{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T43XKKAABKAU245X7KHVJ4TWXJ","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":"da7c0eb180587fa8773aefcd084a9af3158ff64707b3ef2f098f587e98bb6db0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-05T13:23:59Z","title_canon_sha256":"9f3f9014137fd27359ae9a2eef2290bfa180627a08d55ead57365d646744bc40"},"schema_version":"1.0","source":{"id":"1112.0920","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0920","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0920v4","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0920","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"T43XKKAABKAU","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T43XKKAABKAU245X","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T43XKKAA","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:416a802f9c88f0b5e467cd04aeac735befa5bddefcade919be4abc98f63c9339","target":"graph","created_at":"2026-05-18T01:20:12Z","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":"Consider the algebraic dynamics on a torus T=G_m^n given by a matrix M in GL_n(Z). Assume that the characteristic polynomial of M is prime to all polynomials X^m-1. We show that any finite equivariant map from another algebraic dynamics onto (T,M) arises from a finite isogeny T \\to T. A similar and more general statement is shown for Abelian and semi-abelian varieties.\n  In model-theoretic terms, our result says: Working in an existentially closed difference field, we consider a definable subgroup B of a semi-abelian variety A; assume B does not have a subgroup isogenous to A'(F) for some twis","authors_text":"Ehud Hrushovski, Zo\\'e Chatzidakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-05T13:23:59Z","title":"On subgroups of semi-abelian varieties defined by difference equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0920","kind":"arxiv","version":4},"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:d5614056ea94c77a9f5663e4f908d057612657ff9676894ed8812d9fa22ef3ae","target":"record","created_at":"2026-05-18T01:20:12Z","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":"da7c0eb180587fa8773aefcd084a9af3158ff64707b3ef2f098f587e98bb6db0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-05T13:23:59Z","title_canon_sha256":"9f3f9014137fd27359ae9a2eef2290bfa180627a08d55ead57365d646744bc40"},"schema_version":"1.0","source":{"id":"1112.0920","kind":"arxiv","version":4}},"canonical_sha256":"9f377528000a814d73b7fa8f54f276ba6b7c14069fe944b8c8a83dcd2ed7f44a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f377528000a814d73b7fa8f54f276ba6b7c14069fe944b8c8a83dcd2ed7f44a","first_computed_at":"2026-05-18T01:20:12.681779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:12.681779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxE4sVmsW/Eh2Nakd0nbs88c1I3BfmQZsyejzOhBu8Eky29qhvtSc8t7fzYPcz+BTS73YPTaKG4s3ozeHTihDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:12.682435Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0920","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5614056ea94c77a9f5663e4f908d057612657ff9676894ed8812d9fa22ef3ae","sha256:416a802f9c88f0b5e467cd04aeac735befa5bddefcade919be4abc98f63c9339"],"state_sha256":"1775bc66f1fc56500518ef6eadb690aed1065a25646816990ce23e2d0b7a5655"}