{"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"}