{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VSTPPA3A32T2TJ7DPNVG4WVZIG","short_pith_number":"pith:VSTPPA3A","schema_version":"1.0","canonical_sha256":"aca6f78360dea7a9a7e37b6a6e5ab941933e9e2bfe53109ef3360b49ce360c71","source":{"kind":"arxiv","id":"1412.1236","version":1},"attestation_state":"computed","paper":{"title":"The best constant of discrete Sobolev inequality on the C60 fullerene buckyball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Atsushi Nagai, Hiroyuki Yamagishi, Kazuo Takemura, Kohtaro Watanabe, Yoshinori Kametaka","submitted_at":"2014-12-03T08:50:21Z","abstract_excerpt":"The best constants of two kinds of discrete Sobolev inequalities on the C60 fullerene buckyball are obtained. All the eigenvalues of discrete Laplacian $A$ corresponding to the buckyball are found. They are roots of algebraic equation at most degree $4$ with integer coefficients. Green matrix $G(a)=(A+a I)^{-1}\\ (0<a<\\infty)$ and the pseudo Green matrix $G_*=A^{\\dagger}$ are obtained by using computer software Mathematica. Diagonal values of $G_*$ and $G(a)$ are identical and they are equal to the best constants of discrete Sobolev inequalities."},"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":"1412.1236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-03T08:50:21Z","cross_cats_sorted":[],"title_canon_sha256":"1d44db9eb4a64c8fde02970815ec35cd5500b3e865f0dcf56cc6d70b017925bc","abstract_canon_sha256":"304c72104058f49eefbec0338fa60fdf69c323a4c08fd33fa80626a58a6002c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:13.050892Z","signature_b64":"A0IXjCa3izkc26YR/uRJbGpEI0iIioolARM3ON5uaXS1wRZuDdVjBhGzXH7a+HN3iJHUrg6VIwZJWCYsd0xZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aca6f78360dea7a9a7e37b6a6e5ab941933e9e2bfe53109ef3360b49ce360c71","last_reissued_at":"2026-05-18T02:32:13.050434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:13.050434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The best constant of discrete Sobolev inequality on the C60 fullerene buckyball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Atsushi Nagai, Hiroyuki Yamagishi, Kazuo Takemura, Kohtaro Watanabe, Yoshinori Kametaka","submitted_at":"2014-12-03T08:50:21Z","abstract_excerpt":"The best constants of two kinds of discrete Sobolev inequalities on the C60 fullerene buckyball are obtained. All the eigenvalues of discrete Laplacian $A$ corresponding to the buckyball are found. They are roots of algebraic equation at most degree $4$ with integer coefficients. Green matrix $G(a)=(A+a I)^{-1}\\ (0<a<\\infty)$ and the pseudo Green matrix $G_*=A^{\\dagger}$ are obtained by using computer software Mathematica. Diagonal values of $G_*$ and $G(a)$ are identical and they are equal to the best constants of discrete Sobolev inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1236","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":"1412.1236","created_at":"2026-05-18T02:32:13.050489+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1236v1","created_at":"2026-05-18T02:32:13.050489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1236","created_at":"2026-05-18T02:32:13.050489+00:00"},{"alias_kind":"pith_short_12","alias_value":"VSTPPA3A32T2","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VSTPPA3A32T2TJ7D","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VSTPPA3A","created_at":"2026-05-18T12:28:54.890064+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/VSTPPA3A32T2TJ7DPNVG4WVZIG","json":"https://pith.science/pith/VSTPPA3A32T2TJ7DPNVG4WVZIG.json","graph_json":"https://pith.science/api/pith-number/VSTPPA3A32T2TJ7DPNVG4WVZIG/graph.json","events_json":"https://pith.science/api/pith-number/VSTPPA3A32T2TJ7DPNVG4WVZIG/events.json","paper":"https://pith.science/paper/VSTPPA3A"},"agent_actions":{"view_html":"https://pith.science/pith/VSTPPA3A32T2TJ7DPNVG4WVZIG","download_json":"https://pith.science/pith/VSTPPA3A32T2TJ7DPNVG4WVZIG.json","view_paper":"https://pith.science/paper/VSTPPA3A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1236&json=true","fetch_graph":"https://pith.science/api/pith-number/VSTPPA3A32T2TJ7DPNVG4WVZIG/graph.json","fetch_events":"https://pith.science/api/pith-number/VSTPPA3A32T2TJ7DPNVG4WVZIG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VSTPPA3A32T2TJ7DPNVG4WVZIG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VSTPPA3A32T2TJ7DPNVG4WVZIG/action/storage_attestation","attest_author":"https://pith.science/pith/VSTPPA3A32T2TJ7DPNVG4WVZIG/action/author_attestation","sign_citation":"https://pith.science/pith/VSTPPA3A32T2TJ7DPNVG4WVZIG/action/citation_signature","submit_replication":"https://pith.science/pith/VSTPPA3A32T2TJ7DPNVG4WVZIG/action/replication_record"}},"created_at":"2026-05-18T02:32:13.050489+00:00","updated_at":"2026-05-18T02:32:13.050489+00:00"}