{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WW3NR26MEHHQSIASXVYTNFGWEZ","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":"b53ce2b0ee664f152d6133562976069cab0e8fbcea41c7ecb8c5bca2d4191ab0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-23T13:50:13Z","title_canon_sha256":"fd4312cbf0fc8e264bae64b5bc665c74277dbb293a198e4ab7e456fb6063481f"},"schema_version":"1.0","source":{"id":"1802.08527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08527","created_at":"2026-07-05T02:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08527v1","created_at":"2026-07-05T02:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08527","created_at":"2026-07-05T02:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"WW3NR26MEHHQ","created_at":"2026-07-05T02:54:09Z"},{"alias_kind":"pith_short_16","alias_value":"WW3NR26MEHHQSIAS","created_at":"2026-07-05T02:54:09Z"},{"alias_kind":"pith_short_8","alias_value":"WW3NR26M","created_at":"2026-07-05T02:54:09Z"}],"graph_snapshots":[{"event_id":"sha256:59602feed05d9384adb4b08a1802a3fea1e043c2e6f9250d1bc9ba12289171e3","target":"graph","created_at":"2026-07-05T02:54:09Z","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/1802.08527/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $A$ be the product of an abelian variety and a torus over a number field $K$, and let $m$ be a positive integer. If $\\alpha \\in A(K)$ is a point of infinite order, we consider the set of primes $\\mathfrak p$ of $K$ such that the reduction $(\\alpha \\bmod \\mathfrak p)$ is well defined and has order coprime to $m$. This set admits a natural density, which we are able to express as a finite sum of products of $\\ell$-adic integrals, where $\\ell$ varies in the set of prime divisors of $m$. We deduce that the density is a rational number, whose denominator is bounded (up to powers of $m$) in a ve","authors_text":"Antonella Perucca, Peter Bruin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-23T13:50:13Z","title":"Reductions of points on algebraic groups, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08527","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:bc1b704e1a1fe600e101100a58227b8c686494f1527b93ec29d10be18473ad98","target":"record","created_at":"2026-07-05T02:54:09Z","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":"b53ce2b0ee664f152d6133562976069cab0e8fbcea41c7ecb8c5bca2d4191ab0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-23T13:50:13Z","title_canon_sha256":"fd4312cbf0fc8e264bae64b5bc665c74277dbb293a198e4ab7e456fb6063481f"},"schema_version":"1.0","source":{"id":"1802.08527","kind":"arxiv","version":1}},"canonical_sha256":"b5b6d8ebcc21cf092012bd713694d626493200d9c40c28279e282cbb8d154375","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5b6d8ebcc21cf092012bd713694d626493200d9c40c28279e282cbb8d154375","first_computed_at":"2026-07-05T02:54:09.420467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:54:09.420467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hqD9yJcE7UnmuL02Eh1azdNPYfNp3qJAInOyJ/wE5Fcc3KiFwSz+T2YllaOs98Yckx7reFxIvJlxMReEGlj5Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T02:54:09.420865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc1b704e1a1fe600e101100a58227b8c686494f1527b93ec29d10be18473ad98","sha256:59602feed05d9384adb4b08a1802a3fea1e043c2e6f9250d1bc9ba12289171e3"],"state_sha256":"75d17b2978e9a7dc3441c2e257290111bf181d6a756c7c5f6550b1f2e8fbc9b6"}