{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VIW5JW2DU35QHGIVEIOGNTUNCG","short_pith_number":"pith:VIW5JW2D","schema_version":"1.0","canonical_sha256":"aa2dd4db43a6fb039915221c66ce8d11a8a0ae4c2497c0776582e3ede40419e7","source":{"kind":"arxiv","id":"1907.08285","version":1},"attestation_state":"computed","paper":{"title":"Patterns of primes in the Sato-Tate conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Pascadi, Ashwin Sah, Junyao Peng, Michael Kural, Nate Gillman","submitted_at":"2019-07-18T21:17:41Z","abstract_excerpt":"Fix a non-CM elliptic curve $E/\\mathbb{Q}$, and let $a_E(p) = p + 1 - \\#E(\\mathbb{F}_p)$ denote the trace of Frobenius at $p$. The Sato-Tate conjecture gives the limiting distribution $\\mu_{ST}$ of $a_E(p)/(2\\sqrt{p})$ within $[-1, 1]$. We establish bounded gaps for primes in the context of this distribution. More precisely, given an interval $I\\subseteq [-1, 1]$, let $p_{I,n}$ denote the $n$th prime such that $a_E(p)/(2\\sqrt{p})\\in I$. We show $\\liminf_{n\\to\\infty}(p_{I,n+m}-p_{I,n}) < \\infty$ for all $m\\ge 1$ for \"most\" intervals, and in particular, for all $I$ with $\\mu_{ST}(I)\\ge 0.36$. Fu"},"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":"1907.08285","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-18T21:17:41Z","cross_cats_sorted":[],"title_canon_sha256":"9dcd05762d2f4242da3f787f0fd4501579216bb268551492a3db4fb83967623a","abstract_canon_sha256":"0b68fded9aa345dcba850756d11b9c61e60d0587258d244dec3f812232ce6564"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:30:18.457807Z","signature_b64":"uHVKxKV56r0+8VioJbxV9LIz3a65sxGFZLxW3xdXddbLz7BVycUSzzCWcAx8kPtP7298JSPo3HWQtDOnubjrAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa2dd4db43a6fb039915221c66ce8d11a8a0ae4c2497c0776582e3ede40419e7","last_reissued_at":"2026-07-05T00:30:18.457364Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:30:18.457364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Patterns of primes in the Sato-Tate conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Pascadi, Ashwin Sah, Junyao Peng, Michael Kural, Nate Gillman","submitted_at":"2019-07-18T21:17:41Z","abstract_excerpt":"Fix a non-CM elliptic curve $E/\\mathbb{Q}$, and let $a_E(p) = p + 1 - \\#E(\\mathbb{F}_p)$ denote the trace of Frobenius at $p$. The Sato-Tate conjecture gives the limiting distribution $\\mu_{ST}$ of $a_E(p)/(2\\sqrt{p})$ within $[-1, 1]$. We establish bounded gaps for primes in the context of this distribution. More precisely, given an interval $I\\subseteq [-1, 1]$, let $p_{I,n}$ denote the $n$th prime such that $a_E(p)/(2\\sqrt{p})\\in I$. We show $\\liminf_{n\\to\\infty}(p_{I,n+m}-p_{I,n}) < \\infty$ for all $m\\ge 1$ for \"most\" intervals, and in particular, for all $I$ with $\\mu_{ST}(I)\\ge 0.36$. Fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08285","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.08285/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1907.08285","created_at":"2026-07-05T00:30:18.457424+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.08285v1","created_at":"2026-07-05T00:30:18.457424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08285","created_at":"2026-07-05T00:30:18.457424+00:00"},{"alias_kind":"pith_short_12","alias_value":"VIW5JW2DU35Q","created_at":"2026-07-05T00:30:18.457424+00:00"},{"alias_kind":"pith_short_16","alias_value":"VIW5JW2DU35QHGIV","created_at":"2026-07-05T00:30:18.457424+00:00"},{"alias_kind":"pith_short_8","alias_value":"VIW5JW2D","created_at":"2026-07-05T00:30:18.457424+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/VIW5JW2DU35QHGIVEIOGNTUNCG","json":"https://pith.science/pith/VIW5JW2DU35QHGIVEIOGNTUNCG.json","graph_json":"https://pith.science/api/pith-number/VIW5JW2DU35QHGIVEIOGNTUNCG/graph.json","events_json":"https://pith.science/api/pith-number/VIW5JW2DU35QHGIVEIOGNTUNCG/events.json","paper":"https://pith.science/paper/VIW5JW2D"},"agent_actions":{"view_html":"https://pith.science/pith/VIW5JW2DU35QHGIVEIOGNTUNCG","download_json":"https://pith.science/pith/VIW5JW2DU35QHGIVEIOGNTUNCG.json","view_paper":"https://pith.science/paper/VIW5JW2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.08285&json=true","fetch_graph":"https://pith.science/api/pith-number/VIW5JW2DU35QHGIVEIOGNTUNCG/graph.json","fetch_events":"https://pith.science/api/pith-number/VIW5JW2DU35QHGIVEIOGNTUNCG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VIW5JW2DU35QHGIVEIOGNTUNCG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VIW5JW2DU35QHGIVEIOGNTUNCG/action/storage_attestation","attest_author":"https://pith.science/pith/VIW5JW2DU35QHGIVEIOGNTUNCG/action/author_attestation","sign_citation":"https://pith.science/pith/VIW5JW2DU35QHGIVEIOGNTUNCG/action/citation_signature","submit_replication":"https://pith.science/pith/VIW5JW2DU35QHGIVEIOGNTUNCG/action/replication_record"}},"created_at":"2026-07-05T00:30:18.457424+00:00","updated_at":"2026-07-05T00:30:18.457424+00:00"}