{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BD7EX3OA6UCVT5AX74PJUMWNWQ","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":"28cc2100322bf75be5ca314edc34bf81de517e18cec62ef2e43c4e0189949c94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-01-08T10:57:30Z","title_canon_sha256":"0f3d574c1d57becff12e373e3f19c17dea763f8e1856d8a59928b11dba16f2bd"},"schema_version":"1.0","source":{"id":"2501.04412","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04412","created_at":"2026-07-05T10:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04412v2","created_at":"2026-07-05T10:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04412","created_at":"2026-07-05T10:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"BD7EX3OA6UCV","created_at":"2026-07-05T10:18:47Z"},{"alias_kind":"pith_short_16","alias_value":"BD7EX3OA6UCVT5AX","created_at":"2026-07-05T10:18:47Z"},{"alias_kind":"pith_short_8","alias_value":"BD7EX3OA","created_at":"2026-07-05T10:18:47Z"}],"graph_snapshots":[{"event_id":"sha256:c103fabe40a19a9670f0be80ab8a1a3d8caa3c6eb989244ed12fdf792fa5b30a","target":"graph","created_at":"2026-07-05T10:18:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.04412/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We take up Dedekind's question ''Was sind und was sollen die Zahlen?'' (''What are numbers, and would should they be?''), with the aim to describe the place that Conway's (Surreal) Numbers and Games take, or deserve to take, in the whole of mathematics. Rather than just reviewing the work of Conway, and subsequent one by Gonshor, Alling, Ehrlich, and others, we propose a new setting which puts the theory of surreal numbers onto the firm ground of ''pure'' set theory. This approach is closely related to Gonshor's one by ''sign expansions'', but appears to be significantly simpler and clearer, a","authors_text":"Wolfgang Bertram (IECL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-01-08T10:57:30Z","title":"On Conway's Numbers and Games, the Von Neumann Universe, and Pure Set Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04412","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:c18f3b265e8c31c08329cced42586f9b8ed391316068eb4488b0be40ffb7eab8","target":"record","created_at":"2026-07-05T10:18:47Z","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":"28cc2100322bf75be5ca314edc34bf81de517e18cec62ef2e43c4e0189949c94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-01-08T10:57:30Z","title_canon_sha256":"0f3d574c1d57becff12e373e3f19c17dea763f8e1856d8a59928b11dba16f2bd"},"schema_version":"1.0","source":{"id":"2501.04412","kind":"arxiv","version":2}},"canonical_sha256":"08fe4bedc0f50559f417ff1e9a32cdb40cd29a637960bb4c3adb2d38931195ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08fe4bedc0f50559f417ff1e9a32cdb40cd29a637960bb4c3adb2d38931195ed","first_computed_at":"2026-07-05T10:18:47.976803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:47.976803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"umi8ZZwdRAkw8GNvuYJSdxYCFzVq6+DSb6BcaQkYZFwXGbX47p9iJPqQDZLu81044bHmMtsjZ+TvWJKeVswODw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:47.977301Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.04412","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c18f3b265e8c31c08329cced42586f9b8ed391316068eb4488b0be40ffb7eab8","sha256:c103fabe40a19a9670f0be80ab8a1a3d8caa3c6eb989244ed12fdf792fa5b30a"],"state_sha256":"64c80d006b812cbb96c52b35b656aebf8768b3c9cf319a3f18d3ca61ebaaeee2"}