{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:R3NA7P6QW3WEDENV65H6LLBBWY","short_pith_number":"pith:R3NA7P6Q","canonical_record":{"source":{"id":"1801.04866","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T16:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"f2eebc8f9b6e74ac3339967c6829a545f47a8536c55d5d97035cd6ce9967f141","abstract_canon_sha256":"2ce5d1ad272b2cf30ea4b112c444364a2f40e2b7d01e3b051417c7476f665a8b"},"schema_version":"1.0"},"canonical_sha256":"8eda0fbfd0b6ec4191b5f74fe5ac21b6208bcadd331e7016e8f21533896185da","source":{"kind":"arxiv","id":"1801.04866","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04866","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04866v3","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04866","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"R3NA7P6QW3WE","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R3NA7P6QW3WEDENV","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R3NA7P6Q","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:R3NA7P6QW3WEDENV65H6LLBBWY","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04866","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T16:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"f2eebc8f9b6e74ac3339967c6829a545f47a8536c55d5d97035cd6ce9967f141","abstract_canon_sha256":"2ce5d1ad272b2cf30ea4b112c444364a2f40e2b7d01e3b051417c7476f665a8b"},"schema_version":"1.0"},"canonical_sha256":"8eda0fbfd0b6ec4191b5f74fe5ac21b6208bcadd331e7016e8f21533896185da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:49.079257Z","signature_b64":"B8ALVzrV2qjxcXexstxXYqG+yATDYrKSw5MpyuKLUjkL/J3wjYkyaFNJIO7854XpfQw4RM0n3xXfJvKltdcxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8eda0fbfd0b6ec4191b5f74fe5ac21b6208bcadd331e7016e8f21533896185da","last_reissued_at":"2026-05-17T23:42:49.078670Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:49.078670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04866","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8vYfdOWxELbit9s41pyKkPEacesR01Mx+2C4gR9F5uqCIStpav/bao3LjtVE0iR0Fin2Zse4OI8n1mGa/ZZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:31:58.476642Z"},"content_sha256":"1f3bd89c2254d2949595e0ad32c63bd901492ab88aec44d9cfafc1e9154de460","schema_version":"1.0","event_id":"sha256:1f3bd89c2254d2949595e0ad32c63bd901492ab88aec44d9cfafc1e9154de460"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:R3NA7P6QW3WEDENV65H6LLBBWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An inverse problem for the relativistic Schr\\\"odinger equation with partial boundary data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Manmohan Vashisth, Venkateswaran P. Krishnan","submitted_at":"2018-01-15T16:26:33Z","abstract_excerpt":"We study the inverse problem of determining the vector and scalar potentials $\\mathcal{A}(t,x)=\\left(A_{0},A_{1},\\cdots,A_{n}\\right)$ and $q(t,x)$, respectively, in the relativistic Schr\\\"odinger equation\n  \\begin{equation*}\n  \\Big{(}\\left(\\partial_{t}+A_{0}(t,x)\\right)^{2}-\\sum_{j=1}^{n}\\left(\\partial_{j}+A_{j}(t,x)\\right)^{2}+q(t,x)\\Big{)}u(t,x)=0\n  \\end{equation*}\n  in the region $Q=(0,T)\\times\\Omega$, where $\\Omega$ is a $C^{2}$ bounded domain in $\\mathbb{R}^{n}$ for $n\\geq 3$ and $T>\\mbox{diam}(\\Omega)$ from partial data on the boundary $\\partial Q$. We prove the unique determination of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04866","kind":"arxiv","version":3},"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":"2026-05-17T23:42:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V8tbhkg9G8+HcGUFAaANjqux7IXo2XTo347NXGVdUcHuqyLoh2O+/1jaxvd+zThSE7fdktYaY9IjMpa7rOEvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:31:58.476972Z"},"content_sha256":"c3f97d49b648ee88c8c332ac3e6759b468897b8db26b2bcf452a8ba91caa50ac","schema_version":"1.0","event_id":"sha256:c3f97d49b648ee88c8c332ac3e6759b468897b8db26b2bcf452a8ba91caa50ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R3NA7P6QW3WEDENV65H6LLBBWY/bundle.json","state_url":"https://pith.science/pith/R3NA7P6QW3WEDENV65H6LLBBWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R3NA7P6QW3WEDENV65H6LLBBWY/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":"2026-06-21T22:31:58Z","links":{"resolver":"https://pith.science/pith/R3NA7P6QW3WEDENV65H6LLBBWY","bundle":"https://pith.science/pith/R3NA7P6QW3WEDENV65H6LLBBWY/bundle.json","state":"https://pith.science/pith/R3NA7P6QW3WEDENV65H6LLBBWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R3NA7P6QW3WEDENV65H6LLBBWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R3NA7P6QW3WEDENV65H6LLBBWY","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":"2ce5d1ad272b2cf30ea4b112c444364a2f40e2b7d01e3b051417c7476f665a8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T16:26:33Z","title_canon_sha256":"f2eebc8f9b6e74ac3339967c6829a545f47a8536c55d5d97035cd6ce9967f141"},"schema_version":"1.0","source":{"id":"1801.04866","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04866","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04866v3","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04866","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"R3NA7P6QW3WE","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R3NA7P6QW3WEDENV","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R3NA7P6Q","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:c3f97d49b648ee88c8c332ac3e6759b468897b8db26b2bcf452a8ba91caa50ac","target":"graph","created_at":"2026-05-17T23:42:49Z","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 inverse problem of determining the vector and scalar potentials $\\mathcal{A}(t,x)=\\left(A_{0},A_{1},\\cdots,A_{n}\\right)$ and $q(t,x)$, respectively, in the relativistic Schr\\\"odinger equation\n  \\begin{equation*}\n  \\Big{(}\\left(\\partial_{t}+A_{0}(t,x)\\right)^{2}-\\sum_{j=1}^{n}\\left(\\partial_{j}+A_{j}(t,x)\\right)^{2}+q(t,x)\\Big{)}u(t,x)=0\n  \\end{equation*}\n  in the region $Q=(0,T)\\times\\Omega$, where $\\Omega$ is a $C^{2}$ bounded domain in $\\mathbb{R}^{n}$ for $n\\geq 3$ and $T>\\mbox{diam}(\\Omega)$ from partial data on the boundary $\\partial Q$. We prove the unique determination of t","authors_text":"Manmohan Vashisth, Venkateswaran P. Krishnan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T16:26:33Z","title":"An inverse problem for the relativistic Schr\\\"odinger equation with partial boundary data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04866","kind":"arxiv","version":3},"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":"sha256:1f3bd89c2254d2949595e0ad32c63bd901492ab88aec44d9cfafc1e9154de460","target":"record","created_at":"2026-05-17T23:42:49Z","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":"2ce5d1ad272b2cf30ea4b112c444364a2f40e2b7d01e3b051417c7476f665a8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T16:26:33Z","title_canon_sha256":"f2eebc8f9b6e74ac3339967c6829a545f47a8536c55d5d97035cd6ce9967f141"},"schema_version":"1.0","source":{"id":"1801.04866","kind":"arxiv","version":3}},"canonical_sha256":"8eda0fbfd0b6ec4191b5f74fe5ac21b6208bcadd331e7016e8f21533896185da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8eda0fbfd0b6ec4191b5f74fe5ac21b6208bcadd331e7016e8f21533896185da","first_computed_at":"2026-05-17T23:42:49.078670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:49.078670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B8ALVzrV2qjxcXexstxXYqG+yATDYrKSw5MpyuKLUjkL/J3wjYkyaFNJIO7854XpfQw4RM0n3xXfJvKltdcxCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:49.079257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04866","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f3bd89c2254d2949595e0ad32c63bd901492ab88aec44d9cfafc1e9154de460","sha256:c3f97d49b648ee88c8c332ac3e6759b468897b8db26b2bcf452a8ba91caa50ac"],"state_sha256":"3c2af333619af8f9ad0c9ca331ddc8623f85337918f76c94fdd34024a77f48c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OdYBbE3DJR6IGzWgVetJ4X7EAHV+THwDRD7KfCm/Y5qQfW+pIS64T12M2DLCdqNUQ2ZvnsAfHYGrQ9mFHq1MDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:31:58.478858Z","bundle_sha256":"9b048bb8437f083707b2d7523d3ab970ac15806bd329d1505c157ac0c5e467b8"}}