{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DX4EFFB7XBIHCQ4S774BQ6WSLQ","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":"7343ddefd6b9038db1f8a200bdcf4a07447877aea5b0b5cbb98f3edd46e7057b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-21T04:06:26Z","title_canon_sha256":"bdadf4348c1d2c4f3103b31093b89fd69ad65ddc17e2ab38925625b7c28dcd96"},"schema_version":"1.0","source":{"id":"2405.12485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.12485","created_at":"2026-07-05T08:21:20Z"},{"alias_kind":"arxiv_version","alias_value":"2405.12485v1","created_at":"2026-07-05T08:21:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.12485","created_at":"2026-07-05T08:21:20Z"},{"alias_kind":"pith_short_12","alias_value":"DX4EFFB7XBIH","created_at":"2026-07-05T08:21:20Z"},{"alias_kind":"pith_short_16","alias_value":"DX4EFFB7XBIHCQ4S","created_at":"2026-07-05T08:21:20Z"},{"alias_kind":"pith_short_8","alias_value":"DX4EFFB7","created_at":"2026-07-05T08:21:20Z"}],"graph_snapshots":[{"event_id":"sha256:c484d6a8d8124d1872dcb0c132ed41191802d522445fd9aa9bd03c08cec2b6a9","target":"graph","created_at":"2026-07-05T08:21:20Z","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/2405.12485/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a categorical formalism for context-free languages with morphisms given by correspondences obtained from rational transductions. We show that D0L-systems are a special case of the correspondences that define morphisms in this category. We construct a functorial mapping to aperiodic spin chains. We then generalize this construction to a class of mildly context sensitive grammars, the multiple-context-free grammars (MCFG), with a similar functorial mapping to spin systems in higher dimensions, with Boltzmann weights describing interacting spins on vertices of hypercubes. We show that ","authors_text":"Francesca Fernandes, Matilde Marcolli","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-21T04:06:26Z","title":"Formal languages, spin systems, and quasicrystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.12485","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:e4b69d9d30211c576100afcb253bc2a28302201173b03727635a0ed5f842ea28","target":"record","created_at":"2026-07-05T08:21:20Z","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":"7343ddefd6b9038db1f8a200bdcf4a07447877aea5b0b5cbb98f3edd46e7057b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-21T04:06:26Z","title_canon_sha256":"bdadf4348c1d2c4f3103b31093b89fd69ad65ddc17e2ab38925625b7c28dcd96"},"schema_version":"1.0","source":{"id":"2405.12485","kind":"arxiv","version":1}},"canonical_sha256":"1df842943fb850714392fff8187ad25c3d53d639c4d3c7657dddfa23b6e675f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1df842943fb850714392fff8187ad25c3d53d639c4d3c7657dddfa23b6e675f4","first_computed_at":"2026-07-05T08:21:20.758269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:21:20.758269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0wGYZSTvRDZPejuoybZN1OO3vzScAYJUSZejdCTyOWOnUWwumKE5SyZlcdlEHCIVaPEcq8XoDWo1a1d9XjFoBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:21:20.758710Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.12485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4b69d9d30211c576100afcb253bc2a28302201173b03727635a0ed5f842ea28","sha256:c484d6a8d8124d1872dcb0c132ed41191802d522445fd9aa9bd03c08cec2b6a9"],"state_sha256":"6d037a93d786e4eb031cefe1c36b4c43424bfece8f3926f7582e6f2ba2c19dd3"}