{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3FWNW5L7CICPNB32VTK37Z2VL2","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":"f82dd7cd7e2c98424f9aa2f6b7701eb20058681f66aae4f8532479a6ef7ba8e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-19T15:53:38Z","title_canon_sha256":"5216bc0bdabadebef9b55a3d06233061160c99f741a04469f16b46beab78c6cf"},"schema_version":"1.0","source":{"id":"1406.5089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5089","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5089v1","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5089","created_at":"2026-05-18T02:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"3FWNW5L7CICP","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3FWNW5L7CICPNB32","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3FWNW5L7","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:f98d60e41344250f1a171d5d300b6aeab95de0409558b6488f56dbd1a0a361c3","target":"graph","created_at":"2026-05-18T02:49:20Z","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 study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.","authors_text":"Erwan Hillion","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-19T15:53:38Z","title":"Entropy along W_{1,+}-geodesics on graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5089","kind":"arxiv","version":1},"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:a0b8e9b3bb33dc256b561cf2187d1ae98d928b8b249ec8e9bb85712442aaafa9","target":"record","created_at":"2026-05-18T02:49:20Z","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":"f82dd7cd7e2c98424f9aa2f6b7701eb20058681f66aae4f8532479a6ef7ba8e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-19T15:53:38Z","title_canon_sha256":"5216bc0bdabadebef9b55a3d06233061160c99f741a04469f16b46beab78c6cf"},"schema_version":"1.0","source":{"id":"1406.5089","kind":"arxiv","version":1}},"canonical_sha256":"d96cdb757f1204f6877aacd5bfe7555ea82b5b8794ed32e7a12e9757dbfe055a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d96cdb757f1204f6877aacd5bfe7555ea82b5b8794ed32e7a12e9757dbfe055a","first_computed_at":"2026-05-18T02:49:20.963437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:20.963437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bEDraZxC8uHF4BpMZjttuhjIrYNdvsBz4nuf4mR2ORyE87YxLfa9oAdc4zNcTO8/9l0PKqc1B19tuOQgyNPUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:20.964647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0b8e9b3bb33dc256b561cf2187d1ae98d928b8b249ec8e9bb85712442aaafa9","sha256:f98d60e41344250f1a171d5d300b6aeab95de0409558b6488f56dbd1a0a361c3"],"state_sha256":"72cbb6243f6056d1a85d1ea26de7fe18153626768528cd53562280e6e9a5d04f"}