{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JW72BQJRMEQGZ2UKEPDJCQQ6QN","short_pith_number":"pith:JW72BQJR","schema_version":"1.0","canonical_sha256":"4dbfa0c13161206cea8a23c691421e835faf36a65731cfb4d725acd6b11bb345","source":{"kind":"arxiv","id":"1808.08902","version":2},"attestation_state":"computed","paper":{"title":"Phase transition for the interchange and quantum Heisenberg models on the Hamming graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Micha{\\l} Kotowski, Piotr Mi{\\l}o\\'s, Rados{\\l}aw Adamczak","submitted_at":"2018-08-27T16:10:02Z","abstract_excerpt":"We study a family of random permutation models on the Hamming graph $H(2,n)$ (i.e., the $2$-fold Cartesian product of complete graphs), containing the interchange process and the cycle-weighted interchange process with parameter $\\theta > 0$. This family contains the random walk representation of the quantum Heisenberg ferromagnet. We show that in these models the cycle structure of permutations undergoes a \\textit{phase transition} -- when the number of transpositions defining the permutation is $\\leq c n^2$, for small enough $c > 0$, all cycles are microscopic, while for more than $\\geq C n^"},"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":"1808.08902","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-27T16:10:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d00734bd131788b706a3f7b390f35a8494390a1cd2d583cb49d4d4d848b8f9d6","abstract_canon_sha256":"9fbfed33271117e8f2ef8722e6070df0aaaa9173686a729a4fedf5dbf765f28e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:25:09.452966Z","signature_b64":"cqu+KG6Yw5wrAvtgZwiH7helL/v4EYmN1p2VVdjCdoYqVNqhaptlGzhOQ4AOfOMbbsO42By+0nSQABKrFQbUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dbfa0c13161206cea8a23c691421e835faf36a65731cfb4d725acd6b11bb345","last_reissued_at":"2026-07-05T02:25:09.452477Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:25:09.452477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase transition for the interchange and quantum Heisenberg models on the Hamming graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Micha{\\l} Kotowski, Piotr Mi{\\l}o\\'s, Rados{\\l}aw Adamczak","submitted_at":"2018-08-27T16:10:02Z","abstract_excerpt":"We study a family of random permutation models on the Hamming graph $H(2,n)$ (i.e., the $2$-fold Cartesian product of complete graphs), containing the interchange process and the cycle-weighted interchange process with parameter $\\theta > 0$. This family contains the random walk representation of the quantum Heisenberg ferromagnet. We show that in these models the cycle structure of permutations undergoes a \\textit{phase transition} -- when the number of transpositions defining the permutation is $\\leq c n^2$, for small enough $c > 0$, all cycles are microscopic, while for more than $\\geq C n^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08902","kind":"arxiv","version":2},"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/1808.08902/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":"1808.08902","created_at":"2026-07-05T02:25:09.452527+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.08902v2","created_at":"2026-07-05T02:25:09.452527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08902","created_at":"2026-07-05T02:25:09.452527+00:00"},{"alias_kind":"pith_short_12","alias_value":"JW72BQJRMEQG","created_at":"2026-07-05T02:25:09.452527+00:00"},{"alias_kind":"pith_short_16","alias_value":"JW72BQJRMEQGZ2UK","created_at":"2026-07-05T02:25:09.452527+00:00"},{"alias_kind":"pith_short_8","alias_value":"JW72BQJR","created_at":"2026-07-05T02:25:09.452527+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.10213","citing_title":"Critical Parameters for Loop and Bernoulli Percolation","ref_index":51,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN","json":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN.json","graph_json":"https://pith.science/api/pith-number/JW72BQJRMEQGZ2UKEPDJCQQ6QN/graph.json","events_json":"https://pith.science/api/pith-number/JW72BQJRMEQGZ2UKEPDJCQQ6QN/events.json","paper":"https://pith.science/paper/JW72BQJR"},"agent_actions":{"view_html":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN","download_json":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN.json","view_paper":"https://pith.science/paper/JW72BQJR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.08902&json=true","fetch_graph":"https://pith.science/api/pith-number/JW72BQJRMEQGZ2UKEPDJCQQ6QN/graph.json","fetch_events":"https://pith.science/api/pith-number/JW72BQJRMEQGZ2UKEPDJCQQ6QN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN/action/storage_attestation","attest_author":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN/action/author_attestation","sign_citation":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN/action/citation_signature","submit_replication":"https://pith.science/pith/JW72BQJRMEQGZ2UKEPDJCQQ6QN/action/replication_record"}},"created_at":"2026-07-05T02:25:09.452527+00:00","updated_at":"2026-07-05T02:25:09.452527+00:00"}