{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KD27T4RKZHY3ZGFBCAYAP5UWKZ","short_pith_number":"pith:KD27T4RK","canonical_record":{"source":{"id":"1904.06573","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.HO","submitted_at":"2019-04-13T17:18:07Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3bfbbbe9e52307861f8637128dd43dd796b14ece3b16e69d8c6ed08b1d7ef095","abstract_canon_sha256":"4a819962f7261ff13ad1ffbadd97793628a3e7dcd62562746022f7164d0ec16a"},"schema_version":"1.0"},"canonical_sha256":"50f5f9f22ac9f1bc98a1103007f696565536f3c346f18cc93a3843d67e7eeceb","source":{"kind":"arxiv","id":"1904.06573","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06573","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06573v1","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06573","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"KD27T4RKZHY3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KD27T4RKZHY3ZGFB","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KD27T4RK","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KD27T4RKZHY3ZGFBCAYAP5UWKZ","target":"record","payload":{"canonical_record":{"source":{"id":"1904.06573","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.HO","submitted_at":"2019-04-13T17:18:07Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3bfbbbe9e52307861f8637128dd43dd796b14ece3b16e69d8c6ed08b1d7ef095","abstract_canon_sha256":"4a819962f7261ff13ad1ffbadd97793628a3e7dcd62562746022f7164d0ec16a"},"schema_version":"1.0"},"canonical_sha256":"50f5f9f22ac9f1bc98a1103007f696565536f3c346f18cc93a3843d67e7eeceb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:38.813744Z","signature_b64":"0xHiuxHihQbtZzRJ/cLd0EIEfOWeP4B/1wDZF3hX3GlhXBmrpBkysvHIHk67wZsGhnUhzmhTFQxNMX3At+ngCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50f5f9f22ac9f1bc98a1103007f696565536f3c346f18cc93a3843d67e7eeceb","last_reissued_at":"2026-05-17T23:48:38.813352Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:38.813352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.06573","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nm1+vK5rjwfO+zThIFoCnh69tgFPzdAzFZMt+pcSuHs/FWq46DYphJHtLgrGYRw/yuWLLFCUZg4E9oDcywVmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:54:17.644214Z"},"content_sha256":"6793f11ce7b042b88d53babd8bc84d1131636d2128aa61e4368be4e3c304b600","schema_version":"1.0","event_id":"sha256:6793f11ce7b042b88d53babd8bc84d1131636d2128aa61e4368be4e3c304b600"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KD27T4RKZHY3ZGFBCAYAP5UWKZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Frobenius's last proof","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.HO","authors_text":"Peter G. Doyle","submitted_at":"2019-04-13T17:18:07Z","abstract_excerpt":"Around about 1917, Issai Schur rediscovered the Rogers-Ramanujan identities, and proved a system of polynomial identities that imply them. Schur wrote that Georg Frobenius (his former advisor) had shown him a simple, direct proof of these polynomial identities. Schur did not see fit to reveal Frobenius's proof, preferring his own rather complicated proof. But it is easy enough to guess what this `simple, direct' proof must have been. As Frobenius died in 1917, we may call this `Frobenius's last proof'."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06573","kind":"arxiv","version":1},"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":"2026-05-17T23:48:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OWFjAmF9/o7wQ27EmHUDoh+slN5E3dQVXB+IXCuhWrMCZ5e0UC+nGCyNsTbYmDqvY8X9m47yBCf6iQ5yrkAWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:54:17.644958Z"},"content_sha256":"1a92066d1066d9d643b9ed6f2434a8e9752732d857613e26a3dea8696d69731b","schema_version":"1.0","event_id":"sha256:1a92066d1066d9d643b9ed6f2434a8e9752732d857613e26a3dea8696d69731b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KD27T4RKZHY3ZGFBCAYAP5UWKZ/bundle.json","state_url":"https://pith.science/pith/KD27T4RKZHY3ZGFBCAYAP5UWKZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KD27T4RKZHY3ZGFBCAYAP5UWKZ/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":"2026-05-31T08:54:17Z","links":{"resolver":"https://pith.science/pith/KD27T4RKZHY3ZGFBCAYAP5UWKZ","bundle":"https://pith.science/pith/KD27T4RKZHY3ZGFBCAYAP5UWKZ/bundle.json","state":"https://pith.science/pith/KD27T4RKZHY3ZGFBCAYAP5UWKZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KD27T4RKZHY3ZGFBCAYAP5UWKZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KD27T4RKZHY3ZGFBCAYAP5UWKZ","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":"4a819962f7261ff13ad1ffbadd97793628a3e7dcd62562746022f7164d0ec16a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.HO","submitted_at":"2019-04-13T17:18:07Z","title_canon_sha256":"3bfbbbe9e52307861f8637128dd43dd796b14ece3b16e69d8c6ed08b1d7ef095"},"schema_version":"1.0","source":{"id":"1904.06573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06573","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06573v1","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06573","created_at":"2026-05-17T23:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"KD27T4RKZHY3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KD27T4RKZHY3ZGFB","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KD27T4RK","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:1a92066d1066d9d643b9ed6f2434a8e9752732d857613e26a3dea8696d69731b","target":"graph","created_at":"2026-05-17T23:48:38Z","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":"Around about 1917, Issai Schur rediscovered the Rogers-Ramanujan identities, and proved a system of polynomial identities that imply them. Schur wrote that Georg Frobenius (his former advisor) had shown him a simple, direct proof of these polynomial identities. Schur did not see fit to reveal Frobenius's proof, preferring his own rather complicated proof. But it is easy enough to guess what this `simple, direct' proof must have been. As Frobenius died in 1917, we may call this `Frobenius's last proof'.","authors_text":"Peter G. Doyle","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.HO","submitted_at":"2019-04-13T17:18:07Z","title":"Frobenius's last proof"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06573","kind":"arxiv","version":1},"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":"sha256:6793f11ce7b042b88d53babd8bc84d1131636d2128aa61e4368be4e3c304b600","target":"record","created_at":"2026-05-17T23:48:38Z","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":"4a819962f7261ff13ad1ffbadd97793628a3e7dcd62562746022f7164d0ec16a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.HO","submitted_at":"2019-04-13T17:18:07Z","title_canon_sha256":"3bfbbbe9e52307861f8637128dd43dd796b14ece3b16e69d8c6ed08b1d7ef095"},"schema_version":"1.0","source":{"id":"1904.06573","kind":"arxiv","version":1}},"canonical_sha256":"50f5f9f22ac9f1bc98a1103007f696565536f3c346f18cc93a3843d67e7eeceb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50f5f9f22ac9f1bc98a1103007f696565536f3c346f18cc93a3843d67e7eeceb","first_computed_at":"2026-05-17T23:48:38.813352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:38.813352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0xHiuxHihQbtZzRJ/cLd0EIEfOWeP4B/1wDZF3hX3GlhXBmrpBkysvHIHk67wZsGhnUhzmhTFQxNMX3At+ngCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:38.813744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.06573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6793f11ce7b042b88d53babd8bc84d1131636d2128aa61e4368be4e3c304b600","sha256:1a92066d1066d9d643b9ed6f2434a8e9752732d857613e26a3dea8696d69731b"],"state_sha256":"4c9d5f57baa51faff54ecc310a93ef35815a3173f179c8e4751f19346cea492a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+OtPH/mCYYdILS1Hogk3TslWlyV3qRevUPC8mGe9OfZ4chgutCZlqlFDZROpE+OkQfriNBk4KLiEoNq0/uNfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:54:17.648804Z","bundle_sha256":"e5074a090f7a6cbcfd152714ab7a7526b31f70703fec4fd4aa7b160ec10b5835"}}