{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:DX4EFFB7XBIHCQ4S774BQ6WSLQ","short_pith_number":"pith:DX4EFFB7","schema_version":"1.0","canonical_sha256":"1df842943fb850714392fff8187ad25c3d53d639c4d3c7657dddfa23b6e675f4","source":{"kind":"arxiv","id":"2405.12485","version":1},"attestation_state":"computed","paper":{"title":"Formal languages, spin systems, and quasicrystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Francesca Fernandes, Matilde Marcolli","submitted_at":"2024-05-21T04:06:26Z","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 "},"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":"2405.12485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-21T04:06:26Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"bdadf4348c1d2c4f3103b31093b89fd69ad65ddc17e2ab38925625b7c28dcd96","abstract_canon_sha256":"7343ddefd6b9038db1f8a200bdcf4a07447877aea5b0b5cbb98f3edd46e7057b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:21:20.758710Z","signature_b64":"0wGYZSTvRDZPejuoybZN1OO3vzScAYJUSZejdCTyOWOnUWwumKE5SyZlcdlEHCIVaPEcq8XoDWo1a1d9XjFoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1df842943fb850714392fff8187ad25c3d53d639c4d3c7657dddfa23b6e675f4","last_reissued_at":"2026-07-05T08:21:20.758269Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:21:20.758269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formal languages, spin systems, and quasicrystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Francesca Fernandes, Matilde Marcolli","submitted_at":"2024-05-21T04:06:26Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.12485","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/2405.12485/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":"2405.12485","created_at":"2026-07-05T08:21:20.758327+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.12485v1","created_at":"2026-07-05T08:21:20.758327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.12485","created_at":"2026-07-05T08:21:20.758327+00:00"},{"alias_kind":"pith_short_12","alias_value":"DX4EFFB7XBIH","created_at":"2026-07-05T08:21:20.758327+00:00"},{"alias_kind":"pith_short_16","alias_value":"DX4EFFB7XBIHCQ4S","created_at":"2026-07-05T08:21:20.758327+00:00"},{"alias_kind":"pith_short_8","alias_value":"DX4EFFB7","created_at":"2026-07-05T08:21:20.758327+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.09688","citing_title":"Formal Languages and TQFTs with Defects","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ","json":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ.json","graph_json":"https://pith.science/api/pith-number/DX4EFFB7XBIHCQ4S774BQ6WSLQ/graph.json","events_json":"https://pith.science/api/pith-number/DX4EFFB7XBIHCQ4S774BQ6WSLQ/events.json","paper":"https://pith.science/paper/DX4EFFB7"},"agent_actions":{"view_html":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ","download_json":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ.json","view_paper":"https://pith.science/paper/DX4EFFB7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.12485&json=true","fetch_graph":"https://pith.science/api/pith-number/DX4EFFB7XBIHCQ4S774BQ6WSLQ/graph.json","fetch_events":"https://pith.science/api/pith-number/DX4EFFB7XBIHCQ4S774BQ6WSLQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ/action/storage_attestation","attest_author":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ/action/author_attestation","sign_citation":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ/action/citation_signature","submit_replication":"https://pith.science/pith/DX4EFFB7XBIHCQ4S774BQ6WSLQ/action/replication_record"}},"created_at":"2026-07-05T08:21:20.758327+00:00","updated_at":"2026-07-05T08:21:20.758327+00:00"}