{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:MZA4BF2ZXSGALVWMB2V4QGM5TH","short_pith_number":"pith:MZA4BF2Z","schema_version":"1.0","canonical_sha256":"6641c09759bc8c05d6cc0eabc8199d99f3090927e60266b4ec07e8ee17678731","source":{"kind":"arxiv","id":"math/0412450","version":1},"attestation_state":"computed","paper":{"title":"Phase ordering after a deep quench: the stochastic Ising and hard core gas models on a tree","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Fabio Martinelli, Pietro Caputo","submitted_at":"2004-12-22T12:12:32Z","abstract_excerpt":"Consider a low temperature stochastic Ising model in the phase coexistence regime with Markov semigroup $P_t$. A fundamental and still largely open problem is the understanding of the long time behavior of $\\d_\\h P_t$ when the initial configuration $\\h$ is sampled from a highly disordered state $\\nu$ (e.g. a product Bernoulli measure or a high temperature Gibbs measure). Exploiting recent progresses in the analysis of the mixing time of Monte Carlo Markov chains for discrete spin models on a regular $b$-ary tree $\\Tree^b$, we tackle the above problem for the Ising and hard core gas (independen"},"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":"math/0412450","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-12-22T12:12:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7c7fbf4d4e9276502853e7de0a060dbc6dbdee51b3b033c8cd8858eb77a35fe0","abstract_canon_sha256":"06d88111abef7d0d836f3ca1f230315584e0f2f23557d38649b5ba542b53d4cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:51.523714Z","signature_b64":"IwY0OQusG3moEhvhhErNAUZPVCS76ZOuCkT+hvOABQcYcrR4Bicms4fsIv8VoMulymPloMZnEtenPZpSZO+hBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6641c09759bc8c05d6cc0eabc8199d99f3090927e60266b4ec07e8ee17678731","last_reissued_at":"2026-05-18T04:39:51.523255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:51.523255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase ordering after a deep quench: the stochastic Ising and hard core gas models on a tree","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Fabio Martinelli, Pietro Caputo","submitted_at":"2004-12-22T12:12:32Z","abstract_excerpt":"Consider a low temperature stochastic Ising model in the phase coexistence regime with Markov semigroup $P_t$. A fundamental and still largely open problem is the understanding of the long time behavior of $\\d_\\h P_t$ when the initial configuration $\\h$ is sampled from a highly disordered state $\\nu$ (e.g. a product Bernoulli measure or a high temperature Gibbs measure). Exploiting recent progresses in the analysis of the mixing time of Monte Carlo Markov chains for discrete spin models on a regular $b$-ary tree $\\Tree^b$, we tackle the above problem for the Ising and hard core gas (independen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412450","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":"math/0412450","created_at":"2026-05-18T04:39:51.523324+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0412450v1","created_at":"2026-05-18T04:39:51.523324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412450","created_at":"2026-05-18T04:39:51.523324+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZA4BF2ZXSGA","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZA4BF2ZXSGALVWM","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZA4BF2Z","created_at":"2026-05-18T12:25:52.687210+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/MZA4BF2ZXSGALVWMB2V4QGM5TH","json":"https://pith.science/pith/MZA4BF2ZXSGALVWMB2V4QGM5TH.json","graph_json":"https://pith.science/api/pith-number/MZA4BF2ZXSGALVWMB2V4QGM5TH/graph.json","events_json":"https://pith.science/api/pith-number/MZA4BF2ZXSGALVWMB2V4QGM5TH/events.json","paper":"https://pith.science/paper/MZA4BF2Z"},"agent_actions":{"view_html":"https://pith.science/pith/MZA4BF2ZXSGALVWMB2V4QGM5TH","download_json":"https://pith.science/pith/MZA4BF2ZXSGALVWMB2V4QGM5TH.json","view_paper":"https://pith.science/paper/MZA4BF2Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0412450&json=true","fetch_graph":"https://pith.science/api/pith-number/MZA4BF2ZXSGALVWMB2V4QGM5TH/graph.json","fetch_events":"https://pith.science/api/pith-number/MZA4BF2ZXSGALVWMB2V4QGM5TH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZA4BF2ZXSGALVWMB2V4QGM5TH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZA4BF2ZXSGALVWMB2V4QGM5TH/action/storage_attestation","attest_author":"https://pith.science/pith/MZA4BF2ZXSGALVWMB2V4QGM5TH/action/author_attestation","sign_citation":"https://pith.science/pith/MZA4BF2ZXSGALVWMB2V4QGM5TH/action/citation_signature","submit_replication":"https://pith.science/pith/MZA4BF2ZXSGALVWMB2V4QGM5TH/action/replication_record"}},"created_at":"2026-05-18T04:39:51.523324+00:00","updated_at":"2026-05-18T04:39:51.523324+00:00"}