{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QKKPJFQXEU4TCGIMTST4KJISSC","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":"5a6c1772ac8800a4786f7e909108adc3729bf0b35069d9797f078d9cdaed6f21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-20T17:51:55Z","title_canon_sha256":"3ead8ecca42ea09be4b061ee030880d6ea2d17095497ee7cb8d05bdb5da07fe1"},"schema_version":"1.0","source":{"id":"1601.05348","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05348","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05348v3","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05348","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"pith_short_12","alias_value":"QKKPJFQXEU4T","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QKKPJFQXEU4TCGIM","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QKKPJFQX","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:9481c6fdd229db262de5c9e8f574dbcff3d36d2ccd9ab70f8d5a6be279f043da","target":"graph","created_at":"2026-05-18T01:20:55Z","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 generalize a result of Frey [Fre88] on the Selmer group of twists of elliptic curves over Q with Q-rational torsion points to elliptic curves defined over number fields of small degree K with a K-rational point. We also provide examples of elliptic curves coming from [Zyw15] that satisfy the conditions of our Theorem B.","authors_text":"Jackson S. Morrow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-20T17:51:55Z","title":"Selmer groups of twists of elliptic curves over K with K-rational torsion points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05348","kind":"arxiv","version":3},"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":"sha256:28a327fdc484e2968657b5491f39fe63715647124c97c2073d487a83cedb3352","target":"record","created_at":"2026-05-18T01:20:55Z","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":"5a6c1772ac8800a4786f7e909108adc3729bf0b35069d9797f078d9cdaed6f21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-20T17:51:55Z","title_canon_sha256":"3ead8ecca42ea09be4b061ee030880d6ea2d17095497ee7cb8d05bdb5da07fe1"},"schema_version":"1.0","source":{"id":"1601.05348","kind":"arxiv","version":3}},"canonical_sha256":"8294f49617253931190c9ca7c52512908c823b5631e9d44f10f38e336b8f4d67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8294f49617253931190c9ca7c52512908c823b5631e9d44f10f38e336b8f4d67","first_computed_at":"2026-05-18T01:20:55.458665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:55.458665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hBDK5g4Qys9V8HqN4ZP0i0x1iwfxSNSjSB8m+9l7U5CJUgWA3v1W4dUYPpl1lKsCB3lrIJezXYDrw0GF+7NsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:55.459310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05348","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28a327fdc484e2968657b5491f39fe63715647124c97c2073d487a83cedb3352","sha256:9481c6fdd229db262de5c9e8f574dbcff3d36d2ccd9ab70f8d5a6be279f043da"],"state_sha256":"30d34bd0139abb4632b5dbb54d928c25a44261b520afecfd2c7f2bd8a3979056"}