{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:VA7OSF3YR4AMVO3UGT5UM32PMP","short_pith_number":"pith:VA7OSF3Y","schema_version":"1.0","canonical_sha256":"a83ee917788f00cabb7434fb466f4f63e9dd772b2088539e0ea453ab1bca2222","source":{"kind":"arxiv","id":"2201.06859","version":4},"attestation_state":"computed","paper":{"title":"Grand-Canonical Optimal Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.OC","authors_text":"Luca Nenna, Mathieu Lewin, Simone Di Marino","submitted_at":"2022-01-18T10:29:31Z","abstract_excerpt":"We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals $N$ and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible $N$'s, while fixing a certain linear combination of the corresponding marginals."},"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":"2201.06859","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-01-18T10:29:31Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"fd2974ab6aaf16c83b299099ae4723b55502a20b37d2a6ada4fe81fec318dd2b","abstract_canon_sha256":"dd7d84213833d879a70f3defaae910eecd94949da955a09c6f3ce788c8e085df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:00:31.274032Z","signature_b64":"UHuy5bHXuJ8rw3xG+oBC7W3GCWE4bj4gOHAECQ1a+Od5HPMGYgMZaNtYc6mvbPKabcgBMFEhYEFEVgy2oKp8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a83ee917788f00cabb7434fb466f4f63e9dd772b2088539e0ea453ab1bca2222","last_reissued_at":"2026-07-05T10:00:31.273612Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:00:31.273612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Grand-Canonical Optimal Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.OC","authors_text":"Luca Nenna, Mathieu Lewin, Simone Di Marino","submitted_at":"2022-01-18T10:29:31Z","abstract_excerpt":"We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals $N$ and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible $N$'s, while fixing a certain linear combination of the corresponding marginals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.06859","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.06859/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2201.06859","created_at":"2026-07-05T10:00:31.273672+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.06859v4","created_at":"2026-07-05T10:00:31.273672+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.06859","created_at":"2026-07-05T10:00:31.273672+00:00"},{"alias_kind":"pith_short_12","alias_value":"VA7OSF3YR4AM","created_at":"2026-07-05T10:00:31.273672+00:00"},{"alias_kind":"pith_short_16","alias_value":"VA7OSF3YR4AMVO3U","created_at":"2026-07-05T10:00:31.273672+00:00"},{"alias_kind":"pith_short_8","alias_value":"VA7OSF3Y","created_at":"2026-07-05T10:00:31.273672+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/VA7OSF3YR4AMVO3UGT5UM32PMP","json":"https://pith.science/pith/VA7OSF3YR4AMVO3UGT5UM32PMP.json","graph_json":"https://pith.science/api/pith-number/VA7OSF3YR4AMVO3UGT5UM32PMP/graph.json","events_json":"https://pith.science/api/pith-number/VA7OSF3YR4AMVO3UGT5UM32PMP/events.json","paper":"https://pith.science/paper/VA7OSF3Y"},"agent_actions":{"view_html":"https://pith.science/pith/VA7OSF3YR4AMVO3UGT5UM32PMP","download_json":"https://pith.science/pith/VA7OSF3YR4AMVO3UGT5UM32PMP.json","view_paper":"https://pith.science/paper/VA7OSF3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.06859&json=true","fetch_graph":"https://pith.science/api/pith-number/VA7OSF3YR4AMVO3UGT5UM32PMP/graph.json","fetch_events":"https://pith.science/api/pith-number/VA7OSF3YR4AMVO3UGT5UM32PMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VA7OSF3YR4AMVO3UGT5UM32PMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VA7OSF3YR4AMVO3UGT5UM32PMP/action/storage_attestation","attest_author":"https://pith.science/pith/VA7OSF3YR4AMVO3UGT5UM32PMP/action/author_attestation","sign_citation":"https://pith.science/pith/VA7OSF3YR4AMVO3UGT5UM32PMP/action/citation_signature","submit_replication":"https://pith.science/pith/VA7OSF3YR4AMVO3UGT5UM32PMP/action/replication_record"}},"created_at":"2026-07-05T10:00:31.273672+00:00","updated_at":"2026-07-05T10:00:31.273672+00:00"}