{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:OLZWYJKXODKKXD54T7BEGJ6CGW","short_pith_number":"pith:OLZWYJKX","schema_version":"1.0","canonical_sha256":"72f36c255770d4ab8fbc9fc24327c2359876e38c01eea5bf4567963e9c529baf","source":{"kind":"arxiv","id":"math/0411184","version":2},"attestation_state":"computed","paper":{"title":"Necessary and sufficient conditions for McShane's identity and variations","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Ser Peow Tan, Yan Loi Wong, Ying Zhang","submitted_at":"2004-11-09T02:01:36Z","abstract_excerpt":"Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators \\Gamma to SL(2,C). In this note we extend Bowditch's result by giving necessary and sufficient conditions for the identity to hold, and also for the generalized McShane identity to hold for arbitrary (not necessarily type preserving) representations. We also give a ve"},"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":"math/0411184","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2004-11-09T02:01:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"68554f3f00cbec19d5afa0d1d4e1129ba54962fbd0139038cb805e78cb83c620","abstract_canon_sha256":"97a865e2cbd47b140305d6e6f5f11c06c2efc368e058453ade190d4cf9a4109d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:58:16.711112Z","signature_b64":"tzOVHZP9WzlVWmJOFtYBSkVN6HPaHCszTGF41xleckQFWmTl6cLdJCEGj3n/sHkm5tYNCtbGaQwu1yUFJG9tCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72f36c255770d4ab8fbc9fc24327c2359876e38c01eea5bf4567963e9c529baf","last_reissued_at":"2026-07-04T14:58:16.710655Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:58:16.710655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Necessary and sufficient conditions for McShane's identity and variations","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Ser Peow Tan, Yan Loi Wong, Ying Zhang","submitted_at":"2004-11-09T02:01:36Z","abstract_excerpt":"Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators \\Gamma to SL(2,C). In this note we extend Bowditch's result by giving necessary and sufficient conditions for the identity to hold, and also for the generalized McShane identity to hold for arbitrary (not necessarily type preserving) representations. We also give a ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411184","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/math/0411184/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":"math/0411184","created_at":"2026-07-04T14:58:16.710729+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0411184v2","created_at":"2026-07-04T14:58:16.710729+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411184","created_at":"2026-07-04T14:58:16.710729+00:00"},{"alias_kind":"pith_short_12","alias_value":"OLZWYJKXODKK","created_at":"2026-07-04T14:58:16.710729+00:00"},{"alias_kind":"pith_short_16","alias_value":"OLZWYJKXODKKXD54","created_at":"2026-07-04T14:58:16.710729+00:00"},{"alias_kind":"pith_short_8","alias_value":"OLZWYJKX","created_at":"2026-07-04T14:58:16.710729+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/OLZWYJKXODKKXD54T7BEGJ6CGW","json":"https://pith.science/pith/OLZWYJKXODKKXD54T7BEGJ6CGW.json","graph_json":"https://pith.science/api/pith-number/OLZWYJKXODKKXD54T7BEGJ6CGW/graph.json","events_json":"https://pith.science/api/pith-number/OLZWYJKXODKKXD54T7BEGJ6CGW/events.json","paper":"https://pith.science/paper/OLZWYJKX"},"agent_actions":{"view_html":"https://pith.science/pith/OLZWYJKXODKKXD54T7BEGJ6CGW","download_json":"https://pith.science/pith/OLZWYJKXODKKXD54T7BEGJ6CGW.json","view_paper":"https://pith.science/paper/OLZWYJKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0411184&json=true","fetch_graph":"https://pith.science/api/pith-number/OLZWYJKXODKKXD54T7BEGJ6CGW/graph.json","fetch_events":"https://pith.science/api/pith-number/OLZWYJKXODKKXD54T7BEGJ6CGW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OLZWYJKXODKKXD54T7BEGJ6CGW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OLZWYJKXODKKXD54T7BEGJ6CGW/action/storage_attestation","attest_author":"https://pith.science/pith/OLZWYJKXODKKXD54T7BEGJ6CGW/action/author_attestation","sign_citation":"https://pith.science/pith/OLZWYJKXODKKXD54T7BEGJ6CGW/action/citation_signature","submit_replication":"https://pith.science/pith/OLZWYJKXODKKXD54T7BEGJ6CGW/action/replication_record"}},"created_at":"2026-07-04T14:58:16.710729+00:00","updated_at":"2026-07-04T14:58:16.710729+00:00"}