{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:RD6SLZWKCDCB5CAQ6OX3MID7RV","short_pith_number":"pith:RD6SLZWK","canonical_record":{"source":{"id":"2308.04521","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-08-08T18:36:03Z","cross_cats_sorted":[],"title_canon_sha256":"c475ca17c5d54fdde1a180ce5c182511e266fbc3424c4109893536e36122e68b","abstract_canon_sha256":"cefc133df701611df48e05c890b24766fb86b8c6a0c84270faae530e0aec36aa"},"schema_version":"1.0"},"canonical_sha256":"88fd25e6ca10c41e8810f3afb6207f8d729a1713cb733efa867d4e421f0c6532","source":{"kind":"arxiv","id":"2308.04521","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04521","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04521v1","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04521","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"RD6SLZWKCDCB","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"pith_short_16","alias_value":"RD6SLZWKCDCB5CAQ","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"pith_short_8","alias_value":"RD6SLZWK","created_at":"2026-07-05T06:39:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:RD6SLZWKCDCB5CAQ6OX3MID7RV","target":"record","payload":{"canonical_record":{"source":{"id":"2308.04521","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-08-08T18:36:03Z","cross_cats_sorted":[],"title_canon_sha256":"c475ca17c5d54fdde1a180ce5c182511e266fbc3424c4109893536e36122e68b","abstract_canon_sha256":"cefc133df701611df48e05c890b24766fb86b8c6a0c84270faae530e0aec36aa"},"schema_version":"1.0"},"canonical_sha256":"88fd25e6ca10c41e8810f3afb6207f8d729a1713cb733efa867d4e421f0c6532","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:39:39.088107Z","signature_b64":"q2yRN0yROZwfdR2wpYU+mYPlFiN6q87Wvc+QYOpeF8G1nYSyJRfsznKwAPMNhlLP7u5TrKXEXCsdAMKk6l+rDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88fd25e6ca10c41e8810f3afb6207f8d729a1713cb733efa867d4e421f0c6532","last_reissued_at":"2026-07-05T06:39:39.087647Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:39:39.087647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.04521","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KrcC2kN8cy5zTPjHvBNdN1UfnB8SGJawd8M9JXc6yMfArfc0rRZ9GJ0DwdCoGXAGQORoT7im3asonFHHkOAYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T09:37:23.528654Z"},"content_sha256":"4e5f5e3dd282e24ae3ef059ff9d77616c438f34393e187a1c349eb211e16ca6d","schema_version":"1.0","event_id":"sha256:4e5f5e3dd282e24ae3ef059ff9d77616c438f34393e187a1c349eb211e16ca6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:RD6SLZWKCDCB5CAQ6OX3MID7RV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semantic Analysis of Subexponential Modalities in Distributive Non-commutative Linear Logic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Daniel Rogozin (University College London)","submitted_at":"2023-08-08T18:36:03Z","abstract_excerpt":"In this paper, we consider the full Lambek calculus enriched with subexponential modalities in a distributive setting. We show that the distributive Lambek calculus with subexponentials is complete with respect to its Kripke frames via canonical extensions.  In this approach, we consider subexponentials as S4-like modalities and each modality is interpreted with a reflexive and transitive relation similarly to usual Kripke semantics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04521","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/2308.04521/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fz+eBtFzKhSBqPUmCbSIN8h0rtzC9JMHETvEhpuZBsFnKJ+DSg7aUR2uMXIT05E9L51jrBONQZe7Uqe5fnKmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T09:37:23.529166Z"},"content_sha256":"833fba5a0dc907767840160ba42af354d14601b2aae6a3ff66c420cc0c4e10e2","schema_version":"1.0","event_id":"sha256:833fba5a0dc907767840160ba42af354d14601b2aae6a3ff66c420cc0c4e10e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RD6SLZWKCDCB5CAQ6OX3MID7RV/bundle.json","state_url":"https://pith.science/pith/RD6SLZWKCDCB5CAQ6OX3MID7RV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RD6SLZWKCDCB5CAQ6OX3MID7RV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T09:37:23Z","links":{"resolver":"https://pith.science/pith/RD6SLZWKCDCB5CAQ6OX3MID7RV","bundle":"https://pith.science/pith/RD6SLZWKCDCB5CAQ6OX3MID7RV/bundle.json","state":"https://pith.science/pith/RD6SLZWKCDCB5CAQ6OX3MID7RV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RD6SLZWKCDCB5CAQ6OX3MID7RV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RD6SLZWKCDCB5CAQ6OX3MID7RV","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":"cefc133df701611df48e05c890b24766fb86b8c6a0c84270faae530e0aec36aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-08-08T18:36:03Z","title_canon_sha256":"c475ca17c5d54fdde1a180ce5c182511e266fbc3424c4109893536e36122e68b"},"schema_version":"1.0","source":{"id":"2308.04521","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.04521","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"2308.04521v1","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.04521","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"RD6SLZWKCDCB","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"pith_short_16","alias_value":"RD6SLZWKCDCB5CAQ","created_at":"2026-07-05T06:39:39Z"},{"alias_kind":"pith_short_8","alias_value":"RD6SLZWK","created_at":"2026-07-05T06:39:39Z"}],"graph_snapshots":[{"event_id":"sha256:833fba5a0dc907767840160ba42af354d14601b2aae6a3ff66c420cc0c4e10e2","target":"graph","created_at":"2026-07-05T06:39:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2308.04521/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider the full Lambek calculus enriched with subexponential modalities in a distributive setting. We show that the distributive Lambek calculus with subexponentials is complete with respect to its Kripke frames via canonical extensions.  In this approach, we consider subexponentials as S4-like modalities and each modality is interpreted with a reflexive and transitive relation similarly to usual Kripke semantics.","authors_text":"Daniel Rogozin (University College London)","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-08-08T18:36:03Z","title":"Semantic Analysis of Subexponential Modalities in Distributive Non-commutative Linear Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.04521","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":"sha256:4e5f5e3dd282e24ae3ef059ff9d77616c438f34393e187a1c349eb211e16ca6d","target":"record","created_at":"2026-07-05T06:39:39Z","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":"cefc133df701611df48e05c890b24766fb86b8c6a0c84270faae530e0aec36aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-08-08T18:36:03Z","title_canon_sha256":"c475ca17c5d54fdde1a180ce5c182511e266fbc3424c4109893536e36122e68b"},"schema_version":"1.0","source":{"id":"2308.04521","kind":"arxiv","version":1}},"canonical_sha256":"88fd25e6ca10c41e8810f3afb6207f8d729a1713cb733efa867d4e421f0c6532","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88fd25e6ca10c41e8810f3afb6207f8d729a1713cb733efa867d4e421f0c6532","first_computed_at":"2026-07-05T06:39:39.087647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:39:39.087647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q2yRN0yROZwfdR2wpYU+mYPlFiN6q87Wvc+QYOpeF8G1nYSyJRfsznKwAPMNhlLP7u5TrKXEXCsdAMKk6l+rDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:39:39.088107Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.04521","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e5f5e3dd282e24ae3ef059ff9d77616c438f34393e187a1c349eb211e16ca6d","sha256:833fba5a0dc907767840160ba42af354d14601b2aae6a3ff66c420cc0c4e10e2"],"state_sha256":"894095abe08159e082880a8df1984c1b022895b902a2dedae8b4e79f51e2af1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uehBqWHcbxNmNDAar5oJIlvLwTcYqwqsgbZE5/qnxEdc8Eu0UQn6AX70mpwhogk2R/cJkQidXp7nqVX7Z8w7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T09:37:23.533002Z","bundle_sha256":"57ddcc1add18314f87c02ce8212005ca688447569a5fc9723db27cc257416f4a"}}