{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S22RBW5VNQEA2JTQKQ2UOL5REP","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":"ac18b3dfeeea9055c8ba54ab01002837e52e4842ab462ab9cbb15fb67374d454","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-08T08:00:45Z","title_canon_sha256":"c327509f7d8b62b614fb66c1ba8fbb22d9c47dd2d737c435ca808a5a163e3288"},"schema_version":"1.0","source":{"id":"1305.1739","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1739","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1739v2","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1739","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"S22RBW5VNQEA","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S22RBW5VNQEA2JTQ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S22RBW5V","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:20794e02f6813ca0c36e90cc1f02dac11e30d44851d416d53fa3f26bc335c11c","target":"graph","created_at":"2026-05-18T03:22:18Z","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 consider inverse problems for the Einstein equation with a time-depending metric on a 4-dimensional globally hyperbolic Lorentzian manifold $(M,g)$. We formulate the concept of active measurements for relativistic models. We do this by coupling the Einstein equation with equations for scalar fields and study the system $Ein(g)=T$, $T=T(g,\\phi)+F_1$, and $\\square_g \\phi=F_2+S(g,\\phi,F_1,F_2)$. Here $F=(F_1,F_2)$ correspond to the perturbations of the physical fields which we control and $S$ is a secondary source corresponding to the adaptation of the system to the perturbation so that the co","authors_text":"Gunther Uhlmann, Matti Lassas, Yaroslav Kurylev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-08T08:00:45Z","title":"Determination of structures in the space-time from local measurements: a detailed exposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1739","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:c001d45fe08115d8bb85006a81efc098fd1ba5d2a0f3051591e26d45ee1381ea","target":"record","created_at":"2026-05-18T03:22:18Z","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":"ac18b3dfeeea9055c8ba54ab01002837e52e4842ab462ab9cbb15fb67374d454","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-08T08:00:45Z","title_canon_sha256":"c327509f7d8b62b614fb66c1ba8fbb22d9c47dd2d737c435ca808a5a163e3288"},"schema_version":"1.0","source":{"id":"1305.1739","kind":"arxiv","version":2}},"canonical_sha256":"96b510dbb56c080d26705435472fb123d4ca539695b12b2767c28d2b1423f8a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96b510dbb56c080d26705435472fb123d4ca539695b12b2767c28d2b1423f8a2","first_computed_at":"2026-05-18T03:22:18.283398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:18.283398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v9QKeE7akcGKryqBPiCa1EMTHklDYHBPb3Gczop3ny0rxddujtIpmj2BW1SM3AEu/utOk/nxGuSqu8Q7kndtDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:18.283937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1739","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c001d45fe08115d8bb85006a81efc098fd1ba5d2a0f3051591e26d45ee1381ea","sha256:20794e02f6813ca0c36e90cc1f02dac11e30d44851d416d53fa3f26bc335c11c"],"state_sha256":"8b75e0a504883bbe160cb166ddc86d655609b7365a88a54d57aab1c50f6318be"}