{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SESR62MHGKB7Z26WDZHMBIHTSH","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":"9a6e8c407e9e8a04e1fd9ad0e3494bff01d3ecdc15d7a9d13cf02a060dbce987","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-05-24T14:34:23Z","title_canon_sha256":"f366932fb79d5b728a90ba434095d6a619414d1d6f76b954ccb153ffbf7d9bf5"},"schema_version":"1.0","source":{"id":"1205.5466","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5466","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5466v2","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5466","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"SESR62MHGKB7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SESR62MHGKB7Z26W","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SESR62MH","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:e2a7e5d305878459117afa380c8be9e23a3a02b8243f1471d74913d0baf842ce","target":"graph","created_at":"2026-05-18T03:29:39Z","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":"We prove the positivity conjecture for skew-symmetric coefficient-free cluster algebras of rank 3.","authors_text":"Kyungyong Lee, Ralf Schiffler","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-05-24T14:34:23Z","title":"Positivity for cluster algebras of rank 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5466","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:e2fb27b8188d69a5b2118805f2caaf4c812dc487c02cd977ea53515fbdc1c7c7","target":"record","created_at":"2026-05-18T03:29:39Z","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":"9a6e8c407e9e8a04e1fd9ad0e3494bff01d3ecdc15d7a9d13cf02a060dbce987","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-05-24T14:34:23Z","title_canon_sha256":"f366932fb79d5b728a90ba434095d6a619414d1d6f76b954ccb153ffbf7d9bf5"},"schema_version":"1.0","source":{"id":"1205.5466","kind":"arxiv","version":2}},"canonical_sha256":"91251f69873283fcebd61e4ec0a0f391f1b46713982a6fde86e3ff7c285af530","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91251f69873283fcebd61e4ec0a0f391f1b46713982a6fde86e3ff7c285af530","first_computed_at":"2026-05-18T03:29:39.180511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:39.180511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MMtWLZzt1uHdFCR/HQedhiDcwHjChJNYZxSas0fFDU6J8ba7KmVR1gTZ7vZ/0Djv31vumgwGodozi5goUWO8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:39.181027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5466","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2fb27b8188d69a5b2118805f2caaf4c812dc487c02cd977ea53515fbdc1c7c7","sha256:e2a7e5d305878459117afa380c8be9e23a3a02b8243f1471d74913d0baf842ce"],"state_sha256":"3fc809151578246cbd17d3cf39a2351d30e8d08e6cdd2614b82a422fd341f551"}