{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7","short_pith_number":"pith:2C2ZMRLM","schema_version":"1.0","canonical_sha256":"d0b596456c87531f2fd920bb7b9ab04ffd845b99e08067a361c8ba125d155b34","source":{"kind":"arxiv","id":"2304.11325","version":1},"attestation_state":"computed","paper":{"title":"Deterministic identity testing paradigms for bounded top-fanin depth-4 circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SC","math.AC"],"primary_cat":"cs.CC","authors_text":"Nitin Saxena, Pranjal Dutta, Prateek Dwivedi","submitted_at":"2023-04-22T05:36:12Z","abstract_excerpt":"Polynomial Identity Testing (PIT) is a fundamental computational problem. The famous depth-$4$ reduction result by Agrawal and Vinay (FOCS 2008) has made PIT for depth-$4$ circuits an enticing pursuit. A restricted depth-4 circuit computing a $n$-variate degree-$d$ polynomial of the form $\\sum_{i = 1}^{k} \\prod_{j} g_{ij}$, where $\\deg g_{ij} \\leq \\delta$ is called $\\Sigma^{[k]}\\Pi\\Sigma\\Pi^{[\\delta]}$ circuit. On further restricting $g_{ij}$ to be sum of univariates we obtain $\\Sigma^{[k]}\\Pi\\Sigma\\wedge$ circuits. The largely open, special-cases of $\\Sigma^{[k]}\\Pi\\Sigma\\Pi^{[\\delta]}$ for c"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2304.11325","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2023-04-22T05:36:12Z","cross_cats_sorted":["cs.SC","math.AC"],"title_canon_sha256":"4bb1d92739a638e4de8d9c76b0c7bce2b17d92376456bbd626caf0cd3da61d61","abstract_canon_sha256":"a2422ac9a8f8a0b4db05a33a97a4211d3f42f9eff55044c91d2ce990534482a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:04:14.829159Z","signature_b64":"7ANrtDwGWufGIALviSGeL9bSevdNkptdAvKXflI8wRq9DLgQeuJCg9KOpuFwIrCEpzQyO/YBkriULrC7W/heAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0b596456c87531f2fd920bb7b9ab04ffd845b99e08067a361c8ba125d155b34","last_reissued_at":"2026-07-05T06:04:14.828612Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:04:14.828612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deterministic identity testing paradigms for bounded top-fanin depth-4 circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SC","math.AC"],"primary_cat":"cs.CC","authors_text":"Nitin Saxena, Pranjal Dutta, Prateek Dwivedi","submitted_at":"2023-04-22T05:36:12Z","abstract_excerpt":"Polynomial Identity Testing (PIT) is a fundamental computational problem. The famous depth-$4$ reduction result by Agrawal and Vinay (FOCS 2008) has made PIT for depth-$4$ circuits an enticing pursuit. A restricted depth-4 circuit computing a $n$-variate degree-$d$ polynomial of the form $\\sum_{i = 1}^{k} \\prod_{j} g_{ij}$, where $\\deg g_{ij} \\leq \\delta$ is called $\\Sigma^{[k]}\\Pi\\Sigma\\Pi^{[\\delta]}$ circuit. On further restricting $g_{ij}$ to be sum of univariates we obtain $\\Sigma^{[k]}\\Pi\\Sigma\\wedge$ circuits. The largely open, special-cases of $\\Sigma^{[k]}\\Pi\\Sigma\\Pi^{[\\delta]}$ for c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.11325","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.11325/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2304.11325","created_at":"2026-07-05T06:04:14.828675+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.11325v1","created_at":"2026-07-05T06:04:14.828675+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.11325","created_at":"2026-07-05T06:04:14.828675+00:00"},{"alias_kind":"pith_short_12","alias_value":"2C2ZMRLMQ5JR","created_at":"2026-07-05T06:04:14.828675+00:00"},{"alias_kind":"pith_short_16","alias_value":"2C2ZMRLMQ5JR6L6Z","created_at":"2026-07-05T06:04:14.828675+00:00"},{"alias_kind":"pith_short_8","alias_value":"2C2ZMRLM","created_at":"2026-07-05T06:04:14.828675+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7","json":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7.json","graph_json":"https://pith.science/api/pith-number/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/graph.json","events_json":"https://pith.science/api/pith-number/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/events.json","paper":"https://pith.science/paper/2C2ZMRLM"},"agent_actions":{"view_html":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7","download_json":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7.json","view_paper":"https://pith.science/paper/2C2ZMRLM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.11325&json=true","fetch_graph":"https://pith.science/api/pith-number/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/graph.json","fetch_events":"https://pith.science/api/pith-number/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/action/storage_attestation","attest_author":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/action/author_attestation","sign_citation":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/action/citation_signature","submit_replication":"https://pith.science/pith/2C2ZMRLMQ5JR6L6ZEC5XXGVQJ7/action/replication_record"}},"created_at":"2026-07-05T06:04:14.828675+00:00","updated_at":"2026-07-05T06:04:14.828675+00:00"}