{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U4XX2FLVE73HOIXDBHEJHFOEFL","short_pith_number":"pith:U4XX2FLV","canonical_record":{"source":{"id":"1307.3994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T15:36:10Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"5c672677c9e84195501c6a6b700f991cf0314745c87efd647f3fa31e1e79ae4b","abstract_canon_sha256":"119c516e141445457796ecd4efc25b382d603d0ead96eefb27c2beb6d0f6848a"},"schema_version":"1.0"},"canonical_sha256":"a72f7d157527f67722e309c89395c42adfc1897d14ae55b310fba415f6afa371","source":{"kind":"arxiv","id":"1307.3994","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3994","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3994v1","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3994","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"U4XX2FLVE73H","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4XX2FLVE73HOIXD","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4XX2FLV","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U4XX2FLVE73HOIXDBHEJHFOEFL","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T15:36:10Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"5c672677c9e84195501c6a6b700f991cf0314745c87efd647f3fa31e1e79ae4b","abstract_canon_sha256":"119c516e141445457796ecd4efc25b382d603d0ead96eefb27c2beb6d0f6848a"},"schema_version":"1.0"},"canonical_sha256":"a72f7d157527f67722e309c89395c42adfc1897d14ae55b310fba415f6afa371","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:27.239173Z","signature_b64":"OXU3OchfqgmMxggfu1Tnv29bG0Y0vwDXb9LPLOhjE3P58TmYGA7Ef/FQiOMO6FVDPohTraG71AMiC9ALFenZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a72f7d157527f67722e309c89395c42adfc1897d14ae55b310fba415f6afa371","last_reissued_at":"2026-05-18T03:18:27.238463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:27.238463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3994","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":"2026-05-18T03:18:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UzFlHQO0mmTI5hPV9QspE6AowsJfH3mAx2GYUDptmHlfg8yRk2GY4X4Zqgc8HmUGdqzM7Hc28Zdx/FYlg5IwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T06:12:40.682793Z"},"content_sha256":"d4eb040cf0e903f30c6498fc9045e9446e2e5c078967032da044667dbf182db5","schema_version":"1.0","event_id":"sha256:d4eb040cf0e903f30c6498fc9045e9446e2e5c078967032da044667dbf182db5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U4XX2FLVE73HOIXDBHEJHFOEFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the rank of the fibers of elliptic K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Cecilia Salgado","submitted_at":"2013-07-15T15:36:10Z","abstract_excerpt":"Let $X$ be an elliptic K3 surface endowed with two distinct Jacobian elliptic fibrations $\\pi_i$, $i=1,2$, defined over a number field $k$. We prove that there is an elliptic curve $C\\subset X$ such that the generic rank over $k$ of $X$ after a base extension by $C$ is strictly larger than the generic rank of $X$. Moreover, if the generic rank of $\\pi_j$ is positive then there are infinitely many fibers of $\\pi_i$ ($j\\neq i$) with rank at least the generic rank of $\\pi_i$ plus one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3994","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":"2026-05-18T03:18:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eg1KqpI4OrwRhJRh7W6+vDqMq/+EdE2AOpkjh7oRoTKPZWc7ee++hOb0TPMYmbG0o+j2DMjqheNOsEJuha5kAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T06:12:40.683135Z"},"content_sha256":"7d6ebd6a2b84bab0d08b8cb5bcabcfc038dc20dc6665b675da660d197f94c44d","schema_version":"1.0","event_id":"sha256:7d6ebd6a2b84bab0d08b8cb5bcabcfc038dc20dc6665b675da660d197f94c44d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4XX2FLVE73HOIXDBHEJHFOEFL/bundle.json","state_url":"https://pith.science/pith/U4XX2FLVE73HOIXDBHEJHFOEFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4XX2FLVE73HOIXDBHEJHFOEFL/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":"2026-06-26T06:12:40Z","links":{"resolver":"https://pith.science/pith/U4XX2FLVE73HOIXDBHEJHFOEFL","bundle":"https://pith.science/pith/U4XX2FLVE73HOIXDBHEJHFOEFL/bundle.json","state":"https://pith.science/pith/U4XX2FLVE73HOIXDBHEJHFOEFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4XX2FLVE73HOIXDBHEJHFOEFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U4XX2FLVE73HOIXDBHEJHFOEFL","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":"119c516e141445457796ecd4efc25b382d603d0ead96eefb27c2beb6d0f6848a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T15:36:10Z","title_canon_sha256":"5c672677c9e84195501c6a6b700f991cf0314745c87efd647f3fa31e1e79ae4b"},"schema_version":"1.0","source":{"id":"1307.3994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3994","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3994v1","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3994","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"U4XX2FLVE73H","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4XX2FLVE73HOIXD","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4XX2FLV","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:7d6ebd6a2b84bab0d08b8cb5bcabcfc038dc20dc6665b675da660d197f94c44d","target":"graph","created_at":"2026-05-18T03:18:27Z","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 $X$ be an elliptic K3 surface endowed with two distinct Jacobian elliptic fibrations $\\pi_i$, $i=1,2$, defined over a number field $k$. We prove that there is an elliptic curve $C\\subset X$ such that the generic rank over $k$ of $X$ after a base extension by $C$ is strictly larger than the generic rank of $X$. Moreover, if the generic rank of $\\pi_j$ is positive then there are infinitely many fibers of $\\pi_i$ ($j\\neq i$) with rank at least the generic rank of $\\pi_i$ plus one.","authors_text":"Cecilia Salgado","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T15:36:10Z","title":"On the rank of the fibers of elliptic K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3994","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:d4eb040cf0e903f30c6498fc9045e9446e2e5c078967032da044667dbf182db5","target":"record","created_at":"2026-05-18T03:18:27Z","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":"119c516e141445457796ecd4efc25b382d603d0ead96eefb27c2beb6d0f6848a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-15T15:36:10Z","title_canon_sha256":"5c672677c9e84195501c6a6b700f991cf0314745c87efd647f3fa31e1e79ae4b"},"schema_version":"1.0","source":{"id":"1307.3994","kind":"arxiv","version":1}},"canonical_sha256":"a72f7d157527f67722e309c89395c42adfc1897d14ae55b310fba415f6afa371","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a72f7d157527f67722e309c89395c42adfc1897d14ae55b310fba415f6afa371","first_computed_at":"2026-05-18T03:18:27.238463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:27.238463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OXU3OchfqgmMxggfu1Tnv29bG0Y0vwDXb9LPLOhjE3P58TmYGA7Ef/FQiOMO6FVDPohTraG71AMiC9ALFenZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:27.239173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4eb040cf0e903f30c6498fc9045e9446e2e5c078967032da044667dbf182db5","sha256:7d6ebd6a2b84bab0d08b8cb5bcabcfc038dc20dc6665b675da660d197f94c44d"],"state_sha256":"c61183073e2f15aa7ff92e45b87bdbcc378ddb655522b4ca61b791410f01fd92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"27LCE055Z69nW8p9RGrZLIzbFwL3nrbJEWhk63Q1m3JFZE1bfKBHk1HWJBIyTb4oxsHqdLZHEQXD6hsFttEgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T06:12:40.685111Z","bundle_sha256":"f0bd377c110429f44b9e33aebe33a7aca093803e28103828a8150b4990e25f38"}}