{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QU7WVYASTS6LJDX4MW2BFGXWRW","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":"70f83ef29ec81bff4c08effa4aa6fb54eec576957ee05263442fee6ebed003a2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-07-29T23:59:29Z","title_canon_sha256":"4f95ad1a3b68c5a3e10056f2bd7ca877bdbf69d1a065145867e60f8e17adae5e"},"schema_version":"1.0","source":{"id":"2407.20468","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.20468","created_at":"2026-07-05T09:37:55Z"},{"alias_kind":"arxiv_version","alias_value":"2407.20468v2","created_at":"2026-07-05T09:37:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20468","created_at":"2026-07-05T09:37:55Z"},{"alias_kind":"pith_short_12","alias_value":"QU7WVYASTS6L","created_at":"2026-07-05T09:37:55Z"},{"alias_kind":"pith_short_16","alias_value":"QU7WVYASTS6LJDX4","created_at":"2026-07-05T09:37:55Z"},{"alias_kind":"pith_short_8","alias_value":"QU7WVYAS","created_at":"2026-07-05T09:37:55Z"}],"graph_snapshots":[{"event_id":"sha256:897b57b4fd3ef535734cde650f85e409e580c86f1ab697946a86e827bb5f27e0","target":"graph","created_at":"2026-07-05T09:37:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.20468/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let E be an elliptic curve over a number field F, A the abelian surface E x E, and T_F(A) the F-rational albanese kernel of A, which is a subgroup of the degree zero part of Chow group of zero cycles on A modulo rational equivalence. The first result is that for all but a finite number of primes p where E has ordinary reduction, the image of T_F(A)/p in the Galois cohomology group H^2(F, sym^2(E[p])) is zero; here E[p] denotes as usual the Galois module of p-division points on E. The second result is that for any prime p where E has good ordinary reduction, there is a finite extension K of F, ","authors_text":"Dinakar Ramakrishnan","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-07-29T23:59:29Z","title":"Global Galois Symbols on E x E"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20468","kind":"arxiv","version":2},"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:ee60826a66fb82a39a9338f524e8ac01dc5f69d2ecc90ea33fa314204e64e929","target":"record","created_at":"2026-07-05T09:37:55Z","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":"70f83ef29ec81bff4c08effa4aa6fb54eec576957ee05263442fee6ebed003a2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-07-29T23:59:29Z","title_canon_sha256":"4f95ad1a3b68c5a3e10056f2bd7ca877bdbf69d1a065145867e60f8e17adae5e"},"schema_version":"1.0","source":{"id":"2407.20468","kind":"arxiv","version":2}},"canonical_sha256":"853f6ae0129cbcb48efc65b4129af68d901f430b9c58da58dfb88dabaaa66ec5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"853f6ae0129cbcb48efc65b4129af68d901f430b9c58da58dfb88dabaaa66ec5","first_computed_at":"2026-07-05T09:37:55.766950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:37:55.766950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Fox5CDpYNd0TIV/e44a3tgDY458YjYkPAcR8O6t4SZu3yru9MMuNK2DH98yKPBXPSMQb63BucQW+bolFTGXCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:37:55.767440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.20468","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee60826a66fb82a39a9338f524e8ac01dc5f69d2ecc90ea33fa314204e64e929","sha256:897b57b4fd3ef535734cde650f85e409e580c86f1ab697946a86e827bb5f27e0"],"state_sha256":"627219547a63dd619ca244233b4a11d4e77b04117ce6f528018b0202bfbc7b16"}