Paper Citation Record · LEDGER

Lower Bounds against the Ideal Proof System in Finite Fields

As of 16 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2506.17210.

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

pith.paper-citation-record.v1
2506.17210 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:23:26.556284Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

17 of 17 outbound references displayed

verified exact4
verified fuzzy3
unresolved9
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 62cdf3b2-d991-4a27-928f-1c20881cf584 · outbound

This paper cites Characterizing Propositional Proofs as Non-Commutative Formulas.

Lower Bounds against the Ideal Proof System in Finite Fields Characterizing Propositional Proofs as Non-Commutative Formulas

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.535531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 660f0b7c-f58e-4af1-8574-2d7a79208bbe · outbound

This paper cites Lower Bounds for Polynomial Cal- culus with Extension Variables over Finite Fields.

Lower Bounds against the Ideal Proof System in Finite Fields Lower Bounds for Polynomial Cal- culus with Extension Variables over Finite Fields

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.486615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1e137f9-8144-4cec-b1b4-f6aa9de70255 · outbound

This paper cites Characterizing Propositional Proofs as Non- commutative Formulas.

Lower Bounds against the Ideal Proof System in Finite Fields Characterizing Propositional Proofs as Non- commutative Formulas

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.530653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fba73930-358d-4ffa-b04b-e53c516a2592 · outbound

This paper cites Iterated Lower Bound Formulas: A Diagonalization- Based Approach to Proof Complexity.

Lower Bounds against the Ideal Proof System in Finite Fields Iterated Lower Bound Formulas: A Diagonalization- Based Approach to Proof Complexity

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.556284Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f57c5b4-7167-43df-aa5a-769b7d794465 · outbound

This paper cites Unsolvable systems of equations and proof complexity.

Lower Bounds against the Ideal Proof System in Finite Fields Unsolvable systems of equations and proof complexity

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:23:27.314761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 813bc3cf-7e09-4e2a-bb40-99764555d558 · outbound

This paper cites Improved Lower Bound, and Proof Barrier, for Constant Depth Algebraic Circuits.

Lower Bounds against the Ideal Proof System in Finite Fields Improved Lower Bound, and Proof Barrier, for Constant Depth Algebraic Circuits

Reference 200

Resolution: verified exact; doi, observed 2026-08-15T19:23:26.743921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c9f690cc-1184-4070-bfb7-058f9be25185 · outbound

This paper cites A Lower Bound for Polynomial Calculus with Extension Rule.

Lower Bounds against the Ideal Proof System in Finite Fields A Lower Bound for Polynomial Calculus with Extension Rule

Reference 261

Resolution: verified exact; doi, observed 2026-08-15T19:23:26.809901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7271c312-8ae7-4ae4-8941-a212168d6d9c · outbound

This paper cites Quasipolynomial-Time Identity Testing of Non- commutative and Read-Once Oblivious Algebraic Branching Programs.

Lower Bounds against the Ideal Proof System in Finite Fields Quasipolynomial-Time Identity Testing of Non- commutative and Read-Once Oblivious Algebraic Branching Programs

Reference 300

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.355189Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42642afa-9f51-45d8-b5b8-bf50bf07c8ed · outbound

This paper cites Low-depth algebraic circuit lower bounds over any field.

Lower Bounds against the Ideal Proof System in Finite Fields Low-depth algebraic circuit lower bounds over any field

Reference 305

Resolution: malformed identifier; no resolver link, observed 2026-08-15T19:23:26.351108Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e97328aa-d1f0-46ff-93a5-cee49d642cbb · outbound

This paper cites Algebraic Proof Complexity: Progress, Frontiers and Challenges.

Lower Bounds against the Ideal Proof System in Finite Fields Algebraic Proof Complexity: Progress, Frontiers and Challenges

Reference 460

Resolution: verified exact; doi, observed 2026-08-15T19:23:26.641626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 320bdeac-9af9-49f6-991f-27068730b419 · outbound

This paper cites Algebraic propositional proof systems.

Lower Bounds against the Ideal Proof System in Finite Fields Algebraic propositional proof systems

Reference 1991

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.539526Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a0d5190-827f-44fd-8150-dd88b70575c9 · outbound

This paper cites (Semi)Algebraic proofs over±1 variables.

Lower Bounds against the Ideal Proof System in Finite Fields (Semi)Algebraic proofs over±1 variables

Reference 2012

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:23:27.301472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fbb1d50b-e4f0-4572-8b3f-2d9cff3fc83e · outbound

This paper cites Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs.

Lower Bounds against the Ideal Proof System in Finite Fields Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.359570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c1b605b-5ab0-4349-b0e1-91ec17e2afee · outbound

This paper cites Low- Depth Arithmetic Circuit Lower Bounds: Bypassing Set-Multilinearization.

Lower Bounds against the Ideal Proof System in Finite Fields Low- Depth Arithmetic Circuit Lower Bounds: Bypassing Set-Multilinearization

Reference 2020

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:23:27.409789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f90b5602-370a-499d-8780-362623b3a910 · outbound

This paper cites Ideals, Determinants, and Straightening: Proving and Using Lower Bounds for Polynomial Ideals.

Lower Bounds against the Ideal Proof System in Finite Fields Ideals, Determinants, and Straightening: Proving and Using Lower Bounds for Polynomial Ideals

Reference 2022

Resolution: verified exact; local_arxiv, observed 2026-08-15T19:23:27.287688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1dae1a1e-3efb-4170-b02d-001e9a62a70a · outbound

This paper cites The Surprising Power of Constant Depth Algebraic Proofs.

Lower Bounds against the Ideal Proof System in Finite Fields The Surprising Power of Constant Depth Algebraic Proofs

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.402200Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f32c96b-aa54-4881-9ada-d2a0c01bf3a6 · outbound

This paper cites TowardsNP-Pvia Proof Complexity and Search.

Lower Bounds against the Ideal Proof System in Finite Fields TowardsNP-Pvia Proof Complexity and Search

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-15T19:23:26.345010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.