{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:BJF3EDTFDY4QQ6ORK26L3A56QD","short_pith_number":"pith:BJF3EDTF","schema_version":"1.0","canonical_sha256":"0a4bb20e651e390879d156bcbd83be80c81c692b8c10adaa628c5841c46bfd83","source":{"kind":"arxiv","id":"0907.2082","version":1},"attestation_state":"computed","paper":{"title":"Length spectra and degeneration of flat metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GT","authors_text":"Christopher J. Leininger, Kasra Rafi, Moon Duchin","submitted_at":"2009-07-13T01:00:40Z","abstract_excerpt":"In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a boundary for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to \"mixed structures\" on the surface: part flat metric and part measured foliation."},"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":"0907.2082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-13T01:00:40Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"261e8ac1347c60a8187e45f4d367eefd75ced3dc15e20d9f264aff82c5573ceb","abstract_canon_sha256":"6787227a69f5e5a1a8c2ee5a398e8267b2c6fbb289f6021aa5a62248293fdcde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:03.614283Z","signature_b64":"RlCBlhZV4xvDiZkd2W60Ob1amBZLEXvxbAE4+rP6zn7X8+U0vcObj2R8f7kwTljqH6LOupXzMLNOgr/ONaAtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a4bb20e651e390879d156bcbd83be80c81c692b8c10adaa628c5841c46bfd83","last_reissued_at":"2026-05-18T02:13:03.613813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:03.613813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Length spectra and degeneration of flat metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GT","authors_text":"Christopher J. Leininger, Kasra Rafi, Moon Duchin","submitted_at":"2009-07-13T01:00:40Z","abstract_excerpt":"In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a boundary for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to \"mixed structures\" on the surface: part flat metric and part measured foliation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2082","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"0907.2082","created_at":"2026-05-18T02:13:03.613877+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.2082v1","created_at":"2026-05-18T02:13:03.613877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2082","created_at":"2026-05-18T02:13:03.613877+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJF3EDTFDY4Q","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJF3EDTFDY4QQ6OR","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJF3EDTF","created_at":"2026-05-18T12:25:58.837520+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD","json":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD.json","graph_json":"https://pith.science/api/pith-number/BJF3EDTFDY4QQ6ORK26L3A56QD/graph.json","events_json":"https://pith.science/api/pith-number/BJF3EDTFDY4QQ6ORK26L3A56QD/events.json","paper":"https://pith.science/paper/BJF3EDTF"},"agent_actions":{"view_html":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD","download_json":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD.json","view_paper":"https://pith.science/paper/BJF3EDTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.2082&json=true","fetch_graph":"https://pith.science/api/pith-number/BJF3EDTFDY4QQ6ORK26L3A56QD/graph.json","fetch_events":"https://pith.science/api/pith-number/BJF3EDTFDY4QQ6ORK26L3A56QD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD/action/storage_attestation","attest_author":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD/action/author_attestation","sign_citation":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD/action/citation_signature","submit_replication":"https://pith.science/pith/BJF3EDTFDY4QQ6ORK26L3A56QD/action/replication_record"}},"created_at":"2026-05-18T02:13:03.613877+00:00","updated_at":"2026-05-18T02:13:03.613877+00:00"}