{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:M2GQBUX4M6TGOFCUYXIRE37IEU","short_pith_number":"pith:M2GQBUX4","canonical_record":{"source":{"id":"1205.5077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-23T00:27:36Z","cross_cats_sorted":[],"title_canon_sha256":"90aad8664dd2c1ca2399e68350b2a003b38c8d9594e2f0c6cf6fbd37453ad7c9","abstract_canon_sha256":"292cdb5927eae9a040f6b120454653e7f8ed39672997db762daabf94fcfb3516"},"schema_version":"1.0"},"canonical_sha256":"668d00d2fc67a6671454c5d1126fe8252820e000bbc8d5a4b19e0397531b8e5b","source":{"kind":"arxiv","id":"1205.5077","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5077","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5077v2","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5077","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"M2GQBUX4M6TG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M2GQBUX4M6TGOFCU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M2GQBUX4","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:M2GQBUX4M6TGOFCUYXIRE37IEU","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-23T00:27:36Z","cross_cats_sorted":[],"title_canon_sha256":"90aad8664dd2c1ca2399e68350b2a003b38c8d9594e2f0c6cf6fbd37453ad7c9","abstract_canon_sha256":"292cdb5927eae9a040f6b120454653e7f8ed39672997db762daabf94fcfb3516"},"schema_version":"1.0"},"canonical_sha256":"668d00d2fc67a6671454c5d1126fe8252820e000bbc8d5a4b19e0397531b8e5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:36.429212Z","signature_b64":"H9DiE0egl6NNI/q+ym7wz841WOwsNOpVIPJh0IHLEhb0SKAyzfvtgKk4jVgrFekYYodWDnTX8wSktX8N+itABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"668d00d2fc67a6671454c5d1126fe8252820e000bbc8d5a4b19e0397531b8e5b","last_reissued_at":"2026-05-18T01:14:36.428492Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:36.428492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5077","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":"2026-05-18T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yudcZiBfBQns9PYJ10iPqvyx0kIJZtmOw1VCYu1zeBrMN1uSVaoQnaAdYfNP6DCjU1QwaNc8MeAw6rVbYIKyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:38:41.057277Z"},"content_sha256":"3aa2a6b93bb9372ed3040a26ff3db9bb0135fe5b7ac46999b0c7744bb1eb4c5d","schema_version":"1.0","event_id":"sha256:3aa2a6b93bb9372ed3040a26ff3db9bb0135fe5b7ac46999b0c7744bb1eb4c5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:M2GQBUX4M6TGOFCUYXIRE37IEU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing weight one modular forms over $\\C$ and $\\Fpbar$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kevin Buzzard","submitted_at":"2012-05-23T00:27:36Z","abstract_excerpt":"We report on a systematic computation of weight one cuspidal eigenforms for the group $\\Gamma_1(N)$ in characteristic zero and in characteristic $p>2$. Perhaps the most surprising result was the existence of a mod 199 weight~1 cusp form of level 82 which does not lift to characteristic zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5077","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":""},"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":"2026-05-18T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TeBCF0QC0ji+QYSLiWGQbraT6NueWCRHlln6NW3zMVWxqrs4S4fgl1Duxboihtl3as4adMmyrIOkWb7S7mxsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:38:41.057638Z"},"content_sha256":"d2434eb5b07651898572b170be26c43d25679b21dced04402e4461436f1e9f7b","schema_version":"1.0","event_id":"sha256:d2434eb5b07651898572b170be26c43d25679b21dced04402e4461436f1e9f7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2GQBUX4M6TGOFCUYXIRE37IEU/bundle.json","state_url":"https://pith.science/pith/M2GQBUX4M6TGOFCUYXIRE37IEU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2GQBUX4M6TGOFCUYXIRE37IEU/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":"2026-06-03T16:38:41Z","links":{"resolver":"https://pith.science/pith/M2GQBUX4M6TGOFCUYXIRE37IEU","bundle":"https://pith.science/pith/M2GQBUX4M6TGOFCUYXIRE37IEU/bundle.json","state":"https://pith.science/pith/M2GQBUX4M6TGOFCUYXIRE37IEU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2GQBUX4M6TGOFCUYXIRE37IEU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M2GQBUX4M6TGOFCUYXIRE37IEU","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":"292cdb5927eae9a040f6b120454653e7f8ed39672997db762daabf94fcfb3516","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-23T00:27:36Z","title_canon_sha256":"90aad8664dd2c1ca2399e68350b2a003b38c8d9594e2f0c6cf6fbd37453ad7c9"},"schema_version":"1.0","source":{"id":"1205.5077","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5077","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5077v2","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5077","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"M2GQBUX4M6TG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M2GQBUX4M6TGOFCU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M2GQBUX4","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:d2434eb5b07651898572b170be26c43d25679b21dced04402e4461436f1e9f7b","target":"graph","created_at":"2026-05-18T01:14:36Z","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 report on a systematic computation of weight one cuspidal eigenforms for the group $\\Gamma_1(N)$ in characteristic zero and in characteristic $p>2$. Perhaps the most surprising result was the existence of a mod 199 weight~1 cusp form of level 82 which does not lift to characteristic zero.","authors_text":"Kevin Buzzard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-23T00:27:36Z","title":"Computing weight one modular forms over $\\C$ and $\\Fpbar$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5077","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":"sha256:3aa2a6b93bb9372ed3040a26ff3db9bb0135fe5b7ac46999b0c7744bb1eb4c5d","target":"record","created_at":"2026-05-18T01:14:36Z","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":"292cdb5927eae9a040f6b120454653e7f8ed39672997db762daabf94fcfb3516","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-23T00:27:36Z","title_canon_sha256":"90aad8664dd2c1ca2399e68350b2a003b38c8d9594e2f0c6cf6fbd37453ad7c9"},"schema_version":"1.0","source":{"id":"1205.5077","kind":"arxiv","version":2}},"canonical_sha256":"668d00d2fc67a6671454c5d1126fe8252820e000bbc8d5a4b19e0397531b8e5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"668d00d2fc67a6671454c5d1126fe8252820e000bbc8d5a4b19e0397531b8e5b","first_computed_at":"2026-05-18T01:14:36.428492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:36.428492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H9DiE0egl6NNI/q+ym7wz841WOwsNOpVIPJh0IHLEhb0SKAyzfvtgKk4jVgrFekYYodWDnTX8wSktX8N+itABA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:36.429212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5077","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3aa2a6b93bb9372ed3040a26ff3db9bb0135fe5b7ac46999b0c7744bb1eb4c5d","sha256:d2434eb5b07651898572b170be26c43d25679b21dced04402e4461436f1e9f7b"],"state_sha256":"c4563fa5a719b1f7b34dbb4319c1bbe6e8722f219949753c6b60273257c5822e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2tc3wJMLm9Xrqmkjg0NYiuxDeZ+u0wN6YaF/WQr/+n43L3QSYCMwj7MpCkCly/VQy4/Zz58ZQbpdsIDCYN/DBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:38:41.059598Z","bundle_sha256":"8a74dfcc27974d3ae1024f6c4b21313b3951d27139eb3c3ead3140b14442caee"}}