{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LMO5A3UWTYMILGMADPJRD4XPDX","short_pith_number":"pith:LMO5A3UW","schema_version":"1.0","canonical_sha256":"5b1dd06e969e188599801bd311f2ef1dc2dc147b382a8841e09e84f2964b5194","source":{"kind":"arxiv","id":"1708.04496","version":4},"attestation_state":"computed","paper":{"title":"Analytic continuations of log-exp-analytic germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.LO","authors_text":"Patrick Speissegger, Tobias Kaiser","submitted_at":"2017-08-15T13:48:56Z","abstract_excerpt":"We describe maximal, in a sense made precise, analytic continuations of germs at infinity of unary functions definable in the o-minimal structure R_an,exp on the Riemann surface of the logarithm. As one application, we give an upper bound on the logarithmic-exponential complexity of the compositional inverse of an infinitely increasing such germ, in terms of its own logarithmic-exponential complexity and its level. As a second application, we strengthen Wilkie's theorem on definable complex analytic continuations of germs belonging to the residue field of the valuation ring of all polynomially"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.04496","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-15T13:48:56Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"4233ee75bce587a4d4dbca4dab5b83160a00cc6270d3de83eba218f48903dfa3","abstract_canon_sha256":"1242afdc630db1967034ad2792d813898acc79bbb3a4b524f75979f2750e94f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:49.824388Z","signature_b64":"i7TQ883gsqpQuqp4IH710TTAXpUGtBwf/qPwYDqkgZJb/90JdNL5lmI6rGSjC/nI4rKxFTFTJIp04VksqlMgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b1dd06e969e188599801bd311f2ef1dc2dc147b382a8841e09e84f2964b5194","last_reissued_at":"2026-05-18T00:02:49.823900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:49.823900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic continuations of log-exp-analytic germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.LO","authors_text":"Patrick Speissegger, Tobias Kaiser","submitted_at":"2017-08-15T13:48:56Z","abstract_excerpt":"We describe maximal, in a sense made precise, analytic continuations of germs at infinity of unary functions definable in the o-minimal structure R_an,exp on the Riemann surface of the logarithm. As one application, we give an upper bound on the logarithmic-exponential complexity of the compositional inverse of an infinitely increasing such germ, in terms of its own logarithmic-exponential complexity and its level. As a second application, we strengthen Wilkie's theorem on definable complex analytic continuations of germs belonging to the residue field of the valuation ring of all polynomially"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04496","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.04496","created_at":"2026-05-18T00:02:49.823975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.04496v4","created_at":"2026-05-18T00:02:49.823975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04496","created_at":"2026-05-18T00:02:49.823975+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMO5A3UWTYMI","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMO5A3UWTYMILGMA","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMO5A3UW","created_at":"2026-05-18T12:31:28.150371+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX","json":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX.json","graph_json":"https://pith.science/api/pith-number/LMO5A3UWTYMILGMADPJRD4XPDX/graph.json","events_json":"https://pith.science/api/pith-number/LMO5A3UWTYMILGMADPJRD4XPDX/events.json","paper":"https://pith.science/paper/LMO5A3UW"},"agent_actions":{"view_html":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX","download_json":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX.json","view_paper":"https://pith.science/paper/LMO5A3UW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.04496&json=true","fetch_graph":"https://pith.science/api/pith-number/LMO5A3UWTYMILGMADPJRD4XPDX/graph.json","fetch_events":"https://pith.science/api/pith-number/LMO5A3UWTYMILGMADPJRD4XPDX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX/action/storage_attestation","attest_author":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX/action/author_attestation","sign_citation":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX/action/citation_signature","submit_replication":"https://pith.science/pith/LMO5A3UWTYMILGMADPJRD4XPDX/action/replication_record"}},"created_at":"2026-05-18T00:02:49.823975+00:00","updated_at":"2026-05-18T00:02:49.823975+00:00"}