{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CCOBWBAZ3EPXLT2ES2QEII4YUX","short_pith_number":"pith:CCOBWBAZ","schema_version":"1.0","canonical_sha256":"109c1b0419d91f75cf4496a0442398a5eae76601734d53e80badb1cf517ac11b","source":{"kind":"arxiv","id":"1611.01029","version":2},"attestation_state":"computed","paper":{"title":"On the Sum of Linear Coefficients of a Boolean Valued Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Sumit Kumar Jha","submitted_at":"2016-11-03T14:10:17Z","abstract_excerpt":"Let $f:\\{-1,1\\}^{n}\\rightarrow \\{-1,1\\}$ be a Boolean valued function having total degree $d$. Then a conjecture due to Servedio and Gopalan asserts that $\\sum_{i=1}^{n}\\widehat{f}(i)\\leq \\sum_{j=1}^{d}\\widehat{\\text{Maj}}_{d}(j)$ where $\\text{Maj}_{d}$ is the majority function on $d$ bits. Here we give some alternative formalisms of this conjecture involving the discrete derivative operators on $f$."},"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":"1611.01029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-03T14:10:17Z","cross_cats_sorted":[],"title_canon_sha256":"1e33751717f8ff4deb4ee680007680c06dd8ada1603d1b62371cf96a8092ce05","abstract_canon_sha256":"b361ff171dc2dceb81b5e6dcf406663e8e80979f751d84efc501d207b1b0452f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:05.143446Z","signature_b64":"boJw8xoduOjZU8zK56dGR5BO89FHy3HF4fVORzGwaKiDHYYMyWdXj6F07YTaQWmqPrt0xDfOH4hPENSAlxkVDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"109c1b0419d91f75cf4496a0442398a5eae76601734d53e80badb1cf517ac11b","last_reissued_at":"2026-05-18T01:00:05.142799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:05.142799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Sum of Linear Coefficients of a Boolean Valued Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Sumit Kumar Jha","submitted_at":"2016-11-03T14:10:17Z","abstract_excerpt":"Let $f:\\{-1,1\\}^{n}\\rightarrow \\{-1,1\\}$ be a Boolean valued function having total degree $d$. Then a conjecture due to Servedio and Gopalan asserts that $\\sum_{i=1}^{n}\\widehat{f}(i)\\leq \\sum_{j=1}^{d}\\widehat{\\text{Maj}}_{d}(j)$ where $\\text{Maj}_{d}$ is the majority function on $d$ bits. Here we give some alternative formalisms of this conjecture involving the discrete derivative operators on $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01029","kind":"arxiv","version":2},"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":"1611.01029","created_at":"2026-05-18T01:00:05.142893+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.01029v2","created_at":"2026-05-18T01:00:05.142893+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01029","created_at":"2026-05-18T01:00:05.142893+00:00"},{"alias_kind":"pith_short_12","alias_value":"CCOBWBAZ3EPX","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CCOBWBAZ3EPXLT2E","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CCOBWBAZ","created_at":"2026-05-18T12:30:09.641336+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/CCOBWBAZ3EPXLT2ES2QEII4YUX","json":"https://pith.science/pith/CCOBWBAZ3EPXLT2ES2QEII4YUX.json","graph_json":"https://pith.science/api/pith-number/CCOBWBAZ3EPXLT2ES2QEII4YUX/graph.json","events_json":"https://pith.science/api/pith-number/CCOBWBAZ3EPXLT2ES2QEII4YUX/events.json","paper":"https://pith.science/paper/CCOBWBAZ"},"agent_actions":{"view_html":"https://pith.science/pith/CCOBWBAZ3EPXLT2ES2QEII4YUX","download_json":"https://pith.science/pith/CCOBWBAZ3EPXLT2ES2QEII4YUX.json","view_paper":"https://pith.science/paper/CCOBWBAZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.01029&json=true","fetch_graph":"https://pith.science/api/pith-number/CCOBWBAZ3EPXLT2ES2QEII4YUX/graph.json","fetch_events":"https://pith.science/api/pith-number/CCOBWBAZ3EPXLT2ES2QEII4YUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CCOBWBAZ3EPXLT2ES2QEII4YUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CCOBWBAZ3EPXLT2ES2QEII4YUX/action/storage_attestation","attest_author":"https://pith.science/pith/CCOBWBAZ3EPXLT2ES2QEII4YUX/action/author_attestation","sign_citation":"https://pith.science/pith/CCOBWBAZ3EPXLT2ES2QEII4YUX/action/citation_signature","submit_replication":"https://pith.science/pith/CCOBWBAZ3EPXLT2ES2QEII4YUX/action/replication_record"}},"created_at":"2026-05-18T01:00:05.142893+00:00","updated_at":"2026-05-18T01:00:05.142893+00:00"}