{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:IYWRPT2UXXDOROT2VEL2SNTBSS","short_pith_number":"pith:IYWRPT2U","schema_version":"1.0","canonical_sha256":"462d17cf54bdc6e8ba7aa917a9366194bf635acb77e0bc9925ff9835252c0b3b","source":{"kind":"arxiv","id":"1907.02854","version":1},"attestation_state":"computed","paper":{"title":"$p$-adic boundary laws and Markov chains on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Le Ny, L. Liao, U. A. Rozikov","submitted_at":"2019-07-05T14:34:23Z","abstract_excerpt":"In this paper we consider $q$-state potential on general infinite trees with a nearest-neighbor $p$-adic interactions given by a stochastic matrix. {We show the uniqueness of the associated Markov chain ({\\em splitting Gibbs measures}) under some sufficient conditions on the stochastic matrix.} Moreover, we find a family of stochastic matrices for which there are at least two $p$-adic Markov chains on an infinite tree (in particular, on a Cayley tree). When the $p$-adic norm of $q$ is greater ({{\\em resp.}} less) than the norm of any element of the stochastic matrix then it is proved that the "},"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":"1907.02854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-07-05T14:34:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"fe21a3bceb6a2756ad6c2478372ab60e9beb14d73131d9de396d50d4452ec192","abstract_canon_sha256":"1c18276093e9493fcc48c1983089fc8793594162db895303c12085cc20c135c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:22.855769Z","signature_b64":"TxOLBIfO0VOvmLf4Y/8FiShJ7L4TwNRtB0a721Uh6Vo7wrbmWCe/T8dxQwQDYb3KSwX8nLIIKACMugAq0RbeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"462d17cf54bdc6e8ba7aa917a9366194bf635acb77e0bc9925ff9835252c0b3b","last_reissued_at":"2026-05-17T23:41:22.855065Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:22.855065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$p$-adic boundary laws and Markov chains on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Le Ny, L. Liao, U. A. Rozikov","submitted_at":"2019-07-05T14:34:23Z","abstract_excerpt":"In this paper we consider $q$-state potential on general infinite trees with a nearest-neighbor $p$-adic interactions given by a stochastic matrix. {We show the uniqueness of the associated Markov chain ({\\em splitting Gibbs measures}) under some sufficient conditions on the stochastic matrix.} Moreover, we find a family of stochastic matrices for which there are at least two $p$-adic Markov chains on an infinite tree (in particular, on a Cayley tree). When the $p$-adic norm of $q$ is greater ({{\\em resp.}} less) than the norm of any element of the stochastic matrix then it is proved that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02854","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":"1907.02854","created_at":"2026-05-17T23:41:22.855175+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02854v1","created_at":"2026-05-17T23:41:22.855175+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02854","created_at":"2026-05-17T23:41:22.855175+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYWRPT2UXXDO","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYWRPT2UXXDOROT2","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYWRPT2U","created_at":"2026-05-18T12:33:18.533446+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/IYWRPT2UXXDOROT2VEL2SNTBSS","json":"https://pith.science/pith/IYWRPT2UXXDOROT2VEL2SNTBSS.json","graph_json":"https://pith.science/api/pith-number/IYWRPT2UXXDOROT2VEL2SNTBSS/graph.json","events_json":"https://pith.science/api/pith-number/IYWRPT2UXXDOROT2VEL2SNTBSS/events.json","paper":"https://pith.science/paper/IYWRPT2U"},"agent_actions":{"view_html":"https://pith.science/pith/IYWRPT2UXXDOROT2VEL2SNTBSS","download_json":"https://pith.science/pith/IYWRPT2UXXDOROT2VEL2SNTBSS.json","view_paper":"https://pith.science/paper/IYWRPT2U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02854&json=true","fetch_graph":"https://pith.science/api/pith-number/IYWRPT2UXXDOROT2VEL2SNTBSS/graph.json","fetch_events":"https://pith.science/api/pith-number/IYWRPT2UXXDOROT2VEL2SNTBSS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYWRPT2UXXDOROT2VEL2SNTBSS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYWRPT2UXXDOROT2VEL2SNTBSS/action/storage_attestation","attest_author":"https://pith.science/pith/IYWRPT2UXXDOROT2VEL2SNTBSS/action/author_attestation","sign_citation":"https://pith.science/pith/IYWRPT2UXXDOROT2VEL2SNTBSS/action/citation_signature","submit_replication":"https://pith.science/pith/IYWRPT2UXXDOROT2VEL2SNTBSS/action/replication_record"}},"created_at":"2026-05-17T23:41:22.855175+00:00","updated_at":"2026-05-17T23:41:22.855175+00:00"}