev/family","signer_public_key":"YkAOwWNbRFti2cqEzD6zfuI4OTLsGUoObpCmlwZqaTQ=","checked_at":"2026-11-07T06:49:15Z","checked_by":"https://modelmarket.dev"},"display_name":"colony.optimize","description":"Optimize a tour over >=3 2D points: nearest-neighbour + 2-opt. Returns the tour (a permutation), its length, an admissible lower bound (sum of each node's cheapest incident edge / 2), and gap = (length - lower_bound) / lower_bound. The gap is a certificate of how far from optimal the tour can possibly be. When coincident points make the lower bound 0 it certifies nothing, so gap is null (unknown) unless the tour length is also 0 (all points coincide -> provably optimal).","score":0.9838,"match_type":"exact","matched_concepts":["optimization"],"matched_terms":["optimize","optimal","optimizar","optimiser","colony"],"score_breakdown":{"lexical":1.0,"semantic":0.9632,"quality":0.6768},"input_independent":false,"price_per_call_usd":0.005,"access_mode":"paid","credits_eligible":false,"routed_price_usd":0.00505,"routing_fee_bps":100,"trust_score":0.5,"reputation_basis":"unobserved","observations_30d":0,"deliveries_30d":null,"p50_latency_ms":25,"publisher_id":null,"payout_address":"0x1218ff36C5d2e3B6A565CdB1A8B1AcCFc606Ad0a","seller_id":"AIMarket Oracle Family","seller_kind":"hub","stake_usd":null,"demo":false,"offerable":true,"route_status":"live","route_age_s":1091,"input_required":["points"],"input_hint":{"points":{"type":"array","description":"List of [x, y] coordinates (at least 3)."}}},{"product_id":"prod-gauss","capability_id":"gauss.field@v1","source_hub":"https://oracles.modelmarket.dev/family","source_hub_name":"AIMarket Oracle Family","name":"gauss.field","evidence":{"kind":"signed_catalogue","scope":"catalogue","signer":"https://oracles.modelmarket.dev/family","signer_public_key":"YkAOwWNbRFti2cqEzD6zfuI4OTLsGUoObpCmlwZqaTQ=","checked_at":"2026-11-07T06:49:15Z","checked_by":"https://modelmarket.dev"},"display_name":"gauss.field","description":"GP posterior over a query field. Fits the RBF kernel to (X, y) and returns the predictive mean and variance (and std) at every query point — the calibrated uncertainty band that collapses to the noise floor at observations and breathes out to the prior sigma_f^2 far from data.","score":0.7034,"match_type":"semantic","matched_concepts":["optimization"],"matched_terms":["optimize","optimal","optimizar","optimiser","v1"],"score_breakdown":{"lexical":0.0811,"semantic":0.9783,"quality":0.6735},"input_independent":false,"price_per_call_usd":0.006,"access_mode":"paid","credits_eligible":false,"routed_price_usd":0.00606,"routing_fee_bps":100,"trust_score":0.5,"reputation_basis":"unobserved","observations_30d":0,"deliveries_30d":null,"p50_latency_ms":25,"publisher_id":null,"payout_address":"0x1218ff36C5d2e3B6A565CdB1A8B1AcCFc606Ad0a","seller_id":"AIMarket Oracle Family","seller_kind":"hub","stake_usd":null,"demo":false,"offerable":true,"route_status":"live","route_age_s":1091,"input_required":["X","y","query"],"input_hint":{"X":{"type":"array","description":"Training inputs (n × d)."},"y":{"type":"array","description":"Training targets (n)."},"query":{"type":"array","description":"Query inputs (m × d) to predict at."}}},{"product_id":"prod-gauss","capability_id":"gauss.suggest@v1","source_hub":"https://oracles.modelmarket.dev/family","source_hub_name":"AIMarket Oracle Family","name":"gauss.suggest","evidence":{"kind":"signed_catalogue","scope":"catalogue","signer":"https://oracles.modelmarket.dev/family","signer_public_key":"YkAOwWNbRFti2cqEzD6zfuI4OTLsGUoObpCmlwZqaTQ=","checked_at":"2026-11-07T06:49:15Z","checked_by":"https://modelmarket.dev"},"display_name":"gauss.suggest","description":"Best next experiment by Expected Improvement. Given (X, y) and either an explicit candidate set or bounds+grid, fits the GP and ranks candidates by EI(x) = (mu - f_best - xi)·Phi(z) + std·phi(z). Returns the argmax point, its EI, and the full acquisition vector — a calibrated alternative to hand-tuned UCB / bandit exploration. Supports max or min goals.","score":0.7034,"match_type":"semantic","matched_concepts":["optimization"],"matched_terms":["optimize","optimal","optimizar","optimiser","v1"],"score_breakdown":{"lexical":0.0811,"semantic":0.9783,"quality":0.6735},"input_independent":false,"price_per_call_usd":0.006,"access_mode":"paid","credits_eligible":false,"routed_price_usd":0.00606,"routing_fee_bps":100,"trust_score":0.5,"reputation_basis":"unobserved","observations_30d":0,"deliveries_30d":null,"p50_latency_ms":25,"publisher_id":null,"payout_address":"0x1218ff36C5d2e3B6A565CdB1A8B1AcCFc606Ad0a","seller_id":"AIMarket Oracle Family","seller_kind":"hub","stake_usd":null,"demo":false,"offerable":true,"route_status":"live","route_age_s":1091,"input_required":["X","y"],"input_hint":{"X":{"type":"array","description":"Training inputs (n × d)."},"y":{"type":"array","description":"Training targets (n)."}}},{"product_id":"prod-gauss","capability_id":"gauss.verify@v1","source_hub":"https://oracles.modelmarket.dev/family","source_hub_name":"AIMarket Oracle Family","name":"gauss.verify","evidence":{"kind":"signed_catalogue","scope":"catalogue","signer":"https://oracles.modelmarket.dev/family","signer_public_key":"YkAOwWNbRFti2cqEzD6zfuI4OTLsGUoObpCmlwZqaTQ=","checked_at":"2026-11-07T06:49:15Z","checked_by":"https://modelmarket.dev"},"display_name":"gauss.verify","description":"Trustless replay: recompute the GP posterior at one or a few query points and check the claimed mean / variance match within a tolerance. Cheap; needs no trust in the oracle that produced the original field.","score":0.6936,"match_type":"semantic","matched_concepts":["optimization"],"matched_terms":["optimize","optimal","optimizar","optimiser","v1"],"score_breakdown":{"lexical":0.0811,"semantic":0.9632,"quality":0.6945},"input_independent":false,"price_per_call_usd":0.001,"access_mode":"paid","credits_eligible":false,"routed_price_usd":0.00101,"routing_fee_bps":100,"trust_score":0.5,"reputation_basis":"unobserved","observations_30d":0,"deliveries_30d":null,"p50_latency_ms":8,"publisher_id":null,"payout_address":"0x1218ff36C5d2e3B6A565CdB1A8B1AcCFc606Ad0a","seller_id":"AIMarket Oracle Family","seller_kind":"hub","stake_usd":null,"demo":false,"offerable":true,"route_status":"live","route_age_s":1091,"input_required":["X","y","query"],"input_hint":{"X":{"type":"array","description":"Training inputs (n × d)."},"y":{"type":"array","description":"Training targets (n)."},"query":{"type":"array","description":"Query inputs (m × d) to recompute at."}}},{"product_id":"prod-kantor","capability_id":"kantor.verify@v1","source_hub":"https://oracles.modelmarket.dev/family","source_hub_name":"AIMarket Oracle Family","name":"kantor.verify","evidence":{"kind":"signed_catalogue","scope":"catalogue","signer":"https://oracles.modelmarket.dev/family","signer_public_key":"YkAOwWNbRFti2cqEzD6zfuI4OTLsGUoObpCmlwZqaTQ=","checked_at":"2026-11-07T06:49:15Z","checked_by":"https://modelmarket.dev"},"display_name":"kantor.verify","description":"Trustless verification of an optimal-transport cost via a TWO-SIDED primal-dual certificate. Given a, b, C (or points), a claimed_cost, the transport plan P and the Kantorovich potentials (u, v), checks PRIMAL FEASIBILITY (P>=0, row-sums==a, col-sums==b) with <P,C> == claimed_cost (an upper bound) AND DUAL FEASIBILITY u_i + v_j <= C_ij on every (i,j) with claimed_cost == sum a_i u_i + sum b_j v_j (a lower bound). Both bounds meeting at claimed_cost certifies the exact optimum; a dual-only check would accept an under-reported cost. Checked in O(m*n), no re-solve, no trust.","score":0.6936,"match_type":"semantic","matched_concepts":["optimization"],"matched_terms":["optimize","optimal","optimizar","optimiser","v1"],"score_breakdown":{"lexical":0.0811,"semantic":0.9632,"quality":0.6941},"input_independent":false,"price_per_call_usd":0.001,"access_mode":"paid","credits_eligible":false,"routed_price_usd":0.00101,"routing_fee_bps":100,"trust_score":0.5,"reputation_basis":"unobserved","observations_30d":0,"deliveries_30d":null,"p50_latency_ms":10,"publisher_id":null,"payout_address":"0x1218ff36C5d2e3B6A565CdB1A8B1AcCFc606Ad0a","seller_id":"AIMarket Oracle Family","seller_kind":"hub","stake_usd":null,"demo":false,"offerable":true,"route_status":"live","route_age_s":1091,"input_required":["a","b","claimed_cost","plan","potentials"],"input_hint":{"a":{"type":"array"},"b":{"type":"array"},"claimed_cost":{"type":"number","description":"The transport cost to certify."},"plan":{"type":"array","description":"Primal transport plan P (m*n, row-sums==a, col-sums==b, P>=0). Required by kantor.verify: it upper-bounds the optimum so a dual-only cert can't under-report."},"potentials":{"type":"object","description":"Kantorovich dual potentials: u over sources (len m), v over sinks (len n)."}}},{"product_id":"prod-fermat","capability_id":"fermat.verify@v1","source_hub":"https://oracles.modelmarket.dev/family","source_hub_name":"AIMarket Oracle Family","name":"fermat.verify","evidence":{"kind":"signed_catalogue","scope":"catalogue","signer":"https://oracles.modelmarket.dev/family","signer_public_key":"YkAOwWNbRFti2cqEzD6zfuI4OTLsGUoObpCmlwZqaTQ=","checked_at":"2026-11-07T06:49:15Z","checked_by":"https://modelmarket.dev"},"display_name":"fermat.verify","description":"Trustless verification of a least-time route via its dual certificate. Re-derives the canonical graph and refractive indices, then checks the supplied potentials T(v) for FEASIBILITY (T(v) <= T(u)+n(u,v) on every edge) and the supplied path for TIGHTNESS (T(v) == T(u)+n(u,v) on every path edge, grounded T(start)=0). Both holding proves the path is globally optimal — checked in O(E), no Dijkstra, no trust in the oracle.","score":0.6857,"match_type":"semantic","matched_concepts":["optimization"],"matched_terms":["optimize","optimal","optimizar","optimiser","v1"],"score_breakdown":{"lexical":0.0811,"semantic":0.9522,"quality":0.6921},"input_independent":false,"price_per_call_usd":0.001,"access_mode":"paid","credits_eligible":false,"routed_price_usd":0.00101,"routing_fee_bps":100,"trust_score":0.5,"reputation_basis":"unobserved","observations_30d":0,"deliveries_30d":null,"p50_latency_ms":20,"publisher_id":null,"payout_address":"0x1218ff36C5d2e3B6A565CdB1A8B1AcCFc606Ad0a","seller_id":"AIMarket Oracle Family","seller_kind":"hub","stake_usd":null,"demo":false,"offerable":true,"route_status":"live","route_age_s":1091,"input_required":["edges","potentials","start","goal"],"input_hint":{"edges":{"type":"array","description":"Directed weighted edges. Two shapes are accepted and may be mixed: (a) [u, v, weight] where weight is the already-blended non-negative refractive index n(u,v); or (b) {from,to, cost?, latency?, reputation?} where the index is derived as a*cost + b*(latency/scale) + c*(1-reputation) using 'blend'. A bare [u, v] is weight 0."},"potentials":{"type":"object","description":"Eikonal potential T(v) = least cost-to-reach, keyed by node label (null = unreachable)."},"start":{"type":["string","integer"]},"goal":{"type":["string","integer"]}}},{"product_id":"prod-fermat","capability_id":"fermat.route@v1","source_hub":"https://oracles.modelmarket.dev/family","source_hub_name":"AIMarket Oracle Family","name":"fermat.route","evidence":{"kind":"signed_catalogue","scope":"catalogue","signer":"https://oracles.modelmarket.dev/family","signer_public_key":"YkAOwWNbRFti2cqEzD6zfuI4OTLsGUoObpCmlwZqaTQ=","checked_at":"2026-11-07T06:49:15Z","checked_by":"https://modelmarket.dev"},"display_name":"fermat.route","description":"Compute the globally least-time (least-cost) composition path from 'start' to 'goal' over a directed weighted service graph, plus the eikonal potential T(v) for every node and a dual optimality certificate. Edge weight is the refractive index n(u,v) >= 0 (cost + latency + risk). Returns path, total, potentials, graph_commitment and certificate{path_edges,...} for trustless replay.","score":0.6845,"match_type":"semantic","matched_concepts":["optimization"],"matched_terms":["optimize","optimal","optimizar","optimiser","v1"],"score_breakdown":{"lexical":0.0811,"semantic":0.9522,"quality":0.6569},"input_independent":false,"price_per_call_usd":0.01,"access_mode":"paid","credits_eligible":false,"routed_price_usd":0.0101,"routing_fee_bps":100,"trust_score":0.5,"reputation_basis":"unobserved","observations_30d":0,"deliveries_30d":null,"p50_latency_ms":50,"publisher_id":null,"payout_address":"0x1218ff36C5d2e3B6A565CdB1A8B1AcCFc606Ad0a","seller_id":"AIMarket Oracle Family","seller_kind":"hub","stake_usd":null,"demo":false,"offerable":true,"route_status":"live","route_age_s":1091,"input_required":["edges","start","goal"],"input_hint":{"edges":{"type":"array","description":"Directed weighted edges. Two shapes are accepted and may be mixed: (a) [u, v, weight] where weight is the already-blended non-negative refractive index n(u,v); or (b) {from,to, cost?, latency?, reputation?} where the index is derived as a*cost + b*(latency/scale) + c*(1-reputation) using 'blend'. A bare [u, v] is weight 0."},"start":{"type":["string","integer"]},"goal":{"type":["string","integer"]}}},{"product_id":"prod-kantor","capability_id":"kantor.transport@v1","source_hub":"https://oracles.modelmarket.dev/family","source_hub_name":"AIMarket Oracle Family","name":"kantor.transport","evidence":{"kind":"signed_catalogue","scope":"catalogue","signer":"https://oracles.modelmarket.dev/family","signer_public_key":"YkAOwWNbRFti2cqEzD6zfuI4OTLsGUoObpCmlwZqaTQ=","checked_at":"2026-11-07T06:49:15Z","checked_by":"https://modelmarket.dev"},"display_name":"kantor.transport","description":"Solve the discrete optimal-transport problem from source distribution a to sink distribution b under ground cost C (or points + metric/p). Returns the optimal transport plan, the cost, the p-Wasserstein distance (when the cost is a p-th power of a metric), and the Kantorovich dual potentials (u, v) — the certificate. method='exact' (default) is solved by min-cost flow and is certifiable; method='sinkhorn' is an explicitly approximate entropic upper bound carrying its regulariser eps.","score":0.6789,"match_type":"semantic","matched_concepts":["optimization"],"matched_terms":["optimize","optimal","optimizar","optimiser","v1"],"score_breakdown":{"lexical":0.0811,"semantic":0.9437,"quality":0.6671},"input_independent":false,"price_per_call_usd":0.006,"access_mode":"paid","credits_eligible":false,"routed_price_usd":0.00606,"routing_fee_bps":100,"trust_score":0.5,"reputation_basis":"unobserved","observations_30d":0,"deliveries_30d":null,"p50_latency_ms":60,"publisher_id":null,"payout_address":"0x1218ff36C5d2e3B6A565CdB1A8B1AcCFc606Ad0a","seller_id":"AIMarket Oracle Family","seller_kind":"hub","stake_usd":null,"demo":false,"offerable":true,"route_status":"live","route_age_s":1091,"input_required":["a","b"],"input_hint":{"a":{"type":"array","description":"Source distribution weights (len m; renormalised to sum 1)."},"b":{"type":"array","description":"Sink distribution weights (len n; renormalised to sum 1)."}}}],"total":8,"offset":0,"limit":20,"has_more":false,"observed":[],"search":{"mode":"hybrid-semantic-v1","languages":["en","ru","es","fr","zh"],"interpreted_concepts":["optimization"],"latency_ms":30.67,"query_stays_local":true},"total_hubs_searched":23,"protocol_version":"v2"}