{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KIVXN7PKW62TDTUP4NERTVESDG","short_pith_number":"pith:KIVXN7PK","canonical_record":{"source":{"id":"2501.10923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-19T02:54:31Z","cross_cats_sorted":[],"title_canon_sha256":"eb2b2250b7789cfbd368a663c74d94c6fc03ba9920ab2bd2c745f58a44ad19e6","abstract_canon_sha256":"6d8276c16331adb6f97cd9917914f040a10ec0b997821a2c8212c83fbaafdcb3"},"schema_version":"1.0"},"canonical_sha256":"522b76fdeab7b531ce8fe34919d492199f9d3e87035e00e53207e498abd386be","source":{"kind":"arxiv","id":"2501.10923","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.10923","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"arxiv_version","alias_value":"2501.10923v2","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.10923","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"pith_short_12","alias_value":"KIVXN7PKW62T","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"pith_short_16","alias_value":"KIVXN7PKW62TDTUP","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"pith_short_8","alias_value":"KIVXN7PK","created_at":"2026-07-05T12:01:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KIVXN7PKW62TDTUP4NERTVESDG","target":"record","payload":{"canonical_record":{"source":{"id":"2501.10923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-19T02:54:31Z","cross_cats_sorted":[],"title_canon_sha256":"eb2b2250b7789cfbd368a663c74d94c6fc03ba9920ab2bd2c745f58a44ad19e6","abstract_canon_sha256":"6d8276c16331adb6f97cd9917914f040a10ec0b997821a2c8212c83fbaafdcb3"},"schema_version":"1.0"},"canonical_sha256":"522b76fdeab7b531ce8fe34919d492199f9d3e87035e00e53207e498abd386be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:01:57.140789Z","signature_b64":"l3DULSimS7v6P8rMjFU37z1dJwomtJPAkYt+Zg9uc7Qr1T1a1svrPfVzrerN1/XgMIp3aV8unZZ4d/01JBKfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"522b76fdeab7b531ce8fe34919d492199f9d3e87035e00e53207e498abd386be","last_reissued_at":"2026-07-05T12:01:57.140224Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:01:57.140224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.10923","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:01:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IHW0La2755kRHC3KHxhh18UuEX7taeg3dEIRlEBNgNHfhyNyrfxGqkIDdwe9u0qZ+EfSMrq/tTj4/dfZHftzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:57:14.667696Z"},"content_sha256":"ed293999cb290e71ea43312e1848794f954b2d726cca79ba2d8f889e5ee50678","schema_version":"1.0","event_id":"sha256:ed293999cb290e71ea43312e1848794f954b2d726cca79ba2d8f889e5ee50678"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KIVXN7PKW62TDTUP4NERTVESDG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Donghui Yang, Jie Zhong, Weijia Wu, Yaozhong Hu","submitted_at":"2025-01-19T02:54:31Z","abstract_excerpt":"This paper investigates the quantitative weak unique continuation property (QWUCP) for a class of high-dimensional elliptic equations with interior point degeneracy. First, we establish well-posedness results in weighted function spaces. Then, using an innovative approximation method, we derive the three-ball theorem at the degenerate point. Finally, we apply the three-ball theorem to prove QWUCP for two different cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.10923","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.10923/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T12:01:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/XGwqKKquEYXkBYswh9f7i5i0wc+2RuuQ3F3OgNKjeAZvgtI7r2gZgf2BJ4usrQ+ywR6fBG9+TBvef2bzSTuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:57:14.670289Z"},"content_sha256":"5feb33dfa2dfa0b6b563e254c33268321f4aa8d5a548ff5e6ad7447f4659ad8f","schema_version":"1.0","event_id":"sha256:5feb33dfa2dfa0b6b563e254c33268321f4aa8d5a548ff5e6ad7447f4659ad8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIVXN7PKW62TDTUP4NERTVESDG/bundle.json","state_url":"https://pith.science/pith/KIVXN7PKW62TDTUP4NERTVESDG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIVXN7PKW62TDTUP4NERTVESDG/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":"2026-08-12T13:57:14Z","links":{"resolver":"https://pith.science/pith/KIVXN7PKW62TDTUP4NERTVESDG","bundle":"https://pith.science/pith/KIVXN7PKW62TDTUP4NERTVESDG/bundle.json","state":"https://pith.science/pith/KIVXN7PKW62TDTUP4NERTVESDG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIVXN7PKW62TDTUP4NERTVESDG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KIVXN7PKW62TDTUP4NERTVESDG","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":"6d8276c16331adb6f97cd9917914f040a10ec0b997821a2c8212c83fbaafdcb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-19T02:54:31Z","title_canon_sha256":"eb2b2250b7789cfbd368a663c74d94c6fc03ba9920ab2bd2c745f58a44ad19e6"},"schema_version":"1.0","source":{"id":"2501.10923","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.10923","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"arxiv_version","alias_value":"2501.10923v2","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.10923","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"pith_short_12","alias_value":"KIVXN7PKW62T","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"pith_short_16","alias_value":"KIVXN7PKW62TDTUP","created_at":"2026-07-05T12:01:57Z"},{"alias_kind":"pith_short_8","alias_value":"KIVXN7PK","created_at":"2026-07-05T12:01:57Z"}],"graph_snapshots":[{"event_id":"sha256:5feb33dfa2dfa0b6b563e254c33268321f4aa8d5a548ff5e6ad7447f4659ad8f","target":"graph","created_at":"2026-07-05T12:01:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.10923/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the quantitative weak unique continuation property (QWUCP) for a class of high-dimensional elliptic equations with interior point degeneracy. First, we establish well-posedness results in weighted function spaces. Then, using an innovative approximation method, we derive the three-ball theorem at the degenerate point. Finally, we apply the three-ball theorem to prove QWUCP for two different cases.","authors_text":"Donghui Yang, Jie Zhong, Weijia Wu, Yaozhong Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-19T02:54:31Z","title":"Approximation of Elliptic Equations with Interior Single-Point Degeneracy and Its Application to Weak Unique Continuation Property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.10923","kind":"arxiv","version":2},"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:ed293999cb290e71ea43312e1848794f954b2d726cca79ba2d8f889e5ee50678","target":"record","created_at":"2026-07-05T12:01:57Z","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":"6d8276c16331adb6f97cd9917914f040a10ec0b997821a2c8212c83fbaafdcb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-19T02:54:31Z","title_canon_sha256":"eb2b2250b7789cfbd368a663c74d94c6fc03ba9920ab2bd2c745f58a44ad19e6"},"schema_version":"1.0","source":{"id":"2501.10923","kind":"arxiv","version":2}},"canonical_sha256":"522b76fdeab7b531ce8fe34919d492199f9d3e87035e00e53207e498abd386be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"522b76fdeab7b531ce8fe34919d492199f9d3e87035e00e53207e498abd386be","first_computed_at":"2026-07-05T12:01:57.140224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:01:57.140224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l3DULSimS7v6P8rMjFU37z1dJwomtJPAkYt+Zg9uc7Qr1T1a1svrPfVzrerN1/XgMIp3aV8unZZ4d/01JBKfCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:01:57.140789Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.10923","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed293999cb290e71ea43312e1848794f954b2d726cca79ba2d8f889e5ee50678","sha256:5feb33dfa2dfa0b6b563e254c33268321f4aa8d5a548ff5e6ad7447f4659ad8f"],"state_sha256":"15219008e51def84a43cce6eac905e1bf251faee2144d3f234b3bb6a31ca2018"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NkIeKn4lsj65fVdQEwHQNkdL1zPD3ossFLqaXo/h+LKiKVfDb3GFRM3rYN/AW6t4QhMsSAbBAFUOoFKhfefqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T13:57:14.695918Z","bundle_sha256":"093a4a3b54c02b72cf65e913d5821f2a9b5aae74a75abdfca41a6358985439b9"}}