{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:PI7YDWBL72EOU2GOKPM4D662DS","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":"9b4b088cbfcae63bdb618e4b46729822969a91e48e2a80a3812921843f961288","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.AC","submitted_at":"1997-08-18T00:00:00Z","title_canon_sha256":"a75c90494869d0a0690b7422c12eace598f3e49bf9d077012e3ead27e65ede0a"},"schema_version":"1.0","source":{"id":"math/9708212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9708212","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/9708212v1","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9708212","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"PI7YDWBL72EO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"PI7YDWBL72EOU2GO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"PI7YDWBL","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:6627d25690f9b1b8b2e61d795c222d03c5dbe85c52893e7fa39f1e8528da1cd4","target":"graph","created_at":"2026-05-18T03:29:16Z","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":"Based on the work of Hahn, Baer, Ostrowski, Krull, Kaplansky and the Artin-Schreier theory, and stimulated by a paper of S. Lang in 1953, the theory of real places and convex valuations has witnessed a remarkable development and has become a basic tool in the theory of ordered fields and real algebraic geometry. In this paper, we take a further step by adding an exponential function to the ordered field.","authors_text":"Franz-Viktor Kuhlmann (Fields Institute), Salma Kuhlmann","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.AC","submitted_at":"1997-08-18T00:00:00Z","title":"The exponential rank of non-Archimedean exponential fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9708212","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":"sha256:9c229bd52a33f2ef86ef49d3e188c6121d55efcebd0da8476053ffef566555f2","target":"record","created_at":"2026-05-18T03:29:16Z","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":"9b4b088cbfcae63bdb618e4b46729822969a91e48e2a80a3812921843f961288","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.AC","submitted_at":"1997-08-18T00:00:00Z","title_canon_sha256":"a75c90494869d0a0690b7422c12eace598f3e49bf9d077012e3ead27e65ede0a"},"schema_version":"1.0","source":{"id":"math/9708212","kind":"arxiv","version":1}},"canonical_sha256":"7a3f81d82bfe88ea68ce53d9c1fbda1c84a2955a8e1f2b9132bce8b2543d7be1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a3f81d82bfe88ea68ce53d9c1fbda1c84a2955a8e1f2b9132bce8b2543d7be1","first_computed_at":"2026-05-18T03:29:16.793056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:16.793056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nb7Jo23X4/bL/AI6HArkKORFlZvGY6Vzl2gZ7GC1u4SuAxYlr9wcBm0Ww79NzEPfSzlHKPzw2aSracAQkpR7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:16.793761Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9708212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c229bd52a33f2ef86ef49d3e188c6121d55efcebd0da8476053ffef566555f2","sha256:6627d25690f9b1b8b2e61d795c222d03c5dbe85c52893e7fa39f1e8528da1cd4"],"state_sha256":"f9a64dc765254b9f2bc446d77be209ea212d9823875e35d275d5d61725830d2a"}