{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LDHP74RST7PBTYIEKC4LB5YSSE","short_pith_number":"pith:LDHP74RS","canonical_record":{"source":{"id":"1210.4799","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-17T17:30:15Z","cross_cats_sorted":[],"title_canon_sha256":"4fd0c25f96996cec40007d222380484d64948e559f9af255906911ace700d31e","abstract_canon_sha256":"faec0219e6c7fa98f182d64ef0772ae8e9021b1e891f3460aa932d16cdda326b"},"schema_version":"1.0"},"canonical_sha256":"58cefff2329fde19e10450b8b0f712913778dd6b298ad090cf74ff62e6bd75fa","source":{"kind":"arxiv","id":"1210.4799","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4799","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4799v3","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4799","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"LDHP74RST7PB","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LDHP74RST7PBTYIE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LDHP74RS","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LDHP74RST7PBTYIEKC4LB5YSSE","target":"record","payload":{"canonical_record":{"source":{"id":"1210.4799","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-17T17:30:15Z","cross_cats_sorted":[],"title_canon_sha256":"4fd0c25f96996cec40007d222380484d64948e559f9af255906911ace700d31e","abstract_canon_sha256":"faec0219e6c7fa98f182d64ef0772ae8e9021b1e891f3460aa932d16cdda326b"},"schema_version":"1.0"},"canonical_sha256":"58cefff2329fde19e10450b8b0f712913778dd6b298ad090cf74ff62e6bd75fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:22.484057Z","signature_b64":"eDY31KArAWa1SW1SygWjol1pyesQpE+AShPwF1p+Z6TM9PJzmXriuH/P+Oim5+5oqaiRALe+qjRfXE8ymhU4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58cefff2329fde19e10450b8b0f712913778dd6b298ad090cf74ff62e6bd75fa","last_reissued_at":"2026-05-18T03:06:22.483370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:22.483370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.4799","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5WVUaIAElN9f/KrWLMzcqK8MMNF0RXAglKXbDT6Wj7SY+IDKBHGYLsvKRHYpT0sToVYRP+nRLY494FPJJ7Y6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:29:27.186733Z"},"content_sha256":"e0d199391e8c3a67686e8792aeed962dc90a6fcd198ee9f80f53668ee18af261","schema_version":"1.0","event_id":"sha256:e0d199391e8c3a67686e8792aeed962dc90a6fcd198ee9f80f53668ee18af261"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LDHP74RST7PBTYIEKC4LB5YSSE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The virtual fibering theorem for 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Stefan Friedl, Takahiro Kitayama","submitted_at":"2012-10-17T17:30:15Z","abstract_excerpt":"In 2007 Agol showed that if N is an aspherical compact 3-manifold with empty or toroidal boundary such that its fundamental group is virtually RFRS, then $N$ is virtually fibered. We give a largely self-contained proof of Agol's theorem using complexities of sutured manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4799","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+IgEJdL0tCVhfSJ6KiKGl3g1kMtF78nXZCdnU3NQRQPJXltO3oKvUQ40lXewdw14r/fKuNLD0Nj2um0gu6bXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:29:27.187408Z"},"content_sha256":"dbeb720f854da479f8bd65786ead2f5c62a97b64da9ebbf6ce3f20766bd28b92","schema_version":"1.0","event_id":"sha256:dbeb720f854da479f8bd65786ead2f5c62a97b64da9ebbf6ce3f20766bd28b92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDHP74RST7PBTYIEKC4LB5YSSE/bundle.json","state_url":"https://pith.science/pith/LDHP74RST7PBTYIEKC4LB5YSSE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDHP74RST7PBTYIEKC4LB5YSSE/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":"2026-05-26T22:29:27Z","links":{"resolver":"https://pith.science/pith/LDHP74RST7PBTYIEKC4LB5YSSE","bundle":"https://pith.science/pith/LDHP74RST7PBTYIEKC4LB5YSSE/bundle.json","state":"https://pith.science/pith/LDHP74RST7PBTYIEKC4LB5YSSE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDHP74RST7PBTYIEKC4LB5YSSE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LDHP74RST7PBTYIEKC4LB5YSSE","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":"faec0219e6c7fa98f182d64ef0772ae8e9021b1e891f3460aa932d16cdda326b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-17T17:30:15Z","title_canon_sha256":"4fd0c25f96996cec40007d222380484d64948e559f9af255906911ace700d31e"},"schema_version":"1.0","source":{"id":"1210.4799","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4799","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4799v3","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4799","created_at":"2026-05-18T03:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"LDHP74RST7PB","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LDHP74RST7PBTYIE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LDHP74RS","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:dbeb720f854da479f8bd65786ead2f5c62a97b64da9ebbf6ce3f20766bd28b92","target":"graph","created_at":"2026-05-18T03:06:22Z","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":"In 2007 Agol showed that if N is an aspherical compact 3-manifold with empty or toroidal boundary such that its fundamental group is virtually RFRS, then $N$ is virtually fibered. We give a largely self-contained proof of Agol's theorem using complexities of sutured manifolds.","authors_text":"Stefan Friedl, Takahiro Kitayama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-17T17:30:15Z","title":"The virtual fibering theorem for 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4799","kind":"arxiv","version":3},"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:e0d199391e8c3a67686e8792aeed962dc90a6fcd198ee9f80f53668ee18af261","target":"record","created_at":"2026-05-18T03:06:22Z","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":"faec0219e6c7fa98f182d64ef0772ae8e9021b1e891f3460aa932d16cdda326b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-17T17:30:15Z","title_canon_sha256":"4fd0c25f96996cec40007d222380484d64948e559f9af255906911ace700d31e"},"schema_version":"1.0","source":{"id":"1210.4799","kind":"arxiv","version":3}},"canonical_sha256":"58cefff2329fde19e10450b8b0f712913778dd6b298ad090cf74ff62e6bd75fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58cefff2329fde19e10450b8b0f712913778dd6b298ad090cf74ff62e6bd75fa","first_computed_at":"2026-05-18T03:06:22.483370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:22.483370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eDY31KArAWa1SW1SygWjol1pyesQpE+AShPwF1p+Z6TM9PJzmXriuH/P+Oim5+5oqaiRALe+qjRfXE8ymhU4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:22.484057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4799","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0d199391e8c3a67686e8792aeed962dc90a6fcd198ee9f80f53668ee18af261","sha256:dbeb720f854da479f8bd65786ead2f5c62a97b64da9ebbf6ce3f20766bd28b92"],"state_sha256":"9b2f79506b201d2c84070ad9e993b5d6927c531e3fa0c9f48f4ff39aff40bd92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oxPoJdT/d72b3/sm4zkuguW1IMPDxIdkMvIeiWkZhxi/XnGvsJurGS1i3YtkAKap0z9jrkMKy3SYz0UxD71NAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:29:27.190830Z","bundle_sha256":"4a024479ecc04094460608941ce247385a216fd562e3b901ae7c6c3aab5ee8e6"}}