{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LYLHU4S7VLNUETRPEHCSXOIVVK","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":"2452921912cb3bf4b11b966848ed6d36e746bec0e6301e7a7bc53fe5fcc9e437","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-05T17:17:15Z","title_canon_sha256":"449e6fa909b707e3898e1ced5b354ddf2ef894173af7d1c5b74bbb2f472ababa"},"schema_version":"1.0","source":{"id":"1409.1878","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1878","created_at":"2026-05-18T00:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1878v2","created_at":"2026-05-18T00:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1878","created_at":"2026-05-18T00:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"LYLHU4S7VLNU","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LYLHU4S7VLNUETRP","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LYLHU4S7","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:341bd196ffc0aeba464621fb6c67fda9944ce2d3bb779ee3fa6f2e0dcd61149e","target":"graph","created_at":"2026-05-18T00:39:48Z","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 show that if the monodromy of a 3-manifold M that fibers over the circle has large translation distance in the curve complex, then the rank of the fundamental group of M is 2g+1, where g is the genus of the fiber.","authors_text":"Ian Biringer, Juan Souto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-05T17:17:15Z","title":"Ranks of mapping tori via the curve complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1878","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:e1dc31ed85f7ab31d1b7347cfb8b1897adacca5ceb4a8990b42c507a0845a75a","target":"record","created_at":"2026-05-18T00:39:48Z","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":"2452921912cb3bf4b11b966848ed6d36e746bec0e6301e7a7bc53fe5fcc9e437","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-05T17:17:15Z","title_canon_sha256":"449e6fa909b707e3898e1ced5b354ddf2ef894173af7d1c5b74bbb2f472ababa"},"schema_version":"1.0","source":{"id":"1409.1878","kind":"arxiv","version":2}},"canonical_sha256":"5e167a725faadb424e2f21c52bb915aab25ca90ba5a60d69d862ae5d2a003c9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e167a725faadb424e2f21c52bb915aab25ca90ba5a60d69d862ae5d2a003c9c","first_computed_at":"2026-05-18T00:39:48.325469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:48.325469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KsFWcWAiIZiQLB7RcrHfUwFm1bNWgxGUkFPjUfMrY17DzIKoEPpsuOpsu7Mpvyn/3K7+2VtKgMZlQPFAEH1gAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:48.325984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1878","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1dc31ed85f7ab31d1b7347cfb8b1897adacca5ceb4a8990b42c507a0845a75a","sha256:341bd196ffc0aeba464621fb6c67fda9944ce2d3bb779ee3fa6f2e0dcd61149e"],"state_sha256":"adfdb81047167ad2515f3d39e107b824d43755beb5b2575ab8933fccc8eb8698"}