Paper Citation Record · LEDGER

Feynman integral reduction with intersection theory made simple

As of 5 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 4 inbound Pith citation observations for arXiv:2604.05025.

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

pith.paper-citation-record.v1
2604.05025 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T19:20:26.449693Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-10T06:51:36.448776Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-10T06:56:52.300060Z

Reference resolution

36 of 36 outbound references displayed

verified exact28
verified fuzzy2
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

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Outbound references

Observation 09c483e0-d07f-44ee-85bf-5b0d88277ac5 · outbound

This paper cites After imposing symmetry relations, 5 the total number of master integrals is reduced from 228 to 216.

Feynman integral reduction with intersection theory made simple After imposing symmetry relations, 5 the total number of master integrals is reduced from 228 to 216

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T05:47:25.068716Z

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Observation ffc52b39-2c80-48bd-8bfa-d00d8a7d9c9f · outbound

This paper cites an unresolved cited work.

Feynman integral reduction with intersection theory made simple Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-05-16T05:47:25.070734Z

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Observation ae8ff6fd-a050-45bc-9b43-885509885aa2 · outbound

This paper cites an unresolved cited work.

Feynman integral reduction with intersection theory made simple Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-05-16T05:47:25.077010Z

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Observation d0c65e6d-ce3f-42c5-a5d5-bc3ada6a578f · outbound

This paper cites an unresolved cited work.

Feynman integral reduction with intersection theory made simple Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-05-16T05:47:25.074854Z

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Observation 5082a3f2-ed32-4e66-9b43-24700e877b27 · outbound

This paper cites an unresolved cited work.

Feynman integral reduction with intersection theory made simple Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-05-16T05:47:25.072600Z

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Observation b4cf0c9f-6773-4df9-82f1-5ceebac31461 · outbound

This paper cites Remiddi, Nuovo Cim.

Feynman integral reduction with intersection theory made simple Remiddi, Nuovo Cim

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.540495Z

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Observation 1f246a7c-00e4-472e-a94b-1e248810ae02 · outbound

This paper cites Differential Equations for Two-Loop Four-Point Functions.

Feynman integral reduction with intersection theory made simple Differential Equations for Two-Loop Four-Point Functions

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.512461Z

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Observation 9af24b8c-1bad-4c93-9922-195d3ca8d3e7 · outbound

This paper cites AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow.

Feynman integral reduction with intersection theory made simple AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.532356Z

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Observation 3eddb035-ae5f-403c-9bc2-8033a185ad41 · outbound

This paper cites Laporta, Phys.

Feynman integral reduction with intersection theory made simple Laporta, Phys

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.545461Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 5abdf437-0d2f-49e9-b983-efcad1260954 · outbound

This paper cites High-precision calculation of multi-loop Feynman integrals by difference equations.

Feynman integral reduction with intersection theory made simple High-precision calculation of multi-loop Feynman integrals by difference equations

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.601032Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 88f83ebb-8c77-4a29-b85a-36a66cbcd4bb · outbound

This paper cites FIRE 6.5: Feynman Integral Reduction with New Simplification Library.

Feynman integral reduction with intersection theory made simple FIRE 6.5: Feynman Integral Reduction with New Simplification Library

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.508482Z

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Observation 09b61298-34a5-45ae-bfea-160b5f8f1a04 · outbound

This paper cites Reduze 2 - Distributed Feynman Integral Reduction.

Feynman integral reduction with intersection theory made simple Reduze 2 - Distributed Feynman Integral Reduction

Reference 12

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T23:05:49.522889Z

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Observation ee7b2460-f336-4659-b190-28f9e4eaf9cb · outbound

This paper cites LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals.

Feynman integral reduction with intersection theory made simple LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.503947Z

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Observation 97ef8f25-0c77-4645-9b77-6cafc025146b · outbound

This paper cites Integral Reduction with Kira 2.0 and Finite Field Methods.

Feynman integral reduction with intersection theory made simple Integral Reduction with Kira 2.0 and Finite Field Methods

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-18T00:11:26.285833Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 3e1aa11d-2f00-45ac-9fe0-06b524f0685a · outbound

This paper cites Kira 3: integral reduction with efficient seeding and optimized equation selection.

Feynman integral reduction with intersection theory made simple Kira 3: integral reduction with efficient seeding and optimized equation selection

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.444148Z

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Observation 1e0f70fb-7ba4-4ea2-83e9-36c425f7f26f · outbound

This paper cites NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals.

Feynman integral reduction with intersection theory made simple NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.449372Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation ed6ef1d8-07ca-487c-af30-11fc6aa55621 · outbound

This paper cites Blade: A package for block-triangular form improved Feynman integrals decomposition.

Feynman integral reduction with intersection theory made simple Blade: A package for block-triangular form improved Feynman integrals decomposition

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.593037Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation cf7f3b8d-c921-4a63-a6d0-11792a64fd25 · outbound

This paper cites Explainable AI-assisted Optimization for Feynman Integral Reduction.

Feynman integral reduction with intersection theory made simple Explainable AI-assisted Optimization for Feynman Integral Reduction

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.576561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation e9f6f5c8-da33-436f-abf5-60741c7b6259 · outbound

This paper cites Scattering Amplitudes from Intersection Theory.

Feynman integral reduction with intersection theory made simple Scattering Amplitudes from Intersection Theory

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.558477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation fc18d1e7-b9da-4916-a9cc-5d9e17279520 · outbound

This paper cites Feynman Integrals and Intersection Theory.

Feynman integral reduction with intersection theory made simple Feynman Integrals and Intersection Theory

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.428287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation d1a0e836-3430-4441-8158-601dc72f3819 · outbound

This paper cites Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers.

Feynman integral reduction with intersection theory made simple Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.422923Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 1d0f7878-4f7e-4082-8ccb-dd8335f6b507 · outbound

This paper cites Vector Space of Feynman Integrals and Multivariate Intersection Numbers.

Feynman integral reduction with intersection theory made simple Vector Space of Feynman Integrals and Multivariate Intersection Numbers

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.566974Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 971dae81-ffe6-475b-8326-839432161bd1 · outbound

This paper cites From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals.

Feynman integral reduction with intersection theory made simple From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.495558Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 22d17712-dd24-4aef-b935-b5e1d003cd42 · outbound

This paper cites Status of Intersection Theory and Feynman Integrals.

Feynman integral reduction with intersection theory made simple Status of Intersection Theory and Feynman Integrals

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.551591Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 44def0e2-cb5d-4c9f-a1e9-88f15116c0ab · outbound

This paper cites Decomposition of Feynman Integrals by Multivariate Intersection Numbers.

Feynman integral reduction with intersection theory made simple Decomposition of Feynman Integrals by Multivariate Intersection Numbers

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.474235Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 607f960c-9073-4648-a878-9bccc75957a9 · outbound

This paper cites Duals of Feynman Integrals, I: Differential Equations.

Feynman integral reduction with intersection theory made simple Duals of Feynman Integrals, I: Differential Equations

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.583059Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 08dc1ba8-370b-4c78-94cd-77fe462040d9 · outbound

This paper cites Duals of Feynman Integrals, 2: Generalized Unitarity.

Feynman integral reduction with intersection theory made simple Duals of Feynman Integrals, 2: Generalized Unitarity

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.469147Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation def28564-5109-44f7-b145-3e7bd12f40ee · outbound

This paper cites Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers.

Feynman integral reduction with intersection theory made simple Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.436125Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 081cb62a-0a5a-40a4-acd8-4f7720d085f3 · outbound

This paper cites Reduction to master integrals via intersection numbers and polynomial expansions.

Feynman integral reduction with intersection theory made simple Reduction to master integrals via intersection numbers and polynomial expansions

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.461810Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 4457fd35-9759-4c4e-a885-03a2c822384c · outbound

This paper cites Intersection Numbers, Polynomial Division and Relative Cohomology.

Feynman integral reduction with intersection theory made simple Intersection Numbers, Polynomial Division and Relative Cohomology

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.490885Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation db733b0d-31d7-4a1d-a733-b7b6d89840d5 · outbound

This paper cites Intersection Numbers from Companion Tensor Algebra.

Feynman integral reduction with intersection theory made simple Intersection Numbers from Companion Tensor Algebra

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.516122Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 79cd3ff0-1a68-42f4-826c-62e8850a0ddc · outbound

This paper cites Intersection theory, relative cohomology and the Feynman parametrization.

Feynman integral reduction with intersection theory made simple Intersection theory, relative cohomology and the Feynman parametrization

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.616021Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 09ba4489-4564-40b8-bab3-7bd9e21080c6 · outbound

This paper cites Critical points and number of master integrals.

Feynman integral reduction with intersection theory made simple Critical points and number of master integrals

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.454968Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a2f410bf-5657-4957-9190-3e60ffe06adc · outbound

This paper cites Tame multi-leg Feynman integrals beyond one loop.

Feynman integral reduction with intersection theory made simple Tame multi-leg Feynman integrals beyond one loop

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:05:49.621230Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation d0c77670-8862-4c64-9a72-2c22115be435 · outbound

This paper cites FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs.

Feynman integral reduction with intersection theory made simple FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs

Reference 35

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T23:05:49.481176Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 37320fcc-4c53-4052-b31d-c0191bde8d9c · outbound

This paper cites However, in that case one needs to compute inter- section numbers separately for each sub-sector (relative boundary).

Feynman integral reduction with intersection theory made simple However, in that case one needs to compute inter- section numbers separately for each sub-sector (relative boundary)

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-16T05:47:25.066512Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Pith citing papers

Observation a64921fc-ab64-4a3b-ad6c-aef0e5c2550c · inbound

Loop integrals in de Sitter spacetime: The parity-split IBP system and $\mathrm{d}\log$-form differential equations cites this paper.

Loop integrals in de Sitter spacetime: The parity-split IBP system and $\mathrm{d}\log$-form differential equations Feynman integral reduction with intersection theory made simple

Reference 109

Resolution: verified exact; local_arxiv, observed 2026-05-10T11:10:08.719122Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation de186e17-d911-4040-8532-56dbf2801c58 · inbound

An Algorithm for the Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions cites this paper.

An Algorithm for the Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions Feynman integral reduction with intersection theory made simple

Reference 57

Resolution: verified exact; local_arxiv, observed 2026-05-12T06:21:26.224938Z

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Observation 0aceda8a-896c-4843-9e1a-b6963a6f8105 · inbound

On the spanning cuts consistency problem in the IBP reductions of Feynman integrals cites this paper.

On the spanning cuts consistency problem in the IBP reductions of Feynman integrals Feynman integral reduction with intersection theory made simple

Reference 64

Resolution: verified exact; local_arxiv, observed 2026-07-02T00:06:23.587116Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation dd7b2f4a-e7eb-407c-9a29-e33602fe0c7e · inbound

AMFlow 2.0: significant algorithmic and software improvements for Feynman integral evaluation cites this paper.

AMFlow 2.0: significant algorithmic and software improvements for Feynman integral evaluation Feynman integral reduction with intersection theory made simple

Reference 53

Resolution: verified exact; local_arxiv, observed 2026-07-10T06:56:52.301558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.