{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:MDLM4AKLW2Y6UV42PGJFGPPPWL","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":"d9a16dc8485c631ff6f80d455dbdaa2722b21a8c9307d5b167bf0511d0a16286","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-12-19T11:38:35Z","title_canon_sha256":"1afb3098930ecdccdfb2d71420797fc5594301a5d4cdcef20e46e3ff68fd3ed5"},"schema_version":"1.0","source":{"id":"0812.3754","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3754","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3754v4","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3754","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"MDLM4AKLW2Y6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"MDLM4AKLW2Y6UV42","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"MDLM4AKL","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:0b73abace71e131cff6d67218c3bedd031ad40368660dbe929c45707f4fcdded","target":"graph","created_at":"2026-05-18T01:04:09Z","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":"The relationship between Heyting algebras (HA) and semirings is explored. A new class of HAs called Symmetric Heyting algebras (SHAs) is proposed, and a necessary condition on SHAs to be consider semirings is given. We define a new mathematical family called Heyting structures, which are similar to semirings, but with Heyting-algebra operators in place of the usual arithmetic operators usually seen in semirings. The impact of the zero-sum free property of semirings on Heyting structures is shown as also the condition under which it is possible to extend one Heyting structure to another. It is ","authors_text":"Amit Raj, Mahesh Rudrachar, Shrisha Rao","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-12-19T11:38:35Z","title":"Semiring Properties of Heyting Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3754","kind":"arxiv","version":4},"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":"sha256:78bbcbc9e6399b58d38a5da6193fe7ce3937e9ff74defbe18419baf19f97273e","target":"record","created_at":"2026-05-18T01:04:09Z","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":"d9a16dc8485c631ff6f80d455dbdaa2722b21a8c9307d5b167bf0511d0a16286","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-12-19T11:38:35Z","title_canon_sha256":"1afb3098930ecdccdfb2d71420797fc5594301a5d4cdcef20e46e3ff68fd3ed5"},"schema_version":"1.0","source":{"id":"0812.3754","kind":"arxiv","version":4}},"canonical_sha256":"60d6ce014bb6b1ea579a7992533defb2f15d73947506385520c3d6d7a15a8659","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60d6ce014bb6b1ea579a7992533defb2f15d73947506385520c3d6d7a15a8659","first_computed_at":"2026-05-18T01:04:09.741730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:09.741730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9an7rzUosuUqLNwO7cxXrxfcTrYDH9h/zKxomH62O48dfn64veBHKnHueX0n0sJWwpLksNsaIshWWQwciraxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:09.742193Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3754","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78bbcbc9e6399b58d38a5da6193fe7ce3937e9ff74defbe18419baf19f97273e","sha256:0b73abace71e131cff6d67218c3bedd031ad40368660dbe929c45707f4fcdded"],"state_sha256":"df1c1f5d2cfbc68ab4fe6842b04f80931e4a535db9e395f20fd13c3f30975585"}