{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:TSGUFVPEJS2S2SFPBUFNQII4L5","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":"7980d08b4561aaef0ff9a689569934d81775fe8b3b877c424d2b572c8d09843b","cross_cats_sorted":["nlin.PS"],"license":"","primary_cat":"math.AP","submitted_at":"2007-06-20T05:41:27Z","title_canon_sha256":"2dc6735843b77491d952cbc6c8dd920733d3c5db53fc185916a68b49e0b5f35d"},"schema_version":"1.0","source":{"id":"0706.2917","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.2917","created_at":"2026-05-18T02:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"0706.2917v1","created_at":"2026-05-18T02:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.2917","created_at":"2026-05-18T02:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"TSGUFVPEJS2S","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TSGUFVPEJS2S2SFP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TSGUFVPE","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:1afea49f0b3eea5f1ea212719b613afb0191fb469da2afd6e99988437df844b3","target":"graph","created_at":"2026-05-18T02:48:43Z","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":"We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.","authors_text":"N. M. Ercolani, S. C. Venkataramani","cross_cats":["nlin.PS"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-06-20T05:41:27Z","title":"A variational theory for point defects in patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.2917","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:b12cb8f33d321ae065c4b626f9e8c3c10ff4bf540b93f5842b9d8b8e45ace415","target":"record","created_at":"2026-05-18T02:48:43Z","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":"7980d08b4561aaef0ff9a689569934d81775fe8b3b877c424d2b572c8d09843b","cross_cats_sorted":["nlin.PS"],"license":"","primary_cat":"math.AP","submitted_at":"2007-06-20T05:41:27Z","title_canon_sha256":"2dc6735843b77491d952cbc6c8dd920733d3c5db53fc185916a68b49e0b5f35d"},"schema_version":"1.0","source":{"id":"0706.2917","kind":"arxiv","version":1}},"canonical_sha256":"9c8d42d5e44cb52d48af0d0ad8211c5f616211ee7b29f76692d9a2bf3f80ab33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c8d42d5e44cb52d48af0d0ad8211c5f616211ee7b29f76692d9a2bf3f80ab33","first_computed_at":"2026-05-18T02:48:43.922218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:43.922218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S2NX01jGvV8AGBh67a+rWH1M5IFJBYPB/o6taIXbInXCt36BbuvQsv2ILp/OnHkAIU3JIhWEKr17zjYBwjcPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:43.922900Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.2917","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b12cb8f33d321ae065c4b626f9e8c3c10ff4bf540b93f5842b9d8b8e45ace415","sha256:1afea49f0b3eea5f1ea212719b613afb0191fb469da2afd6e99988437df844b3"],"state_sha256":"1211b148e7273ebc604f1562fa73052abff77875566c50a192a4a2156efa26a8"}