{"as_of":"2026-08-07T16:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:dd5498c2dc593a0359db0dfa81779be29bd8f7078ecdad6365cafef3d5e7b725","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T14:34:16.851630Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.18758/citation-record","integrity":"/paper/2607.18758/integrity","json":"/paper/2607.18758/citation-record.json","paper":"/paper/2607.18758"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:13.768179Z","title":"A New Approach to Probabilistic Rounding Error Analysis","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:13.768179Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:ddc014034ed935cca334d03944f5ebe2a7f30dac9437d0eb2cd7dd310ca77942","observation_id":"ce6fddd9-0db5-4e10-bda3-1f8fc1e8f8a0","resolution":{"observed_at":"2026-08-01T14:34:13.768179Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:13.840697Z","title":"Precision-aware determin- istic and probabilistic error bounds for floating point summa- tion","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:13.840697Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:5df5a384c9bbf544eae3e7932126177381591a4df979f30c95c9c398eec6bb07","observation_id":"cb8aa322-5c90-47fb-8190-f3149e78e6cc","resolution":{"observed_at":"2026-08-01T14:34:13.840697Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:13.954544Z","title":"The Ancestral Matrix of a Rooted Tree","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:13.954544Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:5f250b50ba8b389d5ed6d562b8f863a3893a1a76f418ca1d519c551586edb9f7","observation_id":"b8620b18-8f38-431b-9f3f-e4b7890275fb","resolution":{"observed_at":"2026-08-01T14:34:13.954544Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.017534Z","title":"A Method for the Construction of Minimum-Redundancy Codes","venue":null,"work_id":null,"year":1952},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.017534Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:01f89c4f45093505f64fef4aa0dfb846125daade4f30cc07b8cb35280fab9ceb","observation_id":"f57157b6-a837-4cb3-9d7d-4c65c146530d","resolution":{"observed_at":"2026-08-01T14:34:14.017534Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.109333Z","title":"Cover and Joy A","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.109333Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:858fd454b9a2d158cbae30b51f6cd6c0c8e9fa282f3940f11a3838ca471e10c0","observation_id":"f4ab3331-1a3e-489c-a8b9-0b2c58c6d934","resolution":{"observed_at":"2026-08-01T14:34:14.109333Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0097539798341594","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Linear-Time Approximation Algorithms for Computing Numerical Summation with Prov- ably Small Errors","venue":"SIAM Journal on Computing","work_id":"d455a4af-6b32-4102-b203-26e6f3b0e218","year":2000},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.166851Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:4b43b79f09113f9bdff253b043a4d33e56d5fa16a6a3dd043fc17d39bf6a3beb","observation_id":"d16a7568-2ef4-448f-8be6-0ddf0ef1fd97","resolution":{"observed_at":"2026-08-01T14:39:35.357920Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.252021Z","title":"A Fast Al- gorithm for Optimal Length-Limited Huffman Codes","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.252021Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:0cc1104f13b71ffdff239c17cff7f7c278964667360a92fa291ca20f26362b50","observation_id":"b629a264-7cf6-42a5-b849-6f0d4d1207f8","resolution":{"observed_at":"2026-08-01T14:34:14.252021Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.315570Z","title":"The Accuracy of Floating Point Sum- mation","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.315570Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:d76b081dbd2927081b94b71967a58818fd1377e4a40bba4e697587e8ee0e5841","observation_id":"6d63e01a-8cda-475e-91f5-5ecb0444e6b8","resolution":{"observed_at":"2026-08-01T14:34:14.315570Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/19m1257780","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A Class of Fast and Accurate Summation Algorithms","venue":"SIAM Journal on Scientific Computing","work_id":"9185c220-1801-4a33-a1cc-68cf4c9477ec","year":2020},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.373173Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:1bfaa4f162113e05f5945205a8fc88c69b287e3fcf5f1c1eb4e1a448af580b09","observation_id":"381b1692-0065-4c67-bb8d-3cfd77904e32","resolution":{"observed_at":"2026-08-01T14:39:35.272559Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/070679946","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Reducing Floating Point Error in Dot Prod- uct Using the Superblock Family of Algorithms","venue":"SIAM Journal on Scientific Computing","work_id":"fb493ce2-f352-4535-8be1-c071ccd425c7","year":2009},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.423863Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:4e82c99c055447e1371165eb84ad23f8a2e250c3776adb3a69b38d116f807b6c","observation_id":"7e9293c0-dfd7-44a5-a4ff-2ae863ffe5b0","resolution":{"observed_at":"2026-08-01T14:39:35.190511Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.473690Z","title":"Revealing Floating-Point Accumulation Orders in Software/Hardware Implementations","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.473690Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:00b0b35927b2873faac7731030a04605dccab80e9f115c22cb2efb61c0e69ce0","observation_id":"3e24a0b2-df98-41ca-80f4-0e56a8800f0e","resolution":{"observed_at":"2026-08-01T14:34:14.473690Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.527056Z","title":"Ver- sion 1.26.4","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.527056Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:cb0be486a7a626468aa5c6cd154abf7014c09710ce5908f377075b946bee4e72","observation_id":"a4ea8573-8c09-4304-8ace-34bcc86375bf","resolution":{"observed_at":"2026-08-01T14:34:14.527056Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.601881Z","title":"Mixed Precision Training","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.601881Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:d62ae08d17a7c7edc71a79103e4df816d8624c77ce6eefd2274f524a1be9fe06","observation_id":"31f949bb-8062-4507-a262-e8fcd4fafe43","resolution":{"observed_at":"2026-08-01T14:34:14.601881Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.750907Z","title":"NumPy pull request 31274; merged 29 April 2026; released in NumPy 2.5.0 on 21 June 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.750907Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:404e055fcda6701a38aca7d6c512b2b0796f4946332478d96df64f71f03f4ca7","observation_id":"cdd82921-9eb8-47e2-9dfb-2ec5e6bb5801","resolution":{"observed_at":"2026-08-01T14:34:14.750907Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.845691Z","title":"Higham.Accuracy and Stability of Numerical Algo- rithms","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.845691Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:2524c9d76b9e98383b21b5ad112184608bd2b2e97995da6e9c285d1ee4a4fcd6","observation_id":"fc905faf-acc2-4191-940d-f08ff237be41","resolution":{"observed_at":"2026-08-01T14:34:14.845691Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.906041Z","title":"Algorithms for arbitrary precision floating point arithmetic","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.906041Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:2853c383e50d4b0dfa1e0b68813b956e96e45b17f4fa359b7db406f1ca261d07","observation_id":"3fdcc5e7-f953-433f-91bc-0715737d9e48","resolution":{"observed_at":"2026-08-01T14:34:14.906041Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:14.997403Z","title":"Fast and Accurate Floating Point Summation with Application to Computational Geome- try","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.997403Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:3b93842ecb4f4ec3129aeb432550d3f77f68bce44bf25e7ff7d42126fd17f033","observation_id":"dc7828cb-264b-4a68-a87b-c6379d9d27b7","resolution":{"observed_at":"2026-08-01T14:34:14.997403Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/030601818","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Accu- rate Sum and Dot Product","venue":"SIAM Journal on Scientific Computing","work_id":"a353839e-bc19-4f68-b564-46ffc4c6af99","year":2005},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.067838Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:b05090bdd7f4a184bd500bd2ce4ce21e7870a52498a07ffa681da31b0feb80bc","observation_id":"72041966-cc90-44ef-b914-71b4675fa2e9","resolution":{"observed_at":"2026-08-01T14:39:35.125573Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.119279Z","title":"Numerical reproducibility for the parallel reduction on multi- and many-core architectures","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.119279Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:1670fc586118a6b691673815a9cdfcd88ff281583a000a1fa0fb7325f0b7ca11","observation_id":"8613a7ad-58ee-4168-9602-616fcf624de1","resolution":{"observed_at":"2026-08-01T14:34:15.119279Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.211623Z","title":"Best “Or- dering","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.211623Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:03dd254585f794217e4267ec37ed094fc71392d6c12c978c0b41d3681621f2e7","observation_id":"fd0921f2-3ecf-46ad-b87b-311fc0e99612","resolution":{"observed_at":"2026-08-01T14:34:15.211623Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/1037130","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On Floating-Point Summation","venue":"SIAM Review","work_id":"df4ddf90-9385-4a58-94d6-472d2a163ba1","year":1995},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.272332Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:1fb0be7f95c366aa0b8149e52b5173d8cfe589e28980c134524ca197cb0dabfd","observation_id":"80bae28a-8c59-4e5d-ba17-91728e5d08e9","resolution":{"observed_at":"2026-08-01T14:39:35.013778Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.324314Z","title":"Numerical inverting of matrices of high order","venue":null,"work_id":null,"year":1947},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.324314Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:42e2d497d1c04f1098bc7268673ce707907fbc5424c336fb94f54c37b2123206","observation_id":"a57ae635-0b73-46d5-b973-06be3c939381","resolution":{"observed_at":"2026-08-01T14:34:15.324314Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.364316Z","title":"Test of probabilistic models for the propagation of roundoff errors","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.364316Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:8eeba322c63a2ecca58ef0857b5d582f047d5ed00fe8edca1f6614d2aab43dbc","observation_id":"74d83c88-a65e-4a4c-828d-482b43912488","resolution":{"observed_at":"2026-08-01T14:34:15.364316Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.422441Z","title":"Tests of probabilistic models for propagation of roundoff errors","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.422441Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:c42e0157bac49da550a56ee1ce6bbec1bf4861559c39e3880f17ddb264750173","observation_id":"a6b9cc81-27e1-4df4-9e42-de2b1d15e3f4","resolution":{"observed_at":"2026-08-01T14:34:15.422441Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02251833","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On roundoff error distributions in floating point and logarithmic arithmetic","venue":"Computing","work_id":"acdd22f8-4f5a-4cb4-8ad8-150549631d36","year":1985},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.508805Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:c5fca9656bc8e75a6798c79846c32285a52137078fae849ede5a61eef6062127","observation_id":"279709c3-5d1e-4f5f-ac38-390c8f9bbeba","resolution":{"observed_at":"2026-08-01T14:39:34.903284Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.590909Z","title":"A proba- bilistic round-off error propagation model. Application to the eigenvalue problem","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.590909Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:d54fbb2aa6012d25854d2d4c770de0916358c9c33fc87d0160413c4d407b0059","observation_id":"ced9b9fe-16b0-4d91-a1ab-56bc18f04548","resolution":{"observed_at":"2026-08-01T14:34:15.590909Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.634699Z","title":"Stochastic Rounding and Its Probabilistic Backward Error Analysis","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.634699Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:40634235557616406d272792530840b1ab158a8aadb1f37872e0ba787b354728","observation_id":"5dd045b2-4d9e-41ea-ae82-724d6f2a0a22","resolution":{"observed_at":"2026-08-01T14:34:15.634699Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.680912Z","title":"Stochastic rounding: implementation, error analysis and applications","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.680912Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:75b7d3fd2cab56ef22e34472f16755ffe51120853a55bd4608e1b027720ddbd5","observation_id":"90873f00-34ff-4402-ba8e-e0dcceb4b8dc","resolution":{"observed_at":"2026-08-01T14:34:15.680912Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:15.846815Z","title":"Stochastic Rounding Variance and Probabilistic Bounds: A New Approach","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:15.846815Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:dc6ad3ce22e9f61efb40e1c70233f96e262bfc6848e12d45c0c5de7ec68cd2a0","observation_id":"01da4a68-1fb9-468e-94a1-d1ff205beb5d","resolution":{"observed_at":"2026-08-01T14:34:15.846815Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0304-3975(00)00183-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Minimizing Roundoff Errors of Prefix Sums via Dynamic Construction of Huffman Trees","venue":"Theoretical Computer Science","work_id":"5d31f774-2e5b-46f6-ac78-8e1ee3bbdf1f","year":2001},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:16.042205Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:9450eeb6c4e4bce5a7eeea063c47d802d1ebc4d23c8d3899a97a3821ee41566c","observation_id":"bef8704b-2a12-49ae-8756-8358fe31d1ed","resolution":{"observed_at":"2026-08-01T14:39:34.818686Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:16.219120Z","title":"Fast Reproducible Floating-Point Summation","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:16.219120Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:7db94b2565f407b98cc9d569be9a0bb380c3cfd5f40487f24dd3da15739d9d77","observation_id":"fe292909-3a30-4959-93f1-36a236c35589","resolution":{"observed_at":"2026-08-01T14:34:16.219120Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-319-31769-4_11","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Reproducible and Accurate Matrix Multiplication","venue":"Lecture notes in computer science","work_id":"9aa1d1cb-a345-4029-8ffe-ffaab9af74ba","year":2016},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:16.341311Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:28155328bf54c89482c24df2e216ba9a2160ca1cfc44dab07bf4fff060538c58","observation_id":"6d0d4f39-3b2d-43c0-a799-516b4c8b7b8d","resolution":{"observed_at":"2026-08-01T14:39:34.740349Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:16.461075Z","title":"A Statistical Analysis of Error in MPI Reduction Operations","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:16.461075Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:517352b5fded36f3cd1e49a01e41adcf7de363b71417501ab14e6e9967952698","observation_id":"88c31dde-9bb0-40c7-adbc-f7efe79e20d5","resolution":{"observed_at":"2026-08-01T14:34:16.461075Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:16.593043Z","title":"Mixed Precision Block Fused Multiply- Add: Error Analysis and Application to GPU Tensor Cores","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:16.593043Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:73d6888faf67ba8e6d043460912b24ca739e49066867816310dc59864c8410ed","observation_id":"451e3b84-a203-4c4f-8dfe-166a7eedfffb","resolution":{"observed_at":"2026-08-01T14:34:16.593043Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:34:16.723772Z","title":"Deep Learning with Limited Numerical Precision","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:16.723772Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:d809557d709e5383e838a9b0d6ee8e32f61256e79c04a0c631764daa11e006d9","observation_id":"2bc53e82-2a74-4b07-b7dc-36edabf273b1","resolution":{"observed_at":"2026-08-01T14:34:16.723772Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2603.24161","doi":"10.48550/arxiv.2603.24161","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"arXiv (Cornell University)","work_id":"cfa4ee14-494e-479c-9ac6-eeb6d01dafcb","year":2026},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:16.851630Z"},"links":{"citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:ad94881c2e086f42258bd99fdb685b781dba851f69167c0e91f85899ee392394","observation_id":"dd81e675-78b2-4b5f-b4e2-14c3a39eb7bb","resolution":{"observed_at":"2026-08-01T14:39:34.649621Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1710.03740","last_updated":"2018-02-15T20:04:02Z","snapshot_observed_at":"2026-07-06T06:03:37.247241Z","submitted_at":"2017-10-10T17:42:04Z","title":"Mixed Precision Training","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.03740","snapshot_observed_at":"2026-08-01T14:34:14.682480Z","title":"net/forum?id=r1gs9JgRZ","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees","version":1},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-01T14:34:14.682480Z"},"links":{"cited_paper":"/paper/1710.03740","citing_paper":"/paper/2607.18758"},"observation_digest":"sha256:092e9e594b4081e2655a6e0a420ca8a2b3a265b6d553770243a46c69bb134d8b","observation_id":"da1f1e15-de38-43c3-8aee-5f7326601c8b","resolution":{"observed_at":"2026-08-01T14:34:14.682480Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.18758","last_updated":"2026-07-21T06:27:43Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-06T02:41:49.878457Z","submitted_at":"2026-07-21T06:27:43Z","title":"A Second-Moment Theory for Floating-Point Reduction Trees"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":8,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":9,"verified_fuzzy":0},"total_outbound_references":37},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2607.18758."}