{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TVAFD666CFREHXFUSCHBQEGSZG","short_pith_number":"pith:TVAFD666","schema_version":"1.0","canonical_sha256":"9d4051fbde116243dcb4908e1810d2c9a6adcb3e80a6d2855face948e123860f","source":{"kind":"arxiv","id":"2606.31853","version":1},"attestation_state":"computed","paper":{"title":"Conditionals and Modalities in Constructive Quantum Logics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Guillaume Massas (Chapman University), Juan P. Aguilera (TU Wien)","submitted_at":"2026-06-30T15:52:18Z","abstract_excerpt":"We investigate logics that generalize both intuitionistic logic and quantum logic. In earlier work, we introduced Ex-logic, an extension of Holliday's fundamental logic that coincides with the intersection of orthologic and the implication-free fragment of intuitionistic logic. In this paper, we add an implication connective to Ex-logic and axiomatize iEx-logic, the intersection of full intuitionistic logic and orthomodular logic with the implication connective interpreted as the Sasaki hook. As a consequence, we obtain a characterization of the lattice of logics extending iEx-logic as the pro"},"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":"2606.31853","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-06-30T15:52:18Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"c0ba6c84340225e634618ccc081ad1d6746682ec4c98f0ae83032a106372aad7","abstract_canon_sha256":"cc39dc54959fb3c440a1aa6a4a67149973fc06aaba382cb1c89489ec6e7aabbb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:18:17.645179Z","signature_b64":"Xd1FZuh7MeM9JUixW49vALT8Kp9v3FDjB+t0RbPe7shLCWDsI6a1m8ZxfPuBSWI70WEh4i+w2RX7YI35pUOtCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d4051fbde116243dcb4908e1810d2c9a6adcb3e80a6d2855face948e123860f","last_reissued_at":"2026-07-01T01:18:17.644728Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:18:17.644728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conditionals and Modalities in Constructive Quantum Logics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Guillaume Massas (Chapman University), Juan P. Aguilera (TU Wien)","submitted_at":"2026-06-30T15:52:18Z","abstract_excerpt":"We investigate logics that generalize both intuitionistic logic and quantum logic. In earlier work, we introduced Ex-logic, an extension of Holliday's fundamental logic that coincides with the intersection of orthologic and the implication-free fragment of intuitionistic logic. In this paper, we add an implication connective to Ex-logic and axiomatize iEx-logic, the intersection of full intuitionistic logic and orthomodular logic with the implication connective interpreted as the Sasaki hook. As a consequence, we obtain a characterization of the lattice of logics extending iEx-logic as the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31853","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/2606.31853/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":"2606.31853","created_at":"2026-07-01T01:18:17.644802+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.31853v1","created_at":"2026-07-01T01:18:17.644802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31853","created_at":"2026-07-01T01:18:17.644802+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVAFD666CFRE","created_at":"2026-07-01T01:18:17.644802+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVAFD666CFREHXFU","created_at":"2026-07-01T01:18:17.644802+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVAFD666","created_at":"2026-07-01T01:18:17.644802+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/TVAFD666CFREHXFUSCHBQEGSZG","json":"https://pith.science/pith/TVAFD666CFREHXFUSCHBQEGSZG.json","graph_json":"https://pith.science/api/pith-number/TVAFD666CFREHXFUSCHBQEGSZG/graph.json","events_json":"https://pith.science/api/pith-number/TVAFD666CFREHXFUSCHBQEGSZG/events.json","paper":"https://pith.science/paper/TVAFD666"},"agent_actions":{"view_html":"https://pith.science/pith/TVAFD666CFREHXFUSCHBQEGSZG","download_json":"https://pith.science/pith/TVAFD666CFREHXFUSCHBQEGSZG.json","view_paper":"https://pith.science/paper/TVAFD666","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.31853&json=true","fetch_graph":"https://pith.science/api/pith-number/TVAFD666CFREHXFUSCHBQEGSZG/graph.json","fetch_events":"https://pith.science/api/pith-number/TVAFD666CFREHXFUSCHBQEGSZG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVAFD666CFREHXFUSCHBQEGSZG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVAFD666CFREHXFUSCHBQEGSZG/action/storage_attestation","attest_author":"https://pith.science/pith/TVAFD666CFREHXFUSCHBQEGSZG/action/author_attestation","sign_citation":"https://pith.science/pith/TVAFD666CFREHXFUSCHBQEGSZG/action/citation_signature","submit_replication":"https://pith.science/pith/TVAFD666CFREHXFUSCHBQEGSZG/action/replication_record"}},"created_at":"2026-07-01T01:18:17.644802+00:00","updated_at":"2026-07-01T01:18:17.644802+00:00"}