{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6TES6JR4HHNF7DDS43SMY6BZFK","short_pith_number":"pith:6TES6JR4","canonical_record":{"source":{"id":"1109.2765","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-13T12:54:39Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"6127b91bea63efbd4b4007b23120ac8374ff1ac03acbf6c30e9d4d3ef7770ca8","abstract_canon_sha256":"ace6bc6888f107280b2c4813fd97e749dbc15b4daea2cbf6e2db741f96177a1d"},"schema_version":"1.0"},"canonical_sha256":"f4c92f263c39da5f8c72e6e4cc78392a9a3bd18545aa7c96ab9f03568d3c15c9","source":{"kind":"arxiv","id":"1109.2765","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2765","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2765v2","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2765","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"6TES6JR4HHNF","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6TES6JR4HHNF7DDS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6TES6JR4","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6TES6JR4HHNF7DDS43SMY6BZFK","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2765","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-13T12:54:39Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"6127b91bea63efbd4b4007b23120ac8374ff1ac03acbf6c30e9d4d3ef7770ca8","abstract_canon_sha256":"ace6bc6888f107280b2c4813fd97e749dbc15b4daea2cbf6e2db741f96177a1d"},"schema_version":"1.0"},"canonical_sha256":"f4c92f263c39da5f8c72e6e4cc78392a9a3bd18545aa7c96ab9f03568d3c15c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:00.489387Z","signature_b64":"oFwApXjpIqhBhL62oi993W+KZDwRIYKQlm0YGr/FGV41NYbIPmBJzwIqhQV1wD8iK37sO8d0YPd4eepdnY2nCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4c92f263c39da5f8c72e6e4cc78392a9a3bd18545aa7c96ab9f03568d3c15c9","last_reissued_at":"2026-05-18T02:58:00.488810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:00.488810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2765","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":"2026-05-18T02:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jel8Vn3nCeAaM1wFcE8lGE9Na6I1MNYEehyZUWM5b2aqjlXkG+JF24QzWw0h9ri7OHZ370LYkebO2BiRshGRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T17:51:34.620546Z"},"content_sha256":"a4015bc857d4704fff86823cfe4b6ed2990a1944f66e395cf2607d09baf45a4e","schema_version":"1.0","event_id":"sha256:a4015bc857d4704fff86823cfe4b6ed2990a1944f66e395cf2607d09baf45a4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6TES6JR4HHNF7DDS43SMY6BZFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separability of double cosets and conjugacy classes in 3-manifold groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Emily Hamilton, Henry Wilton, Pavel Zalesskii","submitted_at":"2011-09-13T12:54:39Z","abstract_excerpt":"Let M = H^3 / \\Gamma be a hyperbolic 3-manifold of finite volume. We show that if H and K are abelian subgroups of \\Gamma and g is in \\Gamma, then the double coset HgK is separable in \\Gamma. As a consequence we prove that if M is a closed, orientable, Haken 3-manifold and the fundamental group of every hyperbolic piece of the torus decomposition of M is conjugacy separable then so is the fundamental group of M. Invoking recent work of Agol and Wise, it follows that if M is a compact, orientable 3-manifold then \\pi_1(M) is conjugacy separable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2765","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":"2026-05-18T02:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kVW02W03IbO2aKcGfnpMqwzm1CX7N5U34zPLh+lkMdAYixO8T0PVTCA2VVev6doA4qKm1iXGXsK400GhI/NvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T17:51:34.620885Z"},"content_sha256":"1cf5f6c48b2a801953988944c7010bde05dcd2da1219f04142df330965f22021","schema_version":"1.0","event_id":"sha256:1cf5f6c48b2a801953988944c7010bde05dcd2da1219f04142df330965f22021"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TES6JR4HHNF7DDS43SMY6BZFK/bundle.json","state_url":"https://pith.science/pith/6TES6JR4HHNF7DDS43SMY6BZFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TES6JR4HHNF7DDS43SMY6BZFK/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":"2026-07-03T17:51:34Z","links":{"resolver":"https://pith.science/pith/6TES6JR4HHNF7DDS43SMY6BZFK","bundle":"https://pith.science/pith/6TES6JR4HHNF7DDS43SMY6BZFK/bundle.json","state":"https://pith.science/pith/6TES6JR4HHNF7DDS43SMY6BZFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TES6JR4HHNF7DDS43SMY6BZFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6TES6JR4HHNF7DDS43SMY6BZFK","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":"ace6bc6888f107280b2c4813fd97e749dbc15b4daea2cbf6e2db741f96177a1d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-13T12:54:39Z","title_canon_sha256":"6127b91bea63efbd4b4007b23120ac8374ff1ac03acbf6c30e9d4d3ef7770ca8"},"schema_version":"1.0","source":{"id":"1109.2765","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2765","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2765v2","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2765","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"6TES6JR4HHNF","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6TES6JR4HHNF7DDS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6TES6JR4","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:1cf5f6c48b2a801953988944c7010bde05dcd2da1219f04142df330965f22021","target":"graph","created_at":"2026-05-18T02:58:00Z","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":"Let M = H^3 / \\Gamma be a hyperbolic 3-manifold of finite volume. We show that if H and K are abelian subgroups of \\Gamma and g is in \\Gamma, then the double coset HgK is separable in \\Gamma. As a consequence we prove that if M is a closed, orientable, Haken 3-manifold and the fundamental group of every hyperbolic piece of the torus decomposition of M is conjugacy separable then so is the fundamental group of M. Invoking recent work of Agol and Wise, it follows that if M is a compact, orientable 3-manifold then \\pi_1(M) is conjugacy separable.","authors_text":"Emily Hamilton, Henry Wilton, Pavel Zalesskii","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-13T12:54:39Z","title":"Separability of double cosets and conjugacy classes in 3-manifold groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2765","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:a4015bc857d4704fff86823cfe4b6ed2990a1944f66e395cf2607d09baf45a4e","target":"record","created_at":"2026-05-18T02:58:00Z","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":"ace6bc6888f107280b2c4813fd97e749dbc15b4daea2cbf6e2db741f96177a1d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-13T12:54:39Z","title_canon_sha256":"6127b91bea63efbd4b4007b23120ac8374ff1ac03acbf6c30e9d4d3ef7770ca8"},"schema_version":"1.0","source":{"id":"1109.2765","kind":"arxiv","version":2}},"canonical_sha256":"f4c92f263c39da5f8c72e6e4cc78392a9a3bd18545aa7c96ab9f03568d3c15c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4c92f263c39da5f8c72e6e4cc78392a9a3bd18545aa7c96ab9f03568d3c15c9","first_computed_at":"2026-05-18T02:58:00.488810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.488810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oFwApXjpIqhBhL62oi993W+KZDwRIYKQlm0YGr/FGV41NYbIPmBJzwIqhQV1wD8iK37sO8d0YPd4eepdnY2nCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.489387Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2765","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4015bc857d4704fff86823cfe4b6ed2990a1944f66e395cf2607d09baf45a4e","sha256:1cf5f6c48b2a801953988944c7010bde05dcd2da1219f04142df330965f22021"],"state_sha256":"b2a88bbbce5331d16ad1ba27fdaca8ef0ea0b81375acb0c85080735ff189251e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LsYl5EIC/5I8CodUBlUkmFBzFC3WdcFJuOqfV7Yh83a0zIa5+XN04gqIvLX2GFdbYBxIpcTpYUOm/IZDA6G3Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T17:51:34.622748Z","bundle_sha256":"0b3555f253cee79e0707e8f5eb356ef4883b8da3030d977369e25134f2c228c4"}}