{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DH4EIHZGYB3B5654PBMENFA4HA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6ba3e94a1084d0a2f9b36bd01e83523c04a4f78ae15042e099361d2caab7b8ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2014-10-22T13:30:43Z","title_canon_sha256":"a143d9433cdd28d06c30336b3038a109539518b1ab666212c48c90e0042ec587"},"schema_version":"1.0","source":{"id":"1410.6037","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6037","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6037v1","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6037","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"DH4EIHZGYB3B","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DH4EIHZGYB3B5654","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DH4EIHZG","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:4768bc6ae5c300db707e7ae18c7b63245d6b640ce637da7a96a9b609af8bdef1","target":"graph","created_at":"2026-05-18T01:41:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones, are found to closely follow a Meixner Pollaczek recurrence; accurate steady crest shapes ensue for N>=3. Squeezed crests ruled by a discretized Burgers equation involve the same polynomials. Such explicit approximate shape still lack for finite-N pole-decomposed periodic flames, despite another empirical recurrence.","authors_text":"Bruno Denet, Guy Joulin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2014-10-22T13:30:43Z","title":"Premixed flame shapes and polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6037","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:223d8b53a7f40972a724988b41e96ec08fb6fae6d52e6e51f0e82a40ea72b290","target":"record","created_at":"2026-05-18T01:41:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6ba3e94a1084d0a2f9b36bd01e83523c04a4f78ae15042e099361d2caab7b8ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2014-10-22T13:30:43Z","title_canon_sha256":"a143d9433cdd28d06c30336b3038a109539518b1ab666212c48c90e0042ec587"},"schema_version":"1.0","source":{"id":"1410.6037","kind":"arxiv","version":1}},"canonical_sha256":"19f8441f26c0761efbbc785846941c3829a379c6f2b545d82a0ee23c8509d318","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19f8441f26c0761efbbc785846941c3829a379c6f2b545d82a0ee23c8509d318","first_computed_at":"2026-05-18T01:41:41.023810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:41.023810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sUeOc3/1cxVGhkOtQTplm5jTzzwmowAOURoV4Wxm9+i2kRUvsEET/kUPgN4kJSq8jvG/tW+xOu/Tbnwdaz3fAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:41.024342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6037","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:223d8b53a7f40972a724988b41e96ec08fb6fae6d52e6e51f0e82a40ea72b290","sha256:4768bc6ae5c300db707e7ae18c7b63245d6b640ce637da7a96a9b609af8bdef1"],"state_sha256":"725bbdfefbd904d2371d73c45ec6f11434fcaa6b996c05854c373a7f8688f701"}