{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6FFPWBSE3YMUHA4SPOPAERSBMA","short_pith_number":"pith:6FFPWBSE","schema_version":"1.0","canonical_sha256":"f14afb0644de194383927b9e0246416018395dec6dcaad02ca5263f5c872ec81","source":{"kind":"arxiv","id":"1503.00315","version":3},"attestation_state":"computed","paper":{"title":"Surreal numbers, derivations and transseries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alessandro Berarducci, Vincenzo Mantova","submitted_at":"2015-03-01T17:33:51Z","abstract_excerpt":"Several authors have conjectured that Conway's field of surreal numbers, equipped with the exponential function of Kruskal and Gonshor, can be described as a field of transseries and admits a compatible differential structure of Hardy-type. In this paper we give a complete positive solution to both problems. We also show that with this new differential structure, the surreal numbers are Liouville closed, namely the derivation is surjective."},"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":"1503.00315","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-01T17:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"9109e8a4687f6f751abbc07baf85401434e625de870a4ee4bd59fc3065252ed6","abstract_canon_sha256":"a2c240848776c9b397d14c6d7bf887211a7bf59956b401fba0952ea3b2b27bcd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:02.159455Z","signature_b64":"PKWLyFbdH9onmUqiOuatei2lUeiZN3UlywSHwLhBY95iBSGoJwa0W1YMS0NQbGyxBSou0M7XBO2uoY4o/k0DAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f14afb0644de194383927b9e0246416018395dec6dcaad02ca5263f5c872ec81","last_reissued_at":"2026-05-18T00:23:02.158882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:02.158882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Surreal numbers, derivations and transseries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alessandro Berarducci, Vincenzo Mantova","submitted_at":"2015-03-01T17:33:51Z","abstract_excerpt":"Several authors have conjectured that Conway's field of surreal numbers, equipped with the exponential function of Kruskal and Gonshor, can be described as a field of transseries and admits a compatible differential structure of Hardy-type. In this paper we give a complete positive solution to both problems. We also show that with this new differential structure, the surreal numbers are Liouville closed, namely the derivation is surjective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00315","kind":"arxiv","version":3},"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":"1503.00315","created_at":"2026-05-18T00:23:02.158982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.00315v3","created_at":"2026-05-18T00:23:02.158982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00315","created_at":"2026-05-18T00:23:02.158982+00:00"},{"alias_kind":"pith_short_12","alias_value":"6FFPWBSE3YMU","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6FFPWBSE3YMUHA4S","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6FFPWBSE","created_at":"2026-05-18T12:29:07.941421+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/6FFPWBSE3YMUHA4SPOPAERSBMA","json":"https://pith.science/pith/6FFPWBSE3YMUHA4SPOPAERSBMA.json","graph_json":"https://pith.science/api/pith-number/6FFPWBSE3YMUHA4SPOPAERSBMA/graph.json","events_json":"https://pith.science/api/pith-number/6FFPWBSE3YMUHA4SPOPAERSBMA/events.json","paper":"https://pith.science/paper/6FFPWBSE"},"agent_actions":{"view_html":"https://pith.science/pith/6FFPWBSE3YMUHA4SPOPAERSBMA","download_json":"https://pith.science/pith/6FFPWBSE3YMUHA4SPOPAERSBMA.json","view_paper":"https://pith.science/paper/6FFPWBSE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.00315&json=true","fetch_graph":"https://pith.science/api/pith-number/6FFPWBSE3YMUHA4SPOPAERSBMA/graph.json","fetch_events":"https://pith.science/api/pith-number/6FFPWBSE3YMUHA4SPOPAERSBMA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6FFPWBSE3YMUHA4SPOPAERSBMA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6FFPWBSE3YMUHA4SPOPAERSBMA/action/storage_attestation","attest_author":"https://pith.science/pith/6FFPWBSE3YMUHA4SPOPAERSBMA/action/author_attestation","sign_citation":"https://pith.science/pith/6FFPWBSE3YMUHA4SPOPAERSBMA/action/citation_signature","submit_replication":"https://pith.science/pith/6FFPWBSE3YMUHA4SPOPAERSBMA/action/replication_record"}},"created_at":"2026-05-18T00:23:02.158982+00:00","updated_at":"2026-05-18T00:23:02.158982+00:00"}