{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WFX3O73JCK6FNWPQAPJF3KGQPN","short_pith_number":"pith:WFX3O73J","canonical_record":{"source":{"id":"1003.0411","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-01T17:51:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"50f7af4af3d35a0364a3c27e1dd2a42bccb0dd482ec0182a32bdc1c87f620ed1","abstract_canon_sha256":"14a747949799543136ea04891aebd7bf0ae4beb97cdcc086059ddff077ee3e84"},"schema_version":"1.0"},"canonical_sha256":"b16fb77f6912bc56d9f003d25da8d07b5e0c955eecdfa66a869df3d8561f5ea1","source":{"kind":"arxiv","id":"1003.0411","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0411","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0411v2","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0411","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"WFX3O73JCK6F","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WFX3O73JCK6FNWPQ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WFX3O73J","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WFX3O73JCK6FNWPQAPJF3KGQPN","target":"record","payload":{"canonical_record":{"source":{"id":"1003.0411","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-01T17:51:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"50f7af4af3d35a0364a3c27e1dd2a42bccb0dd482ec0182a32bdc1c87f620ed1","abstract_canon_sha256":"14a747949799543136ea04891aebd7bf0ae4beb97cdcc086059ddff077ee3e84"},"schema_version":"1.0"},"canonical_sha256":"b16fb77f6912bc56d9f003d25da8d07b5e0c955eecdfa66a869df3d8561f5ea1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:13.321457Z","signature_b64":"lsLxALeegv+DgQoOo9y3QEMjQ3NytN2lNULU+/a4tYfyhhMSeWcOP0bbOcH/zv6doQ0wK57IQGmaN2E+GFqcCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b16fb77f6912bc56d9f003d25da8d07b5e0c955eecdfa66a869df3d8561f5ea1","last_reissued_at":"2026-05-18T04:25:13.320654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:13.320654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.0411","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJEE0THi4Oxdp0Iq8my4B2If/XkwVo5oKVRc/JmFxWvaMSiCpmpy37yIqK0ViL8pSyrhqeHr6DnKvBjDk5P3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:05:54.958111Z"},"content_sha256":"d183805c3039c892a831d36507decd6d567f6eb8be8977ffd27075be3a6e8b21","schema_version":"1.0","event_id":"sha256:d183805c3039c892a831d36507decd6d567f6eb8be8977ffd27075be3a6e8b21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WFX3O73JCK6FNWPQAPJF3KGQPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On fibered commensurability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Danny Calegari, Hongbin Sun, Shicheng Wang","submitted_at":"2010-03-01T17:51:32Z","abstract_excerpt":"This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over the circle. We show that every hyperbolic fibered commensurability class contains a unique minimal element, whereas the class of Seifert manifolds fibering over the circle consists of a single commensurability class with infinitely many minimal elements. The situation for non-geometric manifolds is more complicated, and we illustrate a range of phenomena that can occur in this context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0411","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mUAdzyVTP1ekgYwxSyo4OHAvsdc5jCwqd0G+UdyTuARM/GwoVEof3Tq+CI69BI71pWo2hNbWa65bREHs86HTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:05:54.958797Z"},"content_sha256":"41ab9d8766c4fbfe77a7797b4502114ad9cac989afac5318eab8d23a77aa4fed","schema_version":"1.0","event_id":"sha256:41ab9d8766c4fbfe77a7797b4502114ad9cac989afac5318eab8d23a77aa4fed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFX3O73JCK6FNWPQAPJF3KGQPN/bundle.json","state_url":"https://pith.science/pith/WFX3O73JCK6FNWPQAPJF3KGQPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFX3O73JCK6FNWPQAPJF3KGQPN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T08:05:54Z","links":{"resolver":"https://pith.science/pith/WFX3O73JCK6FNWPQAPJF3KGQPN","bundle":"https://pith.science/pith/WFX3O73JCK6FNWPQAPJF3KGQPN/bundle.json","state":"https://pith.science/pith/WFX3O73JCK6FNWPQAPJF3KGQPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFX3O73JCK6FNWPQAPJF3KGQPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WFX3O73JCK6FNWPQAPJF3KGQPN","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":"14a747949799543136ea04891aebd7bf0ae4beb97cdcc086059ddff077ee3e84","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-01T17:51:32Z","title_canon_sha256":"50f7af4af3d35a0364a3c27e1dd2a42bccb0dd482ec0182a32bdc1c87f620ed1"},"schema_version":"1.0","source":{"id":"1003.0411","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0411","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0411v2","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0411","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"WFX3O73JCK6F","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WFX3O73JCK6FNWPQ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WFX3O73J","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:41ab9d8766c4fbfe77a7797b4502114ad9cac989afac5318eab8d23a77aa4fed","target":"graph","created_at":"2026-05-18T04:25:13Z","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":"This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over the circle. We show that every hyperbolic fibered commensurability class contains a unique minimal element, whereas the class of Seifert manifolds fibering over the circle consists of a single commensurability class with infinitely many minimal elements. The situation for non-geometric manifolds is more complicated, and we illustrate a range of phenomena that can occur in this context.","authors_text":"Danny Calegari, Hongbin Sun, Shicheng Wang","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-01T17:51:32Z","title":"On fibered commensurability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0411","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:d183805c3039c892a831d36507decd6d567f6eb8be8977ffd27075be3a6e8b21","target":"record","created_at":"2026-05-18T04:25:13Z","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":"14a747949799543136ea04891aebd7bf0ae4beb97cdcc086059ddff077ee3e84","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-01T17:51:32Z","title_canon_sha256":"50f7af4af3d35a0364a3c27e1dd2a42bccb0dd482ec0182a32bdc1c87f620ed1"},"schema_version":"1.0","source":{"id":"1003.0411","kind":"arxiv","version":2}},"canonical_sha256":"b16fb77f6912bc56d9f003d25da8d07b5e0c955eecdfa66a869df3d8561f5ea1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b16fb77f6912bc56d9f003d25da8d07b5e0c955eecdfa66a869df3d8561f5ea1","first_computed_at":"2026-05-18T04:25:13.320654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:13.320654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lsLxALeegv+DgQoOo9y3QEMjQ3NytN2lNULU+/a4tYfyhhMSeWcOP0bbOcH/zv6doQ0wK57IQGmaN2E+GFqcCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:13.321457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.0411","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d183805c3039c892a831d36507decd6d567f6eb8be8977ffd27075be3a6e8b21","sha256:41ab9d8766c4fbfe77a7797b4502114ad9cac989afac5318eab8d23a77aa4fed"],"state_sha256":"afe4b0ab18bf07e71bd0a01184ecc922df14cf9e5bda07cb710bf837ff02e267"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MhXxH0r9EDdjejfk1g2Acv5z1VrokT6AFyXfHNkjrD71vOJX2r2DP197mP1aS2IezYwfNMCQWpJlJee/K7XSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:05:54.962622Z","bundle_sha256":"c70a512fef4719e082ffb98f9ecde66090abcb6703328d63584abcc353417936"}}