{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VPULLGJJ4JBLVEUQZRRLGKB657","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":"fe96ab3128122af7e154d100b541945eda75bb042d0edc693935c4bda5407b17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-26T05:35:46Z","title_canon_sha256":"ab3e47d2392964d339268062d4b785d92a135fb56464486f4d96c1a05d1ebc1c"},"schema_version":"1.0","source":{"id":"1607.07544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07544","created_at":"2026-05-18T01:10:28Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07544v1","created_at":"2026-05-18T01:10:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07544","created_at":"2026-05-18T01:10:28Z"},{"alias_kind":"pith_short_12","alias_value":"VPULLGJJ4JBL","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VPULLGJJ4JBLVEUQ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VPULLGJJ","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:f6e8173631a103296dc20645f63818b1d2fa51ce5377453f3080ee5dd712aa99","target":"graph","created_at":"2026-05-18T01:10:28Z","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":"We study higher order tangents and higher order Laplacians on p.c.f. self-similar sets with fully symmetric structures, such as $D3$ or $D4$ symmetric fractals. Firstly, let $x$ be a vertex point in the graphs that approximate the fractal, we prove that for any $f$ defined near $x$, the higher oder weak tangent of $f$ at $x$, if exists, is the uniform limit of local multiharmonic functions that agree with $f$ in some sense near $x$. Secondly, we prove that the higher order Laplacian on a fractal can be expressible as a renormalized uniform limit of higher order graph Laplacians on the graphs t","authors_text":"Hua Qiu, Shiping Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-26T05:35:46Z","title":"Higher order tangents and Higher order Laplacians on Sierpinski Gasket Type Fractals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07544","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":"sha256:0f414653880fc8c378a466b80dfb4b7538e949df95dbd1ccfd9f2c5b77172857","target":"record","created_at":"2026-05-18T01:10:28Z","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":"fe96ab3128122af7e154d100b541945eda75bb042d0edc693935c4bda5407b17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-26T05:35:46Z","title_canon_sha256":"ab3e47d2392964d339268062d4b785d92a135fb56464486f4d96c1a05d1ebc1c"},"schema_version":"1.0","source":{"id":"1607.07544","kind":"arxiv","version":1}},"canonical_sha256":"abe8b59929e242ba9290cc62b3283eefd71f3f31c262b1b99baef85e7b8caacc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abe8b59929e242ba9290cc62b3283eefd71f3f31c262b1b99baef85e7b8caacc","first_computed_at":"2026-05-18T01:10:28.289029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:28.289029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"prliyVgwREuzrSGvitX0Momzss144dZDABSODoUECa0H6zq7lmFJ0XQ2hUeHTIhRCplMg1ncErnv0Kz35aXhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:28.289541Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f414653880fc8c378a466b80dfb4b7538e949df95dbd1ccfd9f2c5b77172857","sha256:f6e8173631a103296dc20645f63818b1d2fa51ce5377453f3080ee5dd712aa99"],"state_sha256":"8d4696aeaa6fb59957c3ec9db5056b0d52adddb53d29c28a027ac90aa3dc923f"}