{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:7FZEJTQ6EXA554KKAL7RPYYX4H","short_pith_number":"pith:7FZEJTQ6","schema_version":"1.0","canonical_sha256":"f97244ce1e25c1def14a02ff17e317e1e1c1deda9aae050bc89cd0d670239edc","source":{"kind":"arxiv","id":"1202.4126","version":2},"attestation_state":"computed","paper":{"title":"Hyperfunctions and Spectral Zeta Functions of Laplacians on Self-Similar Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Michel L. Lapidus, Nishu Lal","submitted_at":"2012-02-19T06:06:40Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1202.4126","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-19T06:06:40Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d4602f934f9bdf7d7c254de31137a1fc7d9dc5a644d7c911ea6ffbf579965aa3","abstract_canon_sha256":"c20582d7f6a11332a922353c36f256bb9bf596680998ebfebbde9096174fbda4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:23.876219Z","signature_b64":"TD8UXjBRsK+peB8sN/Si+bf+1DvtJnLTRRjEfxgLO74ld75MZaFQ7yO3k9BK7+wYh5IDjdfBD74h1kCn+ZY9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f97244ce1e25c1def14a02ff17e317e1e1c1deda9aae050bc89cd0d670239edc","last_reissued_at":"2026-05-18T01:58:23.875770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:23.875770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hyperfunctions and Spectral Zeta Functions of Laplacians on Self-Similar Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Michel L. Lapidus, Nishu Lal","submitted_at":"2012-02-19T06:06:40Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4126","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.4126","created_at":"2026-05-18T01:58:23.875845+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4126v2","created_at":"2026-05-18T01:58:23.875845+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4126","created_at":"2026-05-18T01:58:23.875845+00:00"},{"alias_kind":"pith_short_12","alias_value":"7FZEJTQ6EXA5","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"7FZEJTQ6EXA554KK","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"7FZEJTQ6","created_at":"2026-05-18T12:26:56.085431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H","json":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H.json","graph_json":"https://pith.science/api/pith-number/7FZEJTQ6EXA554KKAL7RPYYX4H/graph.json","events_json":"https://pith.science/api/pith-number/7FZEJTQ6EXA554KKAL7RPYYX4H/events.json","paper":"https://pith.science/paper/7FZEJTQ6"},"agent_actions":{"view_html":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H","download_json":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H.json","view_paper":"https://pith.science/paper/7FZEJTQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4126&json=true","fetch_graph":"https://pith.science/api/pith-number/7FZEJTQ6EXA554KKAL7RPYYX4H/graph.json","fetch_events":"https://pith.science/api/pith-number/7FZEJTQ6EXA554KKAL7RPYYX4H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/action/storage_attestation","attest_author":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/action/author_attestation","sign_citation":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/action/citation_signature","submit_replication":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/action/replication_record"}},"created_at":"2026-05-18T01:58:23.875845+00:00","updated_at":"2026-05-18T01:58:23.875845+00:00"}