{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:AQA3KPB7OISOEH3Y5XD4IUHTCU","short_pith_number":"pith:AQA3KPB7","canonical_record":{"source":{"id":"2002.10300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-24T15:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"3487fb1a27cbe948f2670a8fe3e3e6321e914aa164c9a548a54bec51fab71ca6","abstract_canon_sha256":"18d59eef241a212a6f80989425f58ba2f7e996660fc53818ec015273335f5dae"},"schema_version":"1.0"},"canonical_sha256":"0401b53c3f7224e21f78edc7c450f31502138def91fae21afa734b6a05f255d7","source":{"kind":"arxiv","id":"2002.10300","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.10300","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"arxiv_version","alias_value":"2002.10300v1","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.10300","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"pith_short_12","alias_value":"AQA3KPB7OISO","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"pith_short_16","alias_value":"AQA3KPB7OISOEH3Y","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"pith_short_8","alias_value":"AQA3KPB7","created_at":"2026-07-05T00:43:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:AQA3KPB7OISOEH3Y5XD4IUHTCU","target":"record","payload":{"canonical_record":{"source":{"id":"2002.10300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-24T15:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"3487fb1a27cbe948f2670a8fe3e3e6321e914aa164c9a548a54bec51fab71ca6","abstract_canon_sha256":"18d59eef241a212a6f80989425f58ba2f7e996660fc53818ec015273335f5dae"},"schema_version":"1.0"},"canonical_sha256":"0401b53c3f7224e21f78edc7c450f31502138def91fae21afa734b6a05f255d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:43:16.112496Z","signature_b64":"nk9QBBR6CuhZ9qhBPhI/iMVe268RAzumKsiB78X5ef60hnn+EnJJmQqbCCusk8vveF9maAf9rCHX6vD+GQOFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0401b53c3f7224e21f78edc7c450f31502138def91fae21afa734b6a05f255d7","last_reissued_at":"2026-07-05T00:43:16.112147Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:43:16.112147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.10300","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":"2026-07-05T00:43:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0R0e8W5wPgVZ8yZcUY7tbXxUW1jNEwphiPVfvKKDuGfozkw7n1iLmN3ys8oDmLiSdaPUVnJb7qfLe9rBs06jBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T03:08:35.086308Z"},"content_sha256":"fa34e2b57847bb4b56ee796633776df6b56bbaed60b5454855a5f1ad5f0fe070","schema_version":"1.0","event_id":"sha256:fa34e2b57847bb4b56ee796633776df6b56bbaed60b5454855a5f1ad5f0fe070"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:AQA3KPB7OISOEH3Y5XD4IUHTCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Galois groups over rational function fields over skew fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Elad Paran, Fran\\c{c}ois Legrand, Gil Alon","submitted_at":"2020-02-24T15:10:39Z","abstract_excerpt":"Let $H$ be a skew field of finite dimension over its center $k$. We solve the Inverse Galois Problem over the field of fractions $H(X)$ of the ring of polynomial functions over $H$ in the variable $X$, if $k$ contains an ample field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.10300","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/2002.10300/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":"2026-07-05T00:43:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gb8aEck2JnYxfjMeKEIWM1PFruNgJV50IvPMwSlbTyN8TN3QtPHGxC2apBQxPUXIl9Yn8A7Vc7VCW/vvJhyyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T03:08:35.086989Z"},"content_sha256":"884fe18da75f1f056c79e9cf6a46cbd0b42bcd4dbf88d2b981c7d7347828966c","schema_version":"1.0","event_id":"sha256:884fe18da75f1f056c79e9cf6a46cbd0b42bcd4dbf88d2b981c7d7347828966c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQA3KPB7OISOEH3Y5XD4IUHTCU/bundle.json","state_url":"https://pith.science/pith/AQA3KPB7OISOEH3Y5XD4IUHTCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQA3KPB7OISOEH3Y5XD4IUHTCU/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":"2026-08-22T03:08:35Z","links":{"resolver":"https://pith.science/pith/AQA3KPB7OISOEH3Y5XD4IUHTCU","bundle":"https://pith.science/pith/AQA3KPB7OISOEH3Y5XD4IUHTCU/bundle.json","state":"https://pith.science/pith/AQA3KPB7OISOEH3Y5XD4IUHTCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQA3KPB7OISOEH3Y5XD4IUHTCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:AQA3KPB7OISOEH3Y5XD4IUHTCU","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":"18d59eef241a212a6f80989425f58ba2f7e996660fc53818ec015273335f5dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-24T15:10:39Z","title_canon_sha256":"3487fb1a27cbe948f2670a8fe3e3e6321e914aa164c9a548a54bec51fab71ca6"},"schema_version":"1.0","source":{"id":"2002.10300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.10300","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"arxiv_version","alias_value":"2002.10300v1","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.10300","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"pith_short_12","alias_value":"AQA3KPB7OISO","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"pith_short_16","alias_value":"AQA3KPB7OISOEH3Y","created_at":"2026-07-05T00:43:16Z"},{"alias_kind":"pith_short_8","alias_value":"AQA3KPB7","created_at":"2026-07-05T00:43:16Z"}],"graph_snapshots":[{"event_id":"sha256:884fe18da75f1f056c79e9cf6a46cbd0b42bcd4dbf88d2b981c7d7347828966c","target":"graph","created_at":"2026-07-05T00:43:16Z","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/2002.10300/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $H$ be a skew field of finite dimension over its center $k$. We solve the Inverse Galois Problem over the field of fractions $H(X)$ of the ring of polynomial functions over $H$ in the variable $X$, if $k$ contains an ample field.","authors_text":"Elad Paran, Fran\\c{c}ois Legrand, Gil Alon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-24T15:10:39Z","title":"Galois groups over rational function fields over skew fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.10300","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:fa34e2b57847bb4b56ee796633776df6b56bbaed60b5454855a5f1ad5f0fe070","target":"record","created_at":"2026-07-05T00:43:16Z","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":"18d59eef241a212a6f80989425f58ba2f7e996660fc53818ec015273335f5dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-02-24T15:10:39Z","title_canon_sha256":"3487fb1a27cbe948f2670a8fe3e3e6321e914aa164c9a548a54bec51fab71ca6"},"schema_version":"1.0","source":{"id":"2002.10300","kind":"arxiv","version":1}},"canonical_sha256":"0401b53c3f7224e21f78edc7c450f31502138def91fae21afa734b6a05f255d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0401b53c3f7224e21f78edc7c450f31502138def91fae21afa734b6a05f255d7","first_computed_at":"2026-07-05T00:43:16.112147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:43:16.112147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nk9QBBR6CuhZ9qhBPhI/iMVe268RAzumKsiB78X5ef60hnn+EnJJmQqbCCusk8vveF9maAf9rCHX6vD+GQOFAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:43:16.112496Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.10300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa34e2b57847bb4b56ee796633776df6b56bbaed60b5454855a5f1ad5f0fe070","sha256:884fe18da75f1f056c79e9cf6a46cbd0b42bcd4dbf88d2b981c7d7347828966c"],"state_sha256":"3e217cd9195d8ca91ce4c699bb2d58536daa02b893327c63000f74c72dd6d2e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kSlEi7KPLMXzMrezPDMvtjJDX2Lc3cb2GQZdaZIBNitjJROrz1udTU8ADewv89vELQ4SKkXvGtOhrdEBylpbAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T03:08:35.092572Z","bundle_sha256":"52bbc5e7fb14dcba61fa2beae96b77f9544557f028a48ebae2db73224119a0d8"}}