{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4I3DMEADXAJ77PEKNH22RG57HS","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":"8a2bc22b98567aff87be4c970646efe04e153b6fc1b571c46662c0779d07b523","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-03-21T16:56:54Z","title_canon_sha256":"9da7c8be3ab688ae81633e773d675247dab3f9e8ffa1ebec23d3b844b4da8e0f"},"schema_version":"1.0","source":{"id":"0803.3195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.3195","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"0803.3195v1","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3195","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"4I3DMEADXAJ7","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_16","alias_value":"4I3DMEADXAJ77PEK","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_8","alias_value":"4I3DMEAD","created_at":"2026-07-04T15:10:21Z"}],"graph_snapshots":[{"event_id":"sha256:261619b53b7e3eadd4ec595af28cfc2d3c084ad7044ce2cf6abc8fdbe8779cd9","target":"graph","created_at":"2026-07-04T15:10:21Z","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/0803.3195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss the polynomial representation for long knots and elaborate on how to obtain them with a bound on degrees of the defining polynomials, for any knot-type.","authors_text":"M.Prabhakar, Rama Mishra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-03-21T16:56:54Z","title":"Polynomial representation for long knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3195","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:cd3546b48df4a15b21edb44ecec564aca5518f230e77bbee058c7aa3a2202efa","target":"record","created_at":"2026-07-04T15:10:21Z","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":"8a2bc22b98567aff87be4c970646efe04e153b6fc1b571c46662c0779d07b523","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-03-21T16:56:54Z","title_canon_sha256":"9da7c8be3ab688ae81633e773d675247dab3f9e8ffa1ebec23d3b844b4da8e0f"},"schema_version":"1.0","source":{"id":"0803.3195","kind":"arxiv","version":1}},"canonical_sha256":"e236361003b813ffbc8a69f5a89bbf3cbcdb42f6d6b5fd3127ba3b63f50c13ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e236361003b813ffbc8a69f5a89bbf3cbcdb42f6d6b5fd3127ba3b63f50c13ed","first_computed_at":"2026-07-04T15:10:21.896747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:10:21.896747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vi7uvlOTsiYvNp6Kt4G4LYB1GzIVO7LLRGsXGiR5UUbfSAgaQTse8ceYTQEqaxdeo22f4Gfp4w8eBntaIUAQAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:10:21.897143Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.3195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd3546b48df4a15b21edb44ecec564aca5518f230e77bbee058c7aa3a2202efa","sha256:261619b53b7e3eadd4ec595af28cfc2d3c084ad7044ce2cf6abc8fdbe8779cd9"],"state_sha256":"5b4df0d0df8b352ffe5598b8a9bd36514d7e0d30c3ac8c7b48e01aec8c568bf1"}