{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UJIPZHKEWZUMLSFQ6NV6MCRRKO","short_pith_number":"pith:UJIPZHKE","schema_version":"1.0","canonical_sha256":"a250fc9d44b668c5c8b0f36be60a3153b5f5c8208251e9a3b762a92183a5cd64","source":{"kind":"arxiv","id":"1902.03408","version":1},"attestation_state":"computed","paper":{"title":"Geometry and Laplacian on Discrete Magic Carpets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chun-Yin Siu, Eric Goodman, Robert S. Strichartz","submitted_at":"2019-02-09T11:24:10Z","abstract_excerpt":"We study several variants of the classical Sierpinski Carpet (SC) fractal. The main examples we call infinite magic carpets (IMC), obtained by taking an infinite blowup of a discrete graph approximation to SC and identifying edges using torus, Klein bottle or projective plane type identifications. We use both theoretical and experimental methods. We prove estimates for the size of metric balls that are close to optimal. We obtain numerical approximations to the spectrum of the graph Laplacian on IMC and to solutions of the associated differential equations: Laplace equation, heat equation and "},"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":"1902.03408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-09T11:24:10Z","cross_cats_sorted":[],"title_canon_sha256":"34683675ccb6de9652ef0577013fb7023be52fc2be190cf02853374b14c7e730","abstract_canon_sha256":"347f6c13a0756b8842635c0dd80860354ce0bf95bd53a2e5cd12603187152bcf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:20.940844Z","signature_b64":"4y0n6DFvirfykeJvD0qzUym81nJ6hvWca/8F+w7YxDVtKO3h6Oubdk7m/GQVI1z77iy8thW3HTT4qmLFl0t7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a250fc9d44b668c5c8b0f36be60a3153b5f5c8208251e9a3b762a92183a5cd64","last_reissued_at":"2026-05-17T23:54:20.940240Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:20.940240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry and Laplacian on Discrete Magic Carpets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chun-Yin Siu, Eric Goodman, Robert S. Strichartz","submitted_at":"2019-02-09T11:24:10Z","abstract_excerpt":"We study several variants of the classical Sierpinski Carpet (SC) fractal. The main examples we call infinite magic carpets (IMC), obtained by taking an infinite blowup of a discrete graph approximation to SC and identifying edges using torus, Klein bottle or projective plane type identifications. We use both theoretical and experimental methods. We prove estimates for the size of metric balls that are close to optimal. We obtain numerical approximations to the spectrum of the graph Laplacian on IMC and to solutions of the associated differential equations: Laplace equation, heat equation and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03408","kind":"arxiv","version":1},"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":"1902.03408","created_at":"2026-05-17T23:54:20.940360+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.03408v1","created_at":"2026-05-17T23:54:20.940360+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03408","created_at":"2026-05-17T23:54:20.940360+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJIPZHKEWZUM","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJIPZHKEWZUMLSFQ","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJIPZHKE","created_at":"2026-05-18T12:33:30.264802+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/UJIPZHKEWZUMLSFQ6NV6MCRRKO","json":"https://pith.science/pith/UJIPZHKEWZUMLSFQ6NV6MCRRKO.json","graph_json":"https://pith.science/api/pith-number/UJIPZHKEWZUMLSFQ6NV6MCRRKO/graph.json","events_json":"https://pith.science/api/pith-number/UJIPZHKEWZUMLSFQ6NV6MCRRKO/events.json","paper":"https://pith.science/paper/UJIPZHKE"},"agent_actions":{"view_html":"https://pith.science/pith/UJIPZHKEWZUMLSFQ6NV6MCRRKO","download_json":"https://pith.science/pith/UJIPZHKEWZUMLSFQ6NV6MCRRKO.json","view_paper":"https://pith.science/paper/UJIPZHKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.03408&json=true","fetch_graph":"https://pith.science/api/pith-number/UJIPZHKEWZUMLSFQ6NV6MCRRKO/graph.json","fetch_events":"https://pith.science/api/pith-number/UJIPZHKEWZUMLSFQ6NV6MCRRKO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJIPZHKEWZUMLSFQ6NV6MCRRKO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJIPZHKEWZUMLSFQ6NV6MCRRKO/action/storage_attestation","attest_author":"https://pith.science/pith/UJIPZHKEWZUMLSFQ6NV6MCRRKO/action/author_attestation","sign_citation":"https://pith.science/pith/UJIPZHKEWZUMLSFQ6NV6MCRRKO/action/citation_signature","submit_replication":"https://pith.science/pith/UJIPZHKEWZUMLSFQ6NV6MCRRKO/action/replication_record"}},"created_at":"2026-05-17T23:54:20.940360+00:00","updated_at":"2026-05-17T23:54:20.940360+00:00"}