{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4YMSFBZC4IBPKBZWJ3OHSKNJA6","short_pith_number":"pith:4YMSFBZC","canonical_record":{"source":{"id":"1706.05589","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-17T23:01:44Z","cross_cats_sorted":[],"title_canon_sha256":"8a420953281cf405865250b28d0ebe92b15fd9e2b3d1bf919e0c96e617e6896c","abstract_canon_sha256":"30e10f453c554b2bed0d0590c72565901702f567fe71382ecdac28fdc962ef53"},"schema_version":"1.0"},"canonical_sha256":"e619228722e202f507364edc7929a907a63225aec3fa6aeee72e2f103cb4eb4c","source":{"kind":"arxiv","id":"1706.05589","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05589","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05589v4","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05589","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"4YMSFBZC4IBP","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4YMSFBZC4IBPKBZW","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4YMSFBZC","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4YMSFBZC4IBPKBZWJ3OHSKNJA6","target":"record","payload":{"canonical_record":{"source":{"id":"1706.05589","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-17T23:01:44Z","cross_cats_sorted":[],"title_canon_sha256":"8a420953281cf405865250b28d0ebe92b15fd9e2b3d1bf919e0c96e617e6896c","abstract_canon_sha256":"30e10f453c554b2bed0d0590c72565901702f567fe71382ecdac28fdc962ef53"},"schema_version":"1.0"},"canonical_sha256":"e619228722e202f507364edc7929a907a63225aec3fa6aeee72e2f103cb4eb4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:04.809213Z","signature_b64":"uSARbTBUFLMYZMAZfnCzSoe6zxdeDmWVQu5XFfhyXr/STZ/jq9CxMMUBmg6pORZfJT7kiI6D+FH/ZGR2+leBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e619228722e202f507364edc7929a907a63225aec3fa6aeee72e2f103cb4eb4c","last_reissued_at":"2026-05-17T23:40:04.808519Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:04.808519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.05589","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zD1U84hmSF0BM7PTTenuHBsgGvptUir676r9UBgcpPWpTlnyrNF1V2qC7p94vJOUC6GIw7gy6oBLPddj6F0DDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:29:36.843822Z"},"content_sha256":"4aa18cf5d04925121662be744536b1855e4f7f311475e6c0285ed88824e2632d","schema_version":"1.0","event_id":"sha256:4aa18cf5d04925121662be744536b1855e4f7f311475e6c0285ed88824e2632d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4YMSFBZC4IBPKBZWJ3OHSKNJA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher congruences between newforms and Eisenstein series of squarefree level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. Hsu","submitted_at":"2017-06-17T23:01:44Z","abstract_excerpt":"Let $p\\geq 5$ be prime. For elliptic modular forms of weight 2 and level $\\Gamma_0(N)$ where $N>6$ is squarefree, we bound the depth of Eisenstein congruences modulo $p$ (from below) by a generalized Bernoulli number with correction factors and show how this depth detects the local non-principality of the Eisenstein ideal. We then use admissibility results of Ribet and Yoo to give an infinite class of examples where the Eisenstein ideal is not locally principal. Lastly, we illustrate these results with explicit computations and give an interesting commutative algebra application related to Hil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05589","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7VDnSD4E8jqnJe2XLU/PqzoeZdpe89RuXiIC/qMa11o/D3OpNFHu9L4+Xh3j2hKQXw047EoDCtY4yQOqIKKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:29:36.844527Z"},"content_sha256":"0c4ee52b4169806cee9d5c31873a25c40fb171756891832de5e3d392a995573c","schema_version":"1.0","event_id":"sha256:0c4ee52b4169806cee9d5c31873a25c40fb171756891832de5e3d392a995573c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YMSFBZC4IBPKBZWJ3OHSKNJA6/bundle.json","state_url":"https://pith.science/pith/4YMSFBZC4IBPKBZWJ3OHSKNJA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YMSFBZC4IBPKBZWJ3OHSKNJA6/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":"2026-06-07T15:29:36Z","links":{"resolver":"https://pith.science/pith/4YMSFBZC4IBPKBZWJ3OHSKNJA6","bundle":"https://pith.science/pith/4YMSFBZC4IBPKBZWJ3OHSKNJA6/bundle.json","state":"https://pith.science/pith/4YMSFBZC4IBPKBZWJ3OHSKNJA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YMSFBZC4IBPKBZWJ3OHSKNJA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4YMSFBZC4IBPKBZWJ3OHSKNJA6","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":"30e10f453c554b2bed0d0590c72565901702f567fe71382ecdac28fdc962ef53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-17T23:01:44Z","title_canon_sha256":"8a420953281cf405865250b28d0ebe92b15fd9e2b3d1bf919e0c96e617e6896c"},"schema_version":"1.0","source":{"id":"1706.05589","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05589","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05589v4","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05589","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"4YMSFBZC4IBP","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4YMSFBZC4IBPKBZW","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4YMSFBZC","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:0c4ee52b4169806cee9d5c31873a25c40fb171756891832de5e3d392a995573c","target":"graph","created_at":"2026-05-17T23:40:04Z","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":"Let $p\\geq 5$ be prime. For elliptic modular forms of weight 2 and level $\\Gamma_0(N)$ where $N>6$ is squarefree, we bound the depth of Eisenstein congruences modulo $p$ (from below) by a generalized Bernoulli number with correction factors and show how this depth detects the local non-principality of the Eisenstein ideal. We then use admissibility results of Ribet and Yoo to give an infinite class of examples where the Eisenstein ideal is not locally principal. Lastly, we illustrate these results with explicit computations and give an interesting commutative algebra application related to Hil","authors_text":"C. Hsu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-17T23:01:44Z","title":"Higher congruences between newforms and Eisenstein series of squarefree level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05589","kind":"arxiv","version":4},"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":"sha256:4aa18cf5d04925121662be744536b1855e4f7f311475e6c0285ed88824e2632d","target":"record","created_at":"2026-05-17T23:40:04Z","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":"30e10f453c554b2bed0d0590c72565901702f567fe71382ecdac28fdc962ef53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-17T23:01:44Z","title_canon_sha256":"8a420953281cf405865250b28d0ebe92b15fd9e2b3d1bf919e0c96e617e6896c"},"schema_version":"1.0","source":{"id":"1706.05589","kind":"arxiv","version":4}},"canonical_sha256":"e619228722e202f507364edc7929a907a63225aec3fa6aeee72e2f103cb4eb4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e619228722e202f507364edc7929a907a63225aec3fa6aeee72e2f103cb4eb4c","first_computed_at":"2026-05-17T23:40:04.808519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:04.808519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uSARbTBUFLMYZMAZfnCzSoe6zxdeDmWVQu5XFfhyXr/STZ/jq9CxMMUBmg6pORZfJT7kiI6D+FH/ZGR2+leBAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:04.809213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05589","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aa18cf5d04925121662be744536b1855e4f7f311475e6c0285ed88824e2632d","sha256:0c4ee52b4169806cee9d5c31873a25c40fb171756891832de5e3d392a995573c"],"state_sha256":"2041704390ac25abf4daaf40ad830260294df1d9b0d03f57b2a0a5d9fbb22470"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WP9MiSi65zEGoAhWOnkAV8iHljXRFnaG3y92qhxVNbyBJHFUEujKFdp2k0NpjxAIcm2A+kum43RT9TgGJs5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T15:29:36.848819Z","bundle_sha256":"7168d45898597bc665947088db5692bdd1a1016ecbb6076e69ee0d3c2ecf8d18"}}