{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MYDPMBLNTV67KHB3QIHXLXJBLE","short_pith_number":"pith:MYDPMBLN","schema_version":"1.0","canonical_sha256":"6606f6056d9d7df51c3b820f75dd21593ba7c2ac1d19a6c1c17d359017d6035b","source":{"kind":"arxiv","id":"1712.00586","version":1},"attestation_state":"computed","paper":{"title":"Constant-length random substitutions and Gibbs measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Cesar Maldonado, Edgardo Ugalde, Liliana Trejo-Valencia","submitted_at":"2017-12-02T10:41:39Z","abstract_excerpt":"This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the substitution, and exhibiting polynomial decay of correlations. For constant-length substitutions, we go further by proving that the invariant state is precisely a Gibbs measure which can be obtained as the projective limit of its natural Markovian approximations. We close the paper with a class of substitutions whose invariant state is the unique Gibbs measure for "},"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":"1712.00586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-02T10:41:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"97028a6a14adca064c94660a626320cee70cfbc4105ef3fa2c6022e69f0e0644","abstract_canon_sha256":"7be8e3f340f825ad0d6c8df3c8f584a4bad2bf1a18c9eb158e2115612d47b7f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:24.795765Z","signature_b64":"Xag/6hdkw2Y7aaeHfFzstEbsLfXPbYg+uHFvQHOlDUG9JBCp2j2KqEIk6A40GZV0AQltl0io0kwFE9nak8AUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6606f6056d9d7df51c3b820f75dd21593ba7c2ac1d19a6c1c17d359017d6035b","last_reissued_at":"2026-05-18T00:19:24.795329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:24.795329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constant-length random substitutions and Gibbs measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Cesar Maldonado, Edgardo Ugalde, Liliana Trejo-Valencia","submitted_at":"2017-12-02T10:41:39Z","abstract_excerpt":"This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the substitution, and exhibiting polynomial decay of correlations. For constant-length substitutions, we go further by proving that the invariant state is precisely a Gibbs measure which can be obtained as the projective limit of its natural Markovian approximations. We close the paper with a class of substitutions whose invariant state is the unique Gibbs measure for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00586","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":""},"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":"1712.00586","created_at":"2026-05-18T00:19:24.795393+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.00586v1","created_at":"2026-05-18T00:19:24.795393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00586","created_at":"2026-05-18T00:19:24.795393+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYDPMBLNTV67","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYDPMBLNTV67KHB3","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYDPMBLN","created_at":"2026-05-18T12:31:31.346846+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/MYDPMBLNTV67KHB3QIHXLXJBLE","json":"https://pith.science/pith/MYDPMBLNTV67KHB3QIHXLXJBLE.json","graph_json":"https://pith.science/api/pith-number/MYDPMBLNTV67KHB3QIHXLXJBLE/graph.json","events_json":"https://pith.science/api/pith-number/MYDPMBLNTV67KHB3QIHXLXJBLE/events.json","paper":"https://pith.science/paper/MYDPMBLN"},"agent_actions":{"view_html":"https://pith.science/pith/MYDPMBLNTV67KHB3QIHXLXJBLE","download_json":"https://pith.science/pith/MYDPMBLNTV67KHB3QIHXLXJBLE.json","view_paper":"https://pith.science/paper/MYDPMBLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.00586&json=true","fetch_graph":"https://pith.science/api/pith-number/MYDPMBLNTV67KHB3QIHXLXJBLE/graph.json","fetch_events":"https://pith.science/api/pith-number/MYDPMBLNTV67KHB3QIHXLXJBLE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYDPMBLNTV67KHB3QIHXLXJBLE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYDPMBLNTV67KHB3QIHXLXJBLE/action/storage_attestation","attest_author":"https://pith.science/pith/MYDPMBLNTV67KHB3QIHXLXJBLE/action/author_attestation","sign_citation":"https://pith.science/pith/MYDPMBLNTV67KHB3QIHXLXJBLE/action/citation_signature","submit_replication":"https://pith.science/pith/MYDPMBLNTV67KHB3QIHXLXJBLE/action/replication_record"}},"created_at":"2026-05-18T00:19:24.795393+00:00","updated_at":"2026-05-18T00:19:24.795393+00:00"}