{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Q6Y4KKYV7BJ6THCF4SQSSYQXEM","short_pith_number":"pith:Q6Y4KKYV","canonical_record":{"source":{"id":"1809.09496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T13:59:53Z","cross_cats_sorted":[],"title_canon_sha256":"1cb673d0b1226acf5b93dbfdae315ba4afb96ca4750fbc7cedaa7a9422d10bb8","abstract_canon_sha256":"f3424267425b64e781e31c9365f91ab12954999a4356970073ce83e987b130f3"},"schema_version":"1.0"},"canonical_sha256":"87b1c52b15f853e99c45e4a1296217231eb9a74277b9ab58d68ee2c4ca8af6fe","source":{"kind":"arxiv","id":"1809.09496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09496","created_at":"2026-05-18T00:04:51Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09496v1","created_at":"2026-05-18T00:04:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09496","created_at":"2026-05-18T00:04:51Z"},{"alias_kind":"pith_short_12","alias_value":"Q6Y4KKYV7BJ6","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q6Y4KKYV7BJ6THCF","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q6Y4KKYV","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Q6Y4KKYV7BJ6THCF4SQSSYQXEM","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T13:59:53Z","cross_cats_sorted":[],"title_canon_sha256":"1cb673d0b1226acf5b93dbfdae315ba4afb96ca4750fbc7cedaa7a9422d10bb8","abstract_canon_sha256":"f3424267425b64e781e31c9365f91ab12954999a4356970073ce83e987b130f3"},"schema_version":"1.0"},"canonical_sha256":"87b1c52b15f853e99c45e4a1296217231eb9a74277b9ab58d68ee2c4ca8af6fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:51.023510Z","signature_b64":"c+5b4rfrOs1HVuMgbBjP39aU4so9O9ng4kxMIchQB9cRPa/Q/ToNHHEm/YjgVSp8U2yNBoAWxx/35lxrLVtvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87b1c52b15f853e99c45e4a1296217231eb9a74277b9ab58d68ee2c4ca8af6fe","last_reissued_at":"2026-05-18T00:04:51.022878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:51.022878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09496","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/fZxV1kPSy6IS6yk6pQgH16dLphlOWlDTFHVSwsT368uZOLmoVnmKDQAb5Th79nyLkfQVA4N28rTjQhbujL6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:52:54.689454Z"},"content_sha256":"1de88d2eea0ee158c7a0e0546d02beeec52bb871567a2b8614ed49cc4aecb07e","schema_version":"1.0","event_id":"sha256:1de88d2eea0ee158c7a0e0546d02beeec52bb871567a2b8614ed49cc4aecb07e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Q6Y4KKYV7BJ6THCF4SQSSYQXEM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unique continuation principles for a higher order fractional Laplace equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Ferrero, Veronica Felli","submitted_at":"2018-09-25T13:59:53Z","abstract_excerpt":"In this paper we prove strong unique continuation principle and unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the Caffarelli-Silvestre extension method combined with an Almgren type monotonicity formula. The corresponding extended problem is formulated as a systems of two second order equations with singular or degenerate weights in a half-space, for which asymptotics estimates are derived by a blow-up analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09496","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLOUXyazUm5MpTWN6ejVIIWuSxJ3cSmDer4ISX98fOJOWdclUPyFXfzDGnruYQ0Kl68UAfXLA7BWGK6J2jgjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:52:54.690136Z"},"content_sha256":"4266bf943b44468ad2528e725875997e29de85b4b95d47997e38f317ac90f93e","schema_version":"1.0","event_id":"sha256:4266bf943b44468ad2528e725875997e29de85b4b95d47997e38f317ac90f93e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q6Y4KKYV7BJ6THCF4SQSSYQXEM/bundle.json","state_url":"https://pith.science/pith/Q6Y4KKYV7BJ6THCF4SQSSYQXEM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q6Y4KKYV7BJ6THCF4SQSSYQXEM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T08:52:54Z","links":{"resolver":"https://pith.science/pith/Q6Y4KKYV7BJ6THCF4SQSSYQXEM","bundle":"https://pith.science/pith/Q6Y4KKYV7BJ6THCF4SQSSYQXEM/bundle.json","state":"https://pith.science/pith/Q6Y4KKYV7BJ6THCF4SQSSYQXEM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q6Y4KKYV7BJ6THCF4SQSSYQXEM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q6Y4KKYV7BJ6THCF4SQSSYQXEM","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":"f3424267425b64e781e31c9365f91ab12954999a4356970073ce83e987b130f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T13:59:53Z","title_canon_sha256":"1cb673d0b1226acf5b93dbfdae315ba4afb96ca4750fbc7cedaa7a9422d10bb8"},"schema_version":"1.0","source":{"id":"1809.09496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09496","created_at":"2026-05-18T00:04:51Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09496v1","created_at":"2026-05-18T00:04:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09496","created_at":"2026-05-18T00:04:51Z"},{"alias_kind":"pith_short_12","alias_value":"Q6Y4KKYV7BJ6","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q6Y4KKYV7BJ6THCF","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q6Y4KKYV","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:4266bf943b44468ad2528e725875997e29de85b4b95d47997e38f317ac90f93e","target":"graph","created_at":"2026-05-18T00:04:51Z","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":"In this paper we prove strong unique continuation principle and unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the Caffarelli-Silvestre extension method combined with an Almgren type monotonicity formula. The corresponding extended problem is formulated as a systems of two second order equations with singular or degenerate weights in a half-space, for which asymptotics estimates are derived by a blow-up analysis.","authors_text":"Alberto Ferrero, Veronica Felli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T13:59:53Z","title":"Unique continuation principles for a higher order fractional Laplace equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09496","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":"sha256:1de88d2eea0ee158c7a0e0546d02beeec52bb871567a2b8614ed49cc4aecb07e","target":"record","created_at":"2026-05-18T00:04:51Z","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":"f3424267425b64e781e31c9365f91ab12954999a4356970073ce83e987b130f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T13:59:53Z","title_canon_sha256":"1cb673d0b1226acf5b93dbfdae315ba4afb96ca4750fbc7cedaa7a9422d10bb8"},"schema_version":"1.0","source":{"id":"1809.09496","kind":"arxiv","version":1}},"canonical_sha256":"87b1c52b15f853e99c45e4a1296217231eb9a74277b9ab58d68ee2c4ca8af6fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87b1c52b15f853e99c45e4a1296217231eb9a74277b9ab58d68ee2c4ca8af6fe","first_computed_at":"2026-05-18T00:04:51.022878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:51.022878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c+5b4rfrOs1HVuMgbBjP39aU4so9O9ng4kxMIchQB9cRPa/Q/ToNHHEm/YjgVSp8U2yNBoAWxx/35lxrLVtvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:51.023510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1de88d2eea0ee158c7a0e0546d02beeec52bb871567a2b8614ed49cc4aecb07e","sha256:4266bf943b44468ad2528e725875997e29de85b4b95d47997e38f317ac90f93e"],"state_sha256":"207a733a6e71f294b4c8a21eee19f4c822c34af25dbbb5a0e5a1306ad4747135"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h18HQkyfmJ3PUEAH/OwHiPFs9+KjlBSZwcG39pI0KR082vfmqZ3FD6udEfWLbbfESqCSDE/o2j3X5wAn6OgaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:52:54.693537Z","bundle_sha256":"8366d1b71e2906ea7aed5e5de1ac963286e616ba307ffee9718845e0106b2ea5"}}