{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KHZ4I7W2TKISUOL2T3XTI64WK2","short_pith_number":"pith:KHZ4I7W2","canonical_record":{"source":{"id":"1505.05571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-05-21T01:17:04Z","cross_cats_sorted":["cs.DC","stat.CO"],"title_canon_sha256":"3d09bdb317bb2ae53b6ec6f53fab35c16b7d076711f5a76d3fefffabb889c1c2","abstract_canon_sha256":"26005704186e15c687fde7ee7a5ac9661b5d237543fc30549018bd3cd8c4be66"},"schema_version":"1.0"},"canonical_sha256":"51f3c47eda9a912a397a9eef347b9656919012e8c4a008e610797f5dbc40ea3b","source":{"kind":"arxiv","id":"1505.05571","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05571","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05571v1","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05571","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"KHZ4I7W2TKIS","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KHZ4I7W2TKISUOL2","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KHZ4I7W2","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KHZ4I7W2TKISUOL2T3XTI64WK2","target":"record","payload":{"canonical_record":{"source":{"id":"1505.05571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-05-21T01:17:04Z","cross_cats_sorted":["cs.DC","stat.CO"],"title_canon_sha256":"3d09bdb317bb2ae53b6ec6f53fab35c16b7d076711f5a76d3fefffabb889c1c2","abstract_canon_sha256":"26005704186e15c687fde7ee7a5ac9661b5d237543fc30549018bd3cd8c4be66"},"schema_version":"1.0"},"canonical_sha256":"51f3c47eda9a912a397a9eef347b9656919012e8c4a008e610797f5dbc40ea3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:54.152374Z","signature_b64":"Ba9CQuR9MVqQX3pCMx6mPFSc1/3MWH+e+vBRita6Ihdx05DExMbDJJrmDJ2aSvU7qERdqAklD01kzvpbR/ytAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51f3c47eda9a912a397a9eef347b9656919012e8c4a008e610797f5dbc40ea3b","last_reissued_at":"2026-05-18T02:03:54.151844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:54.151844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.05571","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":"2026-05-18T02:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K+KV15+6ZVXZn4+y7TjAhET+ASL/8bW+9Sk/MQD/LXVcLXxmLgKbXCesci3tHvE1Hk3iyR6Db9O0GXkWXc5XCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:05:46.839796Z"},"content_sha256":"772c0b914ca210678ba50ca396aee422cb1d4799c31d8605e8d3c732ed270de8","schema_version":"1.0","event_id":"sha256:772c0b914ca210678ba50ca396aee422cb1d4799c31d8605e8d3c732ed270de8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KHZ4I7W2TKISUOL2T3XTI64WK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast exact summation using small and large superaccumulators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","stat.CO"],"primary_cat":"cs.NA","authors_text":"Radford M. Neal","submitted_at":"2015-05-21T01:17:04Z","abstract_excerpt":"I present two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-point number. Higher accuracy than simple summation (rounding after each addition) is important in many applications, such as finding the sample mean of data. Exact summation also guarantees identical results with parallel and serial implementations, since the exact sum is independent of order. The new methods use variations on the concept of a \"superaccumulator\" - a large fixed-point number that can exactly represent the sum of any reasonable number of floating-po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05571","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":"2026-05-18T02:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LJx1eVjABAg971AQAoW2+pOw0tjzAZkYsyD4HrKmM9qpmlqI6ewmNdm93yGHyFgymnDYeLN9pii6LvLNkuyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:05:46.840615Z"},"content_sha256":"a8ca62e6b361ad67584631c6ef8a9a42f28e367d0ab159aa924726636ecdca02","schema_version":"1.0","event_id":"sha256:a8ca62e6b361ad67584631c6ef8a9a42f28e367d0ab159aa924726636ecdca02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KHZ4I7W2TKISUOL2T3XTI64WK2/bundle.json","state_url":"https://pith.science/pith/KHZ4I7W2TKISUOL2T3XTI64WK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KHZ4I7W2TKISUOL2T3XTI64WK2/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":"2026-08-05T01:05:46Z","links":{"resolver":"https://pith.science/pith/KHZ4I7W2TKISUOL2T3XTI64WK2","bundle":"https://pith.science/pith/KHZ4I7W2TKISUOL2T3XTI64WK2/bundle.json","state":"https://pith.science/pith/KHZ4I7W2TKISUOL2T3XTI64WK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KHZ4I7W2TKISUOL2T3XTI64WK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KHZ4I7W2TKISUOL2T3XTI64WK2","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":"26005704186e15c687fde7ee7a5ac9661b5d237543fc30549018bd3cd8c4be66","cross_cats_sorted":["cs.DC","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-05-21T01:17:04Z","title_canon_sha256":"3d09bdb317bb2ae53b6ec6f53fab35c16b7d076711f5a76d3fefffabb889c1c2"},"schema_version":"1.0","source":{"id":"1505.05571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05571","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05571v1","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05571","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"KHZ4I7W2TKIS","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KHZ4I7W2TKISUOL2","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KHZ4I7W2","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:a8ca62e6b361ad67584631c6ef8a9a42f28e367d0ab159aa924726636ecdca02","target":"graph","created_at":"2026-05-18T02:03:54Z","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":"I present two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-point number. Higher accuracy than simple summation (rounding after each addition) is important in many applications, such as finding the sample mean of data. Exact summation also guarantees identical results with parallel and serial implementations, since the exact sum is independent of order. The new methods use variations on the concept of a \"superaccumulator\" - a large fixed-point number that can exactly represent the sum of any reasonable number of floating-po","authors_text":"Radford M. Neal","cross_cats":["cs.DC","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-05-21T01:17:04Z","title":"Fast exact summation using small and large superaccumulators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05571","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":"sha256:772c0b914ca210678ba50ca396aee422cb1d4799c31d8605e8d3c732ed270de8","target":"record","created_at":"2026-05-18T02:03:54Z","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":"26005704186e15c687fde7ee7a5ac9661b5d237543fc30549018bd3cd8c4be66","cross_cats_sorted":["cs.DC","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-05-21T01:17:04Z","title_canon_sha256":"3d09bdb317bb2ae53b6ec6f53fab35c16b7d076711f5a76d3fefffabb889c1c2"},"schema_version":"1.0","source":{"id":"1505.05571","kind":"arxiv","version":1}},"canonical_sha256":"51f3c47eda9a912a397a9eef347b9656919012e8c4a008e610797f5dbc40ea3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51f3c47eda9a912a397a9eef347b9656919012e8c4a008e610797f5dbc40ea3b","first_computed_at":"2026-05-18T02:03:54.151844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:54.151844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ba9CQuR9MVqQX3pCMx6mPFSc1/3MWH+e+vBRita6Ihdx05DExMbDJJrmDJ2aSvU7qERdqAklD01kzvpbR/ytAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:54.152374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:772c0b914ca210678ba50ca396aee422cb1d4799c31d8605e8d3c732ed270de8","sha256:a8ca62e6b361ad67584631c6ef8a9a42f28e367d0ab159aa924726636ecdca02"],"state_sha256":"5e2752d3cf095f6058c9288d10fa6a3d263d52c14785bdeb40eb5d1b62aadda2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VmWti69PMhPUWhYnVh5hBgp4WwVedFd5gpTLmg4GNW1LdWwhHxMvYLzbnonDf6Xo+ukLTeFLyXjb+kftv6CrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T01:05:46.847844Z","bundle_sha256":"e75cac7eb77e6d20833207cd0e4e422849b1c4a9dbfa4309800ec31622d7010b"}}