{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:X2TMRJNQEQVQFBIRKRBDZ7U5EC","short_pith_number":"pith:X2TMRJNQ","schema_version":"1.0","canonical_sha256":"bea6c8a5b0242b02851154423cfe9d20b96c8670fee885a7276a589b276a3927","source":{"kind":"arxiv","id":"math/0407422","version":3},"attestation_state":"computed","paper":{"title":"Tetra and Didi, the cosmic spectral twins","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Juan Pablo Rossetti, Peter G Doyle","submitted_at":"2004-07-25T01:13:53Z","abstract_excerpt":"We introduce a pair of isospectral but non-isometric compact flat 3-manifolds called Tetra (a tetracosm) and Didi (a didicosm). The closed geodesics of Tetra and Didi are very different. Where Tetra has two quarter-twisting geodesics of the shortest length, Didi has four half-twisting geodesics. Nevertheless, these spaces are isospectral. This isospectrality can be proven directly by matching eigenfunctions having the same eigenvalue. However, the real interest of this pair--and what led us to discover it--is the way isospectrality emerges from the Selberg trace formula, as the result of a del"},"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/0407422","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2004-07-25T01:13:53Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"69229c3ced70431203b8a6d7874b352ed096acccd8fa0e9f7ed050198d949b16","abstract_canon_sha256":"a109be9a999a28fc9a52811a067e74bcf83b079e84d28c8163c2e384a2f08630"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:00.009221Z","signature_b64":"P7PipLc2h5VUlqZ3ibsyUGM0bKOl3ojcNuECWRM1NbQlV5JjCouQ5PGR19eXEqyCdHOqQuF9JBGJH3NKhXM1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bea6c8a5b0242b02851154423cfe9d20b96c8670fee885a7276a589b276a3927","last_reissued_at":"2026-05-18T02:38:00.008813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:00.008813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tetra and Didi, the cosmic spectral twins","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Juan Pablo Rossetti, Peter G Doyle","submitted_at":"2004-07-25T01:13:53Z","abstract_excerpt":"We introduce a pair of isospectral but non-isometric compact flat 3-manifolds called Tetra (a tetracosm) and Didi (a didicosm). The closed geodesics of Tetra and Didi are very different. Where Tetra has two quarter-twisting geodesics of the shortest length, Didi has four half-twisting geodesics. Nevertheless, these spaces are isospectral. This isospectrality can be proven directly by matching eigenfunctions having the same eigenvalue. However, the real interest of this pair--and what led us to discover it--is the way isospectrality emerges from the Selberg trace formula, as the result of a del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407422","kind":"arxiv","version":3},"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":"math/0407422","created_at":"2026-05-18T02:38:00.008870+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0407422v3","created_at":"2026-05-18T02:38:00.008870+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407422","created_at":"2026-05-18T02:38:00.008870+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2TMRJNQEQVQ","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2TMRJNQEQVQFBIR","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2TMRJNQ","created_at":"2026-05-18T12:25:52.687210+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/X2TMRJNQEQVQFBIRKRBDZ7U5EC","json":"https://pith.science/pith/X2TMRJNQEQVQFBIRKRBDZ7U5EC.json","graph_json":"https://pith.science/api/pith-number/X2TMRJNQEQVQFBIRKRBDZ7U5EC/graph.json","events_json":"https://pith.science/api/pith-number/X2TMRJNQEQVQFBIRKRBDZ7U5EC/events.json","paper":"https://pith.science/paper/X2TMRJNQ"},"agent_actions":{"view_html":"https://pith.science/pith/X2TMRJNQEQVQFBIRKRBDZ7U5EC","download_json":"https://pith.science/pith/X2TMRJNQEQVQFBIRKRBDZ7U5EC.json","view_paper":"https://pith.science/paper/X2TMRJNQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0407422&json=true","fetch_graph":"https://pith.science/api/pith-number/X2TMRJNQEQVQFBIRKRBDZ7U5EC/graph.json","fetch_events":"https://pith.science/api/pith-number/X2TMRJNQEQVQFBIRKRBDZ7U5EC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2TMRJNQEQVQFBIRKRBDZ7U5EC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2TMRJNQEQVQFBIRKRBDZ7U5EC/action/storage_attestation","attest_author":"https://pith.science/pith/X2TMRJNQEQVQFBIRKRBDZ7U5EC/action/author_attestation","sign_citation":"https://pith.science/pith/X2TMRJNQEQVQFBIRKRBDZ7U5EC/action/citation_signature","submit_replication":"https://pith.science/pith/X2TMRJNQEQVQFBIRKRBDZ7U5EC/action/replication_record"}},"created_at":"2026-05-18T02:38:00.008870+00:00","updated_at":"2026-05-18T02:38:00.008870+00:00"}