{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TR37FYGJZJ2KMX7EAZL3BLAG5F","short_pith_number":"pith:TR37FYGJ","canonical_record":{"source":{"id":"1704.03851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-04-12T17:35:34Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"bc583b3530f88f9492d8204dd8c51266af34fd2da4198d56a182efc52b6f64c3","abstract_canon_sha256":"085c578c7e39118628b54a16a228813a3916dbd4dbec4afa8a0c216d848a57f9"},"schema_version":"1.0"},"canonical_sha256":"9c77f2e0c9ca74a65fe40657b0ac06e97ea05313d746e9d56a4fb4e66f54a93b","source":{"kind":"arxiv","id":"1704.03851","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03851","created_at":"2026-05-18T00:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03851v1","created_at":"2026-05-18T00:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03851","created_at":"2026-05-18T00:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"TR37FYGJZJ2K","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TR37FYGJZJ2KMX7E","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TR37FYGJ","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TR37FYGJZJ2KMX7EAZL3BLAG5F","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-04-12T17:35:34Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"bc583b3530f88f9492d8204dd8c51266af34fd2da4198d56a182efc52b6f64c3","abstract_canon_sha256":"085c578c7e39118628b54a16a228813a3916dbd4dbec4afa8a0c216d848a57f9"},"schema_version":"1.0"},"canonical_sha256":"9c77f2e0c9ca74a65fe40657b0ac06e97ea05313d746e9d56a4fb4e66f54a93b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:32.275035Z","signature_b64":"Q7ALCKBTTwDun9wiRSibTe4BoUF2fkIoOSS/HYgYeJSXza/gt7xCOfj9BHhhyRGjeI7o+dTRHphdigXRt66NAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c77f2e0c9ca74a65fe40657b0ac06e97ea05313d746e9d56a4fb4e66f54a93b","last_reissued_at":"2026-05-18T00:16:32.274697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:32.274697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03851","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":"2026-05-18T00:16:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aKOZNxaLqMiEXyGfchXTTaCT/A5YPakk0v6S+s7BAFOe4kaT4Sm5p0k1tVnqWv3jzc8eH1VflMYN03GO8AhDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:17:04.932935Z"},"content_sha256":"9dc27f35143d3ebf02affd27045384fce013cd025fb161fda4dd7776804c0b31","schema_version":"1.0","event_id":"sha256:9dc27f35143d3ebf02affd27045384fce013cd025fb161fda4dd7776804c0b31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TR37FYGJZJ2KMX7EAZL3BLAG5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical solution of time-dependent problems with fractional power elliptic operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.NA","authors_text":"Petr N. Vabishchevich","submitted_at":"2017-04-12T17:35:34Z","abstract_excerpt":"An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is employed. To construct approximation in time, standard two-level schemes are used. The approximate solution at a new time-level is obtained as a solution of a discrete problem with the fractional power of the elliptic operator. A Pade-type approximation is constructed on the basis of special quadrature formulas for an integral representation of the fractional power"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03851","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":"2026-05-18T00:16:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZaESlt9eyid8YTQkxraPPf0Obwa2AOVQv3VDzt2lEeuG+t3R5HhxWsWS7U+GEDX64zJXluCH4X8D46mjthdEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:17:04.933672Z"},"content_sha256":"c8d90157e3be8d3f8aca0269e8603d3061d6702691cda437314a846895fc8359","schema_version":"1.0","event_id":"sha256:c8d90157e3be8d3f8aca0269e8603d3061d6702691cda437314a846895fc8359"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TR37FYGJZJ2KMX7EAZL3BLAG5F/bundle.json","state_url":"https://pith.science/pith/TR37FYGJZJ2KMX7EAZL3BLAG5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TR37FYGJZJ2KMX7EAZL3BLAG5F/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":"2026-06-10T11:17:04Z","links":{"resolver":"https://pith.science/pith/TR37FYGJZJ2KMX7EAZL3BLAG5F","bundle":"https://pith.science/pith/TR37FYGJZJ2KMX7EAZL3BLAG5F/bundle.json","state":"https://pith.science/pith/TR37FYGJZJ2KMX7EAZL3BLAG5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TR37FYGJZJ2KMX7EAZL3BLAG5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TR37FYGJZJ2KMX7EAZL3BLAG5F","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":"085c578c7e39118628b54a16a228813a3916dbd4dbec4afa8a0c216d848a57f9","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-04-12T17:35:34Z","title_canon_sha256":"bc583b3530f88f9492d8204dd8c51266af34fd2da4198d56a182efc52b6f64c3"},"schema_version":"1.0","source":{"id":"1704.03851","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03851","created_at":"2026-05-18T00:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03851v1","created_at":"2026-05-18T00:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03851","created_at":"2026-05-18T00:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"TR37FYGJZJ2K","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TR37FYGJZJ2KMX7E","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TR37FYGJ","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:c8d90157e3be8d3f8aca0269e8603d3061d6702691cda437314a846895fc8359","target":"graph","created_at":"2026-05-18T00:16:32Z","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":"An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is employed. To construct approximation in time, standard two-level schemes are used. The approximate solution at a new time-level is obtained as a solution of a discrete problem with the fractional power of the elliptic operator. A Pade-type approximation is constructed on the basis of special quadrature formulas for an integral representation of the fractional power","authors_text":"Petr N. Vabishchevich","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-04-12T17:35:34Z","title":"Numerical solution of time-dependent problems with fractional power elliptic operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03851","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":"sha256:9dc27f35143d3ebf02affd27045384fce013cd025fb161fda4dd7776804c0b31","target":"record","created_at":"2026-05-18T00:16:32Z","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":"085c578c7e39118628b54a16a228813a3916dbd4dbec4afa8a0c216d848a57f9","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-04-12T17:35:34Z","title_canon_sha256":"bc583b3530f88f9492d8204dd8c51266af34fd2da4198d56a182efc52b6f64c3"},"schema_version":"1.0","source":{"id":"1704.03851","kind":"arxiv","version":1}},"canonical_sha256":"9c77f2e0c9ca74a65fe40657b0ac06e97ea05313d746e9d56a4fb4e66f54a93b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c77f2e0c9ca74a65fe40657b0ac06e97ea05313d746e9d56a4fb4e66f54a93b","first_computed_at":"2026-05-18T00:16:32.274697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:32.274697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q7ALCKBTTwDun9wiRSibTe4BoUF2fkIoOSS/HYgYeJSXza/gt7xCOfj9BHhhyRGjeI7o+dTRHphdigXRt66NAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:32.275035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03851","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dc27f35143d3ebf02affd27045384fce013cd025fb161fda4dd7776804c0b31","sha256:c8d90157e3be8d3f8aca0269e8603d3061d6702691cda437314a846895fc8359"],"state_sha256":"5e884bbacb487c56647ce8a6a6c892b88bf3ab2157168ee70277792ca7136978"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WmWVur4ODxc1qbQFdqxqiK99LFbgHAWJMkuodBsJEZj8CPpz0LGEiwo5/7KXMDB/SPGA2J5VkT4m7wmE6qEZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:17:04.937592Z","bundle_sha256":"bcf0f6a0f6aabf54354e11a373a8fd9ddb9c269c0a2db5fc040762393e301d28"}}