{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3J5RAPZ5EKNUPHQKTNC4WABG64","short_pith_number":"pith:3J5RAPZ5","canonical_record":{"source":{"id":"1307.7392","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-28T19:14:21Z","cross_cats_sorted":["math.GN","math.LO"],"title_canon_sha256":"995fa18890c0065ad8b982557b3178bb91703fd8072db347f0c38e073a2ba2f1","abstract_canon_sha256":"6480eda45294281003638a5021736b421a8dabae9b0615ebca58abba2c1e25ba"},"schema_version":"1.0"},"canonical_sha256":"da7b103f3d229b479e0a9b45cb0026f7167212648e28fd4ba2454f0d4b7e7556","source":{"kind":"arxiv","id":"1307.7392","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7392","created_at":"2026-05-18T02:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7392v3","created_at":"2026-05-18T02:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7392","created_at":"2026-05-18T02:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"3J5RAPZ5EKNU","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3J5RAPZ5EKNUPHQK","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3J5RAPZ5","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3J5RAPZ5EKNUPHQKTNC4WABG64","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7392","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-28T19:14:21Z","cross_cats_sorted":["math.GN","math.LO"],"title_canon_sha256":"995fa18890c0065ad8b982557b3178bb91703fd8072db347f0c38e073a2ba2f1","abstract_canon_sha256":"6480eda45294281003638a5021736b421a8dabae9b0615ebca58abba2c1e25ba"},"schema_version":"1.0"},"canonical_sha256":"da7b103f3d229b479e0a9b45cb0026f7167212648e28fd4ba2454f0d4b7e7556","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:00.586799Z","signature_b64":"DJ3BiAHhSaxwDg5zmkNs1Z54P6P9v/v3J7eXJBX3YNfVxIfGfoXTplPgabp4a7sXhwDyOVJb6GZuygo0XUj2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da7b103f3d229b479e0a9b45cb0026f7167212648e28fd4ba2454f0d4b7e7556","last_reissued_at":"2026-05-18T02:04:00.586033Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:00.586033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7392","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":"2026-05-18T02:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"83CK8df96q/Q78ajUZBgLumhF6PMA4YCjgOyRn0pLtZScRcDDucSuN846XeTGe+zUsjhWlSwTGtYThOW7z9OCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:48:00.023766Z"},"content_sha256":"b59996bc20e9c9f5d107227bbc2e7ee10f26aade89a1eb32fdd6f661d5b7e92d","schema_version":"1.0","event_id":"sha256:b59996bc20e9c9f5d107227bbc2e7ee10f26aade89a1eb32fdd6f661d5b7e92d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3J5RAPZ5EKNUPHQKTNC4WABG64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis on Surreal Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.LO"],"primary_cat":"math.CA","authors_text":"Ashvin Swaminathan, Simon Rubinstein-Salzedo","submitted_at":"2013-07-28T19:14:21Z","abstract_excerpt":"The class $\\mathbf{No}$ of surreal numbers, which John Conway discovered while studying combinatorial games, possesses a rich numerical structure and shares many arithmetic and algebraic properties with the real numbers. Some work has also been done to develop analysis on $\\mathbf{No}$. In this paper, we extend this work with a treatment of functions, limits, derivatives, power series, and integrals.\n  We propose surreal definitions of the arctangent and logarithm functions using truncations of Maclaurin series. Using a new representation of surreals, we present a formula for the limit of a se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7392","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":"2026-05-18T02:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/1MAQFn288visrsHDO+NaAKovLZncNhri2eoTBRl8s3h8RQj4fgcKEk3eDJ1hN7xsHA/PVtefYNYaFDFZicBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:48:00.024105Z"},"content_sha256":"05e04ede236c605c1acce83f345a382586e103ced2f65288210657c83d063759","schema_version":"1.0","event_id":"sha256:05e04ede236c605c1acce83f345a382586e103ced2f65288210657c83d063759"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3J5RAPZ5EKNUPHQKTNC4WABG64/bundle.json","state_url":"https://pith.science/pith/3J5RAPZ5EKNUPHQKTNC4WABG64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3J5RAPZ5EKNUPHQKTNC4WABG64/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":"2026-06-27T13:48:00Z","links":{"resolver":"https://pith.science/pith/3J5RAPZ5EKNUPHQKTNC4WABG64","bundle":"https://pith.science/pith/3J5RAPZ5EKNUPHQKTNC4WABG64/bundle.json","state":"https://pith.science/pith/3J5RAPZ5EKNUPHQKTNC4WABG64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3J5RAPZ5EKNUPHQKTNC4WABG64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3J5RAPZ5EKNUPHQKTNC4WABG64","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":"6480eda45294281003638a5021736b421a8dabae9b0615ebca58abba2c1e25ba","cross_cats_sorted":["math.GN","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-28T19:14:21Z","title_canon_sha256":"995fa18890c0065ad8b982557b3178bb91703fd8072db347f0c38e073a2ba2f1"},"schema_version":"1.0","source":{"id":"1307.7392","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7392","created_at":"2026-05-18T02:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7392v3","created_at":"2026-05-18T02:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7392","created_at":"2026-05-18T02:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"3J5RAPZ5EKNU","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3J5RAPZ5EKNUPHQK","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3J5RAPZ5","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:05e04ede236c605c1acce83f345a382586e103ced2f65288210657c83d063759","target":"graph","created_at":"2026-05-18T02:04:00Z","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":"The class $\\mathbf{No}$ of surreal numbers, which John Conway discovered while studying combinatorial games, possesses a rich numerical structure and shares many arithmetic and algebraic properties with the real numbers. Some work has also been done to develop analysis on $\\mathbf{No}$. In this paper, we extend this work with a treatment of functions, limits, derivatives, power series, and integrals.\n  We propose surreal definitions of the arctangent and logarithm functions using truncations of Maclaurin series. Using a new representation of surreals, we present a formula for the limit of a se","authors_text":"Ashvin Swaminathan, Simon Rubinstein-Salzedo","cross_cats":["math.GN","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-28T19:14:21Z","title":"Analysis on Surreal Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7392","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:b59996bc20e9c9f5d107227bbc2e7ee10f26aade89a1eb32fdd6f661d5b7e92d","target":"record","created_at":"2026-05-18T02:04:00Z","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":"6480eda45294281003638a5021736b421a8dabae9b0615ebca58abba2c1e25ba","cross_cats_sorted":["math.GN","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-28T19:14:21Z","title_canon_sha256":"995fa18890c0065ad8b982557b3178bb91703fd8072db347f0c38e073a2ba2f1"},"schema_version":"1.0","source":{"id":"1307.7392","kind":"arxiv","version":3}},"canonical_sha256":"da7b103f3d229b479e0a9b45cb0026f7167212648e28fd4ba2454f0d4b7e7556","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da7b103f3d229b479e0a9b45cb0026f7167212648e28fd4ba2454f0d4b7e7556","first_computed_at":"2026-05-18T02:04:00.586033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:00.586033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DJ3BiAHhSaxwDg5zmkNs1Z54P6P9v/v3J7eXJBX3YNfVxIfGfoXTplPgabp4a7sXhwDyOVJb6GZuygo0XUj2Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:00.586799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7392","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b59996bc20e9c9f5d107227bbc2e7ee10f26aade89a1eb32fdd6f661d5b7e92d","sha256:05e04ede236c605c1acce83f345a382586e103ced2f65288210657c83d063759"],"state_sha256":"f6d9b0c990be8d8e787dd3b5ed643eece4da9672954d2357846006adcd02b0e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jeW4je2CkL/G+vU5kCfBz8LkKaC+ItNdVVdXiMToft+l49FznlnJemp1dLTbKmwSkTGEGtWhSA7jOxldxr18BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:48:00.025975Z","bundle_sha256":"3f6b28eb4792d86b032da3fc6c9546111b0d8c49754129b29fc9457f0147a41e"}}