{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KRUW353LXV66FLANYAULXFEOSP","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":"f221c41aa7f17370b58476ecce185f422bc8504755d65fea423435c28dacf9c0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2018-10-23T07:38:43Z","title_canon_sha256":"ca91b821860a20b636941a2c89b2da8e1c2da75e04b8b68ae0915ce737760879"},"schema_version":"1.0","source":{"id":"1810.09701","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09701","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09701v2","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09701","created_at":"2026-05-17T23:48:50Z"},{"alias_kind":"pith_short_12","alias_value":"KRUW353LXV66","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KRUW353LXV66FLAN","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KRUW353L","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:195b13e0292b6201f00834f76a36d63703e458e371a000891df23261dc0d2595","target":"graph","created_at":"2026-05-17T23:48:50Z","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":"A general framework to construct fractal interpolation surfaces (FISs) on rectangular grids was presented and bilinear FIS was deduced by Ruan and Xu [Bull. Aust. Math. Soc. 91(3), 2015, pp. 435-446]. From the view point of operator theory and the stand point of developing some approximation aspects, we revisit the aforementioned construction to obtain a fractal analogue of a prescribed continuous function defined on a rectangular region in $R^2$. This approach leads to a bounded linear operator analogous to the so-called $\\alpha$-fractal operator associated with the univariate fractal interpo","authors_text":"P. Viswanathan, S. Verma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2018-10-23T07:38:43Z","title":"A fractal operator associated to bivariate fractal interpolation functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09701","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":"sha256:7137b3be8d198b832ebebc2c10d5da02cee670bfef413686488eda81380a2255","target":"record","created_at":"2026-05-17T23:48:50Z","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":"f221c41aa7f17370b58476ecce185f422bc8504755d65fea423435c28dacf9c0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2018-10-23T07:38:43Z","title_canon_sha256":"ca91b821860a20b636941a2c89b2da8e1c2da75e04b8b68ae0915ce737760879"},"schema_version":"1.0","source":{"id":"1810.09701","kind":"arxiv","version":2}},"canonical_sha256":"54696df76bbd7de2ac0dc028bb948e93f33e8d44cb582204073f7c39dabd4424","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54696df76bbd7de2ac0dc028bb948e93f33e8d44cb582204073f7c39dabd4424","first_computed_at":"2026-05-17T23:48:50.660691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:50.660691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0/RDqC1GVx3AllXn2OMUTfHOuccZr5g2Ek3/gMshMZm2+Uke8lXVgEnasg4U7ly74gHVxW2eUs/ph+/duH8ACw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:50.661353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09701","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7137b3be8d198b832ebebc2c10d5da02cee670bfef413686488eda81380a2255","sha256:195b13e0292b6201f00834f76a36d63703e458e371a000891df23261dc0d2595"],"state_sha256":"13ce828388a789645af3b8d49b19e7b4928fa60dc80a9a1ce645adc1b370361b"}