{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XDD64XYZTTHUMRYAZW7GLDKDFZ","short_pith_number":"pith:XDD64XYZ","canonical_record":{"source":{"id":"1110.3952","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-18T12:27:22Z","cross_cats_sorted":[],"title_canon_sha256":"add1ca6cffe0ff64b62c73f291675bae5c67caf95ddbfb0decb27afc19921beb","abstract_canon_sha256":"2e1c2bb4ef5f9cfc921b2b0a6afcc33f37a9063401aed4933bcb5d9ad78be88d"},"schema_version":"1.0"},"canonical_sha256":"b8c7ee5f199ccf464700cdbe658d432e66c6c0eb866b09abdf649f1e3f8e0181","source":{"kind":"arxiv","id":"1110.3952","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3952","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3952v2","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3952","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"XDD64XYZTTHU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XDD64XYZTTHUMRYA","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XDD64XYZ","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XDD64XYZTTHUMRYAZW7GLDKDFZ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3952","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-18T12:27:22Z","cross_cats_sorted":[],"title_canon_sha256":"add1ca6cffe0ff64b62c73f291675bae5c67caf95ddbfb0decb27afc19921beb","abstract_canon_sha256":"2e1c2bb4ef5f9cfc921b2b0a6afcc33f37a9063401aed4933bcb5d9ad78be88d"},"schema_version":"1.0"},"canonical_sha256":"b8c7ee5f199ccf464700cdbe658d432e66c6c0eb866b09abdf649f1e3f8e0181","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:23.737027Z","signature_b64":"p0gGMikhsYvBsNFLY/Q11cGcaEQLh6walo9R7neRYtBh/sgmuZYPppFjmlrhsDwYPL+f4xdCxEactUPgeP+eAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8c7ee5f199ccf464700cdbe658d432e66c6c0eb866b09abdf649f1e3f8e0181","last_reissued_at":"2026-05-18T04:01:23.736388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:23.736388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3952","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":"2026-05-18T04:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVqg+PAsSBMWHuuheNDCfO726DaWr0FOnbC6m1khLTPWjHyWzgrRUN5M33754U3Ch9OSsN9lXGNqdT5A9EotDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:44:06.167600Z"},"content_sha256":"a2493b08b35e0f4672a347928d10d74138d8fa0aec6c586d2c717e8a9c775864","schema_version":"1.0","event_id":"sha256:a2493b08b35e0f4672a347928d10d74138d8fa0aec6c586d2c717e8a9c775864"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XDD64XYZTTHUMRYAZW7GLDKDFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On linear $n$-colorings for knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Chuichiro Hayashi, Kanako Oshiro, Miwa Hayashi","submitted_at":"2011-10-18T12:27:22Z","abstract_excerpt":"If a knot has the Alexander polynomial not equal to 1, then it is linear $n$-colorable.\n  By means of such a coloring, such a knot is given an upper bound for the minimal quandle order, i.e., the minimal order of a quandle with which the knot is quandle colorable.\n  For twist knots, we study the minimal quandle orders in detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3952","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":"2026-05-18T04:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OuVr1haovivob/xjBBdgwjOv6k+sMjUWhAqGo3JIHTS/YToq1HdJj54Tq8oDcy2tQ7XbHwDbwg2AvZGQ1OngBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:44:06.167962Z"},"content_sha256":"fb819a49e536929989d6541a31d81a4a37c9d2f6596492c7c73fd1ea828bbb54","schema_version":"1.0","event_id":"sha256:fb819a49e536929989d6541a31d81a4a37c9d2f6596492c7c73fd1ea828bbb54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XDD64XYZTTHUMRYAZW7GLDKDFZ/bundle.json","state_url":"https://pith.science/pith/XDD64XYZTTHUMRYAZW7GLDKDFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XDD64XYZTTHUMRYAZW7GLDKDFZ/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":"2026-06-05T15:44:06Z","links":{"resolver":"https://pith.science/pith/XDD64XYZTTHUMRYAZW7GLDKDFZ","bundle":"https://pith.science/pith/XDD64XYZTTHUMRYAZW7GLDKDFZ/bundle.json","state":"https://pith.science/pith/XDD64XYZTTHUMRYAZW7GLDKDFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XDD64XYZTTHUMRYAZW7GLDKDFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XDD64XYZTTHUMRYAZW7GLDKDFZ","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":"2e1c2bb4ef5f9cfc921b2b0a6afcc33f37a9063401aed4933bcb5d9ad78be88d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-18T12:27:22Z","title_canon_sha256":"add1ca6cffe0ff64b62c73f291675bae5c67caf95ddbfb0decb27afc19921beb"},"schema_version":"1.0","source":{"id":"1110.3952","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3952","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3952v2","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3952","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"XDD64XYZTTHU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XDD64XYZTTHUMRYA","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XDD64XYZ","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:fb819a49e536929989d6541a31d81a4a37c9d2f6596492c7c73fd1ea828bbb54","target":"graph","created_at":"2026-05-18T04:01:23Z","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":"If a knot has the Alexander polynomial not equal to 1, then it is linear $n$-colorable.\n  By means of such a coloring, such a knot is given an upper bound for the minimal quandle order, i.e., the minimal order of a quandle with which the knot is quandle colorable.\n  For twist knots, we study the minimal quandle orders in detail.","authors_text":"Chuichiro Hayashi, Kanako Oshiro, Miwa Hayashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-18T12:27:22Z","title":"On linear $n$-colorings for knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3952","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:a2493b08b35e0f4672a347928d10d74138d8fa0aec6c586d2c717e8a9c775864","target":"record","created_at":"2026-05-18T04:01:23Z","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":"2e1c2bb4ef5f9cfc921b2b0a6afcc33f37a9063401aed4933bcb5d9ad78be88d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-18T12:27:22Z","title_canon_sha256":"add1ca6cffe0ff64b62c73f291675bae5c67caf95ddbfb0decb27afc19921beb"},"schema_version":"1.0","source":{"id":"1110.3952","kind":"arxiv","version":2}},"canonical_sha256":"b8c7ee5f199ccf464700cdbe658d432e66c6c0eb866b09abdf649f1e3f8e0181","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8c7ee5f199ccf464700cdbe658d432e66c6c0eb866b09abdf649f1e3f8e0181","first_computed_at":"2026-05-18T04:01:23.736388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:23.736388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p0gGMikhsYvBsNFLY/Q11cGcaEQLh6walo9R7neRYtBh/sgmuZYPppFjmlrhsDwYPL+f4xdCxEactUPgeP+eAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:23.737027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3952","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2493b08b35e0f4672a347928d10d74138d8fa0aec6c586d2c717e8a9c775864","sha256:fb819a49e536929989d6541a31d81a4a37c9d2f6596492c7c73fd1ea828bbb54"],"state_sha256":"99e4458b9140134049d14af8213637b12d28a184408c498a160a7a659e7be052"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jk3ILJtjvlLk08128bEXVyRHl6m8+3mr0MbU6uYuJyKRdIlSQKdEWrC43uYXfBQcZcINeZipQ2BZECTdiOSyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:44:06.170631Z","bundle_sha256":"6a59b959393acbb4cd79a702f42a83e41298caaf8a5535f82aadd370671c144b"}}