Paper Citation Record · LEDGER

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation

As of 18 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2506.09529.

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

pith.paper-citation-record.v1
2506.09529 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:56:29.603325Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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 exact0
verified fuzzy33
unresolved2
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7bb64087-781a-471b-b9fc-09fcf6d81538 · outbound

This paper cites Stable border bases for ideals of points.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Stable border bases for ideals of points

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.164241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ce47f3fb-9001-4d36-8cf6-8eb848d6b65e · outbound

This paper cites Analytic Manifold Learning: Unifying and Evaluating Representations for Continuous Control.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Analytic Manifold Learning: Unifying and Evaluating Representations for Continuous Control

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T04:56:29.447038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4dd761a9-d662-47b3-a4a0-18b93b63abe7 · outbound

This paper cites Ideals, varieties, and algorithms , volume 3.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Ideals, varieties, and algorithms , volume 3

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.147915Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 99c7cff8-8735-4738-804b-7564999a7403 · outbound

This paper cites Emiris, editors.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Emiris, editors

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.132713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2469eae2-4195-440f-a4bc-1ccb1f998f75 · outbound

This paper cites Symboli-numeric methods for solving polynomial equa- tions.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Symboli-numeric methods for solving polynomial equa- tions

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.118102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cb9033d2-98e3-420b-8115-d2c81a835848 · outbound

This paper cites Almost vanishing polynomials for sets of limited precision points.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Almost vanishing polynomials for sets of limited precision points

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.103541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d1a07dbf-df36-47b1-a47b-b628d7679dba · outbound

This paper cites Simple varieties for limited precision points.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Simple varieties for limited precision points

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.088088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f37690ff-b30a-45b4-a02c-e389f7913142 · outbound

This paper cites Approximate computation of zero-dimensional polynomial ideals.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Approximate computation of zero-dimensional polynomial ideals

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.071646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5ba7ee56-ac00-4c0b-9913-a059733bf99f · outbound

This paper cites Discriminative vanishing component analysis.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Discriminative vanishing component analysis

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.055638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5ed38f1b-52e6-4c01-b0f3-d9a06a8193fe · outbound

This paper cites Principal variety analysis.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Principal variety analysis

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.039764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0788de50-8360-4869-b2a6-061138826367 · outbound

This paper cites Nepomuceno, Aleksandra Tutueva, and Denis Butusov.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Nepomuceno, Aleksandra Tutueva, and Denis Butusov

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.023759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2d076560-750d-4c66-a9cd-002410dd0170 · outbound

This paper cites Identifying empirical equations of chaotic circuit from data.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Identifying empirical equations of chaotic circuit from data

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:30.007381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 36a42283-7542-4daa-9352-21863d32d604 · outbound

This paper cites Characterizations of border bases.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Characterizations of border bases

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.991653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation daffff7c-a768-4069-b8a1-caa35d6ddbe5 · outbound

This paper cites An algebraist’s view on border bases.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation An algebraist’s view on border bases

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.976395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3f5d30e5-8bf3-4861-8896-345014eba4e7 · outbound

This paper cites Border basis computation with gradient-weighted normalization.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Border basis computation with gradient-weighted normalization

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.961105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5e97c507-22cb-4c30-9485-cddc6ebc48f6 · outbound

This paper cites Noise-tolerant algebraic method for reconstruction of non- linear dynamical systems.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Noise-tolerant algebraic method for reconstruction of non- linear dynamical systems

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.945933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8089ef00-732c-41f1-bc2d-baa7da7fd5fe · outbound

This paper cites Approximate vanishing ideal via data knotting.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Approximate vanishing ideal via data knotting

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.931820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 02431a28-c876-42b5-967e-97c3e109a7c3 · outbound

This paper cites Spurious vanishing problem in approximate vanishing ideal.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Spurious vanishing problem in approximate vanishing ideal

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.917581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ab02879a-5e9e-4c00-8a9d-6c6267e5938c · outbound

This paper cites Gradient boosts the approximate vanishing ideal.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Gradient boosts the approximate vanishing ideal

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.903205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8000933c-f358-4b09-8c7a-72ca94ad565e · outbound

This paper cites Monomial-agnostic computation of vanishing ideals.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Monomial-agnostic computation of vanishing ideals

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.888785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8250002b-a82e-4923-9c1f-a1a6449b9ce3 · outbound

This paper cites Vanishing ideal genetic programming.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Vanishing ideal genetic programming

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.874138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e051240f-b97f-4003-806e-b1fa26532db8 · outbound

This paper cites Dual-to-kernel learning with ideals.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Dual-to-kernel learning with ideals

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.858847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4d55f81a-aa3f-4dfe-a604-7d216f31744f · outbound

This paper cites Computational commutative algebra 2 , volume 2.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Computational commutative algebra 2 , volume 2

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.844535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 151612a3-5cda-4971-8b12-2609be74b488 · outbound

This paper cites Computation of approximate border bases and applications.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Computation of approximate border bases and applications

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.829809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cfe6542c-5520-4adf-a5b1-36ff7428daf4 · outbound

This paper cites Vanishing component analysis.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Vanishing component analysis

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.814918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cbf16748-fd00-47d0-8c81-2f25f1eb42ed · outbound

This paper cites Approximating latent manifolds in neural networks via vanishing ideals, 2025.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Approximating latent manifolds in neural networks via vanishing ideals, 2025

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.800108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 25986325-cbce-46fb-9e7d-fae017442c3d · outbound

This paper cites Approximate Commutative Algebra.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Approximate Commutative Algebra

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.784952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 88b48ee5-4e23-4835-bf56-16d1dae35bd0 · outbound

This paper cites an unresolved cited work.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:56:29.770328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2fb81fd8-f010-43dd-aa08-0c2b901d64cd · outbound

This paper cites Application of algebra in the oil industry.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Application of algebra in the oil industry

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.755510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1c1766da-9d14-446d-a96c-35404fa492a4 · outbound

This paper cites Wang and T.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Wang and T

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.739362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 93857726-5d48-43a9-a6fb-4aa339552d0c · outbound

This paper cites Polynomial representation for persistence diagram.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Polynomial representation for persistence diagram

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.722904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9da2a9ae-cb24-4eac-ae7a-d23fc7158a52 · outbound

This paper cites Conditional gradients for the approximately vanishing ideal.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Conditional gradients for the approximately vanishing ideal

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.707232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4a841db9-4543-4a92-824f-f660a1a44385 · outbound

This paper cites Approximate vanishing ideal computa- tions at scale.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Approximate vanishing ideal computa- tions at scale

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.691952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3c5716e5-548b-42d3-8a46-5c5fa64e950c · outbound

This paper cites Deep vanishing component analysis network for pattern classification.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Deep vanishing component analysis network for pattern classification

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.675848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6f0713ff-3be1-4dde-9210-367810b163f3 · outbound

This paper cites Hand posture recognition using approximate vanishing ideal genera- tors.

Gradient-Weighted, Data-Driven Normalization for Approximate Border Bases -- Concept and Computation Hand posture recognition using approximate vanishing ideal genera- tors

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:56:29.659595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

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