{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:4M2I6HLVC4TRFSU637NQLTAMIK","short_pith_number":"pith:4M2I6HLV","canonical_record":{"source":{"id":"0803.1682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-03-11T23:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"eaf97601aa32f20a1e6d5197348657bd0f2bd0708cd39b9df21371273c14d0d6","abstract_canon_sha256":"836983c16c294b8b5c994c26899a32fbc7e425f88b31075a9bd6283f68cb5c75"},"schema_version":"1.0"},"canonical_sha256":"e3348f1d75172712ca9edfdb05cc0c42b7983985c530496ca965169d09f18d7e","source":{"kind":"arxiv","id":"0803.1682","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1682","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1682v1","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1682","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"4M2I6HLVC4TR","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4M2I6HLVC4TRFSU6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4M2I6HLV","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:4M2I6HLVC4TRFSU637NQLTAMIK","target":"record","payload":{"canonical_record":{"source":{"id":"0803.1682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-03-11T23:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"eaf97601aa32f20a1e6d5197348657bd0f2bd0708cd39b9df21371273c14d0d6","abstract_canon_sha256":"836983c16c294b8b5c994c26899a32fbc7e425f88b31075a9bd6283f68cb5c75"},"schema_version":"1.0"},"canonical_sha256":"e3348f1d75172712ca9edfdb05cc0c42b7983985c530496ca965169d09f18d7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:11.720212Z","signature_b64":"i7Wub5O2sC+RZTa6rRXcYEw7t663ak+3zvV7SVa5h4686MJXV+D0KlzR8rspxhqgCZx3SdezOc2ps1eiN9CwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3348f1d75172712ca9edfdb05cc0c42b7983985c530496ca965169d09f18d7e","last_reissued_at":"2026-05-18T02:58:11.719459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:11.719459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0803.1682","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jquwuR/FLmZHGTeQTfn/g5/31ubW3TpaiCrqIQywetWb+iuOFuTos59s03Cl4cHtCvsX84mTzEbUtFPxGaobDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:59:32.062880Z"},"content_sha256":"97145610862a5edf9dc5cbdfcf100d4e15767a9c6771eb64ac75d01b45eac446","schema_version":"1.0","event_id":"sha256:97145610862a5edf9dc5cbdfcf100d4e15767a9c6771eb64ac75d01b45eac446"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:4M2I6HLVC4TRFSU637NQLTAMIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An open image theorem for a general class of abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chris Hall","submitted_at":"2008-03-11T23:01:02Z","abstract_excerpt":"Let K be a number field and A/K be a polarized abelian variety with absolutely trivial endomorphism ring. We show that if the Neron model of A/K has at least one fiber with potential toric dimension one, then for almost all rational primes ell, the Galois group of the splitting field of the ell-torsion of A is GSp_{2g}(Z/ell)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1682","kind":"arxiv","version":1},"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":"2026-05-18T02:58:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HEZe24adwso212XLo7oNshrZBsytAwrBgFimVDWcm/eAX/MVG3F2do2IwT11aAJSyzwBNY1ig3gY+ps+RL7BCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:59:32.063228Z"},"content_sha256":"d3ccc4c9fa0acc4f67631db75e17c43af2ce3444207a916da94dc77b452e76b7","schema_version":"1.0","event_id":"sha256:d3ccc4c9fa0acc4f67631db75e17c43af2ce3444207a916da94dc77b452e76b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4M2I6HLVC4TRFSU637NQLTAMIK/bundle.json","state_url":"https://pith.science/pith/4M2I6HLVC4TRFSU637NQLTAMIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4M2I6HLVC4TRFSU637NQLTAMIK/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":"2026-06-23T13:59:32Z","links":{"resolver":"https://pith.science/pith/4M2I6HLVC4TRFSU637NQLTAMIK","bundle":"https://pith.science/pith/4M2I6HLVC4TRFSU637NQLTAMIK/bundle.json","state":"https://pith.science/pith/4M2I6HLVC4TRFSU637NQLTAMIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4M2I6HLVC4TRFSU637NQLTAMIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4M2I6HLVC4TRFSU637NQLTAMIK","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":"836983c16c294b8b5c994c26899a32fbc7e425f88b31075a9bd6283f68cb5c75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-03-11T23:01:02Z","title_canon_sha256":"eaf97601aa32f20a1e6d5197348657bd0f2bd0708cd39b9df21371273c14d0d6"},"schema_version":"1.0","source":{"id":"0803.1682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1682","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1682v1","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1682","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"4M2I6HLVC4TR","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4M2I6HLVC4TRFSU6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4M2I6HLV","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d3ccc4c9fa0acc4f67631db75e17c43af2ce3444207a916da94dc77b452e76b7","target":"graph","created_at":"2026-05-18T02:58:11Z","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 K be a number field and A/K be a polarized abelian variety with absolutely trivial endomorphism ring. We show that if the Neron model of A/K has at least one fiber with potential toric dimension one, then for almost all rational primes ell, the Galois group of the splitting field of the ell-torsion of A is GSp_{2g}(Z/ell).","authors_text":"Chris Hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-03-11T23:01:02Z","title":"An open image theorem for a general class of abelian varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1682","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":"sha256:97145610862a5edf9dc5cbdfcf100d4e15767a9c6771eb64ac75d01b45eac446","target":"record","created_at":"2026-05-18T02:58:11Z","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":"836983c16c294b8b5c994c26899a32fbc7e425f88b31075a9bd6283f68cb5c75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-03-11T23:01:02Z","title_canon_sha256":"eaf97601aa32f20a1e6d5197348657bd0f2bd0708cd39b9df21371273c14d0d6"},"schema_version":"1.0","source":{"id":"0803.1682","kind":"arxiv","version":1}},"canonical_sha256":"e3348f1d75172712ca9edfdb05cc0c42b7983985c530496ca965169d09f18d7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3348f1d75172712ca9edfdb05cc0c42b7983985c530496ca965169d09f18d7e","first_computed_at":"2026-05-18T02:58:11.719459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:11.719459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7Wub5O2sC+RZTa6rRXcYEw7t663ak+3zvV7SVa5h4686MJXV+D0KlzR8rspxhqgCZx3SdezOc2ps1eiN9CwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:11.720212Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.1682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97145610862a5edf9dc5cbdfcf100d4e15767a9c6771eb64ac75d01b45eac446","sha256:d3ccc4c9fa0acc4f67631db75e17c43af2ce3444207a916da94dc77b452e76b7"],"state_sha256":"15f072398471f99c92770ba597d83e8424e4b62cc482b14d1e0d30126a006c93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Icyd5S4EVETZxxqiS/BG28e9UlhbuOsNGnEvIUk5Np07uP15aXca1Ub8Mr9pCTl1LkbtswhYhlMzTnkFSKSSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:59:32.065283Z","bundle_sha256":"692d85eea258dc7927efc09e7cfdff2d2e1f1a5c316fd4cee818eec3122bd9c7"}}