{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:77D4DCURX55Y6IV76DLNC4EYWD","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":"7f8f9feb4454b730a8cad8cde9dfa79aff06cc3084d044fc8f6b0e7be6005a77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-19T11:56:58Z","title_canon_sha256":"375c7ee6dcf1d8ec53f2ff741220e7fa463e6a06fb2f037e48eb0c62a622651d"},"schema_version":"1.0","source":{"id":"1008.3278","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3278","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3278v2","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3278","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"pith_short_12","alias_value":"77D4DCURX55Y","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"77D4DCURX55Y6IV7","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"77D4DCUR","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:a509fe0a55be5eac674623522da8aff6c06a8458ce40a9928df938aed685249c","target":"graph","created_at":"2026-05-18T03:56:24Z","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":"The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.","authors_text":"Adrien Boussicault (LaBRI, Alain Lascoux (LIGM), LIGM), Valentin Feray (LaBRI), Victor Reiner (UMN-MATH)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-19T11:56:58Z","title":"Linear extension sums as valuations of cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3278","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:c3b6f002a0b4ce56ea3f8fcc3c28b9a9ab0fc5bda397bd38f42bd3ca634f8934","target":"record","created_at":"2026-05-18T03:56:24Z","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":"7f8f9feb4454b730a8cad8cde9dfa79aff06cc3084d044fc8f6b0e7be6005a77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-19T11:56:58Z","title_canon_sha256":"375c7ee6dcf1d8ec53f2ff741220e7fa463e6a06fb2f037e48eb0c62a622651d"},"schema_version":"1.0","source":{"id":"1008.3278","kind":"arxiv","version":2}},"canonical_sha256":"ffc7c18a91bf7b8f22bff0d6d17098b0ed5160af937075aeb45f7496e81f5ab1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffc7c18a91bf7b8f22bff0d6d17098b0ed5160af937075aeb45f7496e81f5ab1","first_computed_at":"2026-05-18T03:56:24.383453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:24.383453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2RaMsviVm/lVmrwxiRiBpxIcVO2hBrrtMfLAPapenq4mXx0Hx8f8ac0JSiWqRFc63cApGMqBZA0jceE/xOCCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:24.384094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3278","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3b6f002a0b4ce56ea3f8fcc3c28b9a9ab0fc5bda397bd38f42bd3ca634f8934","sha256:a509fe0a55be5eac674623522da8aff6c06a8458ce40a9928df938aed685249c"],"state_sha256":"9d574a09db7e2baed86426e230ce212a430ac5f7610806592a5f52c024069546"}