{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AAHZ4QD6YR56SPNVYGVGFB3CUV","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":"45896bba1680185d6888f9d3ef9fcf7985b7b352644aa4b0b7096a0fae8c637e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-18T20:00:42Z","title_canon_sha256":"5744288794a2e8b9962ec12a71bde1c114705da701940f164414e7c3f00fb77f"},"schema_version":"1.0","source":{"id":"1408.4134","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4134","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4134v2","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4134","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"pith_short_12","alias_value":"AAHZ4QD6YR56","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AAHZ4QD6YR56SPNV","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AAHZ4QD6","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:4d083a1ef18fc71e9005a5621d88d95a227ffe1e3be85774993b46ca057ce838","target":"graph","created_at":"2026-05-18T01:35:22Z","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 complex of curves $\\mathcal{C}(S_g)$ of a closed orientable surface of genus $g \\geq 2$ is the simplicial complex having its vertices, $\\mathcal{C}^0(S_g)$, are isotopy classes of essential curves in $S_g$. Two vertices co-bound an edge of the $1$-skeleton, $\\mathcal{C}^1(S_g)$, if there are disjoint representatives in $S_g$. A metric is obtained on $\\mathcal{C}^0(S_g)$ by assigning unit length to each edge of $\\mathcal{C}^1(S_g)$. Thus, the distance between two vertices, $d(v,w)$, corresponds to the length of a geodesic---a shortest edge-path between $v$ and $w$ in $\\mathcal{C}^1 (S_g)$. ","authors_text":"Kayla Morrell, Matthew Morse, Paul Glenn, William W. Menasco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-18T20:00:42Z","title":"MICC: A tool for computing short distances in the curve complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4134","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:b2b2a547b46af2b53e7435724c4d1409a26c5644cd56fe76475b99ba79870369","target":"record","created_at":"2026-05-18T01:35:22Z","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":"45896bba1680185d6888f9d3ef9fcf7985b7b352644aa4b0b7096a0fae8c637e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-18T20:00:42Z","title_canon_sha256":"5744288794a2e8b9962ec12a71bde1c114705da701940f164414e7c3f00fb77f"},"schema_version":"1.0","source":{"id":"1408.4134","kind":"arxiv","version":2}},"canonical_sha256":"000f9e407ec47be93db5c1aa628762a55f592bdd6586f1e218c2fe3c88dbab9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"000f9e407ec47be93db5c1aa628762a55f592bdd6586f1e218c2fe3c88dbab9a","first_computed_at":"2026-05-18T01:35:22.637386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:22.637386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MKTk09F9GEmo3doq2ZtjcJnBwGik/C+quLdvuIwIDnwQWy32CPXq3y3yHaJ1EJbMnhac+u7DmcnxvoJ8+FZOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:22.637981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4134","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2b2a547b46af2b53e7435724c4d1409a26c5644cd56fe76475b99ba79870369","sha256:4d083a1ef18fc71e9005a5621d88d95a227ffe1e3be85774993b46ca057ce838"],"state_sha256":"eba19521228af70d71d3c01dfe27af65cf77d70a76240101d0e12e86e4bd779c"}