Paper Citation Record · LEDGER

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation

As of 8 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2506.00796.

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

pith.paper-citation-record.v1
2506.00796 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:01:23.428707Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

35 of 35 outbound references displayed

verified exact10
verified fuzzy11
unresolved8
parse uncertain0
malformed identifier6
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 41ccc668-1141-41b8-93e0-24143bec74b8 · outbound

This paper cites A high order method for estimation of dynamic systems,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation A high order method for estimation of dynamic systems,

Reference 1

Resolution: verified exact; doi, observed 2026-08-07T12:01:24.825003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8403c7b6-1e1c-4547-a3b0-e644db660f63 · outbound

This paper cites High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD,

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T12:01:20.110752Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12960737-3f9c-45e0-9ce6-32821b31c435 · outbound

This paper cites Arbitrary-order derivatives of quantum chemical methods via automatic differentiation,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Arbitrary-order derivatives of quantum chemical methods via automatic differentiation,

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T12:01:20.205741Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 062c0a60-5360-4923-aa5a-5e81d05bc969 · outbound

This paper cites Automatic differentiation applied for optimization of dynamical systems,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Automatic differentiation applied for optimization of dynamical systems,

Reference 4

Resolution: malformed identifier; no resolver link, observed 2026-08-07T12:01:20.292529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0947503-5305-4004-9491-ff345bdf26bc · outbound

This paper cites Meta-Learning with Implicit Gradients.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Meta-Learning with Implicit Gradients

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T12:01:20.406654Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f848275-7c4c-41dd-a07b-85c99c0ba222 · outbound

This paper cites Automatic differentiation in machine learning: A survey,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Automatic differentiation in machine learning: A survey,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:26.431242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e2ebde44-a26b-4097-bbc1-0c886585ebf2 · outbound

This paper cites Applications of differentiation arithmetic,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Applications of differentiation arithmetic,

Reference 7

Resolution: verified exact; doi, observed 2026-08-07T12:01:24.714416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d9b997bc-1803-4b1f-826c-c62bab3de533 · outbound

This paper cites Analytical differentiation on a digital computer,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Analytical differentiation on a digital computer,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:26.308846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 142ec3a7-6f4b-4b1c-bc6b-6cac258dae8a · outbound

This paper cites A simple automatic derivative evaluation program,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation A simple automatic derivative evaluation program,

Reference 9

Resolution: verified exact; raw_fallback, observed 2026-08-07T12:01:25.090327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 44cebf95-41f2-41fa-8100-0ea7d6af8940 · outbound

This paper cites Compiling fast partial derivatives of functions given by algorithms,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Compiling fast partial derivatives of functions given by algorithms,

Reference 10

Resolution: verified exact; doi, observed 2026-08-07T12:01:24.622406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 563a02ac-2f96-4348-be7e-1bd39ff20931 · outbound

This paper cites Perspectives on automatic differentiation: Past, present, and future?.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Perspectives on automatic differentiation: Past, present, and future?

Reference 11

Resolution: malformed identifier; no resolver link, observed 2026-08-07T12:01:20.910660Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 96fe6250-93a9-4941-8a98-01d50626995b · outbound

This paper cites The method of power series tracking for the mathematical description of beam dynamics,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation The method of power series tracking for the mathematical description of beam dynamics,

Reference 12

Resolution: malformed identifier; doi_truncated, observed 2026-08-07T12:01:24.505743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a00eacd9-d63b-4f61-9935-826304a0044a · outbound

This paper cites Differential algebraic description of beam dynamics to very high orders,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Differential algebraic description of beam dynamics to very high orders,

Reference 13

Resolution: verified exact; doi, observed 2026-08-07T12:01:24.378699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4eea5dc1-cbc7-4172-9bc3-c97b265b9fbe · outbound

This paper cites Arbitrary order description of arbitrary particle optical systems,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Arbitrary order description of arbitrary particle optical systems,

Reference 14

Resolution: verified exact; doi, observed 2026-08-07T12:01:24.239134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bb3ba181-1583-41ea-8be7-e1873823464f · outbound

This paper cites Modern map methods for charged particle optics,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Modern map methods for charged particle optics,

Reference 15

Resolution: verified exact; doi, observed 2026-08-07T12:01:24.116852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c6f840c4-a325-4670-959b-bfc1aa2a79c0 · outbound

This paper cites Symplectic tracking in circular accelerators with high order maps,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Symplectic tracking in circular accelerators with high order maps,

Reference 16

Resolution: verified exact; doi, observed 2026-08-07T12:01:24.004627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ef7b4f39-8e68-4f3f-8243-5cd5469dfd98 · outbound

This paper cites High-order computation and normal form analysis of repetitive systems, in: M. month (ed), physics of particle accelerators,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation High-order computation and normal form analysis of repetitive systems, in: M. month (ed), physics of particle accelerators,

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T12:01:21.408364Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8af97df-a958-4602-b94f-765732c1c714 · outbound

This paper cites Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models,

Reference 18

Resolution: malformed identifier; no resolver link, observed 2026-08-07T12:01:21.504931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 495fe723-5f2d-43e0-bb99-f9872a07b3ab · outbound

This paper cites Verified global optimization with Taylor model-based range bounders,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Verified global optimization with Taylor model-based range bounders,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:26.165843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 83572673-106a-4745-8a85-27938a653f93 · outbound

This paper cites The fast multipole method in the differential algebra framework,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation The fast multipole method in the differential algebra framework,

Reference 20

Resolution: verified exact; doi, observed 2026-08-07T12:01:23.894588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 98db6851-d124-4ec7-85a9-3454c02d1635 · outbound

This paper cites Berz, Modern Map Methods in Particle Beam Physics.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Berz, Modern Map Methods in Particle Beam Physics

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:26.043190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8b881929-b58b-45f9-94c4-627678508d65 · outbound

This paper cites an unresolved cited work.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Unresolved cited work

Reference 22

Resolution: malformed identifier; doi_truncated, observed 2026-08-07T12:01:23.748161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 26205753-47c7-40e8-8b25-7f912eb2f341 · outbound

This paper cites Zhang, SDA: A Symbolic Differential Algebra package in C++, version v1.0.0, Accessed: 2024-09-13,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Zhang, SDA: A Symbolic Differential Algebra package in C++, version v1.0.0, Accessed: 2024-09-13,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:25.908542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7955c138-4f90-446d-81d4-e925002d3c18 · outbound

This paper cites cppTPSA/pyTPSA: A C++/Python package for truncated power series algebra,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation cppTPSA/pyTPSA: A C++/Python package for truncated power series algebra,

Reference 24

Resolution: verified exact; doi, observed 2026-08-07T12:01:23.620952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 969f7c39-142d-4aa3-be59-85587a45b8a1 · outbound

This paper cites Symengine.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Symengine

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:25.692596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dc2e000d-74ab-499f-935a-a1223f0c2dba · outbound

This paper cites Chatgpt.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Chatgpt

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:25.562322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d2b0809e-e8af-4965-b8eb-acc600e544f8 · outbound

This paper cites ChatGPT and Open-AI models: A preliminary review,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation ChatGPT and Open-AI models: A preliminary review,

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T12:01:22.703905Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a31403b-24e5-4e01-bb3a-b851564a192d · outbound

This paper cites Generalised truncated power series algebra for fast particle accelerator transport maps,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Generalised truncated power series algebra for fast particle accelerator transport maps,

Reference 28

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T12:01:25.454539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 713cc88b-2f95-45b8-99ac-5b3b1436c26d · outbound

This paper cites Forward-Mode Automatic Differentiation in Julia.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Forward-Mode Automatic Differentiation in Julia

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T12:01:22.883586Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3eed651b-bb48-422f-adb7-40f0008a4651 · outbound

This paper cites Julia: A Fast Dynamic Language for Technical Computing.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Julia: A Fast Dynamic Language for Technical Computing

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T12:01:22.987274Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 280a9e39-92c4-4f34-a468-d6b511eee89d · outbound

This paper cites Julia: A fresh approach to numerical computing,.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Julia: A fresh approach to numerical computing,

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-07T12:01:23.093833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d6c5158-bd89-4373-866d-1f73e1ca65d1 · outbound

This paper cites Juliaprogramminglanguage.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Juliaprogramminglanguage

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:25.378088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f23f856c-f9a6-420e-a4f7-cc7ffe1016d6 · outbound

This paper cites Signorelli and D.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Signorelli and D

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:25.331233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 09fbe57e-abc7-4ac6-899a-4a696508e4db · outbound

This paper cites Revels, V.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Revels, V

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:25.265337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 74c39673-8fe5-455c-8643-c5f21fed4aa1 · outbound

This paper cites Available:https://github.com/zhanghe9704/tpsa_sym.

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation Available:https://github.com/zhanghe9704/tpsa_sym

Reference 2024

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:01:25.831916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.