{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PEJNTGF2EJHSVS57QL6LNJREZA","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":"3e63290a8e6c248df8e4f4fa3a1e90d46835a9dbfeee71ca02c65864a77be882","cross_cats_sorted":["math.AC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T18:01:20Z","title_canon_sha256":"f06d782d094e282cc4a720cf0102a70998a51505239f181da66fdeff62088259"},"schema_version":"1.0","source":{"id":"2606.23814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23814","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23814v1","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23814","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"PEJNTGF2EJHS","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_16","alias_value":"PEJNTGF2EJHSVS57","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_8","alias_value":"PEJNTGF2","created_at":"2026-06-24T00:14:27Z"}],"graph_snapshots":[{"event_id":"sha256:14204ef912604453e53dfb28d46538230c85c7ab7531ac9b6056d8bc41262efd","target":"graph","created_at":"2026-06-24T00:14:27Z","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/2606.23814/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use the correspondence between iterated multiplication tensors of Gorenstein algebras and homogeneous polynomials of minimal smoothable rank to classify polynomials of minimal border rank of sufficiently high degree in up to 7 variables.","authors_text":"Cosimo Flavi, Tim Seynnaeve, Weronika Obcowska","cross_cats":["math.AC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T18:01:20Z","title":"Polynomials of minimal border rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23814","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":"sha256:089da7f8d467194834192bbaaabc061de68da05e824dc3e41e22410064926017","target":"record","created_at":"2026-06-24T00:14:27Z","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":"3e63290a8e6c248df8e4f4fa3a1e90d46835a9dbfeee71ca02c65864a77be882","cross_cats_sorted":["math.AC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T18:01:20Z","title_canon_sha256":"f06d782d094e282cc4a720cf0102a70998a51505239f181da66fdeff62088259"},"schema_version":"1.0","source":{"id":"2606.23814","kind":"arxiv","version":1}},"canonical_sha256":"7912d998ba224f2acbbf82fcb6a624c82586ca4f4cdb9c89d538a8f85c94e8df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7912d998ba224f2acbbf82fcb6a624c82586ca4f4cdb9c89d538a8f85c94e8df","first_computed_at":"2026-06-24T00:14:27.635231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T00:14:27.635231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"24O87wivMOIH4nX0FBKkNKK8SZ2hwYLyP1SJws8IlmoJ9ZcY0Yg9RKUmHIq79hVLIn3wEkwwhih/F9KwpV/cAQ==","signature_status":"signed_v1","signed_at":"2026-06-24T00:14:27.635615Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:089da7f8d467194834192bbaaabc061de68da05e824dc3e41e22410064926017","sha256:14204ef912604453e53dfb28d46538230c85c7ab7531ac9b6056d8bc41262efd"],"state_sha256":"7edc2abbd4e83b93701eae1eae177becddfdd0a185dc32efe2a20e8337d1f509"}