{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:F5ZHRZC64WTVO4P5Z7QMZTQOOT","short_pith_number":"pith:F5ZHRZC6","canonical_record":{"source":{"id":"1709.06430","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-19T13:52:54Z","cross_cats_sorted":[],"title_canon_sha256":"3d8d51a8bdea1f7cfb8b3f825513f95ebde34bf4a356792b61debc8197a47df3","abstract_canon_sha256":"4c826809bc0795b1ac0d96c3feab83908d38e44399662c87b8684bd92b89673b"},"schema_version":"1.0"},"canonical_sha256":"2f7278e45ee5a75771fdcfe0ccce0e74c73e457ff4ab5005c37302b203c7e9c4","source":{"kind":"arxiv","id":"1709.06430","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06430","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06430v5","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06430","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"F5ZHRZC64WTV","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F5ZHRZC64WTVO4P5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F5ZHRZC6","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:F5ZHRZC64WTVO4P5Z7QMZTQOOT","target":"record","payload":{"canonical_record":{"source":{"id":"1709.06430","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-19T13:52:54Z","cross_cats_sorted":[],"title_canon_sha256":"3d8d51a8bdea1f7cfb8b3f825513f95ebde34bf4a356792b61debc8197a47df3","abstract_canon_sha256":"4c826809bc0795b1ac0d96c3feab83908d38e44399662c87b8684bd92b89673b"},"schema_version":"1.0"},"canonical_sha256":"2f7278e45ee5a75771fdcfe0ccce0e74c73e457ff4ab5005c37302b203c7e9c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:34.445188Z","signature_b64":"y30fdu4m54fV1aF9LR1w1/qWtJcVKPp9RNe1eLxTn1kBeBSPO/2x8B9QK586BQnnnf0Y0C/AybtPc0fDsCmNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f7278e45ee5a75771fdcfe0ccce0e74c73e457ff4ab5005c37302b203c7e9c4","last_reissued_at":"2026-05-18T00:14:34.444514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:34.444514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.06430","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/RDkJgEsUrGQXaSh2du0NhXrSaxewDCEVehasQP7BUK4b1aZBrf66KCdoSHoBMb0t9S4A/yEVoHnNggqXnO0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T00:12:37.259812Z"},"content_sha256":"3eba0faeeee1bca7f022121a315df108fe22aeef00decb3db206497caba49872","schema_version":"1.0","event_id":"sha256:3eba0faeeee1bca7f022121a315df108fe22aeef00decb3db206497caba49872"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:F5ZHRZC64WTVO4P5Z7QMZTQOOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Black Box Galois Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alejandro Arg\\'aez-Garc\\'ia, John Cremona","submitted_at":"2017-09-19T13:52:54Z","abstract_excerpt":"We develop methods to study $2$-dimensional $2$-adic Galois representations $\\rho$ of the absolute Galois group of a number field $K$, unramified outside a known finite set of primes $S$ of $K$, which are presented as Black Box representations, where we only have access to the characteristic polynomials of Frobenius automorphisms at a finite set of primes. Using suitable finite test sets of primes, depending only on $K$ and $S$, we show how to determine the determinant $\\det\\rho$, whether or not $\\rho$ is residually reducible, and further information about the size of the isogeny graph of $\\rh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06430","kind":"arxiv","version":5},"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":"2026-05-18T00:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jlmLSJ7FioCDfTEehWbBzeyLBNCSIfDKajKqa3N7N/sUSdRoHSPxeO573mSMMGWdffm+vQb6gC5C8R6BpqcXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T00:12:37.260470Z"},"content_sha256":"0573910326c771129c4d1366173466c7ad633b78625e08b47ec64fee57d20fd5","schema_version":"1.0","event_id":"sha256:0573910326c771129c4d1366173466c7ad633b78625e08b47ec64fee57d20fd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5ZHRZC64WTVO4P5Z7QMZTQOOT/bundle.json","state_url":"https://pith.science/pith/F5ZHRZC64WTVO4P5Z7QMZTQOOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5ZHRZC64WTVO4P5Z7QMZTQOOT/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":"2026-06-07T00:12:37Z","links":{"resolver":"https://pith.science/pith/F5ZHRZC64WTVO4P5Z7QMZTQOOT","bundle":"https://pith.science/pith/F5ZHRZC64WTVO4P5Z7QMZTQOOT/bundle.json","state":"https://pith.science/pith/F5ZHRZC64WTVO4P5Z7QMZTQOOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5ZHRZC64WTVO4P5Z7QMZTQOOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F5ZHRZC64WTVO4P5Z7QMZTQOOT","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":"4c826809bc0795b1ac0d96c3feab83908d38e44399662c87b8684bd92b89673b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-19T13:52:54Z","title_canon_sha256":"3d8d51a8bdea1f7cfb8b3f825513f95ebde34bf4a356792b61debc8197a47df3"},"schema_version":"1.0","source":{"id":"1709.06430","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06430","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06430v5","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06430","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"F5ZHRZC64WTV","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F5ZHRZC64WTVO4P5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F5ZHRZC6","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:0573910326c771129c4d1366173466c7ad633b78625e08b47ec64fee57d20fd5","target":"graph","created_at":"2026-05-18T00:14:34Z","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":"We develop methods to study $2$-dimensional $2$-adic Galois representations $\\rho$ of the absolute Galois group of a number field $K$, unramified outside a known finite set of primes $S$ of $K$, which are presented as Black Box representations, where we only have access to the characteristic polynomials of Frobenius automorphisms at a finite set of primes. Using suitable finite test sets of primes, depending only on $K$ and $S$, we show how to determine the determinant $\\det\\rho$, whether or not $\\rho$ is residually reducible, and further information about the size of the isogeny graph of $\\rh","authors_text":"Alejandro Arg\\'aez-Garc\\'ia, John Cremona","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-19T13:52:54Z","title":"Black Box Galois Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06430","kind":"arxiv","version":5},"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":"sha256:3eba0faeeee1bca7f022121a315df108fe22aeef00decb3db206497caba49872","target":"record","created_at":"2026-05-18T00:14:34Z","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":"4c826809bc0795b1ac0d96c3feab83908d38e44399662c87b8684bd92b89673b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-19T13:52:54Z","title_canon_sha256":"3d8d51a8bdea1f7cfb8b3f825513f95ebde34bf4a356792b61debc8197a47df3"},"schema_version":"1.0","source":{"id":"1709.06430","kind":"arxiv","version":5}},"canonical_sha256":"2f7278e45ee5a75771fdcfe0ccce0e74c73e457ff4ab5005c37302b203c7e9c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f7278e45ee5a75771fdcfe0ccce0e74c73e457ff4ab5005c37302b203c7e9c4","first_computed_at":"2026-05-18T00:14:34.444514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:34.444514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y30fdu4m54fV1aF9LR1w1/qWtJcVKPp9RNe1eLxTn1kBeBSPO/2x8B9QK586BQnnnf0Y0C/AybtPc0fDsCmNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:34.445188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06430","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eba0faeeee1bca7f022121a315df108fe22aeef00decb3db206497caba49872","sha256:0573910326c771129c4d1366173466c7ad633b78625e08b47ec64fee57d20fd5"],"state_sha256":"4e94b7f2fbcd47e659a044df1e8540f75d7095f22b3a8dd6945d93a8e1e7a0f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4VwkBibkqaHYWoXWNsPZ40zIXU9GgUT+IYCmJc9WGHXfMh40V1P1Sjj92fs/5vaHnsseF/VWHF2sqdlxIh+cBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T00:12:37.265008Z","bundle_sha256":"0346995e541690c28d53e9ae7416eb7fd5ae4a1358eeea4cc68566e147620b4a"}}