{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XYOIS3UZOI7GP5KPVMKS2HGBM3","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":"5982d7086232ebd5339a706d63cadeefb216f7405fe379dd21c5e58b8683ad60","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-31T13:44:58Z","title_canon_sha256":"8df67244810c6f01fa09f1bc2f5a1e0dd9acf981e0ab421c0d4c4ee308f45827"},"schema_version":"1.0","source":{"id":"1912.13304","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.13304","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1912.13304v3","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.13304","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"XYOIS3UZOI7G","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"XYOIS3UZOI7GP5KP","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"XYOIS3UZ","created_at":"2026-07-05T04:11:22Z"}],"graph_snapshots":[{"event_id":"sha256:3baf26ba6a2919642731138ff6d455e1ac82b10490d7f18b623d9725dcf26830","target":"graph","created_at":"2026-07-05T04:11:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.13304/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is well known that the discretization of fractional diffusion equations (FDEs) with fractional derivatives $\\alpha\\in(1,2)$, using the so-called weighted and shifted Gr\\\"unwald formula, leads to linear systems whose coefficient matrices show a Toeplitz-like structure. More precisely, in the case of variable coefficients, the related matrix sequences belong to the so-called Generalized Locally Toeplitz (GLT) class. Conversely, when the given FDE have constant coefficients, using a suitable discretization, we encounter a Toeplitz structure associated to a nonnegative function $\\mathcal{F}_\\al","authors_text":"Nikos Barakitis, Paris Vassalos, Sven-Erik Ekstr\\\"om","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-31T13:44:58Z","title":"Preconditioners for Fractional Diffusion Equations Based on the Spectral Symbol"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.13304","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:a3be10c408a329103f373f43ef4d5c7f43aa5ff4ef90128d496969086a4f9e7f","target":"record","created_at":"2026-07-05T04:11:22Z","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":"5982d7086232ebd5339a706d63cadeefb216f7405fe379dd21c5e58b8683ad60","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-12-31T13:44:58Z","title_canon_sha256":"8df67244810c6f01fa09f1bc2f5a1e0dd9acf981e0ab421c0d4c4ee308f45827"},"schema_version":"1.0","source":{"id":"1912.13304","kind":"arxiv","version":3}},"canonical_sha256":"be1c896e99723e67f54fab152d1cc166dcac4ee26af425ab0a5fa689ce16615e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be1c896e99723e67f54fab152d1cc166dcac4ee26af425ab0a5fa689ce16615e","first_computed_at":"2026-07-05T04:11:22.491221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:11:22.491221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yj1SZc7r9r/lFCAXaftb6iwTqi1dUucoiMFqwy0AVPUtgZixIdYV6711Z7YGzkdVtTmPTfbPX9w8KXgCntRdDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:11:22.491738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.13304","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3be10c408a329103f373f43ef4d5c7f43aa5ff4ef90128d496969086a4f9e7f","sha256:3baf26ba6a2919642731138ff6d455e1ac82b10490d7f18b623d9725dcf26830"],"state_sha256":"ef4a59abb83b6da744d19808aadef269c2dc4aa8f251df47b3e5095a746cfc85"}