{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:U7BJAL7M3V5ERRKH7OAL566BKB","short_pith_number":"pith:U7BJAL7M","schema_version":"1.0","canonical_sha256":"a7c2902fecdd7a48c547fb80befbc15077a3140dcf28de8f049ea81be4c950a0","source":{"kind":"arxiv","id":"1305.6295","version":1},"attestation_state":"computed","paper":{"title":"A stochastic algorithm finding generalized means on compact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laurent Miclo (IMT), Marc Arnaudon (IMB)","submitted_at":"2013-05-27T19:07:41Z","abstract_excerpt":"A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means for p>0, computed with any continuous distance function, not necessarily the Riemannian distance. They also include means for lengths computed from Finsler metrics, or for divergences. The algorithm is fed sequentially with independent random variables Y_n distributed according to the probability measure on the manifold and this is the only knowledge of this"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.6295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-27T19:07:41Z","cross_cats_sorted":[],"title_canon_sha256":"a725582c6e7bb6d8e8f6fe5132393897e4874f5d9706b5b5eca3e83601731f37","abstract_canon_sha256":"71bd60c68406285966c57733006fd29b35f1f686f9b0888ee5318cd9bf6b4199"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:51.628143Z","signature_b64":"1c2JcLFDE0ZUmf+h2OHGR2IFSycdx4R6dDaAnk3NAXRkF/aO9gwg5swDoajx+LAOcpE40PrQeYDLlfhx6gktDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c2902fecdd7a48c547fb80befbc15077a3140dcf28de8f049ea81be4c950a0","last_reissued_at":"2026-05-18T03:24:51.627404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:51.627404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A stochastic algorithm finding generalized means on compact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laurent Miclo (IMT), Marc Arnaudon (IMB)","submitted_at":"2013-05-27T19:07:41Z","abstract_excerpt":"A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means for p>0, computed with any continuous distance function, not necessarily the Riemannian distance. They also include means for lengths computed from Finsler metrics, or for divergences. The algorithm is fed sequentially with independent random variables Y_n distributed according to the probability measure on the manifold and this is the only knowledge of this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6295","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.6295","created_at":"2026-05-18T03:24:51.627516+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6295v1","created_at":"2026-05-18T03:24:51.627516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6295","created_at":"2026-05-18T03:24:51.627516+00:00"},{"alias_kind":"pith_short_12","alias_value":"U7BJAL7M3V5E","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"U7BJAL7M3V5ERRKH","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"U7BJAL7M","created_at":"2026-05-18T12:28:02.375192+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB","json":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB.json","graph_json":"https://pith.science/api/pith-number/U7BJAL7M3V5ERRKH7OAL566BKB/graph.json","events_json":"https://pith.science/api/pith-number/U7BJAL7M3V5ERRKH7OAL566BKB/events.json","paper":"https://pith.science/paper/U7BJAL7M"},"agent_actions":{"view_html":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB","download_json":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB.json","view_paper":"https://pith.science/paper/U7BJAL7M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6295&json=true","fetch_graph":"https://pith.science/api/pith-number/U7BJAL7M3V5ERRKH7OAL566BKB/graph.json","fetch_events":"https://pith.science/api/pith-number/U7BJAL7M3V5ERRKH7OAL566BKB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB/action/storage_attestation","attest_author":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB/action/author_attestation","sign_citation":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB/action/citation_signature","submit_replication":"https://pith.science/pith/U7BJAL7M3V5ERRKH7OAL566BKB/action/replication_record"}},"created_at":"2026-05-18T03:24:51.627516+00:00","updated_at":"2026-05-18T03:24:51.627516+00:00"}