{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O6LOZD4UXAVHRWBTDYWMSGFSCP","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":"64a9e22eb890add92d4dc088acd37dd8fee1dc16afa5f03164a9fd253384bd7b","cross_cats_sorted":["hep-th","math.CO","math.MP","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-20T01:45:45Z","title_canon_sha256":"320daeb3f1c2f6d73e49495fe11be98adb78bfa982d73116bafd8e4c004517ee"},"schema_version":"1.0","source":{"id":"1612.06482","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06482","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06482v2","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06482","created_at":"2026-05-18T00:47:26Z"},{"alias_kind":"pith_short_12","alias_value":"O6LOZD4UXAVH","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O6LOZD4UXAVHRWBT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O6LOZD4U","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:a5fcb13c4f8f8fc33e30e643de261dce75fc1dafff5b44c5016c22c1f09d8712","target":"graph","created_at":"2026-05-18T00:47:26Z","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 introduce the boundary length and point spectrum, as a joint generalization of the boundary length spectrum and boundary point spectrum in arXiv:1307.0967. We establish by cut-and-join methods that the number of partial chord diagrams filtered by the boundary length and point spectrum satisfies a recursion relation, which combined with an initial condition determines these numbers uniquely. This recursion relation is equivalent to a second order, non-linear, algebraic partial differential equation for the generating function of the numbers of partial chord diagrams filtered by the boundary ","authors_text":"Christian M. Reidys, Hiroyuki Fuji, J{\\o}rgen Ellegaard Andersen, Robert C. Penner","cross_cats":["hep-th","math.CO","math.MP","q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-20T01:45:45Z","title":"The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06482","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":"sha256:196ecb3e28c3f231df9e965765995512664c84880eaf80b85a4a839267759dce","target":"record","created_at":"2026-05-18T00:47:26Z","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":"64a9e22eb890add92d4dc088acd37dd8fee1dc16afa5f03164a9fd253384bd7b","cross_cats_sorted":["hep-th","math.CO","math.MP","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-20T01:45:45Z","title_canon_sha256":"320daeb3f1c2f6d73e49495fe11be98adb78bfa982d73116bafd8e4c004517ee"},"schema_version":"1.0","source":{"id":"1612.06482","kind":"arxiv","version":2}},"canonical_sha256":"7796ec8f94b82a78d8331e2cc918b213d3d83102d4de5a8c331546d76ec355af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7796ec8f94b82a78d8331e2cc918b213d3d83102d4de5a8c331546d76ec355af","first_computed_at":"2026-05-18T00:47:26.436236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:26.436236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PHjKfBhxJK3U6JDJmDSh9Lax7rRvkET+/uPNhK2mb84XFmZPgIB6G5m8Ez9zzrewyjgRVamdcyBDw4PjiUV3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:26.436911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06482","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:196ecb3e28c3f231df9e965765995512664c84880eaf80b85a4a839267759dce","sha256:a5fcb13c4f8f8fc33e30e643de261dce75fc1dafff5b44c5016c22c1f09d8712"],"state_sha256":"ecb5f2b8ab8249e0c0c0ccfc4b33023e08e561b5842a1cd41684f88f38ba0d03"}