{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MR4J2K2YFGYN6CICESG4IDBHMT","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":"84940202687322a8a5e0aa24a5a4d4d5e8ec03458a142b854bfec28a88ff6f00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-07T14:45:55Z","title_canon_sha256":"7b598fdc2f11254afab1bf70fb3635ab8c88be857f69c4ba563de4c977f80a84"},"schema_version":"1.0","source":{"id":"1208.1434","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1434","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1434v3","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1434","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"MR4J2K2YFGYN","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MR4J2K2YFGYN6CIC","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MR4J2K2Y","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:60dd24f5c39f1dde6422e0925f1c901ecf22311e33348e48376df6355fbcb52c","target":"graph","created_at":"2026-05-18T03:08:27Z","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 put forward a new method of constructing the complete ordered field of real numbers from the ordered field of rational numbers. Our method is a generalization of that of A. Knopfmacher and J. Knopfmacher. Our result implies that there exist infinitely many ways of constructing the complete ordered field of real numbers. As an application of our results, we prove the irrationality of certain numbers.","authors_text":"Soichi Ikeda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-07T14:45:55Z","title":"A new construction of the real numbers by alternating series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1434","kind":"arxiv","version":3},"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":"sha256:983be5a5a8f31e711a2081b3b91c75b8af37595f8bf2579fc5d241187cde7de2","target":"record","created_at":"2026-05-18T03:08:27Z","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":"84940202687322a8a5e0aa24a5a4d4d5e8ec03458a142b854bfec28a88ff6f00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-07T14:45:55Z","title_canon_sha256":"7b598fdc2f11254afab1bf70fb3635ab8c88be857f69c4ba563de4c977f80a84"},"schema_version":"1.0","source":{"id":"1208.1434","kind":"arxiv","version":3}},"canonical_sha256":"64789d2b5829b0df0902248dc40c2764dfbf55f13963f9a409f066409b2721c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64789d2b5829b0df0902248dc40c2764dfbf55f13963f9a409f066409b2721c2","first_computed_at":"2026-05-18T03:08:27.322809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:27.322809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b35+QXTRZ4vVzQ78jWQF/i//QjcPKUXYKraON9gvM/25MVv2THnZvFXokTKIRLCKL1ujemuv2+mutVMLuc+VDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:27.323497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1434","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:983be5a5a8f31e711a2081b3b91c75b8af37595f8bf2579fc5d241187cde7de2","sha256:60dd24f5c39f1dde6422e0925f1c901ecf22311e33348e48376df6355fbcb52c"],"state_sha256":"32f65fc209c9d296340d8e3c99b2046608004f34a42063fc9726b83de245f255"}