{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5ANL6GXPCVHAOGMLE2S7Y4Y6CN","short_pith_number":"pith:5ANL6GXP","canonical_record":{"source":{"id":"1604.07490","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-26T01:30:11Z","cross_cats_sorted":[],"title_canon_sha256":"f406f5325f9ba6a36fd8ce257744a956f4f50b0ded55fbf17f3d9af0ba374a9c","abstract_canon_sha256":"002eaecf346f2d70cc1ea6f8037bf189111f2d5906febd6120bbf67d9569fa16"},"schema_version":"1.0"},"canonical_sha256":"e81abf1aef154e07198b26a5fc731e135d0dc631d4eb4d1a98ea11a7c17aea1e","source":{"kind":"arxiv","id":"1604.07490","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07490","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07490v3","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07490","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"5ANL6GXPCVHA","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"5ANL6GXPCVHAOGML","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"5ANL6GXP","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5ANL6GXPCVHAOGMLE2S7Y4Y6CN","target":"record","payload":{"canonical_record":{"source":{"id":"1604.07490","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-26T01:30:11Z","cross_cats_sorted":[],"title_canon_sha256":"f406f5325f9ba6a36fd8ce257744a956f4f50b0ded55fbf17f3d9af0ba374a9c","abstract_canon_sha256":"002eaecf346f2d70cc1ea6f8037bf189111f2d5906febd6120bbf67d9569fa16"},"schema_version":"1.0"},"canonical_sha256":"e81abf1aef154e07198b26a5fc731e135d0dc631d4eb4d1a98ea11a7c17aea1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:22.466840Z","signature_b64":"6xYqy/RgHwqmZs8JljU52zSzHhBPth1P8M+PDvRTVTg9jTkhnQS0Xa2iAD7rYfQCu6Z+biHA8C6j7aAnT3p7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e81abf1aef154e07198b26a5fc731e135d0dc631d4eb4d1a98ea11a7c17aea1e","last_reissued_at":"2026-05-18T00:50:22.466022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:22.466022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.07490","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":"2026-05-18T00:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N48Kx1YJ4CawAU19kO5x0jzk31w+yvlfc2ryDuxvjEB2HXOPxMNvCqcRHSHxASr2YzXu48T629+Ct2JSFfpGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:37:49.672573Z"},"content_sha256":"1efed005d11fbc1677a110ca7a37ca2c5f075068350cbcde30a1bc5dc80afc9b","schema_version":"1.0","event_id":"sha256:1efed005d11fbc1677a110ca7a37ca2c5f075068350cbcde30a1bc5dc80afc9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5ANL6GXPCVHAOGMLE2S7Y4Y6CN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted Alexander invariants and Hyperbolic volume","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hiroshi Goda","submitted_at":"2016-04-26T01:30:11Z","abstract_excerpt":"We give a volume formula of hyperbolic knot complements using twisted Alexander invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07490","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":"2026-05-18T00:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8l7mnodL7oGSM0x1WwhSJCIzJdxBzV6gIJ0vQuai00F/WGHCc44cCMUXXkR6OS7v5xRzk2kqOOBQHooxjytjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:37:49.673202Z"},"content_sha256":"b899c6b88eb3646e288329e10d06cd8e5f3f70c3a5e955377edf0deb46377cbd","schema_version":"1.0","event_id":"sha256:b899c6b88eb3646e288329e10d06cd8e5f3f70c3a5e955377edf0deb46377cbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ANL6GXPCVHAOGMLE2S7Y4Y6CN/bundle.json","state_url":"https://pith.science/pith/5ANL6GXPCVHAOGMLE2S7Y4Y6CN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ANL6GXPCVHAOGMLE2S7Y4Y6CN/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":"2026-05-28T23:37:49Z","links":{"resolver":"https://pith.science/pith/5ANL6GXPCVHAOGMLE2S7Y4Y6CN","bundle":"https://pith.science/pith/5ANL6GXPCVHAOGMLE2S7Y4Y6CN/bundle.json","state":"https://pith.science/pith/5ANL6GXPCVHAOGMLE2S7Y4Y6CN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ANL6GXPCVHAOGMLE2S7Y4Y6CN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5ANL6GXPCVHAOGMLE2S7Y4Y6CN","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":"002eaecf346f2d70cc1ea6f8037bf189111f2d5906febd6120bbf67d9569fa16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-26T01:30:11Z","title_canon_sha256":"f406f5325f9ba6a36fd8ce257744a956f4f50b0ded55fbf17f3d9af0ba374a9c"},"schema_version":"1.0","source":{"id":"1604.07490","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07490","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07490v3","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07490","created_at":"2026-05-18T00:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"5ANL6GXPCVHA","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"5ANL6GXPCVHAOGML","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"5ANL6GXP","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:b899c6b88eb3646e288329e10d06cd8e5f3f70c3a5e955377edf0deb46377cbd","target":"graph","created_at":"2026-05-18T00:50:22Z","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":"We give a volume formula of hyperbolic knot complements using twisted Alexander invariants.","authors_text":"Hiroshi Goda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-26T01:30:11Z","title":"Twisted Alexander invariants and Hyperbolic volume"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07490","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":"sha256:1efed005d11fbc1677a110ca7a37ca2c5f075068350cbcde30a1bc5dc80afc9b","target":"record","created_at":"2026-05-18T00:50:22Z","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":"002eaecf346f2d70cc1ea6f8037bf189111f2d5906febd6120bbf67d9569fa16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-26T01:30:11Z","title_canon_sha256":"f406f5325f9ba6a36fd8ce257744a956f4f50b0ded55fbf17f3d9af0ba374a9c"},"schema_version":"1.0","source":{"id":"1604.07490","kind":"arxiv","version":3}},"canonical_sha256":"e81abf1aef154e07198b26a5fc731e135d0dc631d4eb4d1a98ea11a7c17aea1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e81abf1aef154e07198b26a5fc731e135d0dc631d4eb4d1a98ea11a7c17aea1e","first_computed_at":"2026-05-18T00:50:22.466022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:22.466022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6xYqy/RgHwqmZs8JljU52zSzHhBPth1P8M+PDvRTVTg9jTkhnQS0Xa2iAD7rYfQCu6Z+biHA8C6j7aAnT3p7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:22.466840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.07490","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1efed005d11fbc1677a110ca7a37ca2c5f075068350cbcde30a1bc5dc80afc9b","sha256:b899c6b88eb3646e288329e10d06cd8e5f3f70c3a5e955377edf0deb46377cbd"],"state_sha256":"b2530e7659bc70dd8c7e694e83935e79692c52efb57a1700688584e53e1b645a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Me6yb8PXEZZcpquhEenBs21rhT0KH6wZcDkGuILl4j0gncp3xF/iboiydUKBgbCT4In3YPgBE89dixWcoecSBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:37:49.676789Z","bundle_sha256":"4ef266bdfb5195d887dbc15ee6271cb7192469d6a80bc3cec5e91b413fcf859b"}}