{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:G2Q5Y72MLGRNGYHGDEWXMMRWRP","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":"f9a3d701561ae2df75cef2f7c3f99574fbcd87a93129f15df24a2f04296badc6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-19T01:45:15Z","title_canon_sha256":"5bce19a25fcb2b4232ba2d65123edd0b31e2ca4251277c352715ae526b0802e9"},"schema_version":"1.0","source":{"id":"1208.3799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3799","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3799v1","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3799","created_at":"2026-05-18T03:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"G2Q5Y72MLGRN","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"G2Q5Y72MLGRNGYHG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"G2Q5Y72M","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:b2a1825364fabe77a977b88d5572618195e6cd892373ca851efc140f82c0c734","target":"graph","created_at":"2026-05-18T03:48:26Z","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 improve on the inequality $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq \\frac{1}{\\sqrt p}, {0.2 cm}p\\geq 1,}$ showing that $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq C(p) \\frac{\\sqrt{3/\\pi}}{\\sqrt p},}$ with $\\displaystyle{\\lim_{p\\longrightarrow \\infty} C(p)=1,}$ and indeed that {align*} \\displaystyle{\\lim_{p\\longrightarrow \\infty}\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt/ \\frac{\\sqrt{3/\\pi}}{\\sqrt p}=1.} {align*}","authors_text":"R. Kerman, S. Spektor","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-19T01:45:15Z","title":"A New Proof Of The Asymptotic Limit Of The $Lp$ Norm Of The Sinc Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3799","kind":"arxiv","version":1},"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":"sha256:12794961156b06bb31cbd4e6ead1573ec88e0c004d5ad18a1b0809dc0fa55820","target":"record","created_at":"2026-05-18T03:48:26Z","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":"f9a3d701561ae2df75cef2f7c3f99574fbcd87a93129f15df24a2f04296badc6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-19T01:45:15Z","title_canon_sha256":"5bce19a25fcb2b4232ba2d65123edd0b31e2ca4251277c352715ae526b0802e9"},"schema_version":"1.0","source":{"id":"1208.3799","kind":"arxiv","version":1}},"canonical_sha256":"36a1dc7f4c59a2d360e6192d7632368be10d3652104b7a9f2d5fe6f10808558b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36a1dc7f4c59a2d360e6192d7632368be10d3652104b7a9f2d5fe6f10808558b","first_computed_at":"2026-05-18T03:48:26.186436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:26.186436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k8MCqQxBu2bczggkUvHVmhhUs4igVDhMVKVKl18CcG2SHPX9YTAZ+MKQHMKyx/rOswOvm7/ZE1JFGNKTEtk7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:26.186966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12794961156b06bb31cbd4e6ead1573ec88e0c004d5ad18a1b0809dc0fa55820","sha256:b2a1825364fabe77a977b88d5572618195e6cd892373ca851efc140f82c0c734"],"state_sha256":"e2db69397b1c5325ccbcc833c6849aaf530677851e06ce83c50f177c83624f0e"}