{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FIBNPTLDTRUADJJT37WUFUDCBY","short_pith_number":"pith:FIBNPTLD","canonical_record":{"source":{"id":"1108.6218","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T13:05:38Z","cross_cats_sorted":[],"title_canon_sha256":"5e05027998a73acdfaebbf691e2332bcabdb06378e7d3e5ce3302b7a3d87dced","abstract_canon_sha256":"e5540cdfaddf50ae1cd2a6f53c81a64b90c8b2891cdb0e8869eccb09ffe6f1bc"},"schema_version":"1.0"},"canonical_sha256":"2a02d7cd639c6801a533dfed42d0620e35c9699645b4e219bb92e1d063dfaa66","source":{"kind":"arxiv","id":"1108.6218","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6218","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6218v2","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6218","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"pith_short_12","alias_value":"FIBNPTLDTRUA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FIBNPTLDTRUADJJT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FIBNPTLD","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FIBNPTLDTRUADJJT37WUFUDCBY","target":"record","payload":{"canonical_record":{"source":{"id":"1108.6218","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T13:05:38Z","cross_cats_sorted":[],"title_canon_sha256":"5e05027998a73acdfaebbf691e2332bcabdb06378e7d3e5ce3302b7a3d87dced","abstract_canon_sha256":"e5540cdfaddf50ae1cd2a6f53c81a64b90c8b2891cdb0e8869eccb09ffe6f1bc"},"schema_version":"1.0"},"canonical_sha256":"2a02d7cd639c6801a533dfed42d0620e35c9699645b4e219bb92e1d063dfaa66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:31.368490Z","signature_b64":"0BcnZ7LzQeN+ZEyDcrIoMX+qgbnWpzs4n9eK8KSeRlbWTYupcjMxitEc+wkOph+Uc6y5318UcCiFpROO+1iABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a02d7cd639c6801a533dfed42d0620e35c9699645b4e219bb92e1d063dfaa66","last_reissued_at":"2026-05-18T04:11:31.368017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:31.368017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.6218","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NZ9EWfl4/dNSG681bEyL5nB74lyOjLRhTY8cyglXs0uTFkkI9F++NS1DJXBEz3cEXifesDkz2JJdIvKhXqCvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:05:29.790072Z"},"content_sha256":"199e3ce202a5774603a93a16029f164720f0efe26f07b68f56cae225f5ca993c","schema_version":"1.0","event_id":"sha256:199e3ce202a5774603a93a16029f164720f0efe26f07b68f56cae225f5ca993c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FIBNPTLDTRUADJJT37WUFUDCBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Binomial Squares in Pure Cubic Number Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Franz Lemmermeyer","submitted_at":"2011-08-31T13:05:38Z","abstract_excerpt":"Let K = Q(\\omega) with \\omega^3 = m be a pure cubic number field. We show that the elements\\alpha \\in K^\\times whose squares have the form a - \\omega form a group isomorphic to the group of rational points on the elliptic curve E_m: y^2= x^3 - m. We also show how to apply these results to the construction of unramified quadratic extensions of pure cubic number fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6218","kind":"arxiv","version":2},"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":"2026-05-18T04:11:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fc894/d9FTRJprddYImS3ZZOE1bcSdScG4Gz/L+l9M/Ly9rSlT/haY0XQEViTmqD8MT0pErnsvCFjrTPI0XlAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:05:29.790473Z"},"content_sha256":"7cba4333f0418814f54d8619a062893a5ee58c3700192e7017d118f521780d9c","schema_version":"1.0","event_id":"sha256:7cba4333f0418814f54d8619a062893a5ee58c3700192e7017d118f521780d9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FIBNPTLDTRUADJJT37WUFUDCBY/bundle.json","state_url":"https://pith.science/pith/FIBNPTLDTRUADJJT37WUFUDCBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FIBNPTLDTRUADJJT37WUFUDCBY/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":"2026-06-11T20:05:29Z","links":{"resolver":"https://pith.science/pith/FIBNPTLDTRUADJJT37WUFUDCBY","bundle":"https://pith.science/pith/FIBNPTLDTRUADJJT37WUFUDCBY/bundle.json","state":"https://pith.science/pith/FIBNPTLDTRUADJJT37WUFUDCBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FIBNPTLDTRUADJJT37WUFUDCBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FIBNPTLDTRUADJJT37WUFUDCBY","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":"e5540cdfaddf50ae1cd2a6f53c81a64b90c8b2891cdb0e8869eccb09ffe6f1bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T13:05:38Z","title_canon_sha256":"5e05027998a73acdfaebbf691e2332bcabdb06378e7d3e5ce3302b7a3d87dced"},"schema_version":"1.0","source":{"id":"1108.6218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6218","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6218v2","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6218","created_at":"2026-05-18T04:11:31Z"},{"alias_kind":"pith_short_12","alias_value":"FIBNPTLDTRUA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FIBNPTLDTRUADJJT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FIBNPTLD","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:7cba4333f0418814f54d8619a062893a5ee58c3700192e7017d118f521780d9c","target":"graph","created_at":"2026-05-18T04:11:31Z","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 = Q(\\omega) with \\omega^3 = m be a pure cubic number field. We show that the elements\\alpha \\in K^\\times whose squares have the form a - \\omega form a group isomorphic to the group of rational points on the elliptic curve E_m: y^2= x^3 - m. We also show how to apply these results to the construction of unramified quadratic extensions of pure cubic number fields.","authors_text":"Franz Lemmermeyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T13:05:38Z","title":"Binomial Squares in Pure Cubic Number Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6218","kind":"arxiv","version":2},"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":"sha256:199e3ce202a5774603a93a16029f164720f0efe26f07b68f56cae225f5ca993c","target":"record","created_at":"2026-05-18T04:11:31Z","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":"e5540cdfaddf50ae1cd2a6f53c81a64b90c8b2891cdb0e8869eccb09ffe6f1bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-31T13:05:38Z","title_canon_sha256":"5e05027998a73acdfaebbf691e2332bcabdb06378e7d3e5ce3302b7a3d87dced"},"schema_version":"1.0","source":{"id":"1108.6218","kind":"arxiv","version":2}},"canonical_sha256":"2a02d7cd639c6801a533dfed42d0620e35c9699645b4e219bb92e1d063dfaa66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a02d7cd639c6801a533dfed42d0620e35c9699645b4e219bb92e1d063dfaa66","first_computed_at":"2026-05-18T04:11:31.368017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:31.368017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0BcnZ7LzQeN+ZEyDcrIoMX+qgbnWpzs4n9eK8KSeRlbWTYupcjMxitEc+wkOph+Uc6y5318UcCiFpROO+1iABg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:31.368490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.6218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:199e3ce202a5774603a93a16029f164720f0efe26f07b68f56cae225f5ca993c","sha256:7cba4333f0418814f54d8619a062893a5ee58c3700192e7017d118f521780d9c"],"state_sha256":"39ff8daaf9e0cdb32e82a0ad8d520887ed55faefc7e59cde6dc8ac18dc8e3616"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hiX2m/hAqibDsqYbk24y7AkkqLcGg+tbFuFsWNvgB4QfPbzORri833E20nJS4b7Asy6Oa8Rl5fOLe4dZ5WayCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:05:29.792960Z","bundle_sha256":"296507eb300813e54ba41f4ae1ed17f9727e2c48ab2d15db920f82e861970ee9"}}