{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SJFD5L77NIJRLQNGOESKORD3U4","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":"cb94e52067fa5355aaaafd68f5af468c86ad4e4b0242433c79817eb59d08629b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-28T22:27:34Z","title_canon_sha256":"07c4fcc4cdbe22c13756de4d989274d9aff00144d0c23276d1886f67f23daff3"},"schema_version":"1.0","source":{"id":"1907.00099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00099","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00099v1","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00099","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"SJFD5L77NIJR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SJFD5L77NIJRLQNG","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SJFD5L77","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:6f7b29c945692295ddf74c12fa88d3280ef74e9eaa21611393790eb282e770e3","target":"graph","created_at":"2026-05-17T23:41:57Z","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":"To an extended permutohedron we associate the weighted integer points enumerator, whose principal specialization is the $f$-polynomial. In the case of poset cones it refines Gessel's $\\mathsf{P}$-partitions enumerator. We show that this enumerator is a quasisymmetric function obtained by universal morphism from the Hopf algebra of posets.","authors_text":"Marko Pe\\v{s}ovi\\'c, Tanja Stojadinovi\\'c, Vladimir Gruji\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-28T22:27:34Z","title":"Weighted $\\mathsf{P}-$partitions enumerator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00099","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":"sha256:217f34b6b1940fe1e90d5169aed73ddb5796a649395d18d2a53e1e1db115cdf3","target":"record","created_at":"2026-05-17T23:41:57Z","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":"cb94e52067fa5355aaaafd68f5af468c86ad4e4b0242433c79817eb59d08629b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-28T22:27:34Z","title_canon_sha256":"07c4fcc4cdbe22c13756de4d989274d9aff00144d0c23276d1886f67f23daff3"},"schema_version":"1.0","source":{"id":"1907.00099","kind":"arxiv","version":1}},"canonical_sha256":"924a3eafff6a1315c1a67124a7447ba723e0210bd2b6e3aad472acbc0af89f78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"924a3eafff6a1315c1a67124a7447ba723e0210bd2b6e3aad472acbc0af89f78","first_computed_at":"2026-05-17T23:41:57.469845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:57.469845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HX12hHkOma9gvj604vk7FyFlomu5k5nsT5kBQ1kFebQlgmnIe3NU5e3eH3++aLse+5TTU7eEnSOtCvii00B+Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:57.470393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:217f34b6b1940fe1e90d5169aed73ddb5796a649395d18d2a53e1e1db115cdf3","sha256:6f7b29c945692295ddf74c12fa88d3280ef74e9eaa21611393790eb282e770e3"],"state_sha256":"bde828462e5b619d86fb47f36ec6558bcbc1506bf3e715ced0350992c30469b0"}