{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EWDLLFG5Q7HISATE5QAUVVZQD5","short_pith_number":"pith:EWDLLFG5","canonical_record":{"source":{"id":"1810.10373","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-10-23T05:56:19Z","cross_cats_sorted":[],"title_canon_sha256":"e6e01a1e64873a22e4635aa2fc5db35e8a8f7d86a4c7614469f9f66add36bf6b","abstract_canon_sha256":"38188a2b00974808ebe95125261cd14cc15c7b6b6e72da8fdb4a576faa26f5ca"},"schema_version":"1.0"},"canonical_sha256":"2586b594dd87ce890264ec014ad7301f4f1b1a1b184fd0538e3a36be4be5f292","source":{"kind":"arxiv","id":"1810.10373","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10373","created_at":"2026-05-18T00:02:20Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10373v2","created_at":"2026-05-18T00:02:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10373","created_at":"2026-05-18T00:02:20Z"},{"alias_kind":"pith_short_12","alias_value":"EWDLLFG5Q7HI","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EWDLLFG5Q7HISATE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EWDLLFG5","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EWDLLFG5Q7HISATE5QAUVVZQD5","target":"record","payload":{"canonical_record":{"source":{"id":"1810.10373","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-10-23T05:56:19Z","cross_cats_sorted":[],"title_canon_sha256":"e6e01a1e64873a22e4635aa2fc5db35e8a8f7d86a4c7614469f9f66add36bf6b","abstract_canon_sha256":"38188a2b00974808ebe95125261cd14cc15c7b6b6e72da8fdb4a576faa26f5ca"},"schema_version":"1.0"},"canonical_sha256":"2586b594dd87ce890264ec014ad7301f4f1b1a1b184fd0538e3a36be4be5f292","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:20.195748Z","signature_b64":"sqiwm2fD7siOW7FW912JoIN/XHmVFbQokOrbTPKbuu1kmFyY5jG0TYk/WHzgen3kifHr8+oGSKvckoUKOg7AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2586b594dd87ce890264ec014ad7301f4f1b1a1b184fd0538e3a36be4be5f292","last_reissued_at":"2026-05-18T00:02:20.195295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:20.195295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.10373","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ddalek4kumkrD4Cdec190N1bfSoTdGOKWKRSDZpTYB9CbS7XVAeiueEfhYPmXmv/aHUaUNoSqNquJIrdR/PZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:06:03.628682Z"},"content_sha256":"3eb86f46bb73d690ac093db15962571f0561ea4e2d7c86c13346c469157f4d7b","schema_version":"1.0","event_id":"sha256:3eb86f46bb73d690ac093db15962571f0561ea4e2d7c86c13346c469157f4d7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EWDLLFG5Q7HISATE5QAUVVZQD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Surreal Birthdays and Their Arithmetic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Matthew Roughan","submitted_at":"2018-10-23T05:56:19Z","abstract_excerpt":"Surreal numbers are created recursively, with the \"birthday\" being the depth of the recursion. Birthday arithmetic describes how birthdays of surreal numbers are transformed by standard arithemetic operations. This paper shows that birthday arithmetic follows simple rules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10373","kind":"arxiv","version":2},"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":"2026-05-18T00:02:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KhVYG9SD9ROHquTizeElELtuLqJ2pqbNBuBD3nMKinz+ERYji2tc5ICAfOT9+iDXODgP/H4GyB8QMsBgI+n+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:06:03.629129Z"},"content_sha256":"c81a96d2d7b820550b7df2d9f12f996cc6227881d7f815a1735b9ee9a96c0317","schema_version":"1.0","event_id":"sha256:c81a96d2d7b820550b7df2d9f12f996cc6227881d7f815a1735b9ee9a96c0317"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWDLLFG5Q7HISATE5QAUVVZQD5/bundle.json","state_url":"https://pith.science/pith/EWDLLFG5Q7HISATE5QAUVVZQD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWDLLFG5Q7HISATE5QAUVVZQD5/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":"2026-06-24T06:06:03Z","links":{"resolver":"https://pith.science/pith/EWDLLFG5Q7HISATE5QAUVVZQD5","bundle":"https://pith.science/pith/EWDLLFG5Q7HISATE5QAUVVZQD5/bundle.json","state":"https://pith.science/pith/EWDLLFG5Q7HISATE5QAUVVZQD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWDLLFG5Q7HISATE5QAUVVZQD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EWDLLFG5Q7HISATE5QAUVVZQD5","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":"38188a2b00974808ebe95125261cd14cc15c7b6b6e72da8fdb4a576faa26f5ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-10-23T05:56:19Z","title_canon_sha256":"e6e01a1e64873a22e4635aa2fc5db35e8a8f7d86a4c7614469f9f66add36bf6b"},"schema_version":"1.0","source":{"id":"1810.10373","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10373","created_at":"2026-05-18T00:02:20Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10373v2","created_at":"2026-05-18T00:02:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10373","created_at":"2026-05-18T00:02:20Z"},{"alias_kind":"pith_short_12","alias_value":"EWDLLFG5Q7HI","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EWDLLFG5Q7HISATE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EWDLLFG5","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:c81a96d2d7b820550b7df2d9f12f996cc6227881d7f815a1735b9ee9a96c0317","target":"graph","created_at":"2026-05-18T00:02:20Z","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":"Surreal numbers are created recursively, with the \"birthday\" being the depth of the recursion. Birthday arithmetic describes how birthdays of surreal numbers are transformed by standard arithemetic operations. This paper shows that birthday arithmetic follows simple rules.","authors_text":"Matthew Roughan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-10-23T05:56:19Z","title":"Surreal Birthdays and Their Arithmetic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10373","kind":"arxiv","version":2},"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":"sha256:3eb86f46bb73d690ac093db15962571f0561ea4e2d7c86c13346c469157f4d7b","target":"record","created_at":"2026-05-18T00:02:20Z","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":"38188a2b00974808ebe95125261cd14cc15c7b6b6e72da8fdb4a576faa26f5ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2018-10-23T05:56:19Z","title_canon_sha256":"e6e01a1e64873a22e4635aa2fc5db35e8a8f7d86a4c7614469f9f66add36bf6b"},"schema_version":"1.0","source":{"id":"1810.10373","kind":"arxiv","version":2}},"canonical_sha256":"2586b594dd87ce890264ec014ad7301f4f1b1a1b184fd0538e3a36be4be5f292","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2586b594dd87ce890264ec014ad7301f4f1b1a1b184fd0538e3a36be4be5f292","first_computed_at":"2026-05-18T00:02:20.195295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:20.195295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sqiwm2fD7siOW7FW912JoIN/XHmVFbQokOrbTPKbuu1kmFyY5jG0TYk/WHzgen3kifHr8+oGSKvckoUKOg7AAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:20.195748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10373","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eb86f46bb73d690ac093db15962571f0561ea4e2d7c86c13346c469157f4d7b","sha256:c81a96d2d7b820550b7df2d9f12f996cc6227881d7f815a1735b9ee9a96c0317"],"state_sha256":"153b594dff247a8a31475eddf0fd9fff5aac612f43e5d330303bd05596116e2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b8325HBKPkr2wr42u/tnHEhv6Yn1Se6p9+E+tRVxTYMcxG4sSCU9XRm3/vG1g4bT1XOOffZe7puOL8WyamiGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:06:03.631556Z","bundle_sha256":"0c3b0395797f746a4bd403f63c44ce03efabad7eb64d74557105dfe4f39f05e5"}}