{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EMDCP55Q7AVVNJQCEDSQC7VVE3","short_pith_number":"pith:EMDCP55Q","canonical_record":{"source":{"id":"1609.07819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-26T00:13:57Z","cross_cats_sorted":[],"title_canon_sha256":"458525474b0101985d9c397ee4adac6925d0bba28257919276735a74ff354057","abstract_canon_sha256":"10a5a5860d3964d493758a4699cbbec33ca5d58c321c99c9e750226942140d5c"},"schema_version":"1.0"},"canonical_sha256":"230627f7b0f82b56a60220e5017eb526e79f0a00747183d26f7f6716bc3b1176","source":{"kind":"arxiv","id":"1609.07819","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07819","created_at":"2026-05-18T01:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07819v1","created_at":"2026-05-18T01:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07819","created_at":"2026-05-18T01:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"EMDCP55Q7AVV","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EMDCP55Q7AVVNJQC","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EMDCP55Q","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EMDCP55Q7AVVNJQCEDSQC7VVE3","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-26T00:13:57Z","cross_cats_sorted":[],"title_canon_sha256":"458525474b0101985d9c397ee4adac6925d0bba28257919276735a74ff354057","abstract_canon_sha256":"10a5a5860d3964d493758a4699cbbec33ca5d58c321c99c9e750226942140d5c"},"schema_version":"1.0"},"canonical_sha256":"230627f7b0f82b56a60220e5017eb526e79f0a00747183d26f7f6716bc3b1176","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:55.337290Z","signature_b64":"dYkRlOtRl7N4m4zo2AKXUq0pZ7L8FFMNhLIDGeiih0m5+Vu7AlWmoQguvsuP1TGB6mGOsv6moMazb16CKGucCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"230627f7b0f82b56a60220e5017eb526e79f0a00747183d26f7f6716bc3b1176","last_reissued_at":"2026-05-18T01:03:55.336453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:55.336453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07819","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LJTBoMxuIhkpvJRdCawPW7H/WHhd/h7x9ia53JamNC7ihJG4r2R3/wVLM2sAl/7PY+yqmQXDIsXpgEyb2aK6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:06:49.280634Z"},"content_sha256":"1fb3ec91d6f8a98e4a701b80e08479dcedf777bd26557c94e22330b97f1c225d","schema_version":"1.0","event_id":"sha256:1fb3ec91d6f8a98e4a701b80e08479dcedf777bd26557c94e22330b97f1c225d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EMDCP55Q7AVVNJQCEDSQC7VVE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on Riley polynomials of $2$-bridge knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Takayuki Morifuji, Teruaki Kitano","submitted_at":"2016-09-26T00:13:57Z","abstract_excerpt":"In this short note we show the existence of an epimorphism between groups of $2$-bridge knots by means of an elementary argument using the Riley polynomial. As a corollary, we give a classification of $2$-bridge knots by Riley polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07819","kind":"arxiv","version":1},"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":"2026-05-18T01:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLvlBqsQrEtM8R7RaKzU7HiEY9P8T90X+VXnidRbW4Bg20IGcUTEgz7NpaRsFpXcXUtkSObaZmKS5Zs4A6nTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:06:49.280986Z"},"content_sha256":"699017e80445e7d1816c8baa647f1d611170b849075f60584161321c9d827c09","schema_version":"1.0","event_id":"sha256:699017e80445e7d1816c8baa647f1d611170b849075f60584161321c9d827c09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMDCP55Q7AVVNJQCEDSQC7VVE3/bundle.json","state_url":"https://pith.science/pith/EMDCP55Q7AVVNJQCEDSQC7VVE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMDCP55Q7AVVNJQCEDSQC7VVE3/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":"2026-05-28T20:06:49Z","links":{"resolver":"https://pith.science/pith/EMDCP55Q7AVVNJQCEDSQC7VVE3","bundle":"https://pith.science/pith/EMDCP55Q7AVVNJQCEDSQC7VVE3/bundle.json","state":"https://pith.science/pith/EMDCP55Q7AVVNJQCEDSQC7VVE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMDCP55Q7AVVNJQCEDSQC7VVE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EMDCP55Q7AVVNJQCEDSQC7VVE3","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":"10a5a5860d3964d493758a4699cbbec33ca5d58c321c99c9e750226942140d5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-26T00:13:57Z","title_canon_sha256":"458525474b0101985d9c397ee4adac6925d0bba28257919276735a74ff354057"},"schema_version":"1.0","source":{"id":"1609.07819","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07819","created_at":"2026-05-18T01:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07819v1","created_at":"2026-05-18T01:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07819","created_at":"2026-05-18T01:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"EMDCP55Q7AVV","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EMDCP55Q7AVVNJQC","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EMDCP55Q","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:699017e80445e7d1816c8baa647f1d611170b849075f60584161321c9d827c09","target":"graph","created_at":"2026-05-18T01:03:55Z","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 this short note we show the existence of an epimorphism between groups of $2$-bridge knots by means of an elementary argument using the Riley polynomial. As a corollary, we give a classification of $2$-bridge knots by Riley polynomials.","authors_text":"Takayuki Morifuji, Teruaki Kitano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-26T00:13:57Z","title":"A note on Riley polynomials of $2$-bridge knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07819","kind":"arxiv","version":1},"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":"sha256:1fb3ec91d6f8a98e4a701b80e08479dcedf777bd26557c94e22330b97f1c225d","target":"record","created_at":"2026-05-18T01:03:55Z","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":"10a5a5860d3964d493758a4699cbbec33ca5d58c321c99c9e750226942140d5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-26T00:13:57Z","title_canon_sha256":"458525474b0101985d9c397ee4adac6925d0bba28257919276735a74ff354057"},"schema_version":"1.0","source":{"id":"1609.07819","kind":"arxiv","version":1}},"canonical_sha256":"230627f7b0f82b56a60220e5017eb526e79f0a00747183d26f7f6716bc3b1176","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"230627f7b0f82b56a60220e5017eb526e79f0a00747183d26f7f6716bc3b1176","first_computed_at":"2026-05-18T01:03:55.336453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:55.336453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dYkRlOtRl7N4m4zo2AKXUq0pZ7L8FFMNhLIDGeiih0m5+Vu7AlWmoQguvsuP1TGB6mGOsv6moMazb16CKGucCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:55.337290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07819","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fb3ec91d6f8a98e4a701b80e08479dcedf777bd26557c94e22330b97f1c225d","sha256:699017e80445e7d1816c8baa647f1d611170b849075f60584161321c9d827c09"],"state_sha256":"be253a5d904f6c2e35878c7bd97a8940bbe8b771d0370f8bda29b605521ce4a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dHGaa6qCDN/2kfgo8kJooN3Od6DJ3sUaJ1nVVhKZJUi5+EjKUTXe2fcO4mmIuSDW6dGoxED90Qf9vY4Ym7J/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:06:49.282970Z","bundle_sha256":"62039009e94c1210f9b6754ab0514cf6868b0d3fe9dd8a6b8ab7f0f54139968f"}}