{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:MS3LZUHNECMAXLSWGHW6U57GBM","short_pith_number":"pith:MS3LZUHN","schema_version":"1.0","canonical_sha256":"64b6bcd0ed20980bae5631edea77e60b1616f28cc6f0133b1fa7a8f8d1a5b439","source":{"kind":"arxiv","id":"2510.23634","version":3},"attestation_state":"computed","paper":{"title":"Monotone and Separable Set Functions: Characterizations and Neural Models","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Abir De, Nadav Dym, Soutrik Sarangi, Yonatan Sverdlov","submitted_at":"2025-10-24T09:59:07Z","abstract_excerpt":"Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\\subseteq T \\text{ if and only if } F(S)\\leq F(T) $. We call functions satisfying this property Monotone and Separating (MAS) set functions. % We establish lower and upper bounds for the vector dimension necessary to obtain MAS functions, as a function of the cardinality of the multisets and the underlying ground set. In the important case of an infinite ground set, we show that MAS function"},"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":"2510.23634","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.LG","submitted_at":"2025-10-24T09:59:07Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"8d981755fb415b7fc2d9d5b15925a168ed3097a578acd6134af756f38d27b1c8","abstract_canon_sha256":"3fae75895afccb874001b1164ff0344acb8bce17b8e25b9d1cc5facd1d840032"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:36.404729Z","signature_b64":"zrUP+Mmux6KU3lcOGRQPpRU8HTN49Zu9sS9HUr/7NpjIWYnIqFdpxnF0HJsNY9gvUxolIYiLz+sjWWwy5yilCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64b6bcd0ed20980bae5631edea77e60b1616f28cc6f0133b1fa7a8f8d1a5b439","last_reissued_at":"2026-05-20T00:01:36.403960Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:36.403960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monotone and Separable Set Functions: Characterizations and Neural Models","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Abir De, Nadav Dym, Soutrik Sarangi, Yonatan Sverdlov","submitted_at":"2025-10-24T09:59:07Z","abstract_excerpt":"Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\\subseteq T \\text{ if and only if } F(S)\\leq F(T) $. We call functions satisfying this property Monotone and Separating (MAS) set functions. % We establish lower and upper bounds for the vector dimension necessary to obtain MAS functions, as a function of the cardinality of the multisets and the underlying ground set. In the important case of an infinite ground set, we show that MAS function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.23634","kind":"arxiv","version":3},"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/2510.23634/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":"2510.23634","created_at":"2026-05-20T00:01:36.404070+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.23634v3","created_at":"2026-05-20T00:01:36.404070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.23634","created_at":"2026-05-20T00:01:36.404070+00:00"},{"alias_kind":"pith_short_12","alias_value":"MS3LZUHNECMA","created_at":"2026-05-20T00:01:36.404070+00:00"},{"alias_kind":"pith_short_16","alias_value":"MS3LZUHNECMAXLSW","created_at":"2026-05-20T00:01:36.404070+00:00"},{"alias_kind":"pith_short_8","alias_value":"MS3LZUHN","created_at":"2026-05-20T00:01:36.404070+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/MS3LZUHNECMAXLSWGHW6U57GBM","json":"https://pith.science/pith/MS3LZUHNECMAXLSWGHW6U57GBM.json","graph_json":"https://pith.science/api/pith-number/MS3LZUHNECMAXLSWGHW6U57GBM/graph.json","events_json":"https://pith.science/api/pith-number/MS3LZUHNECMAXLSWGHW6U57GBM/events.json","paper":"https://pith.science/paper/MS3LZUHN"},"agent_actions":{"view_html":"https://pith.science/pith/MS3LZUHNECMAXLSWGHW6U57GBM","download_json":"https://pith.science/pith/MS3LZUHNECMAXLSWGHW6U57GBM.json","view_paper":"https://pith.science/paper/MS3LZUHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.23634&json=true","fetch_graph":"https://pith.science/api/pith-number/MS3LZUHNECMAXLSWGHW6U57GBM/graph.json","fetch_events":"https://pith.science/api/pith-number/MS3LZUHNECMAXLSWGHW6U57GBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MS3LZUHNECMAXLSWGHW6U57GBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MS3LZUHNECMAXLSWGHW6U57GBM/action/storage_attestation","attest_author":"https://pith.science/pith/MS3LZUHNECMAXLSWGHW6U57GBM/action/author_attestation","sign_citation":"https://pith.science/pith/MS3LZUHNECMAXLSWGHW6U57GBM/action/citation_signature","submit_replication":"https://pith.science/pith/MS3LZUHNECMAXLSWGHW6U57GBM/action/replication_record"}},"created_at":"2026-05-20T00:01:36.404070+00:00","updated_at":"2026-05-20T00:01:36.404070+00:00"}