{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SH56KL5FFHXG4LNAKIRATYEJ2I","short_pith_number":"pith:SH56KL5F","canonical_record":{"source":{"id":"1512.02267","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-07T22:27:29Z","cross_cats_sorted":["math.CA","math.RA"],"title_canon_sha256":"e3d0e7b7a1b0e61edc8c4c192abaccfd6bed5cc58a33416277e8ade2f73dbd01","abstract_canon_sha256":"7c4f295527945ae26893eca6a90bd7fb7ab274ae484fbc09cc01221c007ec3c8"},"schema_version":"1.0"},"canonical_sha256":"91fbe52fa529ee6e2da0522209e089d22ff1d63e8c48bd606ba6f7b52e87a1ab","source":{"kind":"arxiv","id":"1512.02267","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02267","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02267v3","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02267","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"SH56KL5FFHXG","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SH56KL5FFHXG4LNA","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SH56KL5F","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SH56KL5FFHXG4LNAKIRATYEJ2I","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02267","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-07T22:27:29Z","cross_cats_sorted":["math.CA","math.RA"],"title_canon_sha256":"e3d0e7b7a1b0e61edc8c4c192abaccfd6bed5cc58a33416277e8ade2f73dbd01","abstract_canon_sha256":"7c4f295527945ae26893eca6a90bd7fb7ab274ae484fbc09cc01221c007ec3c8"},"schema_version":"1.0"},"canonical_sha256":"91fbe52fa529ee6e2da0522209e089d22ff1d63e8c48bd606ba6f7b52e87a1ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:29.636278Z","signature_b64":"zj4ttKxLFQFxNx89GSkEeUtuzJKm7Tb/OYmq4Y/zq4Mj4I3Mz0oi3b9jDDtyu5/nNT2FNHyoJ2lCEq7UjR/9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91fbe52fa529ee6e2da0522209e089d22ff1d63e8c48bd606ba6f7b52e87a1ab","last_reissued_at":"2026-05-18T01:09:29.635829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:29.635829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02267","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qgEfBMvRN+wDM5UPVp140e7WQ9HstFYX1w5/hnP55VijvvILbOlt25pJQiAid2JYgaptiLPxXP0knUxGoywTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:58:14.336099Z"},"content_sha256":"2bae2538232ed7761920c92248ba71d8e161bde6ccd743a20f30be870134987c","schema_version":"1.0","event_id":"sha256:2bae2538232ed7761920c92248ba71d8e161bde6ccd743a20f30be870134987c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SH56KL5FFHXG4LNAKIRATYEJ2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The surreal numbers as a universal H-field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.RA"],"primary_cat":"math.LO","authors_text":"Joris van der Hoeven, Lou van den Dries, Matthias Aschenbrenner","submitted_at":"2015-12-07T22:27:29Z","abstract_excerpt":"We show that the natural embedding of the differential field of transseries into Conway's field of surreal numbers with the Berarducci-Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals with the Berarducci-Mantova derivation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02267","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rSIImR19Y8epEEbEGbzcJ1JG+TBM+ZIO1p+zmWx1HaFhn4a6St8RTnr5PawGQ+hxLhidFgprShJ9zmnnrpp6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:58:14.336451Z"},"content_sha256":"9907a95216218f41e512c1aab3cb74a88f140e80252b4510c6312803fb490a40","schema_version":"1.0","event_id":"sha256:9907a95216218f41e512c1aab3cb74a88f140e80252b4510c6312803fb490a40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SH56KL5FFHXG4LNAKIRATYEJ2I/bundle.json","state_url":"https://pith.science/pith/SH56KL5FFHXG4LNAKIRATYEJ2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SH56KL5FFHXG4LNAKIRATYEJ2I/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":"2026-06-08T14:58:14Z","links":{"resolver":"https://pith.science/pith/SH56KL5FFHXG4LNAKIRATYEJ2I","bundle":"https://pith.science/pith/SH56KL5FFHXG4LNAKIRATYEJ2I/bundle.json","state":"https://pith.science/pith/SH56KL5FFHXG4LNAKIRATYEJ2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SH56KL5FFHXG4LNAKIRATYEJ2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SH56KL5FFHXG4LNAKIRATYEJ2I","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":"7c4f295527945ae26893eca6a90bd7fb7ab274ae484fbc09cc01221c007ec3c8","cross_cats_sorted":["math.CA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-07T22:27:29Z","title_canon_sha256":"e3d0e7b7a1b0e61edc8c4c192abaccfd6bed5cc58a33416277e8ade2f73dbd01"},"schema_version":"1.0","source":{"id":"1512.02267","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02267","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02267v3","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02267","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"SH56KL5FFHXG","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SH56KL5FFHXG4LNA","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SH56KL5F","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:9907a95216218f41e512c1aab3cb74a88f140e80252b4510c6312803fb490a40","target":"graph","created_at":"2026-05-18T01:09:29Z","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 show that the natural embedding of the differential field of transseries into Conway's field of surreal numbers with the Berarducci-Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals with the Berarducci-Mantova derivation.","authors_text":"Joris van der Hoeven, Lou van den Dries, Matthias Aschenbrenner","cross_cats":["math.CA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-07T22:27:29Z","title":"The surreal numbers as a universal H-field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02267","kind":"arxiv","version":3},"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":"sha256:2bae2538232ed7761920c92248ba71d8e161bde6ccd743a20f30be870134987c","target":"record","created_at":"2026-05-18T01:09:29Z","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":"7c4f295527945ae26893eca6a90bd7fb7ab274ae484fbc09cc01221c007ec3c8","cross_cats_sorted":["math.CA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-07T22:27:29Z","title_canon_sha256":"e3d0e7b7a1b0e61edc8c4c192abaccfd6bed5cc58a33416277e8ade2f73dbd01"},"schema_version":"1.0","source":{"id":"1512.02267","kind":"arxiv","version":3}},"canonical_sha256":"91fbe52fa529ee6e2da0522209e089d22ff1d63e8c48bd606ba6f7b52e87a1ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91fbe52fa529ee6e2da0522209e089d22ff1d63e8c48bd606ba6f7b52e87a1ab","first_computed_at":"2026-05-18T01:09:29.635829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:29.635829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zj4ttKxLFQFxNx89GSkEeUtuzJKm7Tb/OYmq4Y/zq4Mj4I3Mz0oi3b9jDDtyu5/nNT2FNHyoJ2lCEq7UjR/9CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:29.636278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02267","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bae2538232ed7761920c92248ba71d8e161bde6ccd743a20f30be870134987c","sha256:9907a95216218f41e512c1aab3cb74a88f140e80252b4510c6312803fb490a40"],"state_sha256":"40470433560431957b3e76300c6bb0ecc68fed8b5e6663ec0aec31a73e3a389c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAfzMlaFqniKNtv/2l4vp90isyjUIckGPqIG4lWgDPyuupxFE3EsuEdiP6LnI/csgJuGub9F+SXjCSZ8pGWBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:58:14.338225Z","bundle_sha256":"c478249e89ced7da9311b1a4654da37d4eb226db90e347e3a68bf2c9db8de056"}}