{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HY55MUPDSDFAH5EX4NQMEHN7YV","short_pith_number":"pith:HY55MUPD","canonical_record":{"source":{"id":"1103.2901","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-15T13:30:17Z","cross_cats_sorted":[],"title_canon_sha256":"7abcf74f11f792342e7c6fe2903f140203bfbd8e0cf776506ba054aca1544022","abstract_canon_sha256":"5b8e7b2dff69a1fa626f11158666faee55e461d41ebbe4c6aaa0dee9f8490336"},"schema_version":"1.0"},"canonical_sha256":"3e3bd651e390ca03f497e360c21dbfc57533ec0b132e38b3c08cd011be7013b0","source":{"kind":"arxiv","id":"1103.2901","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2901","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2901v4","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2901","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"HY55MUPDSDFA","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HY55MUPDSDFAH5EX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HY55MUPD","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HY55MUPDSDFAH5EX4NQMEHN7YV","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2901","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-15T13:30:17Z","cross_cats_sorted":[],"title_canon_sha256":"7abcf74f11f792342e7c6fe2903f140203bfbd8e0cf776506ba054aca1544022","abstract_canon_sha256":"5b8e7b2dff69a1fa626f11158666faee55e461d41ebbe4c6aaa0dee9f8490336"},"schema_version":"1.0"},"canonical_sha256":"3e3bd651e390ca03f497e360c21dbfc57533ec0b132e38b3c08cd011be7013b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:45.015070Z","signature_b64":"KmJ2aIf5AUqvo/ITfesFaZ41fJNfZxWHerAXTC4o9NHzMb75H/gojX8QuhEiSpiIzG0D+BVOOKiMtxEOT72iBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e3bd651e390ca03f497e360c21dbfc57533ec0b132e38b3c08cd011be7013b0","last_reissued_at":"2026-05-18T04:14:45.014655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:45.014655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2901","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BD8YFuDXG5K6wtIFzTZq6Vo2XgVYa6JcPMuXvs+kKSlWIRLxlYFLFNWLqKIklAt9fluTcfjKrZfHw2KkG1qVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:42:23.077274Z"},"content_sha256":"a31983f48d8d46f8224363950ce5e291d958bad70a2f0037d730af01453dd119","schema_version":"1.0","event_id":"sha256:a31983f48d8d46f8224363950ce5e291d958bad70a2f0037d730af01453dd119"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HY55MUPDSDFAH5EX4NQMEHN7YV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algorithm to compute relative cubic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anna Morra","submitted_at":"2011-03-15T13:30:17Z","abstract_excerpt":"Let k be an imaginary quadratic number field (with class number 1). We describe a new, essentially linear-time algorithm, to list all isomorphism classes of cubic extensions L/k up to a bound X on the norm of the relative discriminant ideal. The main tools are Taniguchi's generalization of Davenport-Heilbronn parametrisation of cubic extensions, and reduction theory for binary cubic forms over imaginary quadratic fields. Finally, we give numerical data for k=Q(i), and we compare our results with ray class field algorithm ones, and with asymptotic heuristics, based on a generalization of Robert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2901","kind":"arxiv","version":4},"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":"2026-05-18T04:14:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+Su8yiMWhlm8k9duSQXztsNU7GVLabWVCrBU0TZv7NsXOIxfzW4T516TwBSN5gkuGrrpxwpN0DvXHvrFC7cCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:42:23.077638Z"},"content_sha256":"d39bae6b41c184d1771e5ea8f90e9c019b1a969c2f75afaa3f6701a6c28e46b3","schema_version":"1.0","event_id":"sha256:d39bae6b41c184d1771e5ea8f90e9c019b1a969c2f75afaa3f6701a6c28e46b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY55MUPDSDFAH5EX4NQMEHN7YV/bundle.json","state_url":"https://pith.science/pith/HY55MUPDSDFAH5EX4NQMEHN7YV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY55MUPDSDFAH5EX4NQMEHN7YV/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":"2026-06-02T21:42:23Z","links":{"resolver":"https://pith.science/pith/HY55MUPDSDFAH5EX4NQMEHN7YV","bundle":"https://pith.science/pith/HY55MUPDSDFAH5EX4NQMEHN7YV/bundle.json","state":"https://pith.science/pith/HY55MUPDSDFAH5EX4NQMEHN7YV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY55MUPDSDFAH5EX4NQMEHN7YV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HY55MUPDSDFAH5EX4NQMEHN7YV","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":"5b8e7b2dff69a1fa626f11158666faee55e461d41ebbe4c6aaa0dee9f8490336","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-15T13:30:17Z","title_canon_sha256":"7abcf74f11f792342e7c6fe2903f140203bfbd8e0cf776506ba054aca1544022"},"schema_version":"1.0","source":{"id":"1103.2901","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2901","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2901v4","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2901","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"HY55MUPDSDFA","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HY55MUPDSDFAH5EX","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HY55MUPD","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:d39bae6b41c184d1771e5ea8f90e9c019b1a969c2f75afaa3f6701a6c28e46b3","target":"graph","created_at":"2026-05-18T04:14:45Z","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":"Let k be an imaginary quadratic number field (with class number 1). We describe a new, essentially linear-time algorithm, to list all isomorphism classes of cubic extensions L/k up to a bound X on the norm of the relative discriminant ideal. The main tools are Taniguchi's generalization of Davenport-Heilbronn parametrisation of cubic extensions, and reduction theory for binary cubic forms over imaginary quadratic fields. Finally, we give numerical data for k=Q(i), and we compare our results with ray class field algorithm ones, and with asymptotic heuristics, based on a generalization of Robert","authors_text":"Anna Morra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-15T13:30:17Z","title":"An algorithm to compute relative cubic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2901","kind":"arxiv","version":4},"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:a31983f48d8d46f8224363950ce5e291d958bad70a2f0037d730af01453dd119","target":"record","created_at":"2026-05-18T04:14:45Z","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":"5b8e7b2dff69a1fa626f11158666faee55e461d41ebbe4c6aaa0dee9f8490336","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-15T13:30:17Z","title_canon_sha256":"7abcf74f11f792342e7c6fe2903f140203bfbd8e0cf776506ba054aca1544022"},"schema_version":"1.0","source":{"id":"1103.2901","kind":"arxiv","version":4}},"canonical_sha256":"3e3bd651e390ca03f497e360c21dbfc57533ec0b132e38b3c08cd011be7013b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e3bd651e390ca03f497e360c21dbfc57533ec0b132e38b3c08cd011be7013b0","first_computed_at":"2026-05-18T04:14:45.014655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:45.014655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KmJ2aIf5AUqvo/ITfesFaZ41fJNfZxWHerAXTC4o9NHzMb75H/gojX8QuhEiSpiIzG0D+BVOOKiMtxEOT72iBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:45.015070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2901","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a31983f48d8d46f8224363950ce5e291d958bad70a2f0037d730af01453dd119","sha256:d39bae6b41c184d1771e5ea8f90e9c019b1a969c2f75afaa3f6701a6c28e46b3"],"state_sha256":"f09fcd4ef7fc3c20f224564a0a8530c5b53a5c56477710fc76265ceb375058b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JMv6YBsE2ZJbrglCrsJvmTuV7QSBce9XC7FZ8iDljbRG4QMI4vAAlczwsGpltNavxeISfLPfwHCN0ZAAdBg8CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:42:23.079590Z","bundle_sha256":"b25881e627b65026271db98f77fe1a2c62444a1867b87540d0b423bb2302c022"}}