{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:I4CULLDREJOIQNDK26HOHXFJ3Q","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":"94cb39611bb10d1e80eee2181a5ea7808282ec1b3b850d6849f42052fbf4cd17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-28T18:57:56Z","title_canon_sha256":"9b45edc4914d46c777c4e22969560f1b0c35e014c98424816d3107ab5c163b2b"},"schema_version":"1.0","source":{"id":"1310.7533","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7533","created_at":"2026-05-18T02:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7533v2","created_at":"2026-05-18T02:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7533","created_at":"2026-05-18T02:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"I4CULLDREJOI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"I4CULLDREJOIQNDK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"I4CULLDR","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:76fd1c6b5a582e467c16a3273be7b3c8db4166cc999f5e94083783594a317807","target":"graph","created_at":"2026-05-18T02:57:26Z","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":"Let $\\phi \\in \\mbox{Out}(F_n)$ be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism $\\phi$ determines a free-by-cyclic group $\\Gamma=F_n \\rtimes_\\phi \\mathbb Z,$ and a homomorphism $\\alpha \\in H^1(\\Gamma; \\mathbb Z)$. By work of Neumann, Bieri-Neumann-Strebel and Dowdall-Kapovich-Leininger, $\\alpha$ has an open cone neighborhood $\\mathcal A$ in $H^1(\\Gamma;\\mathbb R)$ whose integral points correspond to other fibrations of $\\Gamma$ whose associated outer automorphisms are themselves representable by expanding irreducible trai","authors_text":"Eriko Hironaka, Kasra Rafi, Yael Algom-Kfir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-28T18:57:56Z","title":"Digraphs and cycle polynomials for free-by-cyclic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7533","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":"sha256:78a5edd801493d56f37b10a91ce7a4a53fa914b94003f1c34f7abb8b9f511437","target":"record","created_at":"2026-05-18T02:57:26Z","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":"94cb39611bb10d1e80eee2181a5ea7808282ec1b3b850d6849f42052fbf4cd17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-28T18:57:56Z","title_canon_sha256":"9b45edc4914d46c777c4e22969560f1b0c35e014c98424816d3107ab5c163b2b"},"schema_version":"1.0","source":{"id":"1310.7533","kind":"arxiv","version":2}},"canonical_sha256":"470545ac71225c88346ad78ee3dca9dc01adc01edbb55e0f403a6a2f923824a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"470545ac71225c88346ad78ee3dca9dc01adc01edbb55e0f403a6a2f923824a8","first_computed_at":"2026-05-18T02:57:26.348852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:26.348852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HgIxL77mH4nu3iJWmogsDAnFnN02/MeveiV5SAmsinoqRUP/kaoxwsyzUWSqBLpk+s4iyQpkBM9ocmaQBNZ7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:26.349528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7533","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78a5edd801493d56f37b10a91ce7a4a53fa914b94003f1c34f7abb8b9f511437","sha256:76fd1c6b5a582e467c16a3273be7b3c8db4166cc999f5e94083783594a317807"],"state_sha256":"0d81d789ac4883ae572b4740345b35953a1057ea0e795fd36b1777c34cb3d18c"}