{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:V4ITZ4CSHHDNPYN57PKITR55Y4","short_pith_number":"pith:V4ITZ4CS","canonical_record":{"source":{"id":"1809.10399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-27T08:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"bb216cecf192df1107b396bb6f403ad68659878b4ae74bfd2514fe97fab2362f","abstract_canon_sha256":"5806e4c6d89f2be3acbde83cb497e99d328ada6d2165e8dded5ad29262d1c0e1"},"schema_version":"1.0"},"canonical_sha256":"af113cf05239c6d7e1bdfbd489c7bdc736724dda83106a82a05a3fcc6fb248c8","source":{"kind":"arxiv","id":"1809.10399","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10399","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10399v1","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10399","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"V4ITZ4CSHHDN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V4ITZ4CSHHDNPYN5","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V4ITZ4CS","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:V4ITZ4CSHHDNPYN57PKITR55Y4","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-27T08:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"bb216cecf192df1107b396bb6f403ad68659878b4ae74bfd2514fe97fab2362f","abstract_canon_sha256":"5806e4c6d89f2be3acbde83cb497e99d328ada6d2165e8dded5ad29262d1c0e1"},"schema_version":"1.0"},"canonical_sha256":"af113cf05239c6d7e1bdfbd489c7bdc736724dda83106a82a05a3fcc6fb248c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:38.436461Z","signature_b64":"xzjGeSc2OMD8/xtp9HnVri8Mpl1bXIZmyyth/rAQsEsRTK8tKpJXfTKtH3ucIK66ty/CtxUoWZjY/A9sfrFdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af113cf05239c6d7e1bdfbd489c7bdc736724dda83106a82a05a3fcc6fb248c8","last_reissued_at":"2026-05-18T00:04:38.435940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:38.435940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10399","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":"2026-05-18T00:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vFeDSvSdmbc+F4ug0ehw4zaf4lIAYxwe3YiZ281TQoInXv9XQMCFtFXA+LPvEuk1yTKNimMOE7ZjDhYrDKviBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:56:18.493083Z"},"content_sha256":"740880d97620b4d331ddafd8c8eea5c716834ddf2b975c404d71a24602d8533e","schema_version":"1.0","event_id":"sha256:740880d97620b4d331ddafd8c8eea5c716834ddf2b975c404d71a24602d8533e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:V4ITZ4CSHHDNPYN57PKITR55Y4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Power integral bases in a family of sextic fields with quadratic subfields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Istv\\'an Ga\\'al, L\\'aszl\\'o Remete","submitted_at":"2018-09-27T08:30:32Z","abstract_excerpt":"Let $M=Q(i\\sqrt{d})$ be any imaginary quadratic field with a positive square-free $d$. Consider the polynomial \\[ f(x)=x^3-ax^2-(a+3)x-1, \\] with a parameter $a\\in Z$. Let $K=M(\\alpha)$, where $\\alpha$ is a root of $f$. This is an infinite parametric family of sextic fields depending on two parameters, $a$ and $d$. Applying relative Thue equations we determine the relative power integral bases of these sextic fields over their quadratic subfields. Using these results we also determine generators of (absolute) power integral bases of the sextic fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10399","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":"2026-05-18T00:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C235tdfbg7vga5w6XLl5HZ49sFgW1kAyRj3FhSizIKQJ4cohguq55wriY8u87GjwiL5gP+KcOXpue/KCAI5/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:56:18.493500Z"},"content_sha256":"d73ab5bc4808893cb94310ce980e7295aecea24470c39eb479c5ffe125822df7","schema_version":"1.0","event_id":"sha256:d73ab5bc4808893cb94310ce980e7295aecea24470c39eb479c5ffe125822df7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4ITZ4CSHHDNPYN57PKITR55Y4/bundle.json","state_url":"https://pith.science/pith/V4ITZ4CSHHDNPYN57PKITR55Y4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4ITZ4CSHHDNPYN57PKITR55Y4/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":"2026-07-01T10:56:18Z","links":{"resolver":"https://pith.science/pith/V4ITZ4CSHHDNPYN57PKITR55Y4","bundle":"https://pith.science/pith/V4ITZ4CSHHDNPYN57PKITR55Y4/bundle.json","state":"https://pith.science/pith/V4ITZ4CSHHDNPYN57PKITR55Y4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4ITZ4CSHHDNPYN57PKITR55Y4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V4ITZ4CSHHDNPYN57PKITR55Y4","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":"5806e4c6d89f2be3acbde83cb497e99d328ada6d2165e8dded5ad29262d1c0e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-27T08:30:32Z","title_canon_sha256":"bb216cecf192df1107b396bb6f403ad68659878b4ae74bfd2514fe97fab2362f"},"schema_version":"1.0","source":{"id":"1809.10399","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10399","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10399v1","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10399","created_at":"2026-05-18T00:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"V4ITZ4CSHHDN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V4ITZ4CSHHDNPYN5","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V4ITZ4CS","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:d73ab5bc4808893cb94310ce980e7295aecea24470c39eb479c5ffe125822df7","target":"graph","created_at":"2026-05-18T00:04:38Z","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 $M=Q(i\\sqrt{d})$ be any imaginary quadratic field with a positive square-free $d$. Consider the polynomial \\[ f(x)=x^3-ax^2-(a+3)x-1, \\] with a parameter $a\\in Z$. Let $K=M(\\alpha)$, where $\\alpha$ is a root of $f$. This is an infinite parametric family of sextic fields depending on two parameters, $a$ and $d$. Applying relative Thue equations we determine the relative power integral bases of these sextic fields over their quadratic subfields. Using these results we also determine generators of (absolute) power integral bases of the sextic fields.","authors_text":"Istv\\'an Ga\\'al, L\\'aszl\\'o Remete","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-27T08:30:32Z","title":"Power integral bases in a family of sextic fields with quadratic subfields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10399","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":"sha256:740880d97620b4d331ddafd8c8eea5c716834ddf2b975c404d71a24602d8533e","target":"record","created_at":"2026-05-18T00:04:38Z","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":"5806e4c6d89f2be3acbde83cb497e99d328ada6d2165e8dded5ad29262d1c0e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-27T08:30:32Z","title_canon_sha256":"bb216cecf192df1107b396bb6f403ad68659878b4ae74bfd2514fe97fab2362f"},"schema_version":"1.0","source":{"id":"1809.10399","kind":"arxiv","version":1}},"canonical_sha256":"af113cf05239c6d7e1bdfbd489c7bdc736724dda83106a82a05a3fcc6fb248c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af113cf05239c6d7e1bdfbd489c7bdc736724dda83106a82a05a3fcc6fb248c8","first_computed_at":"2026-05-18T00:04:38.435940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:38.435940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xzjGeSc2OMD8/xtp9HnVri8Mpl1bXIZmyyth/rAQsEsRTK8tKpJXfTKtH3ucIK66ty/CtxUoWZjY/A9sfrFdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:38.436461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10399","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:740880d97620b4d331ddafd8c8eea5c716834ddf2b975c404d71a24602d8533e","sha256:d73ab5bc4808893cb94310ce980e7295aecea24470c39eb479c5ffe125822df7"],"state_sha256":"44748bc34ed2948a10792ddea1670c32c6b2ac16e21b628bef92e06fbe7d51e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gXw9Zd+MIzNBjdiAx224m3AFDTzYb9EAvtRfYPapH3OFmXnO/PZvN0xQdvbIHgl3Bbth6lx9F2JsyBaZ93+pCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T10:56:18.495662Z","bundle_sha256":"4fb886a0b68fd20fbdaaa99843dd0139a279c8b376d4c8f38da1b1b6a9734155"}}