{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GRBDL4GLW4KH3NJJKDRU2HVDDE","short_pith_number":"pith:GRBDL4GL","schema_version":"1.0","canonical_sha256":"344235f0cbb7147db52950e34d1ea319054b797565acf32de4bc68522aee5bcb","source":{"kind":"arxiv","id":"1603.02605","version":1},"attestation_state":"computed","paper":{"title":"Sums of read-once formulas: How many summands suffice?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anuj Tawari, Meena Mahajan","submitted_at":"2016-03-08T17:58:40Z","abstract_excerpt":"An arithmetic read-once formula (ROF) is a formula (circuit of fan-out 1) over $+,\\times$ where each variable labels at most one leaf. Every multilinear polynomial can be expressed as the sum of ROFs. In this work, we prove, for certain multilinear polynomials, a tight lower bound on the number of summands in such an expression."},"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":"1603.02605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-03-08T17:58:40Z","cross_cats_sorted":[],"title_canon_sha256":"31440a2f929f8fe470b6d047465e0b19b2fac5bcd9b03ae2d519cd12ef4646a1","abstract_canon_sha256":"f988d036011b2956230d72c76b598d5ae99a27dde2bc4fed85072d9471ff241d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:22.807410Z","signature_b64":"IM48KpWuKxoPGg1yBvWLDCxF/l9m/uFP5ecF5ZnL65ezQW7TNBlCoKBlm4uK3FrZhYFM/7+07qr4fYrnCkfUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"344235f0cbb7147db52950e34d1ea319054b797565acf32de4bc68522aee5bcb","last_reissued_at":"2026-05-18T01:19:22.806705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:22.806705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sums of read-once formulas: How many summands suffice?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anuj Tawari, Meena Mahajan","submitted_at":"2016-03-08T17:58:40Z","abstract_excerpt":"An arithmetic read-once formula (ROF) is a formula (circuit of fan-out 1) over $+,\\times$ where each variable labels at most one leaf. Every multilinear polynomial can be expressed as the sum of ROFs. In this work, we prove, for certain multilinear polynomials, a tight lower bound on the number of summands in such an expression."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02605","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":""},"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":"1603.02605","created_at":"2026-05-18T01:19:22.806813+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.02605v1","created_at":"2026-05-18T01:19:22.806813+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02605","created_at":"2026-05-18T01:19:22.806813+00:00"},{"alias_kind":"pith_short_12","alias_value":"GRBDL4GLW4KH","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GRBDL4GLW4KH3NJJ","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GRBDL4GL","created_at":"2026-05-18T12:30:19.053100+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/GRBDL4GLW4KH3NJJKDRU2HVDDE","json":"https://pith.science/pith/GRBDL4GLW4KH3NJJKDRU2HVDDE.json","graph_json":"https://pith.science/api/pith-number/GRBDL4GLW4KH3NJJKDRU2HVDDE/graph.json","events_json":"https://pith.science/api/pith-number/GRBDL4GLW4KH3NJJKDRU2HVDDE/events.json","paper":"https://pith.science/paper/GRBDL4GL"},"agent_actions":{"view_html":"https://pith.science/pith/GRBDL4GLW4KH3NJJKDRU2HVDDE","download_json":"https://pith.science/pith/GRBDL4GLW4KH3NJJKDRU2HVDDE.json","view_paper":"https://pith.science/paper/GRBDL4GL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.02605&json=true","fetch_graph":"https://pith.science/api/pith-number/GRBDL4GLW4KH3NJJKDRU2HVDDE/graph.json","fetch_events":"https://pith.science/api/pith-number/GRBDL4GLW4KH3NJJKDRU2HVDDE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GRBDL4GLW4KH3NJJKDRU2HVDDE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GRBDL4GLW4KH3NJJKDRU2HVDDE/action/storage_attestation","attest_author":"https://pith.science/pith/GRBDL4GLW4KH3NJJKDRU2HVDDE/action/author_attestation","sign_citation":"https://pith.science/pith/GRBDL4GLW4KH3NJJKDRU2HVDDE/action/citation_signature","submit_replication":"https://pith.science/pith/GRBDL4GLW4KH3NJJKDRU2HVDDE/action/replication_record"}},"created_at":"2026-05-18T01:19:22.806813+00:00","updated_at":"2026-05-18T01:19:22.806813+00:00"}