{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DXJDHFVX4FDEUGZKJQ4I5POITG","short_pith_number":"pith:DXJDHFVX","schema_version":"1.0","canonical_sha256":"1dd23396b7e1464a1b2a4c388ebdc899bef530effcf62f581ab46404c4a3612b","source":{"kind":"arxiv","id":"2605.30456","version":1},"attestation_state":"computed","paper":{"title":"DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Can Li, Shraman Pal","submitted_at":"2026-05-28T18:27:39Z","abstract_excerpt":"Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches. At the same time, these problems are often accompanied by rich domain knowledge derived from physical laws, operational requirements, and expert heuristics. Such knowledge is frequently expressed as rules involving logical propositions and linear inequalities. Existing neuro-symbolic methods typically enforce these rules approximately through soft penalties, assume input-independent rules when designing specialized architectures, or rely on non-d"},"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":"2605.30456","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-28T18:27:39Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"575abd324d47eed0085f8d36c902678470d334429387ac48650d25ddd07b6e84","abstract_canon_sha256":"023a9ea9de8130a4fef6f3e46a06abf3df3b9cb62e383a880f84f5d2cbb2552f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:02:55.298017Z","signature_b64":"lxjAb53tAcUH9930dskWgpi4sGwbjhsCYZh71PE5+EvET6TEqCGgT3BV//S/L4awhDUv+k7+Qm6BIjL5W2c9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dd23396b7e1464a1b2a4c388ebdc899bef530effcf62f581ab46404c4a3612b","last_reissued_at":"2026-06-01T01:02:55.297278Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:02:55.297278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Can Li, Shraman Pal","submitted_at":"2026-05-28T18:27:39Z","abstract_excerpt":"Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches. At the same time, these problems are often accompanied by rich domain knowledge derived from physical laws, operational requirements, and expert heuristics. Such knowledge is frequently expressed as rules involving logical propositions and linear inequalities. Existing neuro-symbolic methods typically enforce these rules approximately through soft penalties, assume input-independent rules when designing specialized architectures, or rely on non-d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30456","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/2605.30456/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":"2605.30456","created_at":"2026-06-01T01:02:55.297410+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.30456v1","created_at":"2026-06-01T01:02:55.297410+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30456","created_at":"2026-06-01T01:02:55.297410+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXJDHFVX4FDE","created_at":"2026-06-01T01:02:55.297410+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXJDHFVX4FDEUGZK","created_at":"2026-06-01T01:02:55.297410+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXJDHFVX","created_at":"2026-06-01T01:02:55.297410+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/DXJDHFVX4FDEUGZKJQ4I5POITG","json":"https://pith.science/pith/DXJDHFVX4FDEUGZKJQ4I5POITG.json","graph_json":"https://pith.science/api/pith-number/DXJDHFVX4FDEUGZKJQ4I5POITG/graph.json","events_json":"https://pith.science/api/pith-number/DXJDHFVX4FDEUGZKJQ4I5POITG/events.json","paper":"https://pith.science/paper/DXJDHFVX"},"agent_actions":{"view_html":"https://pith.science/pith/DXJDHFVX4FDEUGZKJQ4I5POITG","download_json":"https://pith.science/pith/DXJDHFVX4FDEUGZKJQ4I5POITG.json","view_paper":"https://pith.science/paper/DXJDHFVX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.30456&json=true","fetch_graph":"https://pith.science/api/pith-number/DXJDHFVX4FDEUGZKJQ4I5POITG/graph.json","fetch_events":"https://pith.science/api/pith-number/DXJDHFVX4FDEUGZKJQ4I5POITG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXJDHFVX4FDEUGZKJQ4I5POITG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXJDHFVX4FDEUGZKJQ4I5POITG/action/storage_attestation","attest_author":"https://pith.science/pith/DXJDHFVX4FDEUGZKJQ4I5POITG/action/author_attestation","sign_citation":"https://pith.science/pith/DXJDHFVX4FDEUGZKJQ4I5POITG/action/citation_signature","submit_replication":"https://pith.science/pith/DXJDHFVX4FDEUGZKJQ4I5POITG/action/replication_record"}},"created_at":"2026-06-01T01:02:55.297410+00:00","updated_at":"2026-06-01T01:02:55.297410+00:00"}