{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UZBCBMO3L7YUAUKBTYY4V456C2","short_pith_number":"pith:UZBCBMO3","canonical_record":{"source":{"id":"1508.00211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-02T09:54:59Z","cross_cats_sorted":[],"title_canon_sha256":"1b6e1838edb477635688384a87f70801e94988ea9f88f61a2bfb75181701bad5","abstract_canon_sha256":"4488ee9d9423ee9c936a640badffc7b451e1bdf12cc9153178d69050c1f83bf0"},"schema_version":"1.0"},"canonical_sha256":"a64220b1db5ff14051419e31caf3be16bd615320f259611de4ef11bb77fb0019","source":{"kind":"arxiv","id":"1508.00211","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00211","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00211v2","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00211","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"UZBCBMO3L7YU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UZBCBMO3L7YUAUKB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UZBCBMO3","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UZBCBMO3L7YUAUKBTYY4V456C2","target":"record","payload":{"canonical_record":{"source":{"id":"1508.00211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-02T09:54:59Z","cross_cats_sorted":[],"title_canon_sha256":"1b6e1838edb477635688384a87f70801e94988ea9f88f61a2bfb75181701bad5","abstract_canon_sha256":"4488ee9d9423ee9c936a640badffc7b451e1bdf12cc9153178d69050c1f83bf0"},"schema_version":"1.0"},"canonical_sha256":"a64220b1db5ff14051419e31caf3be16bd615320f259611de4ef11bb77fb0019","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:25.515206Z","signature_b64":"aVbbE6Aw8txJbkR6cmcJfQS14Hvtes/3m8NaZlM+uUvO8mwsk7naXz26nsTI57iI0OF1fHlbv4hthznXhIQvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a64220b1db5ff14051419e31caf3be16bd615320f259611de4ef11bb77fb0019","last_reissued_at":"2026-05-18T01:17:25.514495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:25.514495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.00211","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"11XvbnMB9uNtwoqFyrKT9ipCZgmOBR1glR0G6IJXcqaflPfIGf601+1wiF+gm5W+lKbqe4zT36MeuPjo/o05Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T19:16:59.713107Z"},"content_sha256":"335c1d53c81905b906216b0627e95df6db4f13041e01c40f97953b83e6404a2e","schema_version":"1.0","event_id":"sha256:335c1d53c81905b906216b0627e95df6db4f13041e01c40f97953b83e6404a2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UZBCBMO3L7YUAUKBTYY4V456C2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Residual Representations of Semistable Principally Polarized Abelian Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pedro Lemos, Samir Siksek, Samuele Anni","submitted_at":"2015-08-02T09:54:59Z","abstract_excerpt":"Let $A$ be a semistable principally polarized abelian variety of dimension $d$ defined over the rationals. Let $\\ell$ be a prime and let $\\bar{\\rho}_{A,\\ell} : G_{\\mathbb{Q}} \\rightarrow \\mathrm{GSp}_{2d}(\\mathbb{F}_\\ell)$ be the representation giving the action of $G_{\\mathrm{Q}} :=\\mathrm{Gal}(\\bar{\\mathrm{Q}}/\\mathrm{Q})$ on the $\\ell$-torsion group $A[\\ell]$. We show that if $\\ell \\ge \\max(5,d+2)$, and if image of $\\bar{\\rho}_{A,\\ell}$ contains a transvection then $\\bar{\\rho}_{A,\\ell}$ is either reducible or surjective.\n  With the help of this we study surjectivity of $\\bar{\\rho}_{A,\\ell}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00211","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xkb14tqCmD1xQP8/V3jrwVpKbug+CXTAEb3Xsc2Za8TGaKVfbrtfrEzAVaB73upvDM2o3HzWhh0iUiTIv/XbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T19:16:59.713480Z"},"content_sha256":"9ccb083e88a8ecaf9b61285819c71025379dc2eded99cdef43c4329cddf8cf55","schema_version":"1.0","event_id":"sha256:9ccb083e88a8ecaf9b61285819c71025379dc2eded99cdef43c4329cddf8cf55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZBCBMO3L7YUAUKBTYY4V456C2/bundle.json","state_url":"https://pith.science/pith/UZBCBMO3L7YUAUKBTYY4V456C2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZBCBMO3L7YUAUKBTYY4V456C2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T19:16:59Z","links":{"resolver":"https://pith.science/pith/UZBCBMO3L7YUAUKBTYY4V456C2","bundle":"https://pith.science/pith/UZBCBMO3L7YUAUKBTYY4V456C2/bundle.json","state":"https://pith.science/pith/UZBCBMO3L7YUAUKBTYY4V456C2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZBCBMO3L7YUAUKBTYY4V456C2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UZBCBMO3L7YUAUKBTYY4V456C2","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":"4488ee9d9423ee9c936a640badffc7b451e1bdf12cc9153178d69050c1f83bf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-02T09:54:59Z","title_canon_sha256":"1b6e1838edb477635688384a87f70801e94988ea9f88f61a2bfb75181701bad5"},"schema_version":"1.0","source":{"id":"1508.00211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00211","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00211v2","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00211","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"UZBCBMO3L7YU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UZBCBMO3L7YUAUKB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UZBCBMO3","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:9ccb083e88a8ecaf9b61285819c71025379dc2eded99cdef43c4329cddf8cf55","target":"graph","created_at":"2026-05-18T01:17:25Z","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 $A$ be a semistable principally polarized abelian variety of dimension $d$ defined over the rationals. Let $\\ell$ be a prime and let $\\bar{\\rho}_{A,\\ell} : G_{\\mathbb{Q}} \\rightarrow \\mathrm{GSp}_{2d}(\\mathbb{F}_\\ell)$ be the representation giving the action of $G_{\\mathrm{Q}} :=\\mathrm{Gal}(\\bar{\\mathrm{Q}}/\\mathrm{Q})$ on the $\\ell$-torsion group $A[\\ell]$. We show that if $\\ell \\ge \\max(5,d+2)$, and if image of $\\bar{\\rho}_{A,\\ell}$ contains a transvection then $\\bar{\\rho}_{A,\\ell}$ is either reducible or surjective.\n  With the help of this we study surjectivity of $\\bar{\\rho}_{A,\\ell}$","authors_text":"Pedro Lemos, Samir Siksek, Samuele Anni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-02T09:54:59Z","title":"Residual Representations of Semistable Principally Polarized Abelian Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00211","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":"sha256:335c1d53c81905b906216b0627e95df6db4f13041e01c40f97953b83e6404a2e","target":"record","created_at":"2026-05-18T01:17:25Z","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":"4488ee9d9423ee9c936a640badffc7b451e1bdf12cc9153178d69050c1f83bf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-02T09:54:59Z","title_canon_sha256":"1b6e1838edb477635688384a87f70801e94988ea9f88f61a2bfb75181701bad5"},"schema_version":"1.0","source":{"id":"1508.00211","kind":"arxiv","version":2}},"canonical_sha256":"a64220b1db5ff14051419e31caf3be16bd615320f259611de4ef11bb77fb0019","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a64220b1db5ff14051419e31caf3be16bd615320f259611de4ef11bb77fb0019","first_computed_at":"2026-05-18T01:17:25.514495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:25.514495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aVbbE6Aw8txJbkR6cmcJfQS14Hvtes/3m8NaZlM+uUvO8mwsk7naXz26nsTI57iI0OF1fHlbv4hthznXhIQvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:25.515206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:335c1d53c81905b906216b0627e95df6db4f13041e01c40f97953b83e6404a2e","sha256:9ccb083e88a8ecaf9b61285819c71025379dc2eded99cdef43c4329cddf8cf55"],"state_sha256":"de2aadcb0372e89d05f93740ad9880444d0c5662563773909556815640aa9a5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CY1oYay/TJjYrnBXmly+e/Etd9w0nCG2fsypjB8/1rHeE8Az8eo8aktXL2iZERijngQ07p4BcDes/BrEneWTCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T19:16:59.715569Z","bundle_sha256":"4de5d751d95e13a90d826508c5e0f609ef8f81f96743db4975f4e3fb99fc18b9"}}