{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NN3CJM3UW4XRNMJGPBSEKV2DHQ","short_pith_number":"pith:NN3CJM3U","canonical_record":{"source":{"id":"1701.04699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-01-15T14:38:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d6f201a65cc71e6ae268352e92fa7b786d0199bb53d99910098998066ce2f463","abstract_canon_sha256":"75a5c82e15ea900b3dc6fa7d8a63103409b451257ce57412186b4e352d644079"},"schema_version":"1.0"},"canonical_sha256":"6b7624b374b72f16b12678644557433c222db1401c1c59470175a0566416f7e5","source":{"kind":"arxiv","id":"1701.04699","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04699","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04699v1","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04699","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"NN3CJM3UW4XR","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NN3CJM3UW4XRNMJG","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NN3CJM3U","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NN3CJM3UW4XRNMJGPBSEKV2DHQ","target":"record","payload":{"canonical_record":{"source":{"id":"1701.04699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-01-15T14:38:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d6f201a65cc71e6ae268352e92fa7b786d0199bb53d99910098998066ce2f463","abstract_canon_sha256":"75a5c82e15ea900b3dc6fa7d8a63103409b451257ce57412186b4e352d644079"},"schema_version":"1.0"},"canonical_sha256":"6b7624b374b72f16b12678644557433c222db1401c1c59470175a0566416f7e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:42.875066Z","signature_b64":"0HxTIC26eSZrvR8wbOapUu3wa4/j385JjyR1IN848MsIAG1X1eE/BXLCiRPKjotqCt4LfMfN+L9YxcvNVk04Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b7624b374b72f16b12678644557433c222db1401c1c59470175a0566416f7e5","last_reissued_at":"2026-05-18T00:52:42.874578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:42.874578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.04699","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":"2026-05-18T00:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xmmxd0aZ78ieYV49xg7xdhm+h+ZYUfwkLaT/3Ar7hYWbySPgzh+G8MWNi+9J8ATTW9j3X8c/bXVgp3vqzasLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:54:43.690378Z"},"content_sha256":"c1a7bcbdb86c76bc4690e3c07de8703213d1520f0e14ca0f26897707ef860638","schema_version":"1.0","event_id":"sha256:c1a7bcbdb86c76bc4690e3c07de8703213d1520f0e14ca0f26897707ef860638"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NN3CJM3UW4XRNMJGPBSEKV2DHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Riemann sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.HO","authors_text":"Toshikazu Sunada","submitted_at":"2017-01-15T14:38:50Z","abstract_excerpt":"The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and elementary, thus available to the \"common mathematician in the streets.\" However one may still see here interesting inter-connection and cohesiveness in mathematics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04699","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":"2026-05-18T00:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+kjxse8zmfsQW3y5XlbmNR2sF9C+KrwvwGObY0Y98SojptSolbqe2GIcbSh5vqtaVI4dbyuIDYsEAB74QJJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:54:43.690735Z"},"content_sha256":"c518af34b02937fbc5ead7a85438a83a1391ea8a4c5cba8642012432358d121f","schema_version":"1.0","event_id":"sha256:c518af34b02937fbc5ead7a85438a83a1391ea8a4c5cba8642012432358d121f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NN3CJM3UW4XRNMJGPBSEKV2DHQ/bundle.json","state_url":"https://pith.science/pith/NN3CJM3UW4XRNMJGPBSEKV2DHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NN3CJM3UW4XRNMJGPBSEKV2DHQ/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":"2026-06-02T15:54:43Z","links":{"resolver":"https://pith.science/pith/NN3CJM3UW4XRNMJGPBSEKV2DHQ","bundle":"https://pith.science/pith/NN3CJM3UW4XRNMJGPBSEKV2DHQ/bundle.json","state":"https://pith.science/pith/NN3CJM3UW4XRNMJGPBSEKV2DHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NN3CJM3UW4XRNMJGPBSEKV2DHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NN3CJM3UW4XRNMJGPBSEKV2DHQ","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":"75a5c82e15ea900b3dc6fa7d8a63103409b451257ce57412186b4e352d644079","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-01-15T14:38:50Z","title_canon_sha256":"d6f201a65cc71e6ae268352e92fa7b786d0199bb53d99910098998066ce2f463"},"schema_version":"1.0","source":{"id":"1701.04699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04699","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04699v1","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04699","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"NN3CJM3UW4XR","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NN3CJM3UW4XRNMJG","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NN3CJM3U","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:c518af34b02937fbc5ead7a85438a83a1391ea8a4c5cba8642012432358d121f","target":"graph","created_at":"2026-05-18T00:52:42Z","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 primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and elementary, thus available to the \"common mathematician in the streets.\" However one may still see here interesting inter-connection and cohesiveness in mathematics.","authors_text":"Toshikazu Sunada","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-01-15T14:38:50Z","title":"Generalized Riemann sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04699","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:c1a7bcbdb86c76bc4690e3c07de8703213d1520f0e14ca0f26897707ef860638","target":"record","created_at":"2026-05-18T00:52:42Z","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":"75a5c82e15ea900b3dc6fa7d8a63103409b451257ce57412186b4e352d644079","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-01-15T14:38:50Z","title_canon_sha256":"d6f201a65cc71e6ae268352e92fa7b786d0199bb53d99910098998066ce2f463"},"schema_version":"1.0","source":{"id":"1701.04699","kind":"arxiv","version":1}},"canonical_sha256":"6b7624b374b72f16b12678644557433c222db1401c1c59470175a0566416f7e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b7624b374b72f16b12678644557433c222db1401c1c59470175a0566416f7e5","first_computed_at":"2026-05-18T00:52:42.874578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:42.874578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0HxTIC26eSZrvR8wbOapUu3wa4/j385JjyR1IN848MsIAG1X1eE/BXLCiRPKjotqCt4LfMfN+L9YxcvNVk04Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:42.875066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1a7bcbdb86c76bc4690e3c07de8703213d1520f0e14ca0f26897707ef860638","sha256:c518af34b02937fbc5ead7a85438a83a1391ea8a4c5cba8642012432358d121f"],"state_sha256":"dfbcffc17fea8fcd2e17acb563cc27950ecca19588ccac948b74d1bfe1f6861f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hug54XHwe6QaGVJyWBHmUbOJN0v/CkCYEcYmBFiN+tWWgNsPExdXMmaN0o/IKkWLEGzvl8ed53+bOepiAIsuDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:54:43.692810Z","bundle_sha256":"17751f91c4011eba0ace29185bf6de388682b6eff2d88dd04d06ae8001b10730"}}