{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:F5BTJ5VKS4N2EKG7MCMQZMR3MA","short_pith_number":"pith:F5BTJ5VK","canonical_record":{"source":{"id":"math/0609465","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-09-16T17:55:39Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ca783410a15f8d8d8a128d60593139579e62c35edaf0c153c8291f298b882106","abstract_canon_sha256":"1bfce09c5248276c2f035d7394a93c1879445801afd793747c1aed388cb43109"},"schema_version":"1.0"},"canonical_sha256":"2f4334f6aa971ba228df60990cb23b6019c5290d51d7e5549207c427db044172","source":{"kind":"arxiv","id":"math/0609465","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609465","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609465v1","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609465","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"F5BTJ5VKS4N2","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"pith_short_16","alias_value":"F5BTJ5VKS4N2EKG7","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"pith_short_8","alias_value":"F5BTJ5VK","created_at":"2026-07-04T14:56:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:F5BTJ5VKS4N2EKG7MCMQZMR3MA","target":"record","payload":{"canonical_record":{"source":{"id":"math/0609465","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-09-16T17:55:39Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ca783410a15f8d8d8a128d60593139579e62c35edaf0c153c8291f298b882106","abstract_canon_sha256":"1bfce09c5248276c2f035d7394a93c1879445801afd793747c1aed388cb43109"},"schema_version":"1.0"},"canonical_sha256":"2f4334f6aa971ba228df60990cb23b6019c5290d51d7e5549207c427db044172","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:56:34.422899Z","signature_b64":"+uTvlEX3K2lv1Ecnna2kg+bKpjNso3oO2dE25l8ii6BSjhivBQEIhQdvHOLCrnc2JeBnwoy42/ACL+IIQRf2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f4334f6aa971ba228df60990cb23b6019c5290d51d7e5549207c427db044172","last_reissued_at":"2026-07-04T14:56:34.422511Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:56:34.422511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0609465","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P0pa+yfrTSZVy2ddJRZG/S4Jbs+oHCt9ISnfGlgWKr1hkt+uqRanZSkibn6zFymbzGfT6UuQk5YTpCwDdoxvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T23:07:01.525790Z"},"content_sha256":"2ba638a4017c335862b7b63bdccdfcf40d356190ea8fbeb17a82b1022f699242","schema_version":"1.0","event_id":"sha256:2ba638a4017c335862b7b63bdccdfcf40d356190ea8fbeb17a82b1022f699242"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:F5BTJ5VKS4N2EKG7MCMQZMR3MA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An \"Anti-Hasse Principle\" for Prime Twists","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Pete L. Clark","submitted_at":"2006-09-16T17:55:39Z","abstract_excerpt":"Given an algebraic curve C/Q having points everywhere locally and endowed with a suitable involution, we show that there exists a positive density family of prime quadratic twists of C violating the Hasse principle. The result applies in particular to w_N-Atkin-Lehner twists of most modular curves X_0(N) and to w_p-Atkin-Lehner twists of certain Shimura curves X^{D+}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609465","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/math/0609465/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":"2026-07-04T14:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W1R+iPugSRBJV6Tt+C1e7erGFuZMPuWtzQvgg5KOc1H5bZeTwlXq3MFYkNS6H/EQx++sFbIS8I4PSDJE+QHDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T23:07:01.526334Z"},"content_sha256":"0e25fa500c040be8dc216210e409404e0154f9e1d5ea4669833279ac332b196a","schema_version":"1.0","event_id":"sha256:0e25fa500c040be8dc216210e409404e0154f9e1d5ea4669833279ac332b196a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5BTJ5VKS4N2EKG7MCMQZMR3MA/bundle.json","state_url":"https://pith.science/pith/F5BTJ5VKS4N2EKG7MCMQZMR3MA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5BTJ5VKS4N2EKG7MCMQZMR3MA/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":"2026-08-04T23:07:01Z","links":{"resolver":"https://pith.science/pith/F5BTJ5VKS4N2EKG7MCMQZMR3MA","bundle":"https://pith.science/pith/F5BTJ5VKS4N2EKG7MCMQZMR3MA/bundle.json","state":"https://pith.science/pith/F5BTJ5VKS4N2EKG7MCMQZMR3MA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5BTJ5VKS4N2EKG7MCMQZMR3MA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:F5BTJ5VKS4N2EKG7MCMQZMR3MA","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":"1bfce09c5248276c2f035d7394a93c1879445801afd793747c1aed388cb43109","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2006-09-16T17:55:39Z","title_canon_sha256":"ca783410a15f8d8d8a128d60593139579e62c35edaf0c153c8291f298b882106"},"schema_version":"1.0","source":{"id":"math/0609465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609465","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609465v1","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609465","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"F5BTJ5VKS4N2","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"pith_short_16","alias_value":"F5BTJ5VKS4N2EKG7","created_at":"2026-07-04T14:56:34Z"},{"alias_kind":"pith_short_8","alias_value":"F5BTJ5VK","created_at":"2026-07-04T14:56:34Z"}],"graph_snapshots":[{"event_id":"sha256:0e25fa500c040be8dc216210e409404e0154f9e1d5ea4669833279ac332b196a","target":"graph","created_at":"2026-07-04T14:56:34Z","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/math/0609465/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given an algebraic curve C/Q having points everywhere locally and endowed with a suitable involution, we show that there exists a positive density family of prime quadratic twists of C violating the Hasse principle. The result applies in particular to w_N-Atkin-Lehner twists of most modular curves X_0(N) and to w_p-Atkin-Lehner twists of certain Shimura curves X^{D+}.","authors_text":"Pete L. Clark","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2006-09-16T17:55:39Z","title":"An \"Anti-Hasse Principle\" for Prime Twists"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609465","kind":"arxiv","version":1},"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":"sha256:2ba638a4017c335862b7b63bdccdfcf40d356190ea8fbeb17a82b1022f699242","target":"record","created_at":"2026-07-04T14:56:34Z","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":"1bfce09c5248276c2f035d7394a93c1879445801afd793747c1aed388cb43109","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2006-09-16T17:55:39Z","title_canon_sha256":"ca783410a15f8d8d8a128d60593139579e62c35edaf0c153c8291f298b882106"},"schema_version":"1.0","source":{"id":"math/0609465","kind":"arxiv","version":1}},"canonical_sha256":"2f4334f6aa971ba228df60990cb23b6019c5290d51d7e5549207c427db044172","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f4334f6aa971ba228df60990cb23b6019c5290d51d7e5549207c427db044172","first_computed_at":"2026-07-04T14:56:34.422511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:56:34.422511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+uTvlEX3K2lv1Ecnna2kg+bKpjNso3oO2dE25l8ii6BSjhivBQEIhQdvHOLCrnc2JeBnwoy42/ACL+IIQRf2Dw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:56:34.422899Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ba638a4017c335862b7b63bdccdfcf40d356190ea8fbeb17a82b1022f699242","sha256:0e25fa500c040be8dc216210e409404e0154f9e1d5ea4669833279ac332b196a"],"state_sha256":"a550b8f3d2100b4ebc7bd222e32355d7dac5c1582ace6e4c4ff244877227065e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d4vJatvxk9VTf6IcNmTjR/Ll5IprWV41YUe6d8aF3sZ66/+eerwHNA9qZDoyJvrAPQfhi9YkT08lzOsk5VvMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T23:07:01.532279Z","bundle_sha256":"a91303ce2fb30023be7d613e9d5bdefb28c978ce5c2a8168058f0ca068b36ea1"}}