{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:USWY64VCLU2MKVE2LLUQIUWYBI","short_pith_number":"pith:USWY64VC","canonical_record":{"source":{"id":"1211.7235","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-30T12:57:06Z","cross_cats_sorted":[],"title_canon_sha256":"9e60579271fa11a27bda78ec0dc7440b4d066e19e0aa51a7fe49640a0cf93c7f","abstract_canon_sha256":"f49596c9e5e67f1341694a745b54d2f7b10b2d6d7d9a4e42f7c2590578082631"},"schema_version":"1.0"},"canonical_sha256":"a4ad8f72a25d34c5549a5ae90452d80a0211b0ff4c36f4bef9398ecbfdc1017a","source":{"kind":"arxiv","id":"1211.7235","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7235","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7235v5","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7235","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"USWY64VCLU2M","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"USWY64VCLU2MKVE2","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"USWY64VC","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:USWY64VCLU2MKVE2LLUQIUWYBI","target":"record","payload":{"canonical_record":{"source":{"id":"1211.7235","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-30T12:57:06Z","cross_cats_sorted":[],"title_canon_sha256":"9e60579271fa11a27bda78ec0dc7440b4d066e19e0aa51a7fe49640a0cf93c7f","abstract_canon_sha256":"f49596c9e5e67f1341694a745b54d2f7b10b2d6d7d9a4e42f7c2590578082631"},"schema_version":"1.0"},"canonical_sha256":"a4ad8f72a25d34c5549a5ae90452d80a0211b0ff4c36f4bef9398ecbfdc1017a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:16.099869Z","signature_b64":"FvIGD5Fcn7Hi0V73NRl4oZOQ3YjQzqFPQoFW6S0xpoMf/7KWXi/vpZqWYWAFj7q9ZBM+u9Mr5YGXiyC1t7WVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4ad8f72a25d34c5549a5ae90452d80a0211b0ff4c36f4bef9398ecbfdc1017a","last_reissued_at":"2026-05-18T02:29:16.099457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:16.099457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.7235","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":"2026-05-18T02:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEqdqa2t3UEsq2dM8eweeMRWlODy70+bieEwFOwc71mJwEGCI2tCizLj1TGz5A8k9+0P5n9+3vkdwi3IkvoFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:11:05.408843Z"},"content_sha256":"739eab8ff62a8dd55cb55f0764860f0fecda44d11a4af0887302b7da6d62b3e8","schema_version":"1.0","event_id":"sha256:739eab8ff62a8dd55cb55f0764860f0fecda44d11a4af0887302b7da6d62b3e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:USWY64VCLU2MKVE2LLUQIUWYBI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Looking for the lost torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Amador Martin-Pizarro, Frank Olaf Wagner, Thomas Blossier","submitted_at":"2012-11-30T12:57:06Z","abstract_excerpt":"We classify the groups definable in the coloured fields obtained by Hrushovski amalgamation. A group definable in the bad green field is isogenous to the quotient of a subgroup of an algebraic group by a Cartesian power of the group of green elements. A definable subgroup of an algebraic group in the green or red field is an extension of the coloured points of a multiplicative or additive algebraic group by an algebraic group. In particular, a simple group in a coloured field is algebraic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7235","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":"2026-05-18T02:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQ5yebhzhIwMU2rBUKhNyxSRmImwBXTlwMA9DV9m2W7TUiWblmhkt6xEwMnFrTWZ3wc4h2eHNdUq5ciqGEM9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:11:05.409214Z"},"content_sha256":"f947851fc5cbb85bd67331a0b19d85fd34c5d86cf1564433d371f000b8dc2cdc","schema_version":"1.0","event_id":"sha256:f947851fc5cbb85bd67331a0b19d85fd34c5d86cf1564433d371f000b8dc2cdc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/USWY64VCLU2MKVE2LLUQIUWYBI/bundle.json","state_url":"https://pith.science/pith/USWY64VCLU2MKVE2LLUQIUWYBI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/USWY64VCLU2MKVE2LLUQIUWYBI/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":"2026-05-30T04:11:05Z","links":{"resolver":"https://pith.science/pith/USWY64VCLU2MKVE2LLUQIUWYBI","bundle":"https://pith.science/pith/USWY64VCLU2MKVE2LLUQIUWYBI/bundle.json","state":"https://pith.science/pith/USWY64VCLU2MKVE2LLUQIUWYBI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/USWY64VCLU2MKVE2LLUQIUWYBI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:USWY64VCLU2MKVE2LLUQIUWYBI","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":"f49596c9e5e67f1341694a745b54d2f7b10b2d6d7d9a4e42f7c2590578082631","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-30T12:57:06Z","title_canon_sha256":"9e60579271fa11a27bda78ec0dc7440b4d066e19e0aa51a7fe49640a0cf93c7f"},"schema_version":"1.0","source":{"id":"1211.7235","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7235","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7235v5","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7235","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"USWY64VCLU2M","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"USWY64VCLU2MKVE2","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"USWY64VC","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:f947851fc5cbb85bd67331a0b19d85fd34c5d86cf1564433d371f000b8dc2cdc","target":"graph","created_at":"2026-05-18T02:29:16Z","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"},"paper":{"abstract_excerpt":"We classify the groups definable in the coloured fields obtained by Hrushovski amalgamation. A group definable in the bad green field is isogenous to the quotient of a subgroup of an algebraic group by a Cartesian power of the group of green elements. A definable subgroup of an algebraic group in the green or red field is an extension of the coloured points of a multiplicative or additive algebraic group by an algebraic group. In particular, a simple group in a coloured field is algebraic.","authors_text":"Amador Martin-Pizarro, Frank Olaf Wagner, Thomas Blossier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-30T12:57:06Z","title":"Looking for the lost torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7235","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":"sha256:739eab8ff62a8dd55cb55f0764860f0fecda44d11a4af0887302b7da6d62b3e8","target":"record","created_at":"2026-05-18T02:29:16Z","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":"f49596c9e5e67f1341694a745b54d2f7b10b2d6d7d9a4e42f7c2590578082631","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-30T12:57:06Z","title_canon_sha256":"9e60579271fa11a27bda78ec0dc7440b4d066e19e0aa51a7fe49640a0cf93c7f"},"schema_version":"1.0","source":{"id":"1211.7235","kind":"arxiv","version":5}},"canonical_sha256":"a4ad8f72a25d34c5549a5ae90452d80a0211b0ff4c36f4bef9398ecbfdc1017a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4ad8f72a25d34c5549a5ae90452d80a0211b0ff4c36f4bef9398ecbfdc1017a","first_computed_at":"2026-05-18T02:29:16.099457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:16.099457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FvIGD5Fcn7Hi0V73NRl4oZOQ3YjQzqFPQoFW6S0xpoMf/7KWXi/vpZqWYWAFj7q9ZBM+u9Mr5YGXiyC1t7WVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:16.099869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.7235","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:739eab8ff62a8dd55cb55f0764860f0fecda44d11a4af0887302b7da6d62b3e8","sha256:f947851fc5cbb85bd67331a0b19d85fd34c5d86cf1564433d371f000b8dc2cdc"],"state_sha256":"bc1399d65d9f497ab09a37a25c3bc983b9754bf40f5fbbb167750d9c0c86fb33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLlMtILkEfq5EB2KibsTsl+aBBm7uJ1GBt52Uu4IJMzFJVD38gmN7BDTVkd+gbKaMnh2LTSZtWKMlrA+maZvAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:11:05.412203Z","bundle_sha256":"a9a8e2d423427af5d473cbe334cf784c3e409ccdee2dbb7439f2bf39893c4656"}}