{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7FZEJTQ6EXA554KKAL7RPYYX4H","short_pith_number":"pith:7FZEJTQ6","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"},"canonical_sha256":"f97244ce1e25c1def14a02ff17e317e1e1c1deda9aae050bc89cd0d670239edc","source":{"kind":"arxiv","id":"1202.4126","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7FZEJTQ6EXA554KKAL7RPYYX4H","target":"record","payload":{"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"},"canonical_sha256":"f97244ce1e25c1def14a02ff17e317e1e1c1deda9aae050bc89cd0d670239edc","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"},"source_kind":"arxiv","source_id":"1202.4126","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjQ8jkMMfDms0Bs/GbWE+0nP20w1BaZjXHtzuKqYrb/1tgya7zVkCPSjg+Y8+rRbY8gcHnc10DNmWL7z5C/oDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T16:39:04.904652Z"},"content_sha256":"a4aa0e16aa48f6024a996d0b5be71bf1b7da85aee65f69062af3ac27f95a2991","schema_version":"1.0","event_id":"sha256:a4aa0e16aa48f6024a996d0b5be71bf1b7da85aee65f69062af3ac27f95a2991"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7FZEJTQ6EXA554KKAL7RPYYX4H","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"esaJtfHC/JnyN4x352W/Tsrys/FeNRbPeX13WMwfuSf22YDf7BAmVoTQEEMsn7Qb/fOSow9PW79e1TyMpIj9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T16:39:04.905011Z"},"content_sha256":"2b1c0b72d921562a31071641cc9934a93b51e15c32ef11d5da579f1e7c682933","schema_version":"1.0","event_id":"sha256:2b1c0b72d921562a31071641cc9934a93b51e15c32ef11d5da579f1e7c682933"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/bundle.json","state_url":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T16:39:04Z","links":{"resolver":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H","bundle":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/bundle.json","state":"https://pith.science/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FZEJTQ6EXA554KKAL7RPYYX4H/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVRjxmQXDmcOb62EY6y/Zs+Y3OSi6v65KT2U03pP7+y/pJzSoMUltmrrHd295CgNIqVmWEgBlZPRgw0+lXP7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T16:39:04.906982Z","bundle_sha256":"c1fa923a25bda16b0bea293796d1a7e94932c282a66e71fa5cd8e366858df0f9"}}