{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YO3P3RFLK34YYG42CA3MRWZGFL","short_pith_number":"pith:YO3P3RFL","canonical_record":{"source":{"id":"1404.2849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-10T15:35:26Z","cross_cats_sorted":[],"title_canon_sha256":"8a5d2274b8445f706af2753f480b5dd9f98ed88f6da812382db7527173793493","abstract_canon_sha256":"0be89481f8d0d2f19ba9bcefaade3f13b7536d6728f7302bb34346331ac7bfc4"},"schema_version":"1.0"},"canonical_sha256":"c3b6fdc4ab56f98c1b9a1036c8db262ace534573d650ceb6b523b2753eb02124","source":{"kind":"arxiv","id":"1404.2849","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2849","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2849v1","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2849","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"YO3P3RFLK34Y","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YO3P3RFLK34YYG42","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YO3P3RFL","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YO3P3RFLK34YYG42CA3MRWZGFL","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-10T15:35:26Z","cross_cats_sorted":[],"title_canon_sha256":"8a5d2274b8445f706af2753f480b5dd9f98ed88f6da812382db7527173793493","abstract_canon_sha256":"0be89481f8d0d2f19ba9bcefaade3f13b7536d6728f7302bb34346331ac7bfc4"},"schema_version":"1.0"},"canonical_sha256":"c3b6fdc4ab56f98c1b9a1036c8db262ace534573d650ceb6b523b2753eb02124","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:28.372285Z","signature_b64":"fBAANQjNAvW8P5V1ztbcJYqNjOTlE+Hf42n3set/zHFN4WlPUf8d7VjerrETQLdEfMKVX+RRwOc5J8SGS/HVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3b6fdc4ab56f98c1b9a1036c8db262ace534573d650ceb6b523b2753eb02124","last_reissued_at":"2026-05-18T02:54:28.371629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:28.371629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2849","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":"2026-05-18T02:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pyWtL74UFArSJiLTl2gTRvtC9kKNLty1n+K212LrPsYrONDUOFqAq2u+Yw72qZbbEwJnWAqjD6zXb6NTLM2SCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:20:27.799133Z"},"content_sha256":"9d9c54581d704dfb133294d9f7b2eeec477881cf42b013b4047a14c4391b9a73","schema_version":"1.0","event_id":"sha256:9d9c54581d704dfb133294d9f7b2eeec477881cf42b013b4047a14c4391b9a73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YO3P3RFLK34YYG42CA3MRWZGFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Finitary Hasse Principle for Diagonal Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean Bourgain, Michael Larsen","submitted_at":"2014-04-10T15:35:26Z","abstract_excerpt":"We prove a Hasse principle for solving equations of the form ax+by+cz=0 where x, y, z belong to a given finite index subgroup of the multiplicative group of rational numbers. From this we deduce a Hasse principle for diagonal curves over fields of algebraic numbers with finitely generated Galois group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2849","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":""},"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":"2026-05-18T02:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQAzjLybPjxxjpXxHjs38oiviCulWAn8RyAlZxNV+2Ptqywv5g1AlLo3wMUmTEIyFIdIYeSeBfvXpt7rMmlcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:20:27.799724Z"},"content_sha256":"8dc6a5ff3e5de6adf120ac329a7e1b6c9d23bdb2928acc4d544e27676a4f51f7","schema_version":"1.0","event_id":"sha256:8dc6a5ff3e5de6adf120ac329a7e1b6c9d23bdb2928acc4d544e27676a4f51f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YO3P3RFLK34YYG42CA3MRWZGFL/bundle.json","state_url":"https://pith.science/pith/YO3P3RFLK34YYG42CA3MRWZGFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YO3P3RFLK34YYG42CA3MRWZGFL/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":"2026-05-29T20:20:27Z","links":{"resolver":"https://pith.science/pith/YO3P3RFLK34YYG42CA3MRWZGFL","bundle":"https://pith.science/pith/YO3P3RFLK34YYG42CA3MRWZGFL/bundle.json","state":"https://pith.science/pith/YO3P3RFLK34YYG42CA3MRWZGFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YO3P3RFLK34YYG42CA3MRWZGFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YO3P3RFLK34YYG42CA3MRWZGFL","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":"0be89481f8d0d2f19ba9bcefaade3f13b7536d6728f7302bb34346331ac7bfc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-10T15:35:26Z","title_canon_sha256":"8a5d2274b8445f706af2753f480b5dd9f98ed88f6da812382db7527173793493"},"schema_version":"1.0","source":{"id":"1404.2849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2849","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2849v1","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2849","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"YO3P3RFLK34Y","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YO3P3RFLK34YYG42","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YO3P3RFL","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:8dc6a5ff3e5de6adf120ac329a7e1b6c9d23bdb2928acc4d544e27676a4f51f7","target":"graph","created_at":"2026-05-18T02:54:28Z","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 prove a Hasse principle for solving equations of the form ax+by+cz=0 where x, y, z belong to a given finite index subgroup of the multiplicative group of rational numbers. From this we deduce a Hasse principle for diagonal curves over fields of algebraic numbers with finitely generated Galois group.","authors_text":"Jean Bourgain, Michael Larsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-10T15:35:26Z","title":"A Finitary Hasse Principle for Diagonal Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2849","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":"sha256:9d9c54581d704dfb133294d9f7b2eeec477881cf42b013b4047a14c4391b9a73","target":"record","created_at":"2026-05-18T02:54:28Z","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":"0be89481f8d0d2f19ba9bcefaade3f13b7536d6728f7302bb34346331ac7bfc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-10T15:35:26Z","title_canon_sha256":"8a5d2274b8445f706af2753f480b5dd9f98ed88f6da812382db7527173793493"},"schema_version":"1.0","source":{"id":"1404.2849","kind":"arxiv","version":1}},"canonical_sha256":"c3b6fdc4ab56f98c1b9a1036c8db262ace534573d650ceb6b523b2753eb02124","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3b6fdc4ab56f98c1b9a1036c8db262ace534573d650ceb6b523b2753eb02124","first_computed_at":"2026-05-18T02:54:28.371629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:28.371629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fBAANQjNAvW8P5V1ztbcJYqNjOTlE+Hf42n3set/zHFN4WlPUf8d7VjerrETQLdEfMKVX+RRwOc5J8SGS/HVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:28.372285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d9c54581d704dfb133294d9f7b2eeec477881cf42b013b4047a14c4391b9a73","sha256:8dc6a5ff3e5de6adf120ac329a7e1b6c9d23bdb2928acc4d544e27676a4f51f7"],"state_sha256":"fdc1d04a9e8e7c73e19c3d3144713fb78b5291e4c40ce147a4420047f3a5780e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NK8b9+oN8GZ0ov+EVp3k7YxHmLR2GHETtfoEdbjiV3LP1oubblyeAwuELyNwXFjCI+4Buj7abs0NF5JGW6IfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:20:27.802836Z","bundle_sha256":"9d47605ffddc6c2305fe344f6b61fcb86b4611683c64704aaa437fe81bb61c93"}}