{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4RRXNEPRQZNK3UZKUICNRTT2LM","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":"8dc2d8aaf2af7ed9f6980491cd12b5f4affcb051ea8d70d20d2ce83ad94aa7eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T20:47:15Z","title_canon_sha256":"07b33eafff1bd278538c037a6585e97ce44b827624b7780ff3350079af7ff953"},"schema_version":"1.0","source":{"id":"1302.0276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0276","created_at":"2026-05-18T03:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0276v1","created_at":"2026-05-18T03:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0276","created_at":"2026-05-18T03:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"4RRXNEPRQZNK","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4RRXNEPRQZNK3UZK","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4RRXNEPR","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:e6b03b08c262245e7b24fcd2049f89e12e89d85717dddde7562138ee6e29f5c0","target":"graph","created_at":"2026-05-18T03:34:46Z","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 prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional Laplacian.","authors_text":"Juan Davila, Manuel del Pino, Yannick Sire","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T20:47:15Z","title":"Non degeneracy of the bubble in the critical case for non local equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0276","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":"sha256:368c3d1f4f3e4b11eb6f03c46145daa70b7eb0b1fbb0a21c399eb0a3ecaafda8","target":"record","created_at":"2026-05-18T03:34:46Z","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":"8dc2d8aaf2af7ed9f6980491cd12b5f4affcb051ea8d70d20d2ce83ad94aa7eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-01T20:47:15Z","title_canon_sha256":"07b33eafff1bd278538c037a6585e97ce44b827624b7780ff3350079af7ff953"},"schema_version":"1.0","source":{"id":"1302.0276","kind":"arxiv","version":1}},"canonical_sha256":"e4637691f1865aadd32aa204d8ce7a5b0138ae08f9589a426ac797facf503b6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4637691f1865aadd32aa204d8ce7a5b0138ae08f9589a426ac797facf503b6b","first_computed_at":"2026-05-18T03:34:46.873263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:46.873263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"91o/1mDBsmzCa/aUH3IfyP9U9pApfKkD/4ccr20T0NPYwiAGW/fqZIaySqtZ2rZxzBwpSeeMPetpMKKljpDXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:46.873963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:368c3d1f4f3e4b11eb6f03c46145daa70b7eb0b1fbb0a21c399eb0a3ecaafda8","sha256:e6b03b08c262245e7b24fcd2049f89e12e89d85717dddde7562138ee6e29f5c0"],"state_sha256":"65cd25ae92547ee4895479c8383171f539c065f665cd94e42da179fc2c0d6da2"}