{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A4SPWR3SKW5K6GN4JJW6M74KJR","short_pith_number":"pith:A4SPWR3S","canonical_record":{"source":{"id":"1608.00449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-01T14:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"f754cdfb3174c73e97c4979441a6f3157bb1fa02be4cacc9ccd44ec35ec03151","abstract_canon_sha256":"e4ab4858d316b57516adf6a18b23b6f3948e2d18430bec88275e1087a15c2901"},"schema_version":"1.0"},"canonical_sha256":"0724fb477255baaf19bc4a6de67f8a4c42a5ad5949eee3fd3174152d2c63b9d8","source":{"kind":"arxiv","id":"1608.00449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00449","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00449v1","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00449","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"A4SPWR3SKW5K","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A4SPWR3SKW5K6GN4","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A4SPWR3S","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A4SPWR3SKW5K6GN4JJW6M74KJR","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-01T14:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"f754cdfb3174c73e97c4979441a6f3157bb1fa02be4cacc9ccd44ec35ec03151","abstract_canon_sha256":"e4ab4858d316b57516adf6a18b23b6f3948e2d18430bec88275e1087a15c2901"},"schema_version":"1.0"},"canonical_sha256":"0724fb477255baaf19bc4a6de67f8a4c42a5ad5949eee3fd3174152d2c63b9d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:24.846855Z","signature_b64":"rYO78PCUpYT8Kc3FDVlfskvLP0u1kUy7UtvX1xkIYgrskVd90qvBnvspLPCcmOSNgz3pLpImlBCoC/r0dM7+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0724fb477255baaf19bc4a6de67f8a4c42a5ad5949eee3fd3174152d2c63b9d8","last_reissued_at":"2026-05-18T00:35:24.846176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:24.846176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00449","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":"2026-05-18T00:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A9814l9pLsAqtBWktKxRA4Rjl/kmRtXwcCbYjizCM+/aV7QtFgMmWquAyUvcY6Vj0i2RCg1FVLfWqmUBRup5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:58:46.892414Z"},"content_sha256":"4c9b029977ae7bb7941e06d981cbe75116d0a412acf822ae198c366e52be42fe","schema_version":"1.0","event_id":"sha256:4c9b029977ae7bb7941e06d981cbe75116d0a412acf822ae198c366e52be42fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A4SPWR3SKW5K6GN4JJW6M74KJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability estimate for an inverse problem for the Schr{\\\"o}dinger equation in a magnetic field with time-dependent coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ibtissem Ben Aicha","submitted_at":"2016-08-01T14:38:02Z","abstract_excerpt":"We study the stability issue in the inverse problem of determining the magnetic field and the time-dependent electric potential appearing in the Schr\\\"odinger equation, from boundary observations. We prove in dimension 3 or greater, that the knowledge of the Dicrichlet-to-Neumann map stably determines the magnetic field and the electric potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00449","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":"2026-05-18T00:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fofLqQdPNi0m02NJysEyhRw05pMi9SJxsUYFc4TqSmERfzmnQW/PIi2NsiRFfyroPUvWuxrOXyYg8qdzAQV+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:58:46.893052Z"},"content_sha256":"c3891358b2ea7790b29c828813be8575bba9b3bee527f267b7da1e3f77da05e5","schema_version":"1.0","event_id":"sha256:c3891358b2ea7790b29c828813be8575bba9b3bee527f267b7da1e3f77da05e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4SPWR3SKW5K6GN4JJW6M74KJR/bundle.json","state_url":"https://pith.science/pith/A4SPWR3SKW5K6GN4JJW6M74KJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4SPWR3SKW5K6GN4JJW6M74KJR/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":"2026-06-09T08:58:46Z","links":{"resolver":"https://pith.science/pith/A4SPWR3SKW5K6GN4JJW6M74KJR","bundle":"https://pith.science/pith/A4SPWR3SKW5K6GN4JJW6M74KJR/bundle.json","state":"https://pith.science/pith/A4SPWR3SKW5K6GN4JJW6M74KJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4SPWR3SKW5K6GN4JJW6M74KJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A4SPWR3SKW5K6GN4JJW6M74KJR","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":"e4ab4858d316b57516adf6a18b23b6f3948e2d18430bec88275e1087a15c2901","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-01T14:38:02Z","title_canon_sha256":"f754cdfb3174c73e97c4979441a6f3157bb1fa02be4cacc9ccd44ec35ec03151"},"schema_version":"1.0","source":{"id":"1608.00449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00449","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00449v1","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00449","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"A4SPWR3SKW5K","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A4SPWR3SKW5K6GN4","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A4SPWR3S","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:c3891358b2ea7790b29c828813be8575bba9b3bee527f267b7da1e3f77da05e5","target":"graph","created_at":"2026-05-18T00:35:24Z","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 study the stability issue in the inverse problem of determining the magnetic field and the time-dependent electric potential appearing in the Schr\\\"odinger equation, from boundary observations. We prove in dimension 3 or greater, that the knowledge of the Dicrichlet-to-Neumann map stably determines the magnetic field and the electric potential.","authors_text":"Ibtissem Ben Aicha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-01T14:38:02Z","title":"Stability estimate for an inverse problem for the Schr{\\\"o}dinger equation in a magnetic field with time-dependent coefficient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00449","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":"sha256:4c9b029977ae7bb7941e06d981cbe75116d0a412acf822ae198c366e52be42fe","target":"record","created_at":"2026-05-18T00:35:24Z","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":"e4ab4858d316b57516adf6a18b23b6f3948e2d18430bec88275e1087a15c2901","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-01T14:38:02Z","title_canon_sha256":"f754cdfb3174c73e97c4979441a6f3157bb1fa02be4cacc9ccd44ec35ec03151"},"schema_version":"1.0","source":{"id":"1608.00449","kind":"arxiv","version":1}},"canonical_sha256":"0724fb477255baaf19bc4a6de67f8a4c42a5ad5949eee3fd3174152d2c63b9d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0724fb477255baaf19bc4a6de67f8a4c42a5ad5949eee3fd3174152d2c63b9d8","first_computed_at":"2026-05-18T00:35:24.846176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:24.846176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rYO78PCUpYT8Kc3FDVlfskvLP0u1kUy7UtvX1xkIYgrskVd90qvBnvspLPCcmOSNgz3pLpImlBCoC/r0dM7+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:24.846855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c9b029977ae7bb7941e06d981cbe75116d0a412acf822ae198c366e52be42fe","sha256:c3891358b2ea7790b29c828813be8575bba9b3bee527f267b7da1e3f77da05e5"],"state_sha256":"c7473594682e38775015ba721d07ea1514251ac5e56066cbdc68c61f8d29edbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0PVZ+7JAcasGNh2hXPlAsJ/GuFnNoWB9slpP8HRVn2jHdC6gfiiLfBDYvYqtPJxyaGOB4CkU8qQR5YLp+5PZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:58:46.896972Z","bundle_sha256":"8622eabf50e6ad34825bc48dbd9d3a698734c1becc30b67e99cad58c77787302"}}