{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PQLULYJ74FDR3K35WELOUTMSZE","short_pith_number":"pith:PQLULYJ7","canonical_record":{"source":{"id":"1505.06595","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-25T11:22:24Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"a8d258ad9464f5d6c9dfbb014579319c6b53281799c9bd1b9145432d358952ad","abstract_canon_sha256":"995b52cca07480545e7e34dacb7f7bc3c26af2473b592f06291325d01b80d661"},"schema_version":"1.0"},"canonical_sha256":"7c1745e13fe1471dab7db116ea4d92c92a2e456d403cc4e4e84827018202bcd5","source":{"kind":"arxiv","id":"1505.06595","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06595","created_at":"2026-05-18T01:19:44Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06595v1","created_at":"2026-05-18T01:19:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06595","created_at":"2026-05-18T01:19:44Z"},{"alias_kind":"pith_short_12","alias_value":"PQLULYJ74FDR","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PQLULYJ74FDR3K35","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PQLULYJ7","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PQLULYJ74FDR3K35WELOUTMSZE","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06595","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-25T11:22:24Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"a8d258ad9464f5d6c9dfbb014579319c6b53281799c9bd1b9145432d358952ad","abstract_canon_sha256":"995b52cca07480545e7e34dacb7f7bc3c26af2473b592f06291325d01b80d661"},"schema_version":"1.0"},"canonical_sha256":"7c1745e13fe1471dab7db116ea4d92c92a2e456d403cc4e4e84827018202bcd5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:44.492225Z","signature_b64":"yssQl2luPtCXA6O6wm3exHI2i8g/UG7vqMDciEiuGo6rnwxvwnDJOo0cRYT9WlcMZ7Yx7x0CgY3lnv9FJORFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c1745e13fe1471dab7db116ea4d92c92a2e456d403cc4e4e84827018202bcd5","last_reissued_at":"2026-05-18T01:19:44.491597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:44.491597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06595","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":"2026-05-18T01:19:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TkQ4O6wY+PvFxR0Lq3PwEESmbkaK6zjXiEh6Q8RoKvFA4uxYaHFk5fil7HhepHPdebb5X2z2k5egGnHBGgX3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:12:41.648423Z"},"content_sha256":"7084a7707ba2e4728ed4bb57cb86cb4008d24cdca401c16741f02efb3efb0f79","schema_version":"1.0","event_id":"sha256:7084a7707ba2e4728ed4bb57cb86cb4008d24cdca401c16741f02efb3efb0f79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PQLULYJ74FDR3K35WELOUTMSZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A combinatorial approach to knot recognition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.GT","authors_text":"Alexei Lisitsa, Andrew Fish, David Stanovsk\\'y","submitted_at":"2015-05-25T11:22:24Z","abstract_excerpt":"This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be ut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06595","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":"2026-05-18T01:19:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D6ezCWvJVvXVbkJGZLppiJSVvRXv0ExTWN31VBM+J+2srx7oWmj225Fi6zaksulKJ0yE3X8PvZKVHJFeSResDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:12:41.649070Z"},"content_sha256":"187cc71ee9439ef4e030091f1b93858aeb6a0195722181440f79641962f2273b","schema_version":"1.0","event_id":"sha256:187cc71ee9439ef4e030091f1b93858aeb6a0195722181440f79641962f2273b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQLULYJ74FDR3K35WELOUTMSZE/bundle.json","state_url":"https://pith.science/pith/PQLULYJ74FDR3K35WELOUTMSZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQLULYJ74FDR3K35WELOUTMSZE/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":"2026-06-07T16:12:41Z","links":{"resolver":"https://pith.science/pith/PQLULYJ74FDR3K35WELOUTMSZE","bundle":"https://pith.science/pith/PQLULYJ74FDR3K35WELOUTMSZE/bundle.json","state":"https://pith.science/pith/PQLULYJ74FDR3K35WELOUTMSZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQLULYJ74FDR3K35WELOUTMSZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PQLULYJ74FDR3K35WELOUTMSZE","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":"995b52cca07480545e7e34dacb7f7bc3c26af2473b592f06291325d01b80d661","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-25T11:22:24Z","title_canon_sha256":"a8d258ad9464f5d6c9dfbb014579319c6b53281799c9bd1b9145432d358952ad"},"schema_version":"1.0","source":{"id":"1505.06595","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06595","created_at":"2026-05-18T01:19:44Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06595v1","created_at":"2026-05-18T01:19:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06595","created_at":"2026-05-18T01:19:44Z"},{"alias_kind":"pith_short_12","alias_value":"PQLULYJ74FDR","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PQLULYJ74FDR3K35","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PQLULYJ7","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:187cc71ee9439ef4e030091f1b93858aeb6a0195722181440f79641962f2273b","target":"graph","created_at":"2026-05-18T01:19:44Z","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":"This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be ut","authors_text":"Alexei Lisitsa, Andrew Fish, David Stanovsk\\'y","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-25T11:22:24Z","title":"A combinatorial approach to knot recognition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06595","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":"sha256:7084a7707ba2e4728ed4bb57cb86cb4008d24cdca401c16741f02efb3efb0f79","target":"record","created_at":"2026-05-18T01:19:44Z","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":"995b52cca07480545e7e34dacb7f7bc3c26af2473b592f06291325d01b80d661","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-25T11:22:24Z","title_canon_sha256":"a8d258ad9464f5d6c9dfbb014579319c6b53281799c9bd1b9145432d358952ad"},"schema_version":"1.0","source":{"id":"1505.06595","kind":"arxiv","version":1}},"canonical_sha256":"7c1745e13fe1471dab7db116ea4d92c92a2e456d403cc4e4e84827018202bcd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c1745e13fe1471dab7db116ea4d92c92a2e456d403cc4e4e84827018202bcd5","first_computed_at":"2026-05-18T01:19:44.491597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:44.491597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yssQl2luPtCXA6O6wm3exHI2i8g/UG7vqMDciEiuGo6rnwxvwnDJOo0cRYT9WlcMZ7Yx7x0CgY3lnv9FJORFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:44.492225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06595","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7084a7707ba2e4728ed4bb57cb86cb4008d24cdca401c16741f02efb3efb0f79","sha256:187cc71ee9439ef4e030091f1b93858aeb6a0195722181440f79641962f2273b"],"state_sha256":"2b05dc869ce4422c6f4474fdf55732533892858fe198f8bb82b137d36cbfea21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDViMce7OYn3+j5pjQ4XVZHdeKzAbxtMhLz4gKM7Sf+p7Z6ZYnHHOx9xTaRVnQHzlg9m77/h4+zmTOYR4ZAtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:12:41.651738Z","bundle_sha256":"bff9669e58c487e46ac479770a5865ed3ad9aa5c1a3be75508476782c21b6a3c"}}