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We use these to establish the supercongruence $B_{np^k} \\equiv B_{np^{k-1}} \\bmod p^{2k}$ for all primes $p \\ge 3$ and integers $n,k \\ge 1$, where $B_n$ is a sequence discovered by Zagier, known as Sequence $\\mathbf{B}$.\n  Additionally, for 14 of the 15 sequen"},"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":"2102.11839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-23T18:14:26Z","cross_cats_sorted":[],"title_canon_sha256":"4f24996314960eb074232db05f82bfa1f2b6011d80719578b24614d8cdc4a57c","abstract_canon_sha256":"606fe0fd71c0a06cfa79e9e1e7c82f74a6ddb93c529388f5307220bd2df3368a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:45.008015Z","signature_b64":"LlfySM+qRffqm/4/F9CSZstGwKBciCFC98Xnwwg+WS+2BODVO3VAzN6KOfsmUNhTnLzysS+xmQJNS/msf42dAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ab82efe83b90dabd4997ba6a57935f3c3185b0a56cceb2bc42453238ea5feaa","last_reissued_at":"2026-07-05T09:56:45.007496Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:45.007496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New representations for all sporadic Ap\\'ery-like sequences, with applications to congruences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ofir Gorodetsky","submitted_at":"2021-02-23T18:14:26Z","abstract_excerpt":"We find new representations, in terms of constant terms of powers of Laurent polynomials, for all the 15 sporadic Ap{\\'e}ry-like sequences discovered by Zagier, Almkvist-Zudilin and Cooper.\n  The new representations lead to binomial expressions for the sequences, which, as opposed to previous expressions, do not involve powers of 3 or 8. We use these to establish the supercongruence $B_{np^k} \\equiv B_{np^{k-1}} \\bmod p^{2k}$ for all primes $p \\ge 3$ and integers $n,k \\ge 1$, where $B_n$ is a sequence discovered by Zagier, known as Sequence $\\mathbf{B}$.\n  Additionally, for 14 of the 15 sequen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11839","kind":"arxiv","version":2},"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/2102.11839/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":"2102.11839","created_at":"2026-07-05T09:56:45.007569+00:00"},{"alias_kind":"arxiv_version","alias_value":"2102.11839v2","created_at":"2026-07-05T09:56:45.007569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11839","created_at":"2026-07-05T09:56:45.007569+00:00"},{"alias_kind":"pith_short_12","alias_value":"RK4C57UDXEG2","created_at":"2026-07-05T09:56:45.007569+00:00"},{"alias_kind":"pith_short_16","alias_value":"RK4C57UDXEG2XVEZ","created_at":"2026-07-05T09:56:45.007569+00:00"},{"alias_kind":"pith_short_8","alias_value":"RK4C57UD","created_at":"2026-07-05T09:56:45.007569+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/RK4C57UDXEG2XVEZPOTKK6JV6P","json":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P.json","graph_json":"https://pith.science/api/pith-number/RK4C57UDXEG2XVEZPOTKK6JV6P/graph.json","events_json":"https://pith.science/api/pith-number/RK4C57UDXEG2XVEZPOTKK6JV6P/events.json","paper":"https://pith.science/paper/RK4C57UD"},"agent_actions":{"view_html":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P","download_json":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P.json","view_paper":"https://pith.science/paper/RK4C57UD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2102.11839&json=true","fetch_graph":"https://pith.science/api/pith-number/RK4C57UDXEG2XVEZPOTKK6JV6P/graph.json","fetch_events":"https://pith.science/api/pith-number/RK4C57UDXEG2XVEZPOTKK6JV6P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/action/storage_attestation","attest_author":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/action/author_attestation","sign_citation":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/action/citation_signature","submit_replication":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/action/replication_record"}},"created_at":"2026-07-05T09:56:45.007569+00:00","updated_at":"2026-07-05T09:56:45.007569+00:00"}