Paper Citation Record · LEDGER

A Second-Moment Theory for Floating-Point Reduction Trees

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.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.18758 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T14:34:16.851630Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

37 of 37 outbound references displayed

verified exact9
verified fuzzy0
unresolved20
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ce6fddd9-0db5-4e10-bda3-1f8fc1e8f8a0 · outbound

This paper cites A New Approach to Probabilistic Rounding Error Analysis.

A Second-Moment Theory for Floating-Point Reduction Trees A New Approach to Probabilistic Rounding Error Analysis

Reference 1

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Source-reported events for the cited work

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Observation cb8aa322-5c90-47fb-8190-f3149e78e6cc · outbound

This paper cites Precision-aware determin- istic and probabilistic error bounds for floating point summa- tion.

A Second-Moment Theory for Floating-Point Reduction Trees Precision-aware determin- istic and probabilistic error bounds for floating point summa- tion

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:13.840697Z

Source-reported events for the cited work

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Observation b8620b18-8f38-431b-9f3f-e4b7890275fb · outbound

This paper cites The Ancestral Matrix of a Rooted Tree.

A Second-Moment Theory for Floating-Point Reduction Trees The Ancestral Matrix of a Rooted Tree

Reference 3

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Observation f57157b6-a837-4cb3-9d7d-4c65c146530d · outbound

This paper cites A Method for the Construction of Minimum-Redundancy Codes.

A Second-Moment Theory for Floating-Point Reduction Trees A Method for the Construction of Minimum-Redundancy Codes

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:14.017534Z

Source-reported events for the cited work

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Observation f4ab3331-1a3e-489c-a8b9-0b2c58c6d934 · outbound

This paper cites Cover and Joy A.

A Second-Moment Theory for Floating-Point Reduction Trees Cover and Joy A

Reference 5

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Source-reported events for the cited work

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Observation d16a7568-2ef4-448f-8be6-0ddf0ef1fd97 · outbound

This paper cites Linear-Time Approximation Algorithms for Computing Numerical Summation with Prov- ably Small Errors.

A Second-Moment Theory for Floating-Point Reduction Trees Linear-Time Approximation Algorithms for Computing Numerical Summation with Prov- ably Small Errors

Reference 6

Resolution: verified exact; doi, observed 2026-08-01T14:39:35.357920Z

Source-reported events for the cited work

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Observation b629a264-7cf6-42a5-b849-6f0d4d1207f8 · outbound

This paper cites A Fast Al- gorithm for Optimal Length-Limited Huffman Codes.

A Second-Moment Theory for Floating-Point Reduction Trees A Fast Al- gorithm for Optimal Length-Limited Huffman Codes

Reference 7

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Observation 6d63e01a-8cda-475e-91f5-5ecb0444e6b8 · outbound

This paper cites The Accuracy of Floating Point Sum- mation.

A Second-Moment Theory for Floating-Point Reduction Trees The Accuracy of Floating Point Sum- mation

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:14.315570Z

Source-reported events for the cited work

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Observation 381b1692-0065-4c67-bb8d-3cfd77904e32 · outbound

This paper cites A Class of Fast and Accurate Summation Algorithms.

A Second-Moment Theory for Floating-Point Reduction Trees A Class of Fast and Accurate Summation Algorithms

Reference 9

Resolution: verified exact; doi, observed 2026-08-01T14:39:35.272559Z

Source-reported events for the cited work

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Observation 7e9293c0-dfd7-44a5-a4ff-2ae863ffe5b0 · outbound

This paper cites Reducing Floating Point Error in Dot Prod- uct Using the Superblock Family of Algorithms.

A Second-Moment Theory for Floating-Point Reduction Trees Reducing Floating Point Error in Dot Prod- uct Using the Superblock Family of Algorithms

Reference 10

Resolution: verified exact; doi, observed 2026-08-01T14:39:35.190511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3e24a0b2-df98-41ca-80f4-0e56a8800f0e · outbound

This paper cites Revealing Floating-Point Accumulation Orders in Software/Hardware Implementations.

A Second-Moment Theory for Floating-Point Reduction Trees Revealing Floating-Point Accumulation Orders in Software/Hardware Implementations

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:14.473690Z

Source-reported events for the cited work

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Observation a4ea8573-8c09-4304-8ace-34bcc86375bf · outbound

This paper cites Ver- sion 1.26.4.

A Second-Moment Theory for Floating-Point Reduction Trees Ver- sion 1.26.4

Reference 12

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Source-reported events for the cited work

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Observation 31f949bb-8062-4507-a262-e8fcd4fafe43 · outbound

This paper cites Mixed Precision Training.

A Second-Moment Theory for Floating-Point Reduction Trees Mixed Precision Training

Reference 13

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Source-reported events for the cited work

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Observation cdd82921-9eb8-47e2-9dfb-2ec5e6bb5801 · outbound

This paper cites NumPy pull request 31274; merged 29 April 2026; released in NumPy 2.5.0 on 21 June 2026.

A Second-Moment Theory for Floating-Point Reduction Trees NumPy pull request 31274; merged 29 April 2026; released in NumPy 2.5.0 on 21 June 2026

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:14.750907Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc905faf-acc2-4191-940d-f08ff237be41 · outbound

This paper cites Higham.Accuracy and Stability of Numerical Algo- rithms.

A Second-Moment Theory for Floating-Point Reduction Trees Higham.Accuracy and Stability of Numerical Algo- rithms

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:14.845691Z

Source-reported events for the cited work

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Observation 3fdcc5e7-f953-433f-91bc-0715737d9e48 · outbound

This paper cites Algorithms for arbitrary precision floating point arithmetic.

A Second-Moment Theory for Floating-Point Reduction Trees Algorithms for arbitrary precision floating point arithmetic

Reference 16

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Source-reported events for the cited work

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Observation dc7828cb-264b-4a68-a87b-c6379d9d27b7 · outbound

This paper cites Fast and Accurate Floating Point Summation with Application to Computational Geome- try.

A Second-Moment Theory for Floating-Point Reduction Trees Fast and Accurate Floating Point Summation with Application to Computational Geome- try

Reference 17

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Source-reported events for the cited work

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Observation 72041966-cc90-44ef-b914-71b4675fa2e9 · outbound

This paper cites Accu- rate Sum and Dot Product.

A Second-Moment Theory for Floating-Point Reduction Trees Accu- rate Sum and Dot Product

Reference 18

Resolution: verified exact; doi, observed 2026-08-01T14:39:35.125573Z

Source-reported events for the cited work

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Observation 8613a7ad-58ee-4168-9602-616fcf624de1 · outbound

This paper cites Numerical reproducibility for the parallel reduction on multi- and many-core architectures.

A Second-Moment Theory for Floating-Point Reduction Trees Numerical reproducibility for the parallel reduction on multi- and many-core architectures

Reference 19

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Source-reported events for the cited work

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Observation fd0921f2-3ecf-46ad-b87b-311fc0e99612 · outbound

This paper cites Best “Or- dering.

A Second-Moment Theory for Floating-Point Reduction Trees Best “Or- dering

Reference 20

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Observation 80bae28a-8c59-4e5d-ba17-91728e5d08e9 · outbound

This paper cites On Floating-Point Summation.

A Second-Moment Theory for Floating-Point Reduction Trees On Floating-Point Summation

Reference 21

Resolution: verified exact; doi, observed 2026-08-01T14:39:35.013778Z

Source-reported events for the cited work

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Observation a57ae635-0b73-46d5-b973-06be3c939381 · outbound

This paper cites Numerical inverting of matrices of high order.

A Second-Moment Theory for Floating-Point Reduction Trees Numerical inverting of matrices of high order

Reference 22

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Observation 74d83c88-a65e-4a4c-828d-482b43912488 · outbound

This paper cites Test of probabilistic models for the propagation of roundoff errors.

A Second-Moment Theory for Floating-Point Reduction Trees Test of probabilistic models for the propagation of roundoff errors

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:15.364316Z

Source-reported events for the cited work

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Observation a6b9cc81-27e1-4df4-9e42-de2b1d15e3f4 · outbound

This paper cites Tests of probabilistic models for propagation of roundoff errors.

A Second-Moment Theory for Floating-Point Reduction Trees Tests of probabilistic models for propagation of roundoff errors

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:15.422441Z

Source-reported events for the cited work

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Observation 279709c3-5d1e-4f5f-ac38-390c8f9bbeba · outbound

This paper cites On roundoff error distributions in floating point and logarithmic arithmetic.

A Second-Moment Theory for Floating-Point Reduction Trees On roundoff error distributions in floating point and logarithmic arithmetic

Reference 25

Resolution: verified exact; doi, observed 2026-08-01T14:39:34.903284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ced9b9fe-16b0-4d91-a1ab-56bc18f04548 · outbound

This paper cites A proba- bilistic round-off error propagation model. Application to the eigenvalue problem.

A Second-Moment Theory for Floating-Point Reduction Trees A proba- bilistic round-off error propagation model. Application to the eigenvalue problem

Reference 26

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Source-reported events for the cited work

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Observation 5dd045b2-4d9e-41ea-ae82-724d6f2a0a22 · outbound

This paper cites Stochastic Rounding and Its Probabilistic Backward Error Analysis.

A Second-Moment Theory for Floating-Point Reduction Trees Stochastic Rounding and Its Probabilistic Backward Error Analysis

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:15.634699Z

Source-reported events for the cited work

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Observation 90873f00-34ff-4402-ba8e-e0dcceb4b8dc · outbound

This paper cites Stochastic rounding: implementation, error analysis and applications.

A Second-Moment Theory for Floating-Point Reduction Trees Stochastic rounding: implementation, error analysis and applications

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:15.680912Z

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Unavailable: canonical work link unavailable.

Observation 01da4a68-1fb9-468e-94a1-d1ff205beb5d · outbound

This paper cites Stochastic Rounding Variance and Probabilistic Bounds: A New Approach.

A Second-Moment Theory for Floating-Point Reduction Trees Stochastic Rounding Variance and Probabilistic Bounds: A New Approach

Reference 29

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Source-reported events for the cited work

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Observation bef8704b-2a12-49ae-8756-8358fe31d1ed · outbound

This paper cites Minimizing Roundoff Errors of Prefix Sums via Dynamic Construction of Huffman Trees.

A Second-Moment Theory for Floating-Point Reduction Trees Minimizing Roundoff Errors of Prefix Sums via Dynamic Construction of Huffman Trees

Reference 30

Resolution: verified exact; doi, observed 2026-08-01T14:39:34.818686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation fe292909-3a30-4959-93f1-36a236c35589 · outbound

This paper cites Fast Reproducible Floating-Point Summation.

A Second-Moment Theory for Floating-Point Reduction Trees Fast Reproducible Floating-Point Summation

Reference 31

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Source-reported events for the cited work

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Observation 6d0d4f39-3b2d-43c0-a799-516b4c8b7b8d · outbound

This paper cites Reproducible and Accurate Matrix Multiplication.

A Second-Moment Theory for Floating-Point Reduction Trees Reproducible and Accurate Matrix Multiplication

Reference 32

Resolution: verified exact; doi, observed 2026-08-01T14:39:34.740349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 88c31dde-9bb0-40c7-adbc-f7efe79e20d5 · outbound

This paper cites A Statistical Analysis of Error in MPI Reduction Operations.

A Second-Moment Theory for Floating-Point Reduction Trees A Statistical Analysis of Error in MPI Reduction Operations

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:16.461075Z

Source-reported events for the cited work

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Observation 451e3b84-a203-4c4f-8dfe-166a7eedfffb · outbound

This paper cites Mixed Precision Block Fused Multiply- Add: Error Analysis and Application to GPU Tensor Cores.

A Second-Moment Theory for Floating-Point Reduction Trees Mixed Precision Block Fused Multiply- Add: Error Analysis and Application to GPU Tensor Cores

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:16.593043Z

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Observation 2bc53e82-2a74-4b07-b7dc-36edabf273b1 · outbound

This paper cites Deep Learning with Limited Numerical Precision.

A Second-Moment Theory for Floating-Point Reduction Trees Deep Learning with Limited Numerical Precision

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:16.723772Z

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Observation dd81e675-78b2-4b5f-b4e2-14c3a39eb7bb · outbound

This paper cites an unresolved cited work.

A Second-Moment Theory for Floating-Point Reduction Trees Unresolved cited work

Reference 36

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation da1f1e15-de38-43c3-8aee-5f7326601c8b · outbound

This paper cites Mixed Precision Training.

A Second-Moment Theory for Floating-Point Reduction Trees Mixed Precision Training

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-01T14:34:14.682480Z

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Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.