{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2SZMWTABZTP5UNTVZKY7SOE6QL","short_pith_number":"pith:2SZMWTAB","canonical_record":{"source":{"id":"1706.07212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-22T08:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"eeca0cedfdcc2e83be4ff2125ae6a10cae51201b4b41609482cae66678eb6b38","abstract_canon_sha256":"85f3fdef542e649191f5b6bb07766a3cecb8695fe04addd3552a161398a96e5e"},"schema_version":"1.0"},"canonical_sha256":"d4b2cb4c01ccdfda3675cab1f9389e82e61db9fb3beabcf28d7889dd9453f25e","source":{"kind":"arxiv","id":"1706.07212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07212","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07212v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07212","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"2SZMWTABZTP5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2SZMWTABZTP5UNTV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2SZMWTAB","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2SZMWTABZTP5UNTVZKY7SOE6QL","target":"record","payload":{"canonical_record":{"source":{"id":"1706.07212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-22T08:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"eeca0cedfdcc2e83be4ff2125ae6a10cae51201b4b41609482cae66678eb6b38","abstract_canon_sha256":"85f3fdef542e649191f5b6bb07766a3cecb8695fe04addd3552a161398a96e5e"},"schema_version":"1.0"},"canonical_sha256":"d4b2cb4c01ccdfda3675cab1f9389e82e61db9fb3beabcf28d7889dd9453f25e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:52.326067Z","signature_b64":"LxsIfwPHxIP6Ji+A+ddhaNBa7Wi16z0SUL1kJVcKNmsp72FnvE0h33TyKSxBgs/gUwochOLcyVYwO6nizqXrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4b2cb4c01ccdfda3675cab1f9389e82e61db9fb3beabcf28d7889dd9453f25e","last_reissued_at":"2026-05-18T00:41:52.325518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:52.325518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.07212","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":"2026-05-18T00:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bdKmGB3T+4E5k3XpCbeQDkgchRgGguUscAqU4FgQ5FWJoNJgqSf1TJCJoEai5x65vXG0lXjWWse/N2Hcc7tYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:50:00.789475Z"},"content_sha256":"14a421d433361d5d0339f000fdddc0ebca2cf4dbd4b91813254e2fed68e2d94f","schema_version":"1.0","event_id":"sha256:14a421d433361d5d0339f000fdddc0ebca2cf4dbd4b91813254e2fed68e2d94f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2SZMWTABZTP5UNTVZKY7SOE6QL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Determination of singular time-dependent coefficients for wave equations from full and partial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guanghui Hu, Yavar Kian","submitted_at":"2017-06-22T08:47:50Z","abstract_excerpt":"We study the problem of determining uniquely a time-dependent singular potential $q$, appearing in the wave equation $\\partial_t^2u-\\Delta_x u+q(t,x)u=0$ in $Q=(0,T)\\times\\Omega$ with $T>0$ and $\\Omega$ a $ \\mathcal C^2$ bounded domain of $\\mathbb R^n$, $n\\geq2$. We start by considering the unique determination of some singular time-dependent coefficients from observations on $\\partial Q$. Then, by weakening the singularities of the set of admissible coefficients, we manage to reduce the set of data that still guaranties unique recovery of such a coefficient. To our best knowledge, this paper "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07212","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":"2026-05-18T00:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPMQ3X0ilTscvBac94dccCFgVsHd5Pj4qCAA0b0bdfOQou8JGvnFOd0Mp5Nr/PI3Dv3FK4YetldGDGYLspxuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:50:00.789820Z"},"content_sha256":"981053e8d965d32344ec171838405dbbe56a0103aed0d42e129ae60896dde5da","schema_version":"1.0","event_id":"sha256:981053e8d965d32344ec171838405dbbe56a0103aed0d42e129ae60896dde5da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2SZMWTABZTP5UNTVZKY7SOE6QL/bundle.json","state_url":"https://pith.science/pith/2SZMWTABZTP5UNTVZKY7SOE6QL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2SZMWTABZTP5UNTVZKY7SOE6QL/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":"2026-05-28T07:50:00Z","links":{"resolver":"https://pith.science/pith/2SZMWTABZTP5UNTVZKY7SOE6QL","bundle":"https://pith.science/pith/2SZMWTABZTP5UNTVZKY7SOE6QL/bundle.json","state":"https://pith.science/pith/2SZMWTABZTP5UNTVZKY7SOE6QL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2SZMWTABZTP5UNTVZKY7SOE6QL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2SZMWTABZTP5UNTVZKY7SOE6QL","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":"85f3fdef542e649191f5b6bb07766a3cecb8695fe04addd3552a161398a96e5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-22T08:47:50Z","title_canon_sha256":"eeca0cedfdcc2e83be4ff2125ae6a10cae51201b4b41609482cae66678eb6b38"},"schema_version":"1.0","source":{"id":"1706.07212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07212","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07212v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07212","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"2SZMWTABZTP5","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2SZMWTABZTP5UNTV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2SZMWTAB","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:981053e8d965d32344ec171838405dbbe56a0103aed0d42e129ae60896dde5da","target":"graph","created_at":"2026-05-18T00:41:52Z","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 problem of determining uniquely a time-dependent singular potential $q$, appearing in the wave equation $\\partial_t^2u-\\Delta_x u+q(t,x)u=0$ in $Q=(0,T)\\times\\Omega$ with $T>0$ and $\\Omega$ a $ \\mathcal C^2$ bounded domain of $\\mathbb R^n$, $n\\geq2$. We start by considering the unique determination of some singular time-dependent coefficients from observations on $\\partial Q$. Then, by weakening the singularities of the set of admissible coefficients, we manage to reduce the set of data that still guaranties unique recovery of such a coefficient. To our best knowledge, this paper ","authors_text":"Guanghui Hu, Yavar Kian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-22T08:47:50Z","title":"Determination of singular time-dependent coefficients for wave equations from full and partial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07212","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":"sha256:14a421d433361d5d0339f000fdddc0ebca2cf4dbd4b91813254e2fed68e2d94f","target":"record","created_at":"2026-05-18T00:41:52Z","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":"85f3fdef542e649191f5b6bb07766a3cecb8695fe04addd3552a161398a96e5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-22T08:47:50Z","title_canon_sha256":"eeca0cedfdcc2e83be4ff2125ae6a10cae51201b4b41609482cae66678eb6b38"},"schema_version":"1.0","source":{"id":"1706.07212","kind":"arxiv","version":1}},"canonical_sha256":"d4b2cb4c01ccdfda3675cab1f9389e82e61db9fb3beabcf28d7889dd9453f25e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4b2cb4c01ccdfda3675cab1f9389e82e61db9fb3beabcf28d7889dd9453f25e","first_computed_at":"2026-05-18T00:41:52.325518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:52.325518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LxsIfwPHxIP6Ji+A+ddhaNBa7Wi16z0SUL1kJVcKNmsp72FnvE0h33TyKSxBgs/gUwochOLcyVYwO6nizqXrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:52.326067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14a421d433361d5d0339f000fdddc0ebca2cf4dbd4b91813254e2fed68e2d94f","sha256:981053e8d965d32344ec171838405dbbe56a0103aed0d42e129ae60896dde5da"],"state_sha256":"3cac4a43943e1ab56b740891e6470d14e9bd1bcf4906c3ad89f605dfc88ee3b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T0HbmqUFenzI0ef7ev0qQTPStTXbtCS9XnoVxFg2GDT+rqj83VPvDBBk/DznR/Axogr/uZATRygzKRd5M0wNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:50:00.791747Z","bundle_sha256":"d26579fd113c7c25b4a00531b34da4561e9adac061c3cc2d4ba2104be1142605"}}