{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RFAJESQOKJALBIDGJ3A3UI5FFX","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":"1d2e08f2fc624c2888f5d65b3138c6ff67a0506558f8e5194c53c2c53184bfed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-02T12:05:22Z","title_canon_sha256":"1f24d7d97a1effbb97230e22dbe16a68e704a5a0b72c0565ee78cac92ee166d6"},"schema_version":"1.0","source":{"id":"1202.0416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0416","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0416v1","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0416","created_at":"2026-05-18T04:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"RFAJESQOKJAL","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RFAJESQOKJALBIDG","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RFAJESQO","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:f9ed14c849f898cb5d533fd9f3cafc7b74c25c3df80c75ae4dd3701618e9cd89","target":"graph","created_at":"2026-05-18T04:03:18Z","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":"Here we present certificates for 5 classes of 6-edged multigraphs whose symmetrized graph monomials may be represented as sum of squares, but not as linear combinations of partition square graphs. This is a complement to the results presented in Discriminants, symmetrized graph monomials, and sums of squares.","authors_text":"Per Alexandersson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-02T12:05:22Z","title":"Discriminants, symmetrized graph monomials, and sums of squares certificates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0416","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":"sha256:253488e5e25366535af9c3310bf75f716d441a93c69d74b92f2f4c3773033dba","target":"record","created_at":"2026-05-18T04:03:18Z","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":"1d2e08f2fc624c2888f5d65b3138c6ff67a0506558f8e5194c53c2c53184bfed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-02T12:05:22Z","title_canon_sha256":"1f24d7d97a1effbb97230e22dbe16a68e704a5a0b72c0565ee78cac92ee166d6"},"schema_version":"1.0","source":{"id":"1202.0416","kind":"arxiv","version":1}},"canonical_sha256":"8940924a0e5240b0a0664ec1ba23a52df2cde16e1d47d891e6dc2aa4d1271b5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8940924a0e5240b0a0664ec1ba23a52df2cde16e1d47d891e6dc2aa4d1271b5b","first_computed_at":"2026-05-18T04:03:18.363256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:18.363256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x1PbpPIlXUxPXvT0SXloQ+OWClmVWdRzaY8+u7gB3EW45DJZSrZ4B5A0nq5ISJEm4VdwGadEmoMgYeF5BfFLAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:18.363978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:253488e5e25366535af9c3310bf75f716d441a93c69d74b92f2f4c3773033dba","sha256:f9ed14c849f898cb5d533fd9f3cafc7b74c25c3df80c75ae4dd3701618e9cd89"],"state_sha256":"9a7fefcd6adaca50a6d0767f28d9c8cecf052b09aa185daa7e47da339bae0c66"}