{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BC5I5ZJLRFPR42I2XXSJA2SMZN","short_pith_number":"pith:BC5I5ZJL","canonical_record":{"source":{"id":"2505.01602","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-02T21:53:19Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"027d8f838672c38dbe959a6365d796315e4a512e9a017678b83e58b3a1dedf0d","abstract_canon_sha256":"a732d07d7d89e4e6cae794c042f07d089a57216f15c6f7742adc19828fc25595"},"schema_version":"1.0"},"canonical_sha256":"08ba8ee52b895f1e691abde4906a4ccb6daa8691d51d11a5af2e9921f2bab290","source":{"kind":"arxiv","id":"2505.01602","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.01602","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"2505.01602v1","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.01602","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"BC5I5ZJLRFPR","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"pith_short_16","alias_value":"BC5I5ZJLRFPR42I2","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"pith_short_8","alias_value":"BC5I5ZJL","created_at":"2026-07-05T10:58:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BC5I5ZJLRFPR42I2XXSJA2SMZN","target":"record","payload":{"canonical_record":{"source":{"id":"2505.01602","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-02T21:53:19Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"027d8f838672c38dbe959a6365d796315e4a512e9a017678b83e58b3a1dedf0d","abstract_canon_sha256":"a732d07d7d89e4e6cae794c042f07d089a57216f15c6f7742adc19828fc25595"},"schema_version":"1.0"},"canonical_sha256":"08ba8ee52b895f1e691abde4906a4ccb6daa8691d51d11a5af2e9921f2bab290","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:00.672265Z","signature_b64":"N+SJ73MJeAgwZcdutleeRqSsQ/5ynyv7YiEzb8aXybIpJStW5x43IehL7PNc0pHm5m2E7xXMOV32ovDjgJxPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08ba8ee52b895f1e691abde4906a4ccb6daa8691d51d11a5af2e9921f2bab290","last_reissued_at":"2026-07-05T10:58:00.671775Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:00.671775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.01602","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":"2026-07-05T10:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFAZ7C35V0jVsy6I2YXcfcR3RoOm83nKNCpPUHaVhxQGaU/WsafGwQ0rvBk5R5TJKShbyEXhedWLoBjhBOCLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T05:13:48.442351Z"},"content_sha256":"a9fdaf98d05e7b7f5f16f8662f0d3df94e5091ba0f086a46ef0cf61c22365dc3","schema_version":"1.0","event_id":"sha256:a9fdaf98d05e7b7f5f16f8662f0d3df94e5091ba0f086a46ef0cf61c22365dc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BC5I5ZJLRFPR42I2XXSJA2SMZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schr\\\"odingerization based quantum algorithms for the fractional Poisson equation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nana Liu, Shi Jin, Yue Yu","submitted_at":"2025-05-02T21:53:19Z","abstract_excerpt":"We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the $d$-dimensional fractional equation is reformulated as a local partial differential equation in $d+1$ dimensions. We propose a quantum algorithm for the finite element discretization of this local problem, by capturing the steady-state of the corresponding differential equations using the Schr\\\"odingerization approach from \\cite{JLY22SchrShort, JLY22SchrLong, analogPDE}. The Schr\\\"odingerization technique transforms general linear partial and ordinary di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01602","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.01602/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":"2026-07-05T10:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jlf9Hubqd29Icuqn/Rs/+KpZW2ZH4vm10MLTDXddLOtOknHBAxq0+WSJO72Ghwd1RNTzupdGkEYotDLSk3pvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T05:13:48.442694Z"},"content_sha256":"440973b9a52312319c9ef1aad4aa3cc6d346921b4e9813aff92b8ff3cb4bee77","schema_version":"1.0","event_id":"sha256:440973b9a52312319c9ef1aad4aa3cc6d346921b4e9813aff92b8ff3cb4bee77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BC5I5ZJLRFPR42I2XXSJA2SMZN/bundle.json","state_url":"https://pith.science/pith/BC5I5ZJLRFPR42I2XXSJA2SMZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BC5I5ZJLRFPR42I2XXSJA2SMZN/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":"2026-08-18T05:13:48Z","links":{"resolver":"https://pith.science/pith/BC5I5ZJLRFPR42I2XXSJA2SMZN","bundle":"https://pith.science/pith/BC5I5ZJLRFPR42I2XXSJA2SMZN/bundle.json","state":"https://pith.science/pith/BC5I5ZJLRFPR42I2XXSJA2SMZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BC5I5ZJLRFPR42I2XXSJA2SMZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BC5I5ZJLRFPR42I2XXSJA2SMZN","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":"a732d07d7d89e4e6cae794c042f07d089a57216f15c6f7742adc19828fc25595","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-02T21:53:19Z","title_canon_sha256":"027d8f838672c38dbe959a6365d796315e4a512e9a017678b83e58b3a1dedf0d"},"schema_version":"1.0","source":{"id":"2505.01602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.01602","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"2505.01602v1","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.01602","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"BC5I5ZJLRFPR","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"pith_short_16","alias_value":"BC5I5ZJLRFPR42I2","created_at":"2026-07-05T10:58:00Z"},{"alias_kind":"pith_short_8","alias_value":"BC5I5ZJL","created_at":"2026-07-05T10:58:00Z"}],"graph_snapshots":[{"event_id":"sha256:440973b9a52312319c9ef1aad4aa3cc6d346921b4e9813aff92b8ff3cb4bee77","target":"graph","created_at":"2026-07-05T10:58:00Z","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/2505.01602/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the $d$-dimensional fractional equation is reformulated as a local partial differential equation in $d+1$ dimensions. We propose a quantum algorithm for the finite element discretization of this local problem, by capturing the steady-state of the corresponding differential equations using the Schr\\\"odingerization approach from \\cite{JLY22SchrShort, JLY22SchrLong, analogPDE}. The Schr\\\"odingerization technique transforms general linear partial and ordinary di","authors_text":"Nana Liu, Shi Jin, Yue Yu","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-02T21:53:19Z","title":"Schr\\\"odingerization based quantum algorithms for the fractional Poisson equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01602","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:a9fdaf98d05e7b7f5f16f8662f0d3df94e5091ba0f086a46ef0cf61c22365dc3","target":"record","created_at":"2026-07-05T10:58:00Z","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":"a732d07d7d89e4e6cae794c042f07d089a57216f15c6f7742adc19828fc25595","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-02T21:53:19Z","title_canon_sha256":"027d8f838672c38dbe959a6365d796315e4a512e9a017678b83e58b3a1dedf0d"},"schema_version":"1.0","source":{"id":"2505.01602","kind":"arxiv","version":1}},"canonical_sha256":"08ba8ee52b895f1e691abde4906a4ccb6daa8691d51d11a5af2e9921f2bab290","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08ba8ee52b895f1e691abde4906a4ccb6daa8691d51d11a5af2e9921f2bab290","first_computed_at":"2026-07-05T10:58:00.671775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:58:00.671775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N+SJ73MJeAgwZcdutleeRqSsQ/5ynyv7YiEzb8aXybIpJStW5x43IehL7PNc0pHm5m2E7xXMOV32ovDjgJxPAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:58:00.672265Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.01602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9fdaf98d05e7b7f5f16f8662f0d3df94e5091ba0f086a46ef0cf61c22365dc3","sha256:440973b9a52312319c9ef1aad4aa3cc6d346921b4e9813aff92b8ff3cb4bee77"],"state_sha256":"619cd3e2812f8b78c3a479e0110319c47c353b81e2eacd600969571bf734e888"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lChdJuff2DtKheuGXfAq+liccAvcu6cNI7E4LcgIA1VOPENEzVTkEwPis5OcValmS9Nc67k1WpyjDh9qVXBBDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T05:13:48.446058Z","bundle_sha256":"7d493b6bf716e3e76481c0c45a9b090623f545e4323bf7c6b947057b7e4f3451"}}