{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:EQTTBEHRBGDQF32SLB6AOLFDHU","short_pith_number":"pith:EQTTBEHR","canonical_record":{"source":{"id":"0906.1267","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OA","submitted_at":"2009-06-06T12:11:03Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"69abf6ae5ca41437698800f92b1b6a305e387bdfe487a28c742dff2e15799005","abstract_canon_sha256":"a090005e734d916da26edf5dbea7187d7603814b63cad687505d5da77d235475"},"schema_version":"1.0"},"canonical_sha256":"24273090f1098702ef52587c072ca33d10a9da837980125d72c611c476c4963a","source":{"kind":"arxiv","id":"0906.1267","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.1267","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"arxiv_version","alias_value":"0906.1267v2","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.1267","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"pith_short_12","alias_value":"EQTTBEHRBGDQ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EQTTBEHRBGDQF32S","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EQTTBEHR","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:EQTTBEHRBGDQF32SLB6AOLFDHU","target":"record","payload":{"canonical_record":{"source":{"id":"0906.1267","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OA","submitted_at":"2009-06-06T12:11:03Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"69abf6ae5ca41437698800f92b1b6a305e387bdfe487a28c742dff2e15799005","abstract_canon_sha256":"a090005e734d916da26edf5dbea7187d7603814b63cad687505d5da77d235475"},"schema_version":"1.0"},"canonical_sha256":"24273090f1098702ef52587c072ca33d10a9da837980125d72c611c476c4963a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:55.533834Z","signature_b64":"WLT6zchs98a8SQuPn+cIsKZQ/rUDfhj9VxFu1MdQOKr72mV1HsnQVW6VzEEuqufvGa/J5Q+8Ge2wyW2b4kXOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24273090f1098702ef52587c072ca33d10a9da837980125d72c611c476c4963a","last_reissued_at":"2026-05-18T02:24:55.533070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:55.533070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.1267","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wlmya3U4Z9jNS0Iuxf9ounsznATPXs4K+CYd4TWxQ58MDtTLfnPveBwU4oiaNeujmm/9pFJgJlTGEN7WZ2ULDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:36:58.267739Z"},"content_sha256":"bbfc3a46c97019aaa08c5c55ae9e4e5201a5449ae98bddd3cb01df123487a9af","schema_version":"1.0","event_id":"sha256:bbfc3a46c97019aaa08c5c55ae9e4e5201a5449ae98bddd3cb01df123487a9af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:EQTTBEHRBGDQF32SLB6AOLFDHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A View on Optimal Transport from Noncommutative Geometry","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Francesco D'Andrea, Pierre Martinetti","submitted_at":"2009-06-06T12:11:03Z","abstract_excerpt":"We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry. Starting from a remark of Rieffel on compact manifolds, we first show that on any - i.e. non-necessary compact - complete Riemannian spin manifolds, the two distances coincide. Then, on convex manifolds in the sense of Nash embedding, we provide some natural upper and lower bounds to the distance between any two probability distributions. Specializing to the Euc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.1267","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SR/f6uDWxHxP7E/HJ7/AttreDejgSb0Hje5nkx4gGR1PzGTclU1h9irjg9SKGphgNrJzDozBsLpwY+UKRfP7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:36:58.268095Z"},"content_sha256":"16c2a50810bb558ca12d5090800dae3b7d0d6e7de75a7255745a04d4d8bf7717","schema_version":"1.0","event_id":"sha256:16c2a50810bb558ca12d5090800dae3b7d0d6e7de75a7255745a04d4d8bf7717"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQTTBEHRBGDQF32SLB6AOLFDHU/bundle.json","state_url":"https://pith.science/pith/EQTTBEHRBGDQF32SLB6AOLFDHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQTTBEHRBGDQF32SLB6AOLFDHU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T20:36:58Z","links":{"resolver":"https://pith.science/pith/EQTTBEHRBGDQF32SLB6AOLFDHU","bundle":"https://pith.science/pith/EQTTBEHRBGDQF32SLB6AOLFDHU/bundle.json","state":"https://pith.science/pith/EQTTBEHRBGDQF32SLB6AOLFDHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQTTBEHRBGDQF32SLB6AOLFDHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EQTTBEHRBGDQF32SLB6AOLFDHU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a090005e734d916da26edf5dbea7187d7603814b63cad687505d5da77d235475","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OA","submitted_at":"2009-06-06T12:11:03Z","title_canon_sha256":"69abf6ae5ca41437698800f92b1b6a305e387bdfe487a28c742dff2e15799005"},"schema_version":"1.0","source":{"id":"0906.1267","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.1267","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"arxiv_version","alias_value":"0906.1267v2","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.1267","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"pith_short_12","alias_value":"EQTTBEHRBGDQ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EQTTBEHRBGDQF32S","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EQTTBEHR","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:16c2a50810bb558ca12d5090800dae3b7d0d6e7de75a7255745a04d4d8bf7717","target":"graph","created_at":"2026-05-18T02:24:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry. Starting from a remark of Rieffel on compact manifolds, we first show that on any - i.e. non-necessary compact - complete Riemannian spin manifolds, the two distances coincide. Then, on convex manifolds in the sense of Nash embedding, we provide some natural upper and lower bounds to the distance between any two probability distributions. Specializing to the Euc","authors_text":"Francesco D'Andrea, Pierre Martinetti","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OA","submitted_at":"2009-06-06T12:11:03Z","title":"A View on Optimal Transport from Noncommutative Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.1267","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bbfc3a46c97019aaa08c5c55ae9e4e5201a5449ae98bddd3cb01df123487a9af","target":"record","created_at":"2026-05-18T02:24:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a090005e734d916da26edf5dbea7187d7603814b63cad687505d5da77d235475","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.OA","submitted_at":"2009-06-06T12:11:03Z","title_canon_sha256":"69abf6ae5ca41437698800f92b1b6a305e387bdfe487a28c742dff2e15799005"},"schema_version":"1.0","source":{"id":"0906.1267","kind":"arxiv","version":2}},"canonical_sha256":"24273090f1098702ef52587c072ca33d10a9da837980125d72c611c476c4963a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24273090f1098702ef52587c072ca33d10a9da837980125d72c611c476c4963a","first_computed_at":"2026-05-18T02:24:55.533070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:55.533070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WLT6zchs98a8SQuPn+cIsKZQ/rUDfhj9VxFu1MdQOKr72mV1HsnQVW6VzEEuqufvGa/J5Q+8Ge2wyW2b4kXOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:55.533834Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.1267","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbfc3a46c97019aaa08c5c55ae9e4e5201a5449ae98bddd3cb01df123487a9af","sha256:16c2a50810bb558ca12d5090800dae3b7d0d6e7de75a7255745a04d4d8bf7717"],"state_sha256":"c0d08c7055e22f658f051b242d834abc08bf146615cefefa34ae1a1ad36753da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/H8l/H3Xac2rD305nEd0br+ziBEI8VqxoOx6b8EgvdiAaQqX6ibcL4jxT/6vWh1HwSh51cQ7RaQa43TOL2frDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:36:58.270034Z","bundle_sha256":"8844d44ad21b1bf759c502cafdbbb21d0dce6d1efee8be80d85cb145611ee505"}}