{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3UKCKGO6RE6AWUH53U5ASHBLHY","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":"22d18f4defea6aa222defd2cef1fa8cfc5948afd4a201a5add20b6f74f215dc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-06-10T15:04:39Z","title_canon_sha256":"1de3cebabf503bf6e25549343c0d4e14b847b6e7352daf26b45ea89e6467489c"},"schema_version":"1.0","source":{"id":"1706.03244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03244","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03244v1","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03244","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"3UKCKGO6RE6A","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3UKCKGO6RE6AWUH5","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3UKCKGO6","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:f3c36646ca679604ce95747488cc5ebee297b65e62729ca8cd2338f96f399ef6","target":"graph","created_at":"2026-05-18T00:42:38Z","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 displacement calculus $\\mathbf{D}$ is a conservative extension of the Lambek calculus $\\mathbf{L1}$ (with empty antecedents allowed in sequents). $\\mathbf{L1}$ can be said to be the logic of concatenation, while $\\mathbf{D}$ can be said to be the logic of concatenation and intercalation. In many senses, it can be claimed that $\\mathbf{D}$ mimics $\\mathbf{L1}$ in that the proof theory, generative capacity and complexity of the former calculus are natural extensions of the latter calculus. In this paper, we strengthen this claim. We present the appropriate classes of models for $\\mathbf{D}$ ","authors_text":"Oriol Valent\\'in","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-06-10T15:04:39Z","title":"Models for the Displacement Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03244","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:d750340f2e225e032ce23dd0113ba7ce5b6d6b719c3ef399099edff39199b838","target":"record","created_at":"2026-05-18T00:42:38Z","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":"22d18f4defea6aa222defd2cef1fa8cfc5948afd4a201a5add20b6f74f215dc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-06-10T15:04:39Z","title_canon_sha256":"1de3cebabf503bf6e25549343c0d4e14b847b6e7352daf26b45ea89e6467489c"},"schema_version":"1.0","source":{"id":"1706.03244","kind":"arxiv","version":1}},"canonical_sha256":"dd142519de893c0b50fddd3a091c2b3e0f77057393bb5ff7b3f0b63790b8bbed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd142519de893c0b50fddd3a091c2b3e0f77057393bb5ff7b3f0b63790b8bbed","first_computed_at":"2026-05-18T00:42:38.075850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:38.075850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rg3+sXpd1yv4uUn4uIIM7BKw7c5p0LsHORwtaCNS0AG671gqGw0trbxlN8M8rGzibn98mu0R+23Z5ts/3cwXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:38.076594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d750340f2e225e032ce23dd0113ba7ce5b6d6b719c3ef399099edff39199b838","sha256:f3c36646ca679604ce95747488cc5ebee297b65e62729ca8cd2338f96f399ef6"],"state_sha256":"19d102e99f771bab675ebe2d61ac0ec4752afa86d93c317153acad55237afa22"}