{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:AYZWI6IUDJDPWNFVUU4XBU5DDZ","short_pith_number":"pith:AYZWI6IU","schema_version":"1.0","canonical_sha256":"06336479141a46fb34b5a53970d3a31e7b4367e8e3de5a594411c25e0972073b","source":{"kind":"arxiv","id":"2412.17625","version":2},"attestation_state":"computed","paper":{"title":"Large scale regularity and correlation length for almost length-minimizing random curves in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Christian Wagner, Tobias Ried","submitted_at":"2024-12-23T14:57:08Z","abstract_excerpt":"We consider a model of random curves in the plane related to the large-scale behavior of the Random Field Ising Model (RFIM) at temperature zero in two space dimensions. Our work is motivated by attempts to quantify the Imry-Ma phenomenon concerning the rounding of the phase transition by quenched disorder, and connects to recent advances regarding the decay of correlations in the RFIM.\n  We study a continuum model of minimal surfaces in two space dimensions subject to an external, quenched random field, and restrict ourselves to isotropic surface integrands. The random fields we consider beha"},"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":"2412.17625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-12-23T14:57:08Z","cross_cats_sorted":["math.AP","math.MP","math.PR"],"title_canon_sha256":"c4ed7afb1f9ecc829f92dbb59c37aa90aa431b5313ac6afd43c169a1e193a756","abstract_canon_sha256":"570a732858fe96d13e500e3d48bed7d94d77e8907da146850ee8e0e76428cfe8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:34.024978Z","signature_b64":"V/piQsIdIkeoNZvy2tn54whjiW9E4Yz28dMRH8ed4Fi2qpRVsPwYEjeEcjkcs6MLwljMHlZ3gkSs02OKp2seAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06336479141a46fb34b5a53970d3a31e7b4367e8e3de5a594411c25e0972073b","last_reissued_at":"2026-06-25T01:18:34.024489Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:34.024489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large scale regularity and correlation length for almost length-minimizing random curves in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Christian Wagner, Tobias Ried","submitted_at":"2024-12-23T14:57:08Z","abstract_excerpt":"We consider a model of random curves in the plane related to the large-scale behavior of the Random Field Ising Model (RFIM) at temperature zero in two space dimensions. Our work is motivated by attempts to quantify the Imry-Ma phenomenon concerning the rounding of the phase transition by quenched disorder, and connects to recent advances regarding the decay of correlations in the RFIM.\n  We study a continuum model of minimal surfaces in two space dimensions subject to an external, quenched random field, and restrict ourselves to isotropic surface integrands. The random fields we consider beha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17625","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/2412.17625/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":"2412.17625","created_at":"2026-06-25T01:18:34.024544+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.17625v2","created_at":"2026-06-25T01:18:34.024544+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.17625","created_at":"2026-06-25T01:18:34.024544+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYZWI6IUDJDP","created_at":"2026-06-25T01:18:34.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYZWI6IUDJDPWNFV","created_at":"2026-06-25T01:18:34.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYZWI6IU","created_at":"2026-06-25T01:18:34.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.27519","citing_title":"Quantitative homogenization of the maximal action of curves in a Brownian potential","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ","json":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ.json","graph_json":"https://pith.science/api/pith-number/AYZWI6IUDJDPWNFVUU4XBU5DDZ/graph.json","events_json":"https://pith.science/api/pith-number/AYZWI6IUDJDPWNFVUU4XBU5DDZ/events.json","paper":"https://pith.science/paper/AYZWI6IU"},"agent_actions":{"view_html":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ","download_json":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ.json","view_paper":"https://pith.science/paper/AYZWI6IU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.17625&json=true","fetch_graph":"https://pith.science/api/pith-number/AYZWI6IUDJDPWNFVUU4XBU5DDZ/graph.json","fetch_events":"https://pith.science/api/pith-number/AYZWI6IUDJDPWNFVUU4XBU5DDZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ/action/storage_attestation","attest_author":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ/action/author_attestation","sign_citation":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ/action/citation_signature","submit_replication":"https://pith.science/pith/AYZWI6IUDJDPWNFVUU4XBU5DDZ/action/replication_record"}},"created_at":"2026-06-25T01:18:34.024544+00:00","updated_at":"2026-06-25T01:18:34.024544+00:00"}