{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TAAFY5PJJZ47QBWMZZ5SANAEYC","short_pith_number":"pith:TAAFY5PJ","canonical_record":{"source":{"id":"1108.6215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T12:59:07Z","cross_cats_sorted":[],"title_canon_sha256":"fd291cb2ce4aa6909a4f89371f040219f72b5b5674e3f223419d5b4ef7f98959","abstract_canon_sha256":"17d28f782732420380ffae69564f68ee6e17be8df39d163c7682e1cfbb7409ef"},"schema_version":"1.0"},"canonical_sha256":"98005c75e94e79f806ccce7b203404c08e9cae53c011bd6b01ae7569d6df8076","source":{"kind":"arxiv","id":"1108.6215","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6215","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6215v1","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6215","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"TAAFY5PJJZ47","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"TAAFY5PJJZ47QBWM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"TAAFY5PJ","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TAAFY5PJJZ47QBWMZZ5SANAEYC","target":"record","payload":{"canonical_record":{"source":{"id":"1108.6215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T12:59:07Z","cross_cats_sorted":[],"title_canon_sha256":"fd291cb2ce4aa6909a4f89371f040219f72b5b5674e3f223419d5b4ef7f98959","abstract_canon_sha256":"17d28f782732420380ffae69564f68ee6e17be8df39d163c7682e1cfbb7409ef"},"schema_version":"1.0"},"canonical_sha256":"98005c75e94e79f806ccce7b203404c08e9cae53c011bd6b01ae7569d6df8076","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:26.806996Z","signature_b64":"L41pCJaWSPDyneD4tGkuMwxq3yUwNwzNWW2YTAlPJ2DDl9nK/N8SuTR+zwKZDyCcT2E+YmUET2JPv36Gl6INBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98005c75e94e79f806ccce7b203404c08e9cae53c011bd6b01ae7569d6df8076","last_reissued_at":"2026-05-18T04:14:26.806280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:26.806280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.6215","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":"2026-05-18T04:14:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I0Jfw+dll/72m0CxDejdI8u30oAA1rrBj4Lbv4Bb/Nkg+IH6Y+axg+yNL8xWa5TcK/IuheLGfY3wl4vTN/S9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:33:46.599482Z"},"content_sha256":"f81cd287732b80eeae870c5d974299498305f048be0fdacc7f8347d8aecd2871","schema_version":"1.0","event_id":"sha256:f81cd287732b80eeae870c5d974299498305f048be0fdacc7f8347d8aecd2871"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TAAFY5PJJZ47QBWMZZ5SANAEYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euclid's Algorithm in quartic CM-fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Franz Lemmermeyer","submitted_at":"2011-08-31T12:59:07Z","abstract_excerpt":"In this note we present techniques to compute inhomogeneous minima of norm forms; as an application, we determine all norm-Euclidean complex bicyclic quartic number fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6215","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":"2026-05-18T04:14:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CmGuTHPPDk66bGVarWfYTCpu5ZhO/KYxD9OBpCxo3Os9RYFjYVnZWimcD5BNCW7mq6ZAm97mxZv6tZaeJCEqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:33:46.599855Z"},"content_sha256":"b7b9549b5a39201fba201d22035998dd5cc8a452820388bb41beb08c96cbaba1","schema_version":"1.0","event_id":"sha256:b7b9549b5a39201fba201d22035998dd5cc8a452820388bb41beb08c96cbaba1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAAFY5PJJZ47QBWMZZ5SANAEYC/bundle.json","state_url":"https://pith.science/pith/TAAFY5PJJZ47QBWMZZ5SANAEYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAAFY5PJJZ47QBWMZZ5SANAEYC/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":"2026-06-11T23:33:46Z","links":{"resolver":"https://pith.science/pith/TAAFY5PJJZ47QBWMZZ5SANAEYC","bundle":"https://pith.science/pith/TAAFY5PJJZ47QBWMZZ5SANAEYC/bundle.json","state":"https://pith.science/pith/TAAFY5PJJZ47QBWMZZ5SANAEYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAAFY5PJJZ47QBWMZZ5SANAEYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TAAFY5PJJZ47QBWMZZ5SANAEYC","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":"17d28f782732420380ffae69564f68ee6e17be8df39d163c7682e1cfbb7409ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T12:59:07Z","title_canon_sha256":"fd291cb2ce4aa6909a4f89371f040219f72b5b5674e3f223419d5b4ef7f98959"},"schema_version":"1.0","source":{"id":"1108.6215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6215","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6215v1","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6215","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"TAAFY5PJJZ47","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"TAAFY5PJJZ47QBWM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"TAAFY5PJ","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:b7b9549b5a39201fba201d22035998dd5cc8a452820388bb41beb08c96cbaba1","target":"graph","created_at":"2026-05-18T04:14:26Z","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":"In this note we present techniques to compute inhomogeneous minima of norm forms; as an application, we determine all norm-Euclidean complex bicyclic quartic number fields.","authors_text":"Franz Lemmermeyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T12:59:07Z","title":"Euclid's Algorithm in quartic CM-fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6215","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:f81cd287732b80eeae870c5d974299498305f048be0fdacc7f8347d8aecd2871","target":"record","created_at":"2026-05-18T04:14:26Z","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":"17d28f782732420380ffae69564f68ee6e17be8df39d163c7682e1cfbb7409ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T12:59:07Z","title_canon_sha256":"fd291cb2ce4aa6909a4f89371f040219f72b5b5674e3f223419d5b4ef7f98959"},"schema_version":"1.0","source":{"id":"1108.6215","kind":"arxiv","version":1}},"canonical_sha256":"98005c75e94e79f806ccce7b203404c08e9cae53c011bd6b01ae7569d6df8076","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98005c75e94e79f806ccce7b203404c08e9cae53c011bd6b01ae7569d6df8076","first_computed_at":"2026-05-18T04:14:26.806280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:26.806280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L41pCJaWSPDyneD4tGkuMwxq3yUwNwzNWW2YTAlPJ2DDl9nK/N8SuTR+zwKZDyCcT2E+YmUET2JPv36Gl6INBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:26.806996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.6215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f81cd287732b80eeae870c5d974299498305f048be0fdacc7f8347d8aecd2871","sha256:b7b9549b5a39201fba201d22035998dd5cc8a452820388bb41beb08c96cbaba1"],"state_sha256":"2bfd6ac83669831614849b55527f3e027db2cf50abb8f28ca99ea9f310115341"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LA/NX08kEvQOEy129SYe8U5dhMh2ukeJ9jreNq1UbLg8rX6j586C9wtNF6rH9Lm95jUvCDaNOrwH3ZC7cfrPAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:33:46.601912Z","bundle_sha256":"7dd08a59490dec2b07ea770a22dd4c90ace0bbc77395ce0aa6234d5a98f66e16"}}