{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U2B7NUIATIYQR54PN5GZB5CWMB","short_pith_number":"pith:U2B7NUIA","canonical_record":{"source":{"id":"1302.3812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T17:21:21Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"15e6345b4484ded9988ffc49b66f6e7f26074382ce197b1f2d369092121c9acf","abstract_canon_sha256":"58f5ce11953505a187b414dc046b9abe34a75c9f8953c3a0fc959e27e526d9b1"},"schema_version":"1.0"},"canonical_sha256":"a683f6d1009a3108f78f6f4d90f45660564d111e13e1ce5b479169c7b20f9b65","source":{"kind":"arxiv","id":"1302.3812","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3812","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3812v2","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3812","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"U2B7NUIATIYQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2B7NUIATIYQR54P","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2B7NUIA","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U2B7NUIATIYQR54PN5GZB5CWMB","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T17:21:21Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"15e6345b4484ded9988ffc49b66f6e7f26074382ce197b1f2d369092121c9acf","abstract_canon_sha256":"58f5ce11953505a187b414dc046b9abe34a75c9f8953c3a0fc959e27e526d9b1"},"schema_version":"1.0"},"canonical_sha256":"a683f6d1009a3108f78f6f4d90f45660564d111e13e1ce5b479169c7b20f9b65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:36.653517Z","signature_b64":"m3DF1l0CFCjZg4NQGAi/NoOzOWzj1keGiSZjamXovAs2KoM+oZPro8S71q40i2TcvjJBEj6QwtxMwraKBIjEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a683f6d1009a3108f78f6f4d90f45660564d111e13e1ce5b479169c7b20f9b65","last_reissued_at":"2026-05-18T01:15:36.652769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:36.652769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3812","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":"2026-05-18T01:15:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oz7rNDjXvvtllqMBgJmnK0yA/O2ehPfGVyoTxsKrqcJ9916ib/ZxcvrybY5Q04Hb4gRGcH8UO0ky0ltK33GTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:07:36.447700Z"},"content_sha256":"e9a2e815097f4b8c786832652b15a95cc7a5bc77f39f3e2185dff2c1b8515d13","schema_version":"1.0","event_id":"sha256:e9a2e815097f4b8c786832652b15a95cc7a5bc77f39f3e2185dff2c1b8515d13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U2B7NUIATIYQR54PN5GZB5CWMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost commensurability of 3-dimensional Anosov flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Pierre Dehornoy","submitted_at":"2013-02-15T17:21:21Z","abstract_excerpt":"Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and all geodesic flows on unit tangent bundles to hyperbolic 2-orbifolds are pairwise almost commensurable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3812","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":"2026-05-18T01:15:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5oiOFQi/y9sfhAegiLadvEt6ac6qHXwBUETOa8jIjHqXCbQduh7C1eZwZL8IFtErLsa7Lzw3B0gVQq36lrRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:07:36.448036Z"},"content_sha256":"ee95eb27c620a244124c02a55a8f170dc09545102932cbb6d4a35dcbbb6a47ff","schema_version":"1.0","event_id":"sha256:ee95eb27c620a244124c02a55a8f170dc09545102932cbb6d4a35dcbbb6a47ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2B7NUIATIYQR54PN5GZB5CWMB/bundle.json","state_url":"https://pith.science/pith/U2B7NUIATIYQR54PN5GZB5CWMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2B7NUIATIYQR54PN5GZB5CWMB/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":"2026-06-27T00:07:36Z","links":{"resolver":"https://pith.science/pith/U2B7NUIATIYQR54PN5GZB5CWMB","bundle":"https://pith.science/pith/U2B7NUIATIYQR54PN5GZB5CWMB/bundle.json","state":"https://pith.science/pith/U2B7NUIATIYQR54PN5GZB5CWMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2B7NUIATIYQR54PN5GZB5CWMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U2B7NUIATIYQR54PN5GZB5CWMB","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":"58f5ce11953505a187b414dc046b9abe34a75c9f8953c3a0fc959e27e526d9b1","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T17:21:21Z","title_canon_sha256":"15e6345b4484ded9988ffc49b66f6e7f26074382ce197b1f2d369092121c9acf"},"schema_version":"1.0","source":{"id":"1302.3812","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3812","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3812v2","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3812","created_at":"2026-05-18T01:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"U2B7NUIATIYQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2B7NUIATIYQR54P","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2B7NUIA","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:ee95eb27c620a244124c02a55a8f170dc09545102932cbb6d4a35dcbbb6a47ff","target":"graph","created_at":"2026-05-18T01:15:36Z","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":"Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and all geodesic flows on unit tangent bundles to hyperbolic 2-orbifolds are pairwise almost commensurable.","authors_text":"Pierre Dehornoy","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T17:21:21Z","title":"Almost commensurability of 3-dimensional Anosov flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3812","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:e9a2e815097f4b8c786832652b15a95cc7a5bc77f39f3e2185dff2c1b8515d13","target":"record","created_at":"2026-05-18T01:15:36Z","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":"58f5ce11953505a187b414dc046b9abe34a75c9f8953c3a0fc959e27e526d9b1","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T17:21:21Z","title_canon_sha256":"15e6345b4484ded9988ffc49b66f6e7f26074382ce197b1f2d369092121c9acf"},"schema_version":"1.0","source":{"id":"1302.3812","kind":"arxiv","version":2}},"canonical_sha256":"a683f6d1009a3108f78f6f4d90f45660564d111e13e1ce5b479169c7b20f9b65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a683f6d1009a3108f78f6f4d90f45660564d111e13e1ce5b479169c7b20f9b65","first_computed_at":"2026-05-18T01:15:36.652769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:36.652769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m3DF1l0CFCjZg4NQGAi/NoOzOWzj1keGiSZjamXovAs2KoM+oZPro8S71q40i2TcvjJBEj6QwtxMwraKBIjEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:36.653517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3812","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9a2e815097f4b8c786832652b15a95cc7a5bc77f39f3e2185dff2c1b8515d13","sha256:ee95eb27c620a244124c02a55a8f170dc09545102932cbb6d4a35dcbbb6a47ff"],"state_sha256":"98e5487a0ae2544cebf0290ea881ccfcbd7d187f64e9e57f4fbbe863a0b0da10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iF9QFxUjB0k6K+Z20yaWeHdesIHdSj3czUjhTCV35EG8u6snvJukw1bX42OlBngK+5m4CnW54Fi9BSi6N2NSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T00:07:36.449882Z","bundle_sha256":"30bb30e14ec3f19cdd603d8d5b756d7ccdf24d427a4648b5d40ff8721db2575c"}}