{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G2S7K6RTGW3LTPLNFYB73ZNBFX","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":"646adecbb025eb98d9966e929fe748818219f5a103a57f180de38183fc0c01b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-24T02:02:10Z","title_canon_sha256":"69ba3e1321de9d33537eb2e42c55224d633d8c8b9d219d5b6c6bc3e592da1cc8"},"schema_version":"1.0","source":{"id":"1607.07436","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07436","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07436v3","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07436","created_at":"2026-05-18T01:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"G2S7K6RTGW3L","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G2S7K6RTGW3LTPLN","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G2S7K6RT","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:4a81c1770bef8e1f036b82889c6b8d3be682379ad3f4b8958015b7aa1cd9fe55","target":"graph","created_at":"2026-05-18T01:09:54Z","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":"In this article, we propose an exponential B-spline collocation method to approximate the solution of the fractional sub-diffusion equation of Caputo type. The present method is generated by use of the Gorenflo-Mainardi-Moretti-Paradisi (GMMP) scheme in time and an efficient exponential B-spline based method in space. The unique solvability is rigorously discussed. Its stability is well illustrated via a procedure closely resembling the classic von Neumann approach. The resulting algebraic system is tri-diagonal that can rapidly be solved by the known algebraic solver with low cost and storage","authors_text":"J. G. Wang, X. G. Zhu, Y. F. Nie, Z. B. Yuan, Z. Z. Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-24T02:02:10Z","title":"An exponential B-spline collocation method for fractional sub-diffusion equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07436","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":"sha256:1b40f63fbd7c4d110ce3bb8324abe8be86eaed226735b13fccd11eaa222e9a0c","target":"record","created_at":"2026-05-18T01:09:54Z","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":"646adecbb025eb98d9966e929fe748818219f5a103a57f180de38183fc0c01b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-24T02:02:10Z","title_canon_sha256":"69ba3e1321de9d33537eb2e42c55224d633d8c8b9d219d5b6c6bc3e592da1cc8"},"schema_version":"1.0","source":{"id":"1607.07436","kind":"arxiv","version":3}},"canonical_sha256":"36a5f57a3335b6b9bd6d2e03fde5a12dea2d1c7b5ef06ed7da9022f430cb494f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36a5f57a3335b6b9bd6d2e03fde5a12dea2d1c7b5ef06ed7da9022f430cb494f","first_computed_at":"2026-05-18T01:09:54.470830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:54.470830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z544Ji8Qccg11qrYvpWp9mPcXl5tq1m97/lke77waDJFdhSS+EkZPgX041bVASLv2KHYsHrxxrgYjuyycRsQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:54.471523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07436","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b40f63fbd7c4d110ce3bb8324abe8be86eaed226735b13fccd11eaa222e9a0c","sha256:4a81c1770bef8e1f036b82889c6b8d3be682379ad3f4b8958015b7aa1cd9fe55"],"state_sha256":"e9269cbcf4ac345bacb696886185ece7563cb78a21c4dff4920ac31f05bd362b"}