{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:QB444EMLSMVDI7PV4JC3ERMHWQ","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":"301a13193475f6099bce58c8ecb382d1127c4c5ec97c1de9a46bcb0317d4f6f1","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-02-13T12:20:01Z","title_canon_sha256":"88dbd39e75e76236112e95ab50fd9955172e30bc0bf78aae7a6ab25f99be8ee5"},"schema_version":"1.0","source":{"id":"math/0502261","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502261","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502261v1","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502261","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"QB444EMLSMVD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"QB444EMLSMVDI7PV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"QB444EML","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:c5dea50ae5838a69d9940e44a943225d726cff108d42e363e0ae0b8f0936171b","target":"graph","created_at":"2026-05-18T01:05:23Z","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":"If A/K is an abelian variety over a number field and P and Q are rational points, the original support conjecture asserted that if the order of Q (mod p) divides the order of P (mod p) for almost all primes p of K, then Q is obtained from P by applying an endomorphism of A. This is now known to be untrue. In this note we prove that it is not even true modulo the torsion of A.","authors_text":"Michael Larsen, Ren\\'e Schoof","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2005-02-13T12:20:01Z","title":"A refined counter-example to the support conjecture for abelian varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502261","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:d68779b37d7f5bd0271b4194033156e8107e4b6abae5be98ab730e5a025fb8d9","target":"record","created_at":"2026-05-18T01:05:23Z","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":"301a13193475f6099bce58c8ecb382d1127c4c5ec97c1de9a46bcb0317d4f6f1","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-02-13T12:20:01Z","title_canon_sha256":"88dbd39e75e76236112e95ab50fd9955172e30bc0bf78aae7a6ab25f99be8ee5"},"schema_version":"1.0","source":{"id":"math/0502261","kind":"arxiv","version":1}},"canonical_sha256":"8079ce118b932a347df5e245b24587b42212846d9bb03fe47c821bb7c69e66f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8079ce118b932a347df5e245b24587b42212846d9bb03fe47c821bb7c69e66f0","first_computed_at":"2026-05-18T01:05:23.742199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:23.742199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bLAdqCwwrA7TEm6MBWvYQeSnaZ5vlPRalFA05WaCFiEJGMfgTRjGiaS1Q5/uiqehG6tsQ34fV/ozKH9cuoluDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:23.742708Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502261","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d68779b37d7f5bd0271b4194033156e8107e4b6abae5be98ab730e5a025fb8d9","sha256:c5dea50ae5838a69d9940e44a943225d726cff108d42e363e0ae0b8f0936171b"],"state_sha256":"eaaed6e619c60add9376497377c89cba3b65909df9d887f9508c09dd0d459f2b"}