{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QZETMK4R5IONKQ5AGDLSIDLMTJ","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":"3c0a86b82f7a4e39af7c57ed3b8327c652a0569cad7997b4888aca87a4b96359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-30T17:40:01Z","title_canon_sha256":"26f38ae794699bd405606a256ec96e60a27dc50bd470981126e2983761afc65c"},"schema_version":"1.0","source":{"id":"1011.6617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6617","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6617v1","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6617","created_at":"2026-05-18T04:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"QZETMK4R5ION","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"QZETMK4R5IONKQ5A","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"QZETMK4R","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:aba350231877f355070156848ef9a8beeede2cf1bab1b2f6e58d0b7e8c007cbf","target":"graph","created_at":"2026-05-18T04:34:26Z","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 consider a functional obtained by adding a trace term to the Allen-Cahn phase segregation model and we prove some density estimates for the level sets of the interfaces.\n  We treat in a unified way also the cases of possible degeneracy and singularity of the ellipticity of the model and the quasiminimal case.","authors_text":"Enrico Valdinoci, Yannick Sire","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-30T17:40:01Z","title":"Density estimates for phase transitions with a trace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6617","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":"sha256:7720d8214a4505118e57d62f18747f8a92e5278c6f177e74b6aac3f56b3a8281","target":"record","created_at":"2026-05-18T04:34:26Z","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":"3c0a86b82f7a4e39af7c57ed3b8327c652a0569cad7997b4888aca87a4b96359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-30T17:40:01Z","title_canon_sha256":"26f38ae794699bd405606a256ec96e60a27dc50bd470981126e2983761afc65c"},"schema_version":"1.0","source":{"id":"1011.6617","kind":"arxiv","version":1}},"canonical_sha256":"8649362b91ea1cd543a030d7240d6c9a52f5fb3361e4c83fb639aa2dfe7a79a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8649362b91ea1cd543a030d7240d6c9a52f5fb3361e4c83fb639aa2dfe7a79a2","first_computed_at":"2026-05-18T04:34:26.493907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:26.493907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OKf57V6t+6eA2oIurmjDROqGkzpExSzck2D+VICh1FU2pFmynVfQrmNnK1hXg5UOeM5KgOk1lWyQMtcNn/nzCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:26.494504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.6617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7720d8214a4505118e57d62f18747f8a92e5278c6f177e74b6aac3f56b3a8281","sha256:aba350231877f355070156848ef9a8beeede2cf1bab1b2f6e58d0b7e8c007cbf"],"state_sha256":"09d4529057cb0bf047f8a93056078b76f053b8c2e588686dab46d592f3a1985f"}