{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:37GYEQ3KIOYR4LKP4BTR4VK3TS","short_pith_number":"pith:37GYEQ3K","canonical_record":{"source":{"id":"math/0106272","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2001-06-18T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"8bd5236516bdfc37ed6c64fa5fb39c11b1d1878b6ab350ba926462e8e6ff9c84","abstract_canon_sha256":"742f545089ec688a6e5101e3361a90627f397a622317644cfafdd3e7f91b23f6"},"schema_version":"1.0"},"canonical_sha256":"dfcd82436a43b11e2d4fe0671e555b9ca2e9241d7326d72df60fec7eebfbf408","source":{"kind":"arxiv","id":"math/0106272","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0106272","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0106272v1","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0106272","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"37GYEQ3KIOYR","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"pith_short_16","alias_value":"37GYEQ3KIOYR4LKP","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"pith_short_8","alias_value":"37GYEQ3K","created_at":"2026-07-04T14:35:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:37GYEQ3KIOYR4LKP4BTR4VK3TS","target":"record","payload":{"canonical_record":{"source":{"id":"math/0106272","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2001-06-18T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"8bd5236516bdfc37ed6c64fa5fb39c11b1d1878b6ab350ba926462e8e6ff9c84","abstract_canon_sha256":"742f545089ec688a6e5101e3361a90627f397a622317644cfafdd3e7f91b23f6"},"schema_version":"1.0"},"canonical_sha256":"dfcd82436a43b11e2d4fe0671e555b9ca2e9241d7326d72df60fec7eebfbf408","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:24.878183Z","signature_b64":"BCfyVFY5+1rDzIvhS73sAUp3oVEsym1eC/OX56WPM8XVILvGO8NiP9xnQ9xRyL52BP3uiuN7IHCH7wUZY28aCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfcd82436a43b11e2d4fe0671e555b9ca2e9241d7326d72df60fec7eebfbf408","last_reissued_at":"2026-07-04T14:35:24.877854Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:24.877854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0106272","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":"2026-07-04T14:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5X6AbrKkwNw85+p3QvpGRgOmKITcGpRtyI/x2jOOu6w47SUBe0/uR613y1Xe1OYSCcvSO3KKOZdyjs//e+8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T20:26:20.320699Z"},"content_sha256":"e738d20b99bbaa99276c1f8dee8cd7a9f988f819794d3d4b454c110b741f8b00","schema_version":"1.0","event_id":"sha256:e738d20b99bbaa99276c1f8dee8cd7a9f988f819794d3d4b454c110b741f8b00"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:37GYEQ3KIOYR4LKP4BTR4VK3TS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Octahedral Galois representations arising from Q-curves of degree 2","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anna Rio, Joan-Carles Lario, Julio Fern\\'andez-Gonz\\'alez","submitted_at":"2001-06-18T00:00:00Z","abstract_excerpt":"Generically, one can attach to a Q-curve C octahedral representations Gal(Qbar/Q) --> GL(2,Fbar_3) coming from the Galois action on the 3-torsion of those abelian varieties of GL_2-type whose building block is C. When C is defined over a quadratic field and has an isogeny of degree 2 to its Galois conjugate, there exist such representations having image into GL(2,F_9). Going the other way, we can ask which mod 3 octahedral representations of Gal(Qbar/Q) arise from Q-curves in the above sense. We characterize those arising from quadratic Q-curves of degree 2. The approach makes use of Galois em"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106272","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0106272/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SC/J/Me3ndqlwUFiAVATHlq5M9EwCg8NGvZQ42QTB55iETN11SYsnXvNx652QomQwVcJAkb1+GiaSL171qVjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T20:26:20.321062Z"},"content_sha256":"0ff7ca26b6cc8c4a43f99726ad3fc14cd2bb21573f84ce99a6d128c5e7da0dd7","schema_version":"1.0","event_id":"sha256:0ff7ca26b6cc8c4a43f99726ad3fc14cd2bb21573f84ce99a6d128c5e7da0dd7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/37GYEQ3KIOYR4LKP4BTR4VK3TS/bundle.json","state_url":"https://pith.science/pith/37GYEQ3KIOYR4LKP4BTR4VK3TS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/37GYEQ3KIOYR4LKP4BTR4VK3TS/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":"2026-07-04T20:26:20Z","links":{"resolver":"https://pith.science/pith/37GYEQ3KIOYR4LKP4BTR4VK3TS","bundle":"https://pith.science/pith/37GYEQ3KIOYR4LKP4BTR4VK3TS/bundle.json","state":"https://pith.science/pith/37GYEQ3KIOYR4LKP4BTR4VK3TS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/37GYEQ3KIOYR4LKP4BTR4VK3TS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:37GYEQ3KIOYR4LKP4BTR4VK3TS","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":"742f545089ec688a6e5101e3361a90627f397a622317644cfafdd3e7f91b23f6","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2001-06-18T00:00:00Z","title_canon_sha256":"8bd5236516bdfc37ed6c64fa5fb39c11b1d1878b6ab350ba926462e8e6ff9c84"},"schema_version":"1.0","source":{"id":"math/0106272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0106272","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0106272v1","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0106272","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"37GYEQ3KIOYR","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"pith_short_16","alias_value":"37GYEQ3KIOYR4LKP","created_at":"2026-07-04T14:35:24Z"},{"alias_kind":"pith_short_8","alias_value":"37GYEQ3K","created_at":"2026-07-04T14:35:24Z"}],"graph_snapshots":[{"event_id":"sha256:0ff7ca26b6cc8c4a43f99726ad3fc14cd2bb21573f84ce99a6d128c5e7da0dd7","target":"graph","created_at":"2026-07-04T14:35:24Z","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/math/0106272/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Generically, one can attach to a Q-curve C octahedral representations Gal(Qbar/Q) --> GL(2,Fbar_3) coming from the Galois action on the 3-torsion of those abelian varieties of GL_2-type whose building block is C. When C is defined over a quadratic field and has an isogeny of degree 2 to its Galois conjugate, there exist such representations having image into GL(2,F_9). Going the other way, we can ask which mod 3 octahedral representations of Gal(Qbar/Q) arise from Q-curves in the above sense. We characterize those arising from quadratic Q-curves of degree 2. The approach makes use of Galois em","authors_text":"Anna Rio, Joan-Carles Lario, Julio Fern\\'andez-Gonz\\'alez","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2001-06-18T00:00:00Z","title":"Octahedral Galois representations arising from Q-curves of degree 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106272","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:e738d20b99bbaa99276c1f8dee8cd7a9f988f819794d3d4b454c110b741f8b00","target":"record","created_at":"2026-07-04T14:35:24Z","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":"742f545089ec688a6e5101e3361a90627f397a622317644cfafdd3e7f91b23f6","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2001-06-18T00:00:00Z","title_canon_sha256":"8bd5236516bdfc37ed6c64fa5fb39c11b1d1878b6ab350ba926462e8e6ff9c84"},"schema_version":"1.0","source":{"id":"math/0106272","kind":"arxiv","version":1}},"canonical_sha256":"dfcd82436a43b11e2d4fe0671e555b9ca2e9241d7326d72df60fec7eebfbf408","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfcd82436a43b11e2d4fe0671e555b9ca2e9241d7326d72df60fec7eebfbf408","first_computed_at":"2026-07-04T14:35:24.877854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:24.877854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BCfyVFY5+1rDzIvhS73sAUp3oVEsym1eC/OX56WPM8XVILvGO8NiP9xnQ9xRyL52BP3uiuN7IHCH7wUZY28aCw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:24.878183Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0106272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e738d20b99bbaa99276c1f8dee8cd7a9f988f819794d3d4b454c110b741f8b00","sha256:0ff7ca26b6cc8c4a43f99726ad3fc14cd2bb21573f84ce99a6d128c5e7da0dd7"],"state_sha256":"615f14d45479f02c4d0e9e3da8a7dde81aeddcd494da1c4803d7f55b6bca214c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fIarbalHDLtvnQ6nEKpyEGmmkoWyV1ML5eDPi+rc4qKKGEAYgpsIWIzCgm/dhMsGZAMzbkbNexn+nt3poi6IAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T20:26:20.322920Z","bundle_sha256":"402130a9f097dcaa59a23ba37ac08c4762d68cb4b44e322e87d03375d8108709"}}