{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:5UBQJTVSCAUJ446WGS2N2XISRB","short_pith_number":"pith:5UBQJTVS","canonical_record":{"source":{"id":"0712.4037","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2007-12-26T09:08:27Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"59d6fd79c29977557bbd1649bb7cff50e32e279b1ccaab1a1364ef76aa3d366c","abstract_canon_sha256":"989c6981b0973d9c905b63216e085fb708104784cc8223676574853417b5396d"},"schema_version":"1.0"},"canonical_sha256":"ed0304ceb210289e73d634b4dd5d1288665bb070309d8acec74a77b9ec2e7f50","source":{"kind":"arxiv","id":"0712.4037","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4037","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4037v1","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4037","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"5UBQJTVSCAUJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5UBQJTVSCAUJ446W","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5UBQJTVS","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:5UBQJTVSCAUJ446WGS2N2XISRB","target":"record","payload":{"canonical_record":{"source":{"id":"0712.4037","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2007-12-26T09:08:27Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"59d6fd79c29977557bbd1649bb7cff50e32e279b1ccaab1a1364ef76aa3d366c","abstract_canon_sha256":"989c6981b0973d9c905b63216e085fb708104784cc8223676574853417b5396d"},"schema_version":"1.0"},"canonical_sha256":"ed0304ceb210289e73d634b4dd5d1288665bb070309d8acec74a77b9ec2e7f50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:28.226102Z","signature_b64":"y55cxEs26fRmKINdoix5Wx5fywiiFBxZmYqEppz3SS7dZRHxWBmd8ZvzCnt3AckGhU6E9W2xClytGMZT7qQRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed0304ceb210289e73d634b4dd5d1288665bb070309d8acec74a77b9ec2e7f50","last_reissued_at":"2026-05-18T03:29:28.225533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:28.225533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.4037","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":"2026-05-18T03:29:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4jD4oSudXVnXYOiAz9VUgEekJgpiTEH0D2vufy5sYCK4By19KMkiAqhZDj9F5mHkjWilmbd2LTEdNASrF3BACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:15:24.371735Z"},"content_sha256":"c69e1ff585b6ed633969786286387172d05dd15dbae125cce243eef16ef6b4f4","schema_version":"1.0","event_id":"sha256:c69e1ff585b6ed633969786286387172d05dd15dbae125cce243eef16ef6b4f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:5UBQJTVSCAUJ446WGS2N2XISRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Valuation bases for generalized algebraic series fields","license":"","headline":"","cross_cats":["math.LO"],"primary_cat":"math.AC","authors_text":"Franz-Viktor Kuhlmann, Jonathan W. Lee, Salma Kuhlmann","submitted_at":"2007-12-26T09:08:27Z","abstract_excerpt":"We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed, or algebraically closed field F, we give a sufficient condition for a valued subfield of the field of generalized power series F((G)) to admit a K-valuation basis. We show that the field of rational functions F(G) and the field F(G) of power series in F((G)) algebraic over F(G) satisfy this condition. It follows that for archimedean F and divisible G the real closed field F(G) admits a restricted exponential function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4037","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":"2026-05-18T03:29:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBWPIkOl0SIKhvXR1ZKDM1A+tQoAkxSlpkmA1BTHJM5EeXT5/MFrXKFTc/F9ydmqjpJbLHG1k8kF5C/vwq5OAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:15:24.372439Z"},"content_sha256":"d391852f35538b8613920bba63120b998d4e33331af046a734aae5238cbf64c6","schema_version":"1.0","event_id":"sha256:d391852f35538b8613920bba63120b998d4e33331af046a734aae5238cbf64c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5UBQJTVSCAUJ446WGS2N2XISRB/bundle.json","state_url":"https://pith.science/pith/5UBQJTVSCAUJ446WGS2N2XISRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5UBQJTVSCAUJ446WGS2N2XISRB/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":"2026-05-30T06:15:24Z","links":{"resolver":"https://pith.science/pith/5UBQJTVSCAUJ446WGS2N2XISRB","bundle":"https://pith.science/pith/5UBQJTVSCAUJ446WGS2N2XISRB/bundle.json","state":"https://pith.science/pith/5UBQJTVSCAUJ446WGS2N2XISRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5UBQJTVSCAUJ446WGS2N2XISRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:5UBQJTVSCAUJ446WGS2N2XISRB","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":"989c6981b0973d9c905b63216e085fb708104784cc8223676574853417b5396d","cross_cats_sorted":["math.LO"],"license":"","primary_cat":"math.AC","submitted_at":"2007-12-26T09:08:27Z","title_canon_sha256":"59d6fd79c29977557bbd1649bb7cff50e32e279b1ccaab1a1364ef76aa3d366c"},"schema_version":"1.0","source":{"id":"0712.4037","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4037","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4037v1","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4037","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"5UBQJTVSCAUJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5UBQJTVSCAUJ446W","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5UBQJTVS","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:d391852f35538b8613920bba63120b998d4e33331af046a734aae5238cbf64c6","target":"graph","created_at":"2026-05-18T03:29:28Z","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 investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed, or algebraically closed field F, we give a sufficient condition for a valued subfield of the field of generalized power series F((G)) to admit a K-valuation basis. We show that the field of rational functions F(G) and the field F(G) of power series in F((G)) algebraic over F(G) satisfy this condition. It follows that for archimedean F and divisible G the real closed field F(G) admits a restricted exponential function.","authors_text":"Franz-Viktor Kuhlmann, Jonathan W. Lee, Salma Kuhlmann","cross_cats":["math.LO"],"headline":"","license":"","primary_cat":"math.AC","submitted_at":"2007-12-26T09:08:27Z","title":"Valuation bases for generalized algebraic series fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4037","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:c69e1ff585b6ed633969786286387172d05dd15dbae125cce243eef16ef6b4f4","target":"record","created_at":"2026-05-18T03:29:28Z","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":"989c6981b0973d9c905b63216e085fb708104784cc8223676574853417b5396d","cross_cats_sorted":["math.LO"],"license":"","primary_cat":"math.AC","submitted_at":"2007-12-26T09:08:27Z","title_canon_sha256":"59d6fd79c29977557bbd1649bb7cff50e32e279b1ccaab1a1364ef76aa3d366c"},"schema_version":"1.0","source":{"id":"0712.4037","kind":"arxiv","version":1}},"canonical_sha256":"ed0304ceb210289e73d634b4dd5d1288665bb070309d8acec74a77b9ec2e7f50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed0304ceb210289e73d634b4dd5d1288665bb070309d8acec74a77b9ec2e7f50","first_computed_at":"2026-05-18T03:29:28.225533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:28.225533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y55cxEs26fRmKINdoix5Wx5fywiiFBxZmYqEppz3SS7dZRHxWBmd8ZvzCnt3AckGhU6E9W2xClytGMZT7qQRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:28.226102Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.4037","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c69e1ff585b6ed633969786286387172d05dd15dbae125cce243eef16ef6b4f4","sha256:d391852f35538b8613920bba63120b998d4e33331af046a734aae5238cbf64c6"],"state_sha256":"34a8447500eddce677e94fd7eaa68fba99953366c266bb2f835fee7ba18bdb1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3c4/rBE2kx49q2Ms+mVac9C3X8gK7GOGQnMxPBKGo5TovGui7dhgaC/NVRT7fh5LYLjVPSGGbYsYEhGGYEZ0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:15:24.376288Z","bundle_sha256":"b3193ad53b163e70e5a2f466553bf30a823f5afab96ef47ae4cfa2d3ad0bd3d9"}}