{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:4URAOBKF36TKLNCXYUIZAG22P2","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":"3f09020af375f08c7ba8a40df7697ffc39172ce4016eb6151b4e6b1307d9e62f","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-11-14T00:26:55Z","title_canon_sha256":"d4d061d1a786e8d16da8b46cc999c4c77c6aaff27a4693b38f4793e401d503e7"},"schema_version":"1.0","source":{"id":"2211.07055","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.07055","created_at":"2026-07-05T11:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"2211.07055v3","created_at":"2026-07-05T11:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.07055","created_at":"2026-07-05T11:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"4URAOBKF36TK","created_at":"2026-07-05T11:11:19Z"},{"alias_kind":"pith_short_16","alias_value":"4URAOBKF36TKLNCX","created_at":"2026-07-05T11:11:19Z"},{"alias_kind":"pith_short_8","alias_value":"4URAOBKF","created_at":"2026-07-05T11:11:19Z"}],"graph_snapshots":[{"event_id":"sha256:2d997b2ab790cbf3ca9982cca38c2c7d85d51ea99850502844126f51c35cef41","target":"graph","created_at":"2026-07-05T11:11:19Z","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/2211.07055/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"According to Kumar's recent surprising result (ToCT'20), a small border Waring rank implies that the polynomial can be approximated as a sum of a constant and a small product of linear polynomials. We prove the converse of Kumar's result and establish a tight connection between border Waring rank and the model of computation in Kumar's result. In this way, we obtain a new formulation of border Waring rank, up to a factor of the degree. We connect this new formulation to the orbit closure problem of the product-plus-power polynomial. We study this orbit closure from two directions: 1. We debord","authors_text":"Christian Ikenmeyer, Fulvio Gesmundo, Gorav Jindal, Pranjal Dutta, Vladimir Lysikov","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-11-14T00:26:55Z","title":"Geometric complexity theory for product-plus-power"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07055","kind":"arxiv","version":3},"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:bb941c3a7d70688be65d12b670f136b2cf7de27a1217bae5a843ef4aea2e06d5","target":"record","created_at":"2026-07-05T11:11:19Z","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":"3f09020af375f08c7ba8a40df7697ffc39172ce4016eb6151b4e6b1307d9e62f","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-11-14T00:26:55Z","title_canon_sha256":"d4d061d1a786e8d16da8b46cc999c4c77c6aaff27a4693b38f4793e401d503e7"},"schema_version":"1.0","source":{"id":"2211.07055","kind":"arxiv","version":3}},"canonical_sha256":"e522070545dfa6a5b457c511901b5a7ea3f5d68a06480519867b31db41fdedaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e522070545dfa6a5b457c511901b5a7ea3f5d68a06480519867b31db41fdedaa","first_computed_at":"2026-07-05T11:11:19.627005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:19.627005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y8ndPp5PF+BgsWH7Ab39nK5cOQWD5HILb2esfBANTw3sAS+Ch0+cfbv5cWUn5uLge+ct1jIUV+jrwjNfJ5NICg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:19.627554Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.07055","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb941c3a7d70688be65d12b670f136b2cf7de27a1217bae5a843ef4aea2e06d5","sha256:2d997b2ab790cbf3ca9982cca38c2c7d85d51ea99850502844126f51c35cef41"],"state_sha256":"88a563dde90326a895b580cc963a693b0e65754f185b643da0a246fa088b166d"}