{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HSZ4LZ3V45EPRI2SZZ3K3BTJYZ","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":"6564fe9ad45287bb951e1ba2dc167a0c5df78fb12cfa2878a6fc10eeb61d769b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-21T02:54:19Z","title_canon_sha256":"be4b540867acf2509ecfed6d556f0363f8bacd8fe63c26ceb4b42223f1046780"},"schema_version":"1.0","source":{"id":"1607.06176","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06176","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06176v2","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06176","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"pith_short_12","alias_value":"HSZ4LZ3V45EP","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HSZ4LZ3V45EPRI2S","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HSZ4LZ3V","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:8e47891abfb78e023e7f386b1325f9921db87a3598790ae6883c5a4983226136","target":"graph","created_at":"2026-05-18T01:00:45Z","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 paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on Sierpinski gasket (SG). As an application, we prove that the solution of the following Dirichlet problem on SG is an FIF with uniform vertical scaling factor $\\frac{1}{5}$: $\\Delta u=0$ on $SG\\setminus \\{q_1,q_2,q_3\\}$, and $u(q_i)=a_i$, $i=1,2,3$, where $q_i$, $i=1,2,3$, are boundary points of SG.","authors_text":"Huo-Jun Ruan, Xiao-Hui Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-21T02:54:19Z","title":"Energy and Laplacian of Fractal Interpolation Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06176","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:ae3271143cbdb5f4b47c71040e92093621728e8e1733ac557abb00cdfb70c3ef","target":"record","created_at":"2026-05-18T01:00:45Z","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":"6564fe9ad45287bb951e1ba2dc167a0c5df78fb12cfa2878a6fc10eeb61d769b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-21T02:54:19Z","title_canon_sha256":"be4b540867acf2509ecfed6d556f0363f8bacd8fe63c26ceb4b42223f1046780"},"schema_version":"1.0","source":{"id":"1607.06176","kind":"arxiv","version":2}},"canonical_sha256":"3cb3c5e775e748f8a352ce76ad8669c674343f526b5a93bed12d4661af7cce3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cb3c5e775e748f8a352ce76ad8669c674343f526b5a93bed12d4661af7cce3f","first_computed_at":"2026-05-18T01:00:45.221547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:45.221547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xsB7L8gVJu70+lYsQziLiuFkbTgmour3q/+j3T5HhtrVDDQoQSbbPoAsXUa1VXCV0h8nCDLCqnC5cS6H8S2+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:45.221919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06176","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae3271143cbdb5f4b47c71040e92093621728e8e1733ac557abb00cdfb70c3ef","sha256:8e47891abfb78e023e7f386b1325f9921db87a3598790ae6883c5a4983226136"],"state_sha256":"a177544f26af3c62e3d3a0ef4cd97ba37e2a448cfa1559363aa045f403b62087"}