{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EU4C4TCKCHAIM7R4SLNM74BJWL","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":"873ae2610bef6b68a6bfb7a002f3935c1c7716da6217559d5896fa03b1b2b18f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-04T12:15:09Z","title_canon_sha256":"a388cd944c7f38e3200fa16db2a14eabcef00d4e0f3e16af6212d59ec2629710"},"schema_version":"1.0","source":{"id":"1506.01559","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01559","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01559v3","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01559","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"pith_short_12","alias_value":"EU4C4TCKCHAI","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EU4C4TCKCHAIM7R4","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EU4C4TCK","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:d5424afa330dac4e199195b42adc8b72cd5c6f6b435fe08282ffc922c9c2feda","target":"graph","created_at":"2026-05-18T01:04:22Z","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 a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient in the interior of an object. The method in this paper relies on solving the forward problem for a whole family of diffusivities by using a spectral Galerkin method in the high-dimensional parameter domain. The evaluation of the parametric solution and its derivatives is then completely independent of spatial and temporal discretizations. In case of a quadra","authors_text":"Lauri Mustonen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-04T12:15:09Z","title":"Numerical study of a parametric parabolic equation and a related inverse boundary value problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01559","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":"sha256:51959eff9edfe183cd3778dc06f29bc867d0a45d22bb821a77d06e1699f79ede","target":"record","created_at":"2026-05-18T01:04:22Z","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":"873ae2610bef6b68a6bfb7a002f3935c1c7716da6217559d5896fa03b1b2b18f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-04T12:15:09Z","title_canon_sha256":"a388cd944c7f38e3200fa16db2a14eabcef00d4e0f3e16af6212d59ec2629710"},"schema_version":"1.0","source":{"id":"1506.01559","kind":"arxiv","version":3}},"canonical_sha256":"25382e4c4a11c0867e3c92dacff029b2cf1dda7775e98f713647d2882c174c91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25382e4c4a11c0867e3c92dacff029b2cf1dda7775e98f713647d2882c174c91","first_computed_at":"2026-05-18T01:04:22.814741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:22.814741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gF5zAZzx+QAhpwcBh//xTBdXTnIPUCm4agB3SPK4A843D2p/LKxm45TXW7BEVtRXs6GYg5ohtndYj2cMApfOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:22.815362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01559","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51959eff9edfe183cd3778dc06f29bc867d0a45d22bb821a77d06e1699f79ede","sha256:d5424afa330dac4e199195b42adc8b72cd5c6f6b435fe08282ffc922c9c2feda"],"state_sha256":"90c5f338baea848cc603ec7901d57b83eaaa567d2e3f3406e2d4217881846066"}