{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4663I3WDI3GXV2VV7PGVHLRZBH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aec617c28a70a7df705d07046b775cc5791a80d0a95018a7833405449c132d7c","cross_cats_sorted":["cs.DM","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-25T17:18:32Z","title_canon_sha256":"2a642fb30604fb35362ab122bb71bd8ec26742cfd9435941ab82b9855716767f"},"schema_version":"1.0","source":{"id":"1012.5486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5486","created_at":"2026-05-18T04:32:23Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5486v1","created_at":"2026-05-18T04:32:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5486","created_at":"2026-05-18T04:32:23Z"},{"alias_kind":"pith_short_12","alias_value":"4663I3WDI3GX","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4663I3WDI3GXV2VV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4663I3WD","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:cc77c96ee13bf810677a4c3161ac65c02a3ec6c41f2c22b937864c14caf88300","target":"graph","created_at":"2026-05-18T04:32:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we introduce the notion of {\\it core} for two specific classes of boolean maps on finite involution posets (which are a generalization of the boolean lattices) and we prove some extension results for such families of boolean maps. Through the properties of the core, we provide a complete characterization of such maps. The main purpose of such abstract results is their application to the study of the compatibility of a particular class of systems of linear inequalities related to a conjecture of Manickam, Mikl\\\"os and Singhi (\\cite{ManSin88}, \\cite{ManMik87}), still unsolved and t","authors_text":"Cinzia Bisi, Giampiero Chiaselotti","cross_cats":["cs.DM","cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-25T17:18:32Z","title":"Extension results for boolean maps and a class of systems of linear inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5486","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:443cd6f6a87f84c122ce06b41bfbab4c340dee333101a23dd2eca9cb6a835fcd","target":"record","created_at":"2026-05-18T04:32:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aec617c28a70a7df705d07046b775cc5791a80d0a95018a7833405449c132d7c","cross_cats_sorted":["cs.DM","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-25T17:18:32Z","title_canon_sha256":"2a642fb30604fb35362ab122bb71bd8ec26742cfd9435941ab82b9855716767f"},"schema_version":"1.0","source":{"id":"1012.5486","kind":"arxiv","version":1}},"canonical_sha256":"e7bdb46ec346cd7aeab5fbcd53ae3909e79d00567c9ee680243597d392f9dd72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7bdb46ec346cd7aeab5fbcd53ae3909e79d00567c9ee680243597d392f9dd72","first_computed_at":"2026-05-18T04:32:23.293120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:23.293120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hGnZAyrSI+btgLkpb9bU48iLwjdkPloX+NNTFFbpR3419AcQfDcsIgjB2pI9Ye3DHN1Zp37cmqo42aLjbdr9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:23.293935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:443cd6f6a87f84c122ce06b41bfbab4c340dee333101a23dd2eca9cb6a835fcd","sha256:cc77c96ee13bf810677a4c3161ac65c02a3ec6c41f2c22b937864c14caf88300"],"state_sha256":"9b58dca46b4380b73afc2138da2e54dea0631ea27a73f9d786259161c3e4b3b2"}