{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UN5ULDAWJQ4KH3LV4WP44PNNNB","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":"9ee142bb4934a22d3de518ff019f4eb10f75d492a57f223470ead328e5bfcaaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-21T16:35:24Z","title_canon_sha256":"291f9d93eef2434dcdfda54ccbac80e37db48fd1465fce5f5c22c6c405a1035f"},"schema_version":"1.0","source":{"id":"1110.4836","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4836","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4836v2","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4836","created_at":"2026-05-18T04:08:23Z"},{"alias_kind":"pith_short_12","alias_value":"UN5ULDAWJQ4K","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UN5ULDAWJQ4KH3LV","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UN5ULDAW","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:f6fa153a3916c29962c188aac6086aec876e645712eb6cb7dacae1734b8c7bc9","target":"graph","created_at":"2026-05-18T04:08:23Z","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":"Let $E$ be an abelian scheme over a geometrically connected variety $X$ defined over $k$, a finitely generated field over $\\mathbb{Q}$. Let $\\eta$ be the generic point of $X$ and $x\\in X$ a closed point. If $\\mathfrak{g}_l$ and $(\\mathfrak{g}_l)_x$ are the Lie algebras of the $l$-adic Galois representations for abelian varieties $E_{\\eta}$ and $E_x$, then $(\\mathfrak{g}_l)_x$ is embedded in $\\mathfrak{g}_l$ by specialization. We prove that the set $\\{x\\in X$ closed point $| (\\mathfrak{g}_l)_x\\subsetneq \\mathfrak{g}_l\\}$ is independent of $l$ and confirm Conjecture 5.5 in [2].","authors_text":"Chun Yin Hui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-21T16:35:24Z","title":"Specialization of monodromy group and l-independence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4836","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":"sha256:25393d53582c829199fe2755648bafac1bdac510491940630d86906c51d16bc6","target":"record","created_at":"2026-05-18T04:08:23Z","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":"9ee142bb4934a22d3de518ff019f4eb10f75d492a57f223470ead328e5bfcaaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-21T16:35:24Z","title_canon_sha256":"291f9d93eef2434dcdfda54ccbac80e37db48fd1465fce5f5c22c6c405a1035f"},"schema_version":"1.0","source":{"id":"1110.4836","kind":"arxiv","version":2}},"canonical_sha256":"a37b458c164c38a3ed75e59fce3dad687cf7b699be1c17f3cea74911af06c988","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a37b458c164c38a3ed75e59fce3dad687cf7b699be1c17f3cea74911af06c988","first_computed_at":"2026-05-18T04:08:23.664793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:23.664793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bo+zui6UJcGqUAKG2pmNMmVxYqY8muHUgN3k6C2hzls3QKImd6lKfepjrwNbwnZoAXgz32/28D6baoI2uREaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:23.665304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4836","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25393d53582c829199fe2755648bafac1bdac510491940630d86906c51d16bc6","sha256:f6fa153a3916c29962c188aac6086aec876e645712eb6cb7dacae1734b8c7bc9"],"state_sha256":"30edc703b081929ecaa4e0bbaa55f69807cbc718c1923123c2ebe825d142dcbb"}