{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HKDPCJ7RWUZ7UT5V6OKHU3GVWB","short_pith_number":"pith:HKDPCJ7R","canonical_record":{"source":{"id":"1504.02343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T15:03:07Z","cross_cats_sorted":[],"title_canon_sha256":"31d746365d07e8f7e44d0b2729581e3ecdd4e7c1329aeb2e4113bd2d0587f15f","abstract_canon_sha256":"74346c6b4051b641ebccd7032bf45c9397f82c65c04eb69246ad50c3e4bca5ce"},"schema_version":"1.0"},"canonical_sha256":"3a86f127f1b533fa4fb5f3947a6cd5b04e2ddef9a60f12bd2a4f15e60391c007","source":{"kind":"arxiv","id":"1504.02343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02343","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02343v1","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02343","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"pith_short_12","alias_value":"HKDPCJ7RWUZ7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HKDPCJ7RWUZ7UT5V","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HKDPCJ7R","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HKDPCJ7RWUZ7UT5V6OKHU3GVWB","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T15:03:07Z","cross_cats_sorted":[],"title_canon_sha256":"31d746365d07e8f7e44d0b2729581e3ecdd4e7c1329aeb2e4113bd2d0587f15f","abstract_canon_sha256":"74346c6b4051b641ebccd7032bf45c9397f82c65c04eb69246ad50c3e4bca5ce"},"schema_version":"1.0"},"canonical_sha256":"3a86f127f1b533fa4fb5f3947a6cd5b04e2ddef9a60f12bd2a4f15e60391c007","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:13.566040Z","signature_b64":"SnK5t06dGPSOfcIfZLayf6ry6Hz06uohchFfPJp8ge9PC+D6D9prgoZf1nBP33jxP7Gf/E1shRhUXbCyURKcAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a86f127f1b533fa4fb5f3947a6cd5b04e2ddef9a60f12bd2a4f15e60391c007","last_reissued_at":"2026-05-18T01:11:13.565558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:13.565558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02343","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":"2026-05-18T01:11:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZNANYY/Ek75URiy6XJ+PPqflvYvpVQsX3dPo0N591EiREw4Qm6f6Lpr5/Qqy/XP0ScU9wqcotxhomsOwiXrHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T23:29:38.878666Z"},"content_sha256":"f12e70af1c9122b3c48762cc1723143b7f439c0436a353e71973f085963b6a9b","schema_version":"1.0","event_id":"sha256:f12e70af1c9122b3c48762cc1723143b7f439c0436a353e71973f085963b6a9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HKDPCJ7RWUZ7UT5V6OKHU3GVWB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hasse principle for generalised Kummer varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexei N. Skorobogatov, Yonatan Harpaz","submitted_at":"2015-04-09T15:03:07Z","abstract_excerpt":"The existence of rational points on Kummer varieties associated to 2-coverings of abelian varieties over number fields can sometimes be proved through the variation of the Selmer group in the family of quadratic twists of the underlying abelian variety, using an idea of Swinnerton-Dyer. Following Mazur and Rubin, we consider the case when the Galois action on the 2-torsion has a large image. Under mild additional hypotheses we prove the Hasse principle for the associated Kummer varieties assuming the finiteness of relevant Shafarevich-Tate groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02343","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":"2026-05-18T01:11:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TgM0fySTw1/MHUl0IV9ohoC95hC/d7mqY5So/4YlKNlo9u/o/mgxKiR9UE+YmrN/yn+S/DSW8TKgk89ft09mCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T23:29:38.879014Z"},"content_sha256":"f1b8b393af83f8635dc9ee85fb3ea1d6ea5d8adb65e068740d24f83ece3a8604","schema_version":"1.0","event_id":"sha256:f1b8b393af83f8635dc9ee85fb3ea1d6ea5d8adb65e068740d24f83ece3a8604"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKDPCJ7RWUZ7UT5V6OKHU3GVWB/bundle.json","state_url":"https://pith.science/pith/HKDPCJ7RWUZ7UT5V6OKHU3GVWB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKDPCJ7RWUZ7UT5V6OKHU3GVWB/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":"2026-07-02T23:29:38Z","links":{"resolver":"https://pith.science/pith/HKDPCJ7RWUZ7UT5V6OKHU3GVWB","bundle":"https://pith.science/pith/HKDPCJ7RWUZ7UT5V6OKHU3GVWB/bundle.json","state":"https://pith.science/pith/HKDPCJ7RWUZ7UT5V6OKHU3GVWB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKDPCJ7RWUZ7UT5V6OKHU3GVWB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HKDPCJ7RWUZ7UT5V6OKHU3GVWB","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":"74346c6b4051b641ebccd7032bf45c9397f82c65c04eb69246ad50c3e4bca5ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T15:03:07Z","title_canon_sha256":"31d746365d07e8f7e44d0b2729581e3ecdd4e7c1329aeb2e4113bd2d0587f15f"},"schema_version":"1.0","source":{"id":"1504.02343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02343","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02343v1","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02343","created_at":"2026-05-18T01:11:13Z"},{"alias_kind":"pith_short_12","alias_value":"HKDPCJ7RWUZ7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HKDPCJ7RWUZ7UT5V","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HKDPCJ7R","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:f1b8b393af83f8635dc9ee85fb3ea1d6ea5d8adb65e068740d24f83ece3a8604","target":"graph","created_at":"2026-05-18T01:11:13Z","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":"The existence of rational points on Kummer varieties associated to 2-coverings of abelian varieties over number fields can sometimes be proved through the variation of the Selmer group in the family of quadratic twists of the underlying abelian variety, using an idea of Swinnerton-Dyer. Following Mazur and Rubin, we consider the case when the Galois action on the 2-torsion has a large image. Under mild additional hypotheses we prove the Hasse principle for the associated Kummer varieties assuming the finiteness of relevant Shafarevich-Tate groups.","authors_text":"Alexei N. Skorobogatov, Yonatan Harpaz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T15:03:07Z","title":"Hasse principle for generalised Kummer varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02343","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:f12e70af1c9122b3c48762cc1723143b7f439c0436a353e71973f085963b6a9b","target":"record","created_at":"2026-05-18T01:11:13Z","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":"74346c6b4051b641ebccd7032bf45c9397f82c65c04eb69246ad50c3e4bca5ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T15:03:07Z","title_canon_sha256":"31d746365d07e8f7e44d0b2729581e3ecdd4e7c1329aeb2e4113bd2d0587f15f"},"schema_version":"1.0","source":{"id":"1504.02343","kind":"arxiv","version":1}},"canonical_sha256":"3a86f127f1b533fa4fb5f3947a6cd5b04e2ddef9a60f12bd2a4f15e60391c007","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a86f127f1b533fa4fb5f3947a6cd5b04e2ddef9a60f12bd2a4f15e60391c007","first_computed_at":"2026-05-18T01:11:13.565558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:13.565558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SnK5t06dGPSOfcIfZLayf6ry6Hz06uohchFfPJp8ge9PC+D6D9prgoZf1nBP33jxP7Gf/E1shRhUXbCyURKcAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:13.566040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f12e70af1c9122b3c48762cc1723143b7f439c0436a353e71973f085963b6a9b","sha256:f1b8b393af83f8635dc9ee85fb3ea1d6ea5d8adb65e068740d24f83ece3a8604"],"state_sha256":"c8d72d5ffd76638c235bbe7ebb11b92fd08168425093e3bc336de7259396ce33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gScyoy67KSTyEUNI4kd/oscWi4tWeyqUCCOfbiamMkhON4WVnWaSKtKQzM4WxJCsdXhaexL/wQ/dW9Y+jKwMBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T23:29:38.880971Z","bundle_sha256":"592f01033652db6429d0b10d757678df25bc6740e9258f9bd86a86be70ebc87a"}}