{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7FZEJTQ6EXA554KKAL7RPYYX4H","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":"c20582d7f6a11332a922353c36f256bb9bf596680998ebfebbde9096174fbda4","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-19T06:06:40Z","title_canon_sha256":"d4602f934f9bdf7d7c254de31137a1fc7d9dc5a644d7c911ea6ffbf579965aa3"},"schema_version":"1.0","source":{"id":"1202.4126","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4126","created_at":"2026-05-18T01:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4126v2","created_at":"2026-05-18T01:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4126","created_at":"2026-05-18T01:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"7FZEJTQ6EXA5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7FZEJTQ6EXA554KK","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7FZEJTQ6","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:2b1c0b72d921562a31071641cc9934a93b51e15c32ef11d5da579f1e7c682933","target":"graph","created_at":"2026-05-18T01:58:23Z","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 investigate the spectral zeta function of fractal differential operators such as the Laplacian on the unbounded (i.e., infinite) Sierpinski gasket and a self-similar Sturm-Liouville operator associated with a fractal self-similar measure on the half-line. In the latter case, C. Sabot discovered the relation between the spectrum of this operator and the iteration of a rational map of several complex variables, called the renormalization map. We obtain a factorization of the spectral zeta function of such an operator, expressed in terms of the Dirac delta hyperfunction, a geometric zeta funct","authors_text":"Michel L. Lapidus, Nishu Lal","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-19T06:06:40Z","title":"Hyperfunctions and Spectral Zeta Functions of Laplacians on Self-Similar Fractals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4126","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:a4aa0e16aa48f6024a996d0b5be71bf1b7da85aee65f69062af3ac27f95a2991","target":"record","created_at":"2026-05-18T01:58:23Z","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":"c20582d7f6a11332a922353c36f256bb9bf596680998ebfebbde9096174fbda4","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-19T06:06:40Z","title_canon_sha256":"d4602f934f9bdf7d7c254de31137a1fc7d9dc5a644d7c911ea6ffbf579965aa3"},"schema_version":"1.0","source":{"id":"1202.4126","kind":"arxiv","version":2}},"canonical_sha256":"f97244ce1e25c1def14a02ff17e317e1e1c1deda9aae050bc89cd0d670239edc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f97244ce1e25c1def14a02ff17e317e1e1c1deda9aae050bc89cd0d670239edc","first_computed_at":"2026-05-18T01:58:23.875770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:23.875770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TD8UXjBRsK+peB8sN/Si+bf+1DvtJnLTRRjEfxgLO74ld75MZaFQ7yO3k9BK7+wYh5IDjdfBD74h1kCn+ZY9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:23.876219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4126","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4aa0e16aa48f6024a996d0b5be71bf1b7da85aee65f69062af3ac27f95a2991","sha256:2b1c0b72d921562a31071641cc9934a93b51e15c32ef11d5da579f1e7c682933"],"state_sha256":"6cd96788c55505236e4c33300ceceb885f0948fa60788da502714362f3b612cb"}