{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:3RQBAPJMV6HUD5W3DDKO67ZIDQ","short_pith_number":"pith:3RQBAPJM","schema_version":"1.0","canonical_sha256":"dc60103d2caf8f41f6db18d4ef7f281c3791ff4201992824eec920c2743e51ac","source":{"kind":"arxiv","id":"2211.00319","version":2},"attestation_state":"computed","paper":{"title":"Random tangled currents for $\\varphi^4$: translation invariant Gibbs measures and continuity of the phase transition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christoforos Panagiotis, Franco Severo, Romain Panis, Trishen S. Gunaratnam","submitted_at":"2022-11-01T08:07:17Z","abstract_excerpt":"We prove that the set of automorphism invariant Gibbs measures for the $\\varphi^4$ model on graphs of polynomial growth has at most two extremal measures at all values of $\\beta$. We also give a sufficient condition to ensure that the set of all Gibbs measures is a singleton. As an application, we show that the spontaneous magnetisation of the nearest-neighbour $\\varphi^4$ model on $\\mathbb{Z}^d$ vanishes at criticality for $d\\geq 3$. The analogous results were established for the Ising model in the seminal works of Aizenman, Duminil-Copin, and Sidoravicius (Comm. Math. Phys., 2015), and Raouf"},"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":"2211.00319","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-11-01T08:07:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"611a39a4fa33d2d2eff789c869929b55e033d3beb185a43027e66a65120d728a","abstract_canon_sha256":"89eff91848b058f9268fc4e45db56e043b63e98e681813155fb5149a46272313"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:37:19.421146Z","signature_b64":"blWfTTFym9w8mcDDUE3szZ+xYPA+hC0ZyexHCf4Nrh0O6am3OpJSajPB+3OM+lP+Y381iZKy/syg5PO7vd4dDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc60103d2caf8f41f6db18d4ef7f281c3791ff4201992824eec920c2743e51ac","last_reissued_at":"2026-07-05T10:37:19.420026Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:37:19.420026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random tangled currents for $\\varphi^4$: translation invariant Gibbs measures and continuity of the phase transition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christoforos Panagiotis, Franco Severo, Romain Panis, Trishen S. Gunaratnam","submitted_at":"2022-11-01T08:07:17Z","abstract_excerpt":"We prove that the set of automorphism invariant Gibbs measures for the $\\varphi^4$ model on graphs of polynomial growth has at most two extremal measures at all values of $\\beta$. We also give a sufficient condition to ensure that the set of all Gibbs measures is a singleton. As an application, we show that the spontaneous magnetisation of the nearest-neighbour $\\varphi^4$ model on $\\mathbb{Z}^d$ vanishes at criticality for $d\\geq 3$. The analogous results were established for the Ising model in the seminal works of Aizenman, Duminil-Copin, and Sidoravicius (Comm. Math. Phys., 2015), and Raouf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.00319","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/2211.00319/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":"2211.00319","created_at":"2026-07-05T10:37:19.420170+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.00319v2","created_at":"2026-07-05T10:37:19.420170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.00319","created_at":"2026-07-05T10:37:19.420170+00:00"},{"alias_kind":"pith_short_12","alias_value":"3RQBAPJMV6HU","created_at":"2026-07-05T10:37:19.420170+00:00"},{"alias_kind":"pith_short_16","alias_value":"3RQBAPJMV6HUD5W3","created_at":"2026-07-05T10:37:19.420170+00:00"},{"alias_kind":"pith_short_8","alias_value":"3RQBAPJM","created_at":"2026-07-05T10:37:19.420170+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.05353","citing_title":"The supercritical phase of the $\\varphi^4$ model is well behaved","ref_index":49,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ","json":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ.json","graph_json":"https://pith.science/api/pith-number/3RQBAPJMV6HUD5W3DDKO67ZIDQ/graph.json","events_json":"https://pith.science/api/pith-number/3RQBAPJMV6HUD5W3DDKO67ZIDQ/events.json","paper":"https://pith.science/paper/3RQBAPJM"},"agent_actions":{"view_html":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ","download_json":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ.json","view_paper":"https://pith.science/paper/3RQBAPJM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.00319&json=true","fetch_graph":"https://pith.science/api/pith-number/3RQBAPJMV6HUD5W3DDKO67ZIDQ/graph.json","fetch_events":"https://pith.science/api/pith-number/3RQBAPJMV6HUD5W3DDKO67ZIDQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ/action/storage_attestation","attest_author":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ/action/author_attestation","sign_citation":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ/action/citation_signature","submit_replication":"https://pith.science/pith/3RQBAPJMV6HUD5W3DDKO67ZIDQ/action/replication_record"}},"created_at":"2026-07-05T10:37:19.420170+00:00","updated_at":"2026-07-05T10:37:19.420170+00:00"}