{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:RK4C57UDXEG2XVEZPOTKK6JV6P","short_pith_number":"pith:RK4C57UD","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"},"canonical_sha256":"8ab82efe83b90dabd4997ba6a57935f3c3185b0a56cceb2bc42453238ea5feaa","source":{"kind":"arxiv","id":"2102.11839","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.11839","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"2102.11839v2","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11839","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"RK4C57UDXEG2","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"pith_short_16","alias_value":"RK4C57UDXEG2XVEZ","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"pith_short_8","alias_value":"RK4C57UD","created_at":"2026-07-05T09:56:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:RK4C57UDXEG2XVEZPOTKK6JV6P","target":"record","payload":{"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"},"canonical_sha256":"8ab82efe83b90dabd4997ba6a57935f3c3185b0a56cceb2bc42453238ea5feaa","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"},"source_kind":"arxiv","source_id":"2102.11839","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aiv/APYbC8nmALMBwipLmPAfY5YxSHV+Gw/8Gaxnfsdn+wS6MR9h7jkkA7YwwpWtjPAt00x10nbIMdOaCx1YDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:54:44.395910Z"},"content_sha256":"82d33cea040585591709c46512e416f40c5e82e82c3f40f183bb236bfc544781","schema_version":"1.0","event_id":"sha256:82d33cea040585591709c46512e416f40c5e82e82c3f40f183bb236bfc544781"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:RK4C57UDXEG2XVEZPOTKK6JV6P","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"44oYFw41Xx8NyS2n4uL12kJDxrnAYnB0G95OjnCIn+CVG6y66NreS999kigFIcOCD1wO/FlneDPXfZ1C7l6aDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:54:44.396506Z"},"content_sha256":"6f08daf6622e531b0814e936b59f5c3f999eaa3c41bc24f968318efc6604017b","schema_version":"1.0","event_id":"sha256:6f08daf6622e531b0814e936b59f5c3f999eaa3c41bc24f968318efc6604017b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/bundle.json","state_url":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T13:54:44Z","links":{"resolver":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P","bundle":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/bundle.json","state":"https://pith.science/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RK4C57UDXEG2XVEZPOTKK6JV6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:RK4C57UDXEG2XVEZPOTKK6JV6P","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":"606fe0fd71c0a06cfa79e9e1e7c82f74a6ddb93c529388f5307220bd2df3368a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-23T18:14:26Z","title_canon_sha256":"4f24996314960eb074232db05f82bfa1f2b6011d80719578b24614d8cdc4a57c"},"schema_version":"1.0","source":{"id":"2102.11839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.11839","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"2102.11839v2","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11839","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"RK4C57UDXEG2","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"pith_short_16","alias_value":"RK4C57UDXEG2XVEZ","created_at":"2026-07-05T09:56:45Z"},{"alias_kind":"pith_short_8","alias_value":"RK4C57UD","created_at":"2026-07-05T09:56:45Z"}],"graph_snapshots":[{"event_id":"sha256:6f08daf6622e531b0814e936b59f5c3f999eaa3c41bc24f968318efc6604017b","target":"graph","created_at":"2026-07-05T09:56:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.11839/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Ofir Gorodetsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-23T18:14:26Z","title":"New representations for all sporadic Ap\\'ery-like sequences, with applications to congruences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11839","kind":"arxiv","version":2},"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":"sha256:82d33cea040585591709c46512e416f40c5e82e82c3f40f183bb236bfc544781","target":"record","created_at":"2026-07-05T09:56:45Z","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":"606fe0fd71c0a06cfa79e9e1e7c82f74a6ddb93c529388f5307220bd2df3368a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-23T18:14:26Z","title_canon_sha256":"4f24996314960eb074232db05f82bfa1f2b6011d80719578b24614d8cdc4a57c"},"schema_version":"1.0","source":{"id":"2102.11839","kind":"arxiv","version":2}},"canonical_sha256":"8ab82efe83b90dabd4997ba6a57935f3c3185b0a56cceb2bc42453238ea5feaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ab82efe83b90dabd4997ba6a57935f3c3185b0a56cceb2bc42453238ea5feaa","first_computed_at":"2026-07-05T09:56:45.007496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:45.007496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LlfySM+qRffqm/4/F9CSZstGwKBciCFC98Xnwwg+WS+2BODVO3VAzN6KOfsmUNhTnLzysS+xmQJNS/msf42dAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:45.008015Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.11839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82d33cea040585591709c46512e416f40c5e82e82c3f40f183bb236bfc544781","sha256:6f08daf6622e531b0814e936b59f5c3f999eaa3c41bc24f968318efc6604017b"],"state_sha256":"494295b4dd7c924fcfeba2c19ba6160a022d0e72f6650edd3ebe58446701c6f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5T0HXgyeNIsJeLj5scwm9AZrlPCFT2cBozJJPzYZsQcMhkHLOUpZM+vpAs/DAsWwL03+c3V9Vq13xIOMBEreAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:54:44.400227Z","bundle_sha256":"e4c9c1261828f226c622c6419beafb0bc201901ec1c405a9899fdc18ab4d9825"}}