{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UAYESYPFY6OG5PCBIL6UF4QP6D","short_pith_number":"pith:UAYESYPF","canonical_record":{"source":{"id":"1112.4784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-20T18:04:57Z","cross_cats_sorted":[],"title_canon_sha256":"eb38d92f244828fb9a77142be33b8b601c48422cb218f1ef6780c5542acd7054","abstract_canon_sha256":"97977f6256783ddfe96eea85decf80951a9fcf9a4e591e73618fe82a0fdd84f8"},"schema_version":"1.0"},"canonical_sha256":"a0304961e5c79c6ebc4142fd42f20ff0c62f67a9c86d69da84cbeb653b47aeba","source":{"kind":"arxiv","id":"1112.4784","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4784","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4784v1","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4784","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"pith_short_12","alias_value":"UAYESYPFY6OG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UAYESYPFY6OG5PCB","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UAYESYPF","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UAYESYPFY6OG5PCBIL6UF4QP6D","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-20T18:04:57Z","cross_cats_sorted":[],"title_canon_sha256":"eb38d92f244828fb9a77142be33b8b601c48422cb218f1ef6780c5542acd7054","abstract_canon_sha256":"97977f6256783ddfe96eea85decf80951a9fcf9a4e591e73618fe82a0fdd84f8"},"schema_version":"1.0"},"canonical_sha256":"a0304961e5c79c6ebc4142fd42f20ff0c62f67a9c86d69da84cbeb653b47aeba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:05.822670Z","signature_b64":"vdSvSUHesfdkDafekDqcEz+bgby7gQvAaZCVgAoDuzcK+gpcjhOswFepR7Xix75+fuJbH9DjrMhszfWP3QnmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0304961e5c79c6ebc4142fd42f20ff0c62f67a9c86d69da84cbeb653b47aeba","last_reissued_at":"2026-05-18T01:21:05.822040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:05.822040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4784","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":"2026-05-18T01:21:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u98/BjdoKsenlknM0zq20a5ZEbn+K+1Vw7fErOSj5QmCbEGvwYFkX2mQDRaUQQZZMxQW9xYiAdXDTkovIVhCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:26:08.347575Z"},"content_sha256":"2c3d009ad819bb2eab21a51b653c6e2da2dae620202c4f3b36c4e96ad4bece99","schema_version":"1.0","event_id":"sha256:2c3d009ad819bb2eab21a51b653c6e2da2dae620202c4f3b36c4e96ad4bece99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UAYESYPFY6OG5PCBIL6UF4QP6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real Closed Exponential Subfields of Pseudoexponential Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ahuva C. Shkop","submitted_at":"2011-12-20T18:04:57Z","abstract_excerpt":"In this paper, we prove that a pseudoexponential field has continuum many non-isomorphic countable real closed exponential subfields, each with an order preserving exponential map which is surjective onto the nonnegative elements. Indeed, this is true of any algebraically closed exponential field satisfying Schanuel's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4784","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":"2026-05-18T01:21:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NAN5NncFJPc0WtPLBd6Z1TGfDpYnaG3vtrMQ2dNziQZokGruh07c4wC2+8qXyCdQRjpZNVW8+954pyNp4SOmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:26:08.348149Z"},"content_sha256":"e0f7da6d1228cf2a85d0211b7124c57a2f8fee3346b81cece707593208221ee2","schema_version":"1.0","event_id":"sha256:e0f7da6d1228cf2a85d0211b7124c57a2f8fee3346b81cece707593208221ee2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAYESYPFY6OG5PCBIL6UF4QP6D/bundle.json","state_url":"https://pith.science/pith/UAYESYPFY6OG5PCBIL6UF4QP6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAYESYPFY6OG5PCBIL6UF4QP6D/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":"2026-05-31T23:26:08Z","links":{"resolver":"https://pith.science/pith/UAYESYPFY6OG5PCBIL6UF4QP6D","bundle":"https://pith.science/pith/UAYESYPFY6OG5PCBIL6UF4QP6D/bundle.json","state":"https://pith.science/pith/UAYESYPFY6OG5PCBIL6UF4QP6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAYESYPFY6OG5PCBIL6UF4QP6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UAYESYPFY6OG5PCBIL6UF4QP6D","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":"97977f6256783ddfe96eea85decf80951a9fcf9a4e591e73618fe82a0fdd84f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-20T18:04:57Z","title_canon_sha256":"eb38d92f244828fb9a77142be33b8b601c48422cb218f1ef6780c5542acd7054"},"schema_version":"1.0","source":{"id":"1112.4784","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4784","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4784v1","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4784","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"pith_short_12","alias_value":"UAYESYPFY6OG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UAYESYPFY6OG5PCB","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UAYESYPF","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:e0f7da6d1228cf2a85d0211b7124c57a2f8fee3346b81cece707593208221ee2","target":"graph","created_at":"2026-05-18T01:21:05Z","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 this paper, we prove that a pseudoexponential field has continuum many non-isomorphic countable real closed exponential subfields, each with an order preserving exponential map which is surjective onto the nonnegative elements. Indeed, this is true of any algebraically closed exponential field satisfying Schanuel's conjecture.","authors_text":"Ahuva C. Shkop","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-20T18:04:57Z","title":"Real Closed Exponential Subfields of Pseudoexponential Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4784","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":"sha256:2c3d009ad819bb2eab21a51b653c6e2da2dae620202c4f3b36c4e96ad4bece99","target":"record","created_at":"2026-05-18T01:21:05Z","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":"97977f6256783ddfe96eea85decf80951a9fcf9a4e591e73618fe82a0fdd84f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-20T18:04:57Z","title_canon_sha256":"eb38d92f244828fb9a77142be33b8b601c48422cb218f1ef6780c5542acd7054"},"schema_version":"1.0","source":{"id":"1112.4784","kind":"arxiv","version":1}},"canonical_sha256":"a0304961e5c79c6ebc4142fd42f20ff0c62f67a9c86d69da84cbeb653b47aeba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0304961e5c79c6ebc4142fd42f20ff0c62f67a9c86d69da84cbeb653b47aeba","first_computed_at":"2026-05-18T01:21:05.822040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:05.822040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vdSvSUHesfdkDafekDqcEz+bgby7gQvAaZCVgAoDuzcK+gpcjhOswFepR7Xix75+fuJbH9DjrMhszfWP3QnmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:05.822670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4784","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c3d009ad819bb2eab21a51b653c6e2da2dae620202c4f3b36c4e96ad4bece99","sha256:e0f7da6d1228cf2a85d0211b7124c57a2f8fee3346b81cece707593208221ee2"],"state_sha256":"ed70480305e8b6f1fe9b240ca54cb7cf856c4c8af95486cb0c1618e4bef5291a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CJ/ZoYmERBpIRyol0O6OOdaDSGQlRdz4sYqPFoRYjDdQuTgt6c9m6FW7I1tFFOd1nD4SCA9t5cRCyCmU9eZVBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:26:08.350614Z","bundle_sha256":"e68418bb43d9a1ce9a8e6d84807d2f7eb2939af618c6bb5176e61ac9747780e2"}}