{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AK3C2HTGFRZQDYW2JLQMQFFQXA","short_pith_number":"pith:AK3C2HTG","schema_version":"1.0","canonical_sha256":"02b62d1e662c7301e2da4ae0c814b0b828454074efc9aa77ff852efe18fbf25d","source":{"kind":"arxiv","id":"1207.5416","version":3},"attestation_state":"computed","paper":{"title":"Resolvent methods for steady premixed flame shapes governed by the Zhdanov-Trubnikov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","nlin.PS"],"primary_cat":"physics.flu-dyn","authors_text":"Bruno Denet, Ga\\\"etan Borot, Guy Joulin","submitted_at":"2012-07-23T14:52:16Z","abstract_excerpt":"Using pole decompositions as starting points, the one parameter (-1 =< c < 1) nonlocal and nonlinear Zhdanov-Trubnikov (ZT) equation for the steady shapes of premixed gaseous flames is studied in the large-wrinkle limit. The singular integral equations for pole densities are closely related to those satisfied by the spectral density in the O(n) matrix model, with n = -2(1 + c)/(1 - c). They can be solved via the introduction of complex resolvents and the use of complex analysis. We retrieve results obtained recently for -1 =< c =< 0, and we explain and cure their pathologies when they are cont"},"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":"1207.5416","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-07-23T14:52:16Z","cross_cats_sorted":["cond-mat.stat-mech","nlin.PS"],"title_canon_sha256":"18c5608c5a8a2bd43ec73170ff5f168c4fdc94dc2f64cfc151abb60ed2db6f25","abstract_canon_sha256":"7d5f4b763f78a6c15ca2a6ceae08df745ec766445148c6abc2364bdb7b660b38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:08.995747Z","signature_b64":"LEf6Cv0BbMStjxbcDPfVFcUph7i1habD+G1kgKB/E8VNGslyd+tHm8aRwK+6cbHlt8T1fTXt8Hrf/GeidZjwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02b62d1e662c7301e2da4ae0c814b0b828454074efc9aa77ff852efe18fbf25d","last_reissued_at":"2026-05-18T01:56:08.994985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:08.994985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resolvent methods for steady premixed flame shapes governed by the Zhdanov-Trubnikov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","nlin.PS"],"primary_cat":"physics.flu-dyn","authors_text":"Bruno Denet, Ga\\\"etan Borot, Guy Joulin","submitted_at":"2012-07-23T14:52:16Z","abstract_excerpt":"Using pole decompositions as starting points, the one parameter (-1 =< c < 1) nonlocal and nonlinear Zhdanov-Trubnikov (ZT) equation for the steady shapes of premixed gaseous flames is studied in the large-wrinkle limit. The singular integral equations for pole densities are closely related to those satisfied by the spectral density in the O(n) matrix model, with n = -2(1 + c)/(1 - c). They can be solved via the introduction of complex resolvents and the use of complex analysis. We retrieve results obtained recently for -1 =< c =< 0, and we explain and cure their pathologies when they are cont"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5416","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":"1207.5416","created_at":"2026-05-18T01:56:08.995113+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.5416v3","created_at":"2026-05-18T01:56:08.995113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5416","created_at":"2026-05-18T01:56:08.995113+00:00"},{"alias_kind":"pith_short_12","alias_value":"AK3C2HTGFRZQ","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AK3C2HTGFRZQDYW2","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AK3C2HTG","created_at":"2026-05-18T12:26:58.693483+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/AK3C2HTGFRZQDYW2JLQMQFFQXA","json":"https://pith.science/pith/AK3C2HTGFRZQDYW2JLQMQFFQXA.json","graph_json":"https://pith.science/api/pith-number/AK3C2HTGFRZQDYW2JLQMQFFQXA/graph.json","events_json":"https://pith.science/api/pith-number/AK3C2HTGFRZQDYW2JLQMQFFQXA/events.json","paper":"https://pith.science/paper/AK3C2HTG"},"agent_actions":{"view_html":"https://pith.science/pith/AK3C2HTGFRZQDYW2JLQMQFFQXA","download_json":"https://pith.science/pith/AK3C2HTGFRZQDYW2JLQMQFFQXA.json","view_paper":"https://pith.science/paper/AK3C2HTG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.5416&json=true","fetch_graph":"https://pith.science/api/pith-number/AK3C2HTGFRZQDYW2JLQMQFFQXA/graph.json","fetch_events":"https://pith.science/api/pith-number/AK3C2HTGFRZQDYW2JLQMQFFQXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AK3C2HTGFRZQDYW2JLQMQFFQXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AK3C2HTGFRZQDYW2JLQMQFFQXA/action/storage_attestation","attest_author":"https://pith.science/pith/AK3C2HTGFRZQDYW2JLQMQFFQXA/action/author_attestation","sign_citation":"https://pith.science/pith/AK3C2HTGFRZQDYW2JLQMQFFQXA/action/citation_signature","submit_replication":"https://pith.science/pith/AK3C2HTGFRZQDYW2JLQMQFFQXA/action/replication_record"}},"created_at":"2026-05-18T01:56:08.995113+00:00","updated_at":"2026-05-18T01:56:08.995113+00:00"}