{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZGQRNOIKQRXFQ5EWMK56WLJTHJ","short_pith_number":"pith:ZGQRNOIK","canonical_record":{"source":{"id":"1112.4062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-17T15:08:31Z","cross_cats_sorted":[],"title_canon_sha256":"2f5c621f07f3e26c1e592fb8f2097cb2dff1029e72fffbb937bcaddb5244d9b2","abstract_canon_sha256":"31808a2c1997264ec2cb155cb9b119f14c0a8452629a2cfe6aec8028a9a5a5be"},"schema_version":"1.0"},"canonical_sha256":"c9a116b90a846e58749662bbeb2d333a4eff1658db67985eec3db525cc6cf595","source":{"kind":"arxiv","id":"1112.4062","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4062","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4062v1","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4062","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZGQRNOIKQRXF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZGQRNOIKQRXFQ5EW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZGQRNOIK","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZGQRNOIKQRXFQ5EWMK56WLJTHJ","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-17T15:08:31Z","cross_cats_sorted":[],"title_canon_sha256":"2f5c621f07f3e26c1e592fb8f2097cb2dff1029e72fffbb937bcaddb5244d9b2","abstract_canon_sha256":"31808a2c1997264ec2cb155cb9b119f14c0a8452629a2cfe6aec8028a9a5a5be"},"schema_version":"1.0"},"canonical_sha256":"c9a116b90a846e58749662bbeb2d333a4eff1658db67985eec3db525cc6cf595","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:41.580748Z","signature_b64":"e6fP98Woq7I8oQ7SJx+JXZfzvlQk20XqBmYUnYkvNw2vLe6P6xVklWaMQdFqWgNdngcOU2i8oPnmtYeXuXQBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9a116b90a846e58749662bbeb2d333a4eff1658db67985eec3db525cc6cf595","last_reissued_at":"2026-05-18T03:37:41.580252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:41.580252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4062","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":"2026-05-18T03:37:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i9151cSSg/P37vdnn5N9YApeDO4lDwjULEEXV7IS1n8IiKwljBe4dUKXqvQ/VixdRwrxwuTfhS9A9YQsy3MYCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:51:08.574536Z"},"content_sha256":"18bd33a22641f55dd726690f4440da1fa6240e545005a1c2d1055aa62c8f86be","schema_version":"1.0","event_id":"sha256:18bd33a22641f55dd726690f4440da1fa6240e545005a1c2d1055aa62c8f86be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZGQRNOIKQRXFQ5EWMK56WLJTHJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real closed exponential fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Julia F. Knight, Karen Lange, Paola D'Aquino, Salma Kuhlmann","submitted_at":"2011-12-17T15:08:31Z","abstract_excerpt":"In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre's construction, which becomes canonical once we fix the real closed exponential field, a residue field section, and a well ordering of the field. The procedure is constructible over these objects; each step looks effective, but may require many steps. We produce an example of an exponential field $R$ with a resi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4062","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":"2026-05-18T03:37:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Td7owixyiJb0Wt+7nsDj0K7m160CH0OEnSrj+y5S46If1h3Zucqdh/j/hSYxCB6C/VeLrMJTdrTU9/aBOSmRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:51:08.574889Z"},"content_sha256":"790e534a3eb36df9bebace5f111f13dd3e7f3f15466c31b61fb6559a8122424e","schema_version":"1.0","event_id":"sha256:790e534a3eb36df9bebace5f111f13dd3e7f3f15466c31b61fb6559a8122424e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGQRNOIKQRXFQ5EWMK56WLJTHJ/bundle.json","state_url":"https://pith.science/pith/ZGQRNOIKQRXFQ5EWMK56WLJTHJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGQRNOIKQRXFQ5EWMK56WLJTHJ/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":"2026-06-01T20:51:08Z","links":{"resolver":"https://pith.science/pith/ZGQRNOIKQRXFQ5EWMK56WLJTHJ","bundle":"https://pith.science/pith/ZGQRNOIKQRXFQ5EWMK56WLJTHJ/bundle.json","state":"https://pith.science/pith/ZGQRNOIKQRXFQ5EWMK56WLJTHJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGQRNOIKQRXFQ5EWMK56WLJTHJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZGQRNOIKQRXFQ5EWMK56WLJTHJ","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":"31808a2c1997264ec2cb155cb9b119f14c0a8452629a2cfe6aec8028a9a5a5be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-17T15:08:31Z","title_canon_sha256":"2f5c621f07f3e26c1e592fb8f2097cb2dff1029e72fffbb937bcaddb5244d9b2"},"schema_version":"1.0","source":{"id":"1112.4062","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4062","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4062v1","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4062","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZGQRNOIKQRXF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZGQRNOIKQRXFQ5EW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZGQRNOIK","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:790e534a3eb36df9bebace5f111f13dd3e7f3f15466c31b61fb6559a8122424e","target":"graph","created_at":"2026-05-18T03:37:41Z","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":"In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre's construction, which becomes canonical once we fix the real closed exponential field, a residue field section, and a well ordering of the field. The procedure is constructible over these objects; each step looks effective, but may require many steps. We produce an example of an exponential field $R$ with a resi","authors_text":"Julia F. Knight, Karen Lange, Paola D'Aquino, Salma Kuhlmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-17T15:08:31Z","title":"Real closed exponential fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4062","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":"sha256:18bd33a22641f55dd726690f4440da1fa6240e545005a1c2d1055aa62c8f86be","target":"record","created_at":"2026-05-18T03:37:41Z","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":"31808a2c1997264ec2cb155cb9b119f14c0a8452629a2cfe6aec8028a9a5a5be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-17T15:08:31Z","title_canon_sha256":"2f5c621f07f3e26c1e592fb8f2097cb2dff1029e72fffbb937bcaddb5244d9b2"},"schema_version":"1.0","source":{"id":"1112.4062","kind":"arxiv","version":1}},"canonical_sha256":"c9a116b90a846e58749662bbeb2d333a4eff1658db67985eec3db525cc6cf595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9a116b90a846e58749662bbeb2d333a4eff1658db67985eec3db525cc6cf595","first_computed_at":"2026-05-18T03:37:41.580252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:41.580252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e6fP98Woq7I8oQ7SJx+JXZfzvlQk20XqBmYUnYkvNw2vLe6P6xVklWaMQdFqWgNdngcOU2i8oPnmtYeXuXQBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:41.580748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4062","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18bd33a22641f55dd726690f4440da1fa6240e545005a1c2d1055aa62c8f86be","sha256:790e534a3eb36df9bebace5f111f13dd3e7f3f15466c31b61fb6559a8122424e"],"state_sha256":"ce14e95889bc6b22271c70a572bbba1199563ead9f20fe276135eb974adea3ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7/urSoiDZ1GztwqKtpGKpD9wF9BcqRiCLkdTbxBm8Z8d3+kWcFW9Emwv+Lrj6cetmucfTs/b9sEVjoiw+O+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:51:08.576807Z","bundle_sha256":"92b342b42db62750256929efc0acafd79be0336d11be6c5ef3f2fa42965993ca"}}