{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ENS432MXEO3RXNTB7ZWNRPKN72","short_pith_number":"pith:ENS432MX","schema_version":"1.0","canonical_sha256":"2365cde99723b71bb661fe6cd8bd4dfe956e1cd70b39802b8c7eb2598103b743","source":{"kind":"arxiv","id":"1202.1322","version":3},"attestation_state":"computed","paper":{"title":"Sharp phase transition in the random stirring model on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alan Hammond","submitted_at":"2012-02-07T00:30:28Z","abstract_excerpt":"We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists d_0 such that, for any d \\geq d_0, the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree d almost surely contains an infinite cycle consists of a semi-infinite interval. The critical point at the left-hand end of this interval is at least 1/d + 1/(2d^2) and at most 1/d + 2/(d^2).\n  This version is a major revision, with a much shorter proof. Principal among the c"},"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":"1202.1322","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-07T00:30:28Z","cross_cats_sorted":[],"title_canon_sha256":"4e055169310b9b169039a25e30f52dbeeebd1c97efa7cc159eeedd63b726649d","abstract_canon_sha256":"71cb125f072bdd3a40a4e3d40ea1fa3a3a368ef7912812b80143328720da33ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:13.820829Z","signature_b64":"Mir4EYykVwIjQLSsaXFHUnQb0RTbj/UU4WQizHBtOlzxVpSseMvI/j9fg/qpacMBNttsNY05WW5OYBVOunh6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2365cde99723b71bb661fe6cd8bd4dfe956e1cd70b39802b8c7eb2598103b743","last_reissued_at":"2026-05-18T03:06:13.820384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:13.820384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp phase transition in the random stirring model on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alan Hammond","submitted_at":"2012-02-07T00:30:28Z","abstract_excerpt":"We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists d_0 such that, for any d \\geq d_0, the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree d almost surely contains an infinite cycle consists of a semi-infinite interval. The critical point at the left-hand end of this interval is at least 1/d + 1/(2d^2) and at most 1/d + 2/(d^2).\n  This version is a major revision, with a much shorter proof. Principal among the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1322","kind":"arxiv","version":3},"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":"1202.1322","created_at":"2026-05-18T03:06:13.820453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.1322v3","created_at":"2026-05-18T03:06:13.820453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1322","created_at":"2026-05-18T03:06:13.820453+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENS432MXEO3R","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENS432MXEO3RXNTB","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENS432MX","created_at":"2026-05-18T12:27:04.183437+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/ENS432MXEO3RXNTB7ZWNRPKN72","json":"https://pith.science/pith/ENS432MXEO3RXNTB7ZWNRPKN72.json","graph_json":"https://pith.science/api/pith-number/ENS432MXEO3RXNTB7ZWNRPKN72/graph.json","events_json":"https://pith.science/api/pith-number/ENS432MXEO3RXNTB7ZWNRPKN72/events.json","paper":"https://pith.science/paper/ENS432MX"},"agent_actions":{"view_html":"https://pith.science/pith/ENS432MXEO3RXNTB7ZWNRPKN72","download_json":"https://pith.science/pith/ENS432MXEO3RXNTB7ZWNRPKN72.json","view_paper":"https://pith.science/paper/ENS432MX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.1322&json=true","fetch_graph":"https://pith.science/api/pith-number/ENS432MXEO3RXNTB7ZWNRPKN72/graph.json","fetch_events":"https://pith.science/api/pith-number/ENS432MXEO3RXNTB7ZWNRPKN72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENS432MXEO3RXNTB7ZWNRPKN72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENS432MXEO3RXNTB7ZWNRPKN72/action/storage_attestation","attest_author":"https://pith.science/pith/ENS432MXEO3RXNTB7ZWNRPKN72/action/author_attestation","sign_citation":"https://pith.science/pith/ENS432MXEO3RXNTB7ZWNRPKN72/action/citation_signature","submit_replication":"https://pith.science/pith/ENS432MXEO3RXNTB7ZWNRPKN72/action/replication_record"}},"created_at":"2026-05-18T03:06:13.820453+00:00","updated_at":"2026-05-18T03:06:13.820453+00:00"}