{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UMEWXKWPSEESAFDOGBYKLOK2NF","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":"052064da961b8c6942b27e3c181e54a893b113048c1c23b65562a32df229619c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T17:03:30Z","title_canon_sha256":"bac97ad773062ac94c5faae4ebc4be9adab7a09b95519facdd9dcc9829332ab1"},"schema_version":"1.0","source":{"id":"1509.00786","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00786","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00786v1","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00786","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"pith_short_12","alias_value":"UMEWXKWPSEES","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UMEWXKWPSEESAFDO","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UMEWXKWP","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:cfb7caef5e0b4ef1a09a0f0666e53404b5b5aa115d45d1a3234ffeb0292330dd","target":"graph","created_at":"2026-05-18T01:34:06Z","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 establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in $\\mathbb R^3$, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature.","authors_text":"Eleonora Cinti, Juan Davila, Manuel del Pino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T17:03:30Z","title":"Solution of the fractional Allen-Cahn equation which are invariant under screw motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00786","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:c483921c20d5f8f8ce4d5baee7d2fde016c9c8c56eeff5d74ccc8365606d2c21","target":"record","created_at":"2026-05-18T01:34:06Z","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":"052064da961b8c6942b27e3c181e54a893b113048c1c23b65562a32df229619c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T17:03:30Z","title_canon_sha256":"bac97ad773062ac94c5faae4ebc4be9adab7a09b95519facdd9dcc9829332ab1"},"schema_version":"1.0","source":{"id":"1509.00786","kind":"arxiv","version":1}},"canonical_sha256":"a3096baacf910920146e3070a5b95a697a1e897f0f6a988b99db83f360f4d937","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3096baacf910920146e3070a5b95a697a1e897f0f6a988b99db83f360f4d937","first_computed_at":"2026-05-18T01:34:06.035232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:06.035232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"92StFCzjzITv0/X83jbQAXL7fiHvgJoqaeEzY4JYDgJogrvDADCiqxb0CQ6QEzAjaYisF4MiGAim6GX8qoXEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:06.035732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00786","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c483921c20d5f8f8ce4d5baee7d2fde016c9c8c56eeff5d74ccc8365606d2c21","sha256:cfb7caef5e0b4ef1a09a0f0666e53404b5b5aa115d45d1a3234ffeb0292330dd"],"state_sha256":"88d4ca376bb2d28e1fce60603c74ce91512b741c44159e44bb29be0e70d5e881"}