{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TOEIKCWZCOKIWS53P6PMFC34CJ","short_pith_number":"pith:TOEIKCWZ","schema_version":"1.0","canonical_sha256":"9b88850ad913948b4bbb7f9ec28b7c12508f25b3787031bfc0b1557cd3f3f18c","source":{"kind":"arxiv","id":"1112.6401","version":3},"attestation_state":"computed","paper":{"title":"Spectral triples for the Sierpinski Gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"D. Guido, F. Cipriani, J-L. Sauvageot, T. Isola","submitted_at":"2011-12-29T20:00:21Z","abstract_excerpt":"We construct a family of spectral triples for the Sierpinski Gasket $K$. For suitable values of the parameters, we determine the dimensional spectrum and recover the Hausdorff measure of $K$ in terms of the residue of the volume functional $a\\to$ tr$(a\\,|D|^{-s})$ at its abscissa of convergence $d_D$, which coincides with the Hausdorff dimension $d_H$ of the fractal. We determine the associated Connes' distance showing that it is bi-Lipschitz equivalent to the distance on $K$ induced by the Euclidean metric of the plane, and show that the pairing of the associated Fredholm module with (odd) $K"},"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":"1112.6401","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-12-29T20:00:21Z","cross_cats_sorted":[],"title_canon_sha256":"4b8146526305dc713df81170e4122fa5f53e74285f64825bec05e78923d56e33","abstract_canon_sha256":"956b334213a2ed69360f15281fffd18c3cbf81a6cf47db88e6ba5a5eb3d5ba46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:04.130688Z","signature_b64":"r609uMfZ7zsYtCdgKM7XqKny7BGEISWOQxS6rnpGJf3QAxI7aj/uLXfYuzGtc+a667Uve3mmwptDgMi3KV0WAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b88850ad913948b4bbb7f9ec28b7c12508f25b3787031bfc0b1557cd3f3f18c","last_reissued_at":"2026-05-18T02:56:04.130227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:04.130227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral triples for the Sierpinski Gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"D. Guido, F. Cipriani, J-L. Sauvageot, T. Isola","submitted_at":"2011-12-29T20:00:21Z","abstract_excerpt":"We construct a family of spectral triples for the Sierpinski Gasket $K$. For suitable values of the parameters, we determine the dimensional spectrum and recover the Hausdorff measure of $K$ in terms of the residue of the volume functional $a\\to$ tr$(a\\,|D|^{-s})$ at its abscissa of convergence $d_D$, which coincides with the Hausdorff dimension $d_H$ of the fractal. We determine the associated Connes' distance showing that it is bi-Lipschitz equivalent to the distance on $K$ induced by the Euclidean metric of the plane, and show that the pairing of the associated Fredholm module with (odd) $K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6401","kind":"arxiv","version":3},"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":"1112.6401","created_at":"2026-05-18T02:56:04.130294+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.6401v3","created_at":"2026-05-18T02:56:04.130294+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6401","created_at":"2026-05-18T02:56:04.130294+00:00"},{"alias_kind":"pith_short_12","alias_value":"TOEIKCWZCOKI","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TOEIKCWZCOKIWS53","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TOEIKCWZ","created_at":"2026-05-18T12:26:42.757692+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/TOEIKCWZCOKIWS53P6PMFC34CJ","json":"https://pith.science/pith/TOEIKCWZCOKIWS53P6PMFC34CJ.json","graph_json":"https://pith.science/api/pith-number/TOEIKCWZCOKIWS53P6PMFC34CJ/graph.json","events_json":"https://pith.science/api/pith-number/TOEIKCWZCOKIWS53P6PMFC34CJ/events.json","paper":"https://pith.science/paper/TOEIKCWZ"},"agent_actions":{"view_html":"https://pith.science/pith/TOEIKCWZCOKIWS53P6PMFC34CJ","download_json":"https://pith.science/pith/TOEIKCWZCOKIWS53P6PMFC34CJ.json","view_paper":"https://pith.science/paper/TOEIKCWZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.6401&json=true","fetch_graph":"https://pith.science/api/pith-number/TOEIKCWZCOKIWS53P6PMFC34CJ/graph.json","fetch_events":"https://pith.science/api/pith-number/TOEIKCWZCOKIWS53P6PMFC34CJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TOEIKCWZCOKIWS53P6PMFC34CJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TOEIKCWZCOKIWS53P6PMFC34CJ/action/storage_attestation","attest_author":"https://pith.science/pith/TOEIKCWZCOKIWS53P6PMFC34CJ/action/author_attestation","sign_citation":"https://pith.science/pith/TOEIKCWZCOKIWS53P6PMFC34CJ/action/citation_signature","submit_replication":"https://pith.science/pith/TOEIKCWZCOKIWS53P6PMFC34CJ/action/replication_record"}},"created_at":"2026-05-18T02:56:04.130294+00:00","updated_at":"2026-05-18T02:56:04.130294+00:00"}