{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:G4NTLRWVFD5LDWS3XC7CFYHCIZ","short_pith_number":"pith:G4NTLRWV","schema_version":"1.0","canonical_sha256":"371b35c6d528fab1da5bb8be22e0e24667ba8b504e0ccad9199002873170bd37","source":{"kind":"arxiv","id":"1810.07236","version":2},"attestation_state":"computed","paper":{"title":"Fibrations of 3-manifolds and asymptotic translation length in the arc complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Bal\\'azs Strenner","submitted_at":"2018-10-16T19:04:34Z","abstract_excerpt":"Given a 3-manifold $M$ fibering over the circle, we investigate how the asymptotic translation lengths of pseudo-Anosov monodromies in the arc complex vary as we vary the fibration. We formalize this problem by defining normalized asymptotic translation length functions $\\mu_d$ for every integer $d \\ge 1$ on the rational points of a fibered face of the unit ball of the Thurston norm on $H^1(M;\\mathbb{R})$. We show that even though the functions $\\mu_d$ themselves are typically nowhere continuous, the sets of accumulation points of their graphs on $d$-dimensional slices of the fibered face are "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.07236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-10-16T19:04:34Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"7bf6d2374089e5d57cfdce67f4bb6a20862698e80ffcaaec05b589d5712ab441","abstract_canon_sha256":"f644005381a79802705625c40a33fe844692e1a2a4c11aad859bb6ee9e258c0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:17:20.492650Z","signature_b64":"bqzlwgv2oduypNMjrjyMt4Vt57bQ++F2JyFllINWY7WmVeYkbbBJXUV0qpSqG4aCp9MCV5IqJZks9tkWzwTKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"371b35c6d528fab1da5bb8be22e0e24667ba8b504e0ccad9199002873170bd37","last_reissued_at":"2026-07-05T07:17:20.492139Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:17:20.492139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fibrations of 3-manifolds and asymptotic translation length in the arc complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Bal\\'azs Strenner","submitted_at":"2018-10-16T19:04:34Z","abstract_excerpt":"Given a 3-manifold $M$ fibering over the circle, we investigate how the asymptotic translation lengths of pseudo-Anosov monodromies in the arc complex vary as we vary the fibration. We formalize this problem by defining normalized asymptotic translation length functions $\\mu_d$ for every integer $d \\ge 1$ on the rational points of a fibered face of the unit ball of the Thurston norm on $H^1(M;\\mathbb{R})$. We show that even though the functions $\\mu_d$ themselves are typically nowhere continuous, the sets of accumulation points of their graphs on $d$-dimensional slices of the fibered face are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07236","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.07236/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.07236","created_at":"2026-07-05T07:17:20.492200+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.07236v2","created_at":"2026-07-05T07:17:20.492200+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07236","created_at":"2026-07-05T07:17:20.492200+00:00"},{"alias_kind":"pith_short_12","alias_value":"G4NTLRWVFD5L","created_at":"2026-07-05T07:17:20.492200+00:00"},{"alias_kind":"pith_short_16","alias_value":"G4NTLRWVFD5LDWS3","created_at":"2026-07-05T07:17:20.492200+00:00"},{"alias_kind":"pith_short_8","alias_value":"G4NTLRWV","created_at":"2026-07-05T07:17:20.492200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.05371","citing_title":"The relative $\\mathcal{L}$-invariant of a compact $4$-manifold","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ","json":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ.json","graph_json":"https://pith.science/api/pith-number/G4NTLRWVFD5LDWS3XC7CFYHCIZ/graph.json","events_json":"https://pith.science/api/pith-number/G4NTLRWVFD5LDWS3XC7CFYHCIZ/events.json","paper":"https://pith.science/paper/G4NTLRWV"},"agent_actions":{"view_html":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ","download_json":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ.json","view_paper":"https://pith.science/paper/G4NTLRWV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.07236&json=true","fetch_graph":"https://pith.science/api/pith-number/G4NTLRWVFD5LDWS3XC7CFYHCIZ/graph.json","fetch_events":"https://pith.science/api/pith-number/G4NTLRWVFD5LDWS3XC7CFYHCIZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ/action/storage_attestation","attest_author":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ/action/author_attestation","sign_citation":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ/action/citation_signature","submit_replication":"https://pith.science/pith/G4NTLRWVFD5LDWS3XC7CFYHCIZ/action/replication_record"}},"created_at":"2026-07-05T07:17:20.492200+00:00","updated_at":"2026-07-05T07:17:20.492200+00:00"}