{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:2EM4KV3LXE5UNPC6GTDDJA2RAN","short_pith_number":"pith:2EM4KV3L","canonical_record":{"source":{"id":"0910.3002","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-10-15T21:36:56Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"470511422ebb4f62629d5d440ff28273f2636c4f0957044d0f2ccae84d9582fe","abstract_canon_sha256":"1f07404721428e105de93304b4c47b6cdd976a9413699692917d4f13274d14d3"},"schema_version":"1.0"},"canonical_sha256":"d119c5576bb93b46bc5e34c63483510365fc7caf06ff518ec2dba458d4d67740","source":{"kind":"arxiv","id":"0910.3002","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3002","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3002v2","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3002","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"2EM4KV3LXE5U","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"pith_short_16","alias_value":"2EM4KV3LXE5UNPC6","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"pith_short_8","alias_value":"2EM4KV3L","created_at":"2026-07-04T17:31:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:2EM4KV3LXE5UNPC6GTDDJA2RAN","target":"record","payload":{"canonical_record":{"source":{"id":"0910.3002","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-10-15T21:36:56Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"470511422ebb4f62629d5d440ff28273f2636c4f0957044d0f2ccae84d9582fe","abstract_canon_sha256":"1f07404721428e105de93304b4c47b6cdd976a9413699692917d4f13274d14d3"},"schema_version":"1.0"},"canonical_sha256":"d119c5576bb93b46bc5e34c63483510365fc7caf06ff518ec2dba458d4d67740","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:31:36.493612Z","signature_b64":"2U77jBMmPLom7XE2QpT86gmGxlSim+ffrYLzLjJ0+uQ2D8F2HhSusO0X/9g603RKWsgeBKunhqXNwExQQG6iDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d119c5576bb93b46bc5e34c63483510365fc7caf06ff518ec2dba458d4d67740","last_reissued_at":"2026-07-04T17:31:36.493154Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:31:36.493154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.3002","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":"2026-07-04T17:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgfIkHXJETFoCS3aLE+nFsGxccnT+yRa7BS49tiBZn6R4A3AR8PkPS3pOiWICmWS8R3l8tCbKFicr8MLBiElBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:42:04.796578Z"},"content_sha256":"dcdb54ac02edbb795ddb8d3e15df3a12bd2fe5f417d94a0091d0611588ae9892","schema_version":"1.0","event_id":"sha256:dcdb54ac02edbb795ddb8d3e15df3a12bd2fe5f417d94a0091d0611588ae9892"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:2EM4KV3LXE5UNPC6GTDDJA2RAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rack shadows and their invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Sam Nelson, Wesley Chang","submitted_at":"2009-10-15T21:36:56Z","abstract_excerpt":"A rack shadow is a set X with a rack action by a rack R, analogous to a vector space over a field. We use shadow colorings of classical link diagrams to define enhanced rack counting invariants and show that the enhanced invariants are stronger than unenhanced counting invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3002","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0910.3002/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z/B4bGNxJ/8UtzHZEs/yOaucp7OrSrzk1ze/EQf0PBDDIVK2n8L5fbucQpXrdEz42MZk2MV4Rc+rAAlubKlrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:42:04.796955Z"},"content_sha256":"00596bf8e5eff895966ea1fa5d85ada709bacd117618390730079c9a74ff585e","schema_version":"1.0","event_id":"sha256:00596bf8e5eff895966ea1fa5d85ada709bacd117618390730079c9a74ff585e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2EM4KV3LXE5UNPC6GTDDJA2RAN/bundle.json","state_url":"https://pith.science/pith/2EM4KV3LXE5UNPC6GTDDJA2RAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2EM4KV3LXE5UNPC6GTDDJA2RAN/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":"2026-07-07T14:42:04Z","links":{"resolver":"https://pith.science/pith/2EM4KV3LXE5UNPC6GTDDJA2RAN","bundle":"https://pith.science/pith/2EM4KV3LXE5UNPC6GTDDJA2RAN/bundle.json","state":"https://pith.science/pith/2EM4KV3LXE5UNPC6GTDDJA2RAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2EM4KV3LXE5UNPC6GTDDJA2RAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:2EM4KV3LXE5UNPC6GTDDJA2RAN","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":"1f07404721428e105de93304b4c47b6cdd976a9413699692917d4f13274d14d3","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-10-15T21:36:56Z","title_canon_sha256":"470511422ebb4f62629d5d440ff28273f2636c4f0957044d0f2ccae84d9582fe"},"schema_version":"1.0","source":{"id":"0910.3002","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3002","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3002v2","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3002","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"2EM4KV3LXE5U","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"pith_short_16","alias_value":"2EM4KV3LXE5UNPC6","created_at":"2026-07-04T17:31:36Z"},{"alias_kind":"pith_short_8","alias_value":"2EM4KV3L","created_at":"2026-07-04T17:31:36Z"}],"graph_snapshots":[{"event_id":"sha256:00596bf8e5eff895966ea1fa5d85ada709bacd117618390730079c9a74ff585e","target":"graph","created_at":"2026-07-04T17:31:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0910.3002/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A rack shadow is a set X with a rack action by a rack R, analogous to a vector space over a field. We use shadow colorings of classical link diagrams to define enhanced rack counting invariants and show that the enhanced invariants are stronger than unenhanced counting invariants.","authors_text":"Sam Nelson, Wesley Chang","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-10-15T21:36:56Z","title":"Rack shadows and their invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3002","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:dcdb54ac02edbb795ddb8d3e15df3a12bd2fe5f417d94a0091d0611588ae9892","target":"record","created_at":"2026-07-04T17:31:36Z","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":"1f07404721428e105de93304b4c47b6cdd976a9413699692917d4f13274d14d3","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-10-15T21:36:56Z","title_canon_sha256":"470511422ebb4f62629d5d440ff28273f2636c4f0957044d0f2ccae84d9582fe"},"schema_version":"1.0","source":{"id":"0910.3002","kind":"arxiv","version":2}},"canonical_sha256":"d119c5576bb93b46bc5e34c63483510365fc7caf06ff518ec2dba458d4d67740","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d119c5576bb93b46bc5e34c63483510365fc7caf06ff518ec2dba458d4d67740","first_computed_at":"2026-07-04T17:31:36.493154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:31:36.493154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2U77jBMmPLom7XE2QpT86gmGxlSim+ffrYLzLjJ0+uQ2D8F2HhSusO0X/9g603RKWsgeBKunhqXNwExQQG6iDA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:31:36.493612Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.3002","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcdb54ac02edbb795ddb8d3e15df3a12bd2fe5f417d94a0091d0611588ae9892","sha256:00596bf8e5eff895966ea1fa5d85ada709bacd117618390730079c9a74ff585e"],"state_sha256":"49a40d48847d9970cc5a19b4cfc340366eddd6d281c7138797a43655ee7f1ac1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Bow3UnDvHx0EoYLizLmlF+QnXREy6oALGjXfmQfGIeu0Qc2xfLou3i0s1oRt7pPJb0CR97DpcDojs9CJE9ZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:42:04.798871Z","bundle_sha256":"07062d3fbf0a8637d8943dc96d096709ecc89befb7eb2300834ef67d16efef25"}}