{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AB5RKMH3ZAW3TWS5XIU4UMJLNV","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":"52493a48fc2340a68e99266bfbd68ab4bc1ed14673c5848f2710aece054928e5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-06-25T17:12:57Z","title_canon_sha256":"637187b284a3ca526eb16c386f47f82d5a6cc378ddf597cfd91d8a867f2346f7"},"schema_version":"1.0","source":{"id":"2606.27293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27293","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27293v1","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27293","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"AB5RKMH3ZAW3","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_16","alias_value":"AB5RKMH3ZAW3TWS5","created_at":"2026-06-26T01:16:17Z"},{"alias_kind":"pith_short_8","alias_value":"AB5RKMH3","created_at":"2026-06-26T01:16:17Z"}],"graph_snapshots":[{"event_id":"sha256:99213bac3551e5951d482b07c74e602311dd5f81e104ec84ac4fa572bf5d1fb5","target":"graph","created_at":"2026-06-26T01:16:17Z","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/2606.27293/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study factoring algorithms for general sparse polynomials and sparse polynomials of bounded individual degree and prove the following results.\n  1. We give a deterministic polynomial-time algorithm which takes as input an $n$-variate $s$-sparse polynomial $f$ of bounded individual degree $d$ and outputs a list of circuits which contains all factors of $f$, although there might be additional spurious circuits in the list. The algorithm runs in time $\\operatorname{poly}(n, s^d)$. Additionally, every circuit in the list has constant depth. Our algorithm works over all fields of characteristic ","authors_text":"Rishabh Kothary, Shanthanu S. Rai, Shubhangi Saraf, Somnath Bhattacharjee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-06-25T17:12:57Z","title":"Deterministic Algorithms for Low Individual Degree Factors of Sparse Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27293","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":"sha256:25175ba16fbd1adee0e693a9c7c85b9186504e8f7c5ac35ed194e2b5f2558f0d","target":"record","created_at":"2026-06-26T01:16:17Z","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":"52493a48fc2340a68e99266bfbd68ab4bc1ed14673c5848f2710aece054928e5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-06-25T17:12:57Z","title_canon_sha256":"637187b284a3ca526eb16c386f47f82d5a6cc378ddf597cfd91d8a867f2346f7"},"schema_version":"1.0","source":{"id":"2606.27293","kind":"arxiv","version":1}},"canonical_sha256":"007b1530fbc82db9da5dba29ca312b6d7ee265bb2037f19eb9a17030854a5e6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"007b1530fbc82db9da5dba29ca312b6d7ee265bb2037f19eb9a17030854a5e6f","first_computed_at":"2026-06-26T01:16:17.942911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:17.942911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OosvpTfOPnfws+fqnbK4gN/sK/6ouZ/LG/RMZnY+vcFlnCnpKzd5JzD2iyi4hGHLFVGk23gXqCp7hMUi59GLAw==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:17.943278Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25175ba16fbd1adee0e693a9c7c85b9186504e8f7c5ac35ed194e2b5f2558f0d","sha256:99213bac3551e5951d482b07c74e602311dd5f81e104ec84ac4fa572bf5d1fb5"],"state_sha256":"d9ae7f8747f9631ed3bd9ddb50041d640385c8823cb35e8089759d9c4412e48c"}