{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:FGCNIYZWXG6CHXPPQQYTI64KKR","short_pith_number":"pith:FGCNIYZW","schema_version":"1.0","canonical_sha256":"2984d46336b9bc23ddef8431347b8a545f5efeaa3bbcb4106f9d65ffd4000869","source":{"kind":"arxiv","id":"2507.11445","version":1},"attestation_state":"computed","paper":{"title":"The stability of long-range order in disordered systems: A generalized Ding-Zhuang argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Hai-Jun Zhou, Jianwen Zhou, Ruifeng Liu, Yejia Chen","submitted_at":"2025-07-15T16:08:00Z","abstract_excerpt":"The stability of long-range order against quenched disorder is a central problem in statistical mechanics. This paper develops a generalized framework extending the Ding-Zhuang method and integrated with the Pirogov-Sinai framework, establishing a systematic scheme for studying phase transitions of long-range order in disordered systems. We axiomatize the Ding-Zhuang approach into a theoretical framework consisting of the Peierls condition and a local symmetry condition. For systems in dimensions $d \\geq 3$ satisfying these conditions, we prove the persistence of long-range order at low temper"},"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":"2507.11445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-07-15T16:08:00Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","math.PR"],"title_canon_sha256":"e0fd9bfed3b19a56ce0b979e89836caa41f45327987c3289b0c92e99471cc325","abstract_canon_sha256":"8ad6d335295a5230dca4cd1e3b9ea055834d093090a8913a2676411118f271c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:37:39.432286Z","signature_b64":"Kf2vjguinhKxVPErsImqCLw0n0TAMO1VSu71eXFo9QAzlISPZVf/HyC3U4O0G7fPmY7p+AkSyR/N/I+ePN5YBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2984d46336b9bc23ddef8431347b8a545f5efeaa3bbcb4106f9d65ffd4000869","last_reissued_at":"2026-07-05T11:37:39.431812Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:37:39.431812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The stability of long-range order in disordered systems: A generalized Ding-Zhuang argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Hai-Jun Zhou, Jianwen Zhou, Ruifeng Liu, Yejia Chen","submitted_at":"2025-07-15T16:08:00Z","abstract_excerpt":"The stability of long-range order against quenched disorder is a central problem in statistical mechanics. This paper develops a generalized framework extending the Ding-Zhuang method and integrated with the Pirogov-Sinai framework, establishing a systematic scheme for studying phase transitions of long-range order in disordered systems. We axiomatize the Ding-Zhuang approach into a theoretical framework consisting of the Peierls condition and a local symmetry condition. For systems in dimensions $d \\geq 3$ satisfying these conditions, we prove the persistence of long-range order at low temper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11445","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.11445/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":"2507.11445","created_at":"2026-07-05T11:37:39.431873+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.11445v1","created_at":"2026-07-05T11:37:39.431873+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.11445","created_at":"2026-07-05T11:37:39.431873+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGCNIYZWXG6C","created_at":"2026-07-05T11:37:39.431873+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGCNIYZWXG6CHXPP","created_at":"2026-07-05T11:37:39.431873+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGCNIYZW","created_at":"2026-07-05T11:37:39.431873+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06205","citing_title":"Thermodynamic phase transitions in lattice spin systems with severe kinetic constraints: Numerical simulation results","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR","json":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR.json","graph_json":"https://pith.science/api/pith-number/FGCNIYZWXG6CHXPPQQYTI64KKR/graph.json","events_json":"https://pith.science/api/pith-number/FGCNIYZWXG6CHXPPQQYTI64KKR/events.json","paper":"https://pith.science/paper/FGCNIYZW"},"agent_actions":{"view_html":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR","download_json":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR.json","view_paper":"https://pith.science/paper/FGCNIYZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.11445&json=true","fetch_graph":"https://pith.science/api/pith-number/FGCNIYZWXG6CHXPPQQYTI64KKR/graph.json","fetch_events":"https://pith.science/api/pith-number/FGCNIYZWXG6CHXPPQQYTI64KKR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR/action/storage_attestation","attest_author":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR/action/author_attestation","sign_citation":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR/action/citation_signature","submit_replication":"https://pith.science/pith/FGCNIYZWXG6CHXPPQQYTI64KKR/action/replication_record"}},"created_at":"2026-07-05T11:37:39.431873+00:00","updated_at":"2026-07-05T11:37:39.431873+00:00"}