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🤖 Gemini PR SummaryCompletes numerous Mathematical Formalization1. Decoding Algorithms
2. Proximity Gaps and Correlated Agreement
3. Bivariate Polynomials and Resultants
Infrastructure and Library Integration
Important Reviewer Note: New assumptions added to Analysis of Changes
Lean Declarations ✏️ **Removed:** 36 declaration(s)
✏️ **Added:** 171 declaration(s)
✏️ **Affected:** 22 declaration(s) (line number changed)
✅ **Removed:** 51 `sorry`(s)
🎨 **Style Guide Adherence**The following violations of the style guide were found: Naming Conventions
Documentation Standards
Syntax and Formatting
Variable Conventions
📄 **Per-File Summaries**
Last updated: 2026-03-03 00:48 UTC. |
FawadHa1der
commented
Jan 30, 2026
Author
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I know probably a way too big of a PR :( but BCIKS is kinda a dependent on many things RationalFunctions, Guruswami etc. So I went ahead tried to prove as much as I could. I am still going and trying to remove any extra assumptions added to the proofs. But hopefully some of these proofs are helpful :) They include Guruswami, BKICS20, DG25, BerleyKamp and RationalFunctions Codex 5.2. |
…ce‑filter implementation
Collaborator
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Hello! Thanks for the PR and sorry for the delay in getting to this. I'll be merging the 4.26 PR soon, which might break a few things, and get back to all the other PRs including this one. |
Author
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Sure I understand, let me know which proofs are useful and I can make a cleaner PR as well if you want. This is definitely too big of a PR for someone who is little new to FV. |
Collaborator
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I think this looks mostly ok although I'll need a bit more time to manually go through all of it since there are some declaration changes. |
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/review External: Internal: Comments: |
🤖 AI Review (with external context)🤖 AI ReviewOverall Summary: 1. TL;DRThe mathematical translation of the BCIKS20, AHIV22, and Guruswami-Sudan algorithms into Lean 4 is extremely impressive, correctly enforcing combinatorial bounds and completely eliminating a vast number of 2. Checklist Coverage
3. Critical Misformalizations
4. Key Lean 4 / Mathlib Issues
5. Overall VerdictVerdict: Changes Requested While the elimination of 📄 **Review for `ArkLib.lean`**Verdict: Approved Checklist Verification:
(Note: The provided diff exclusively contains two Critical Misformalizations: Lean 4 / Mathlib Issues: Nitpicks: 📄 **Review for `ArkLib/Data/CodingTheory/BerlekampWelch/Sorries.lean`**Verdict: Changes Requested Checklist Verification:
Critical Misformalizations: Lean 4 / Mathlib Issues:
Nitpicks:
📄 **Review for `ArkLib/Data/CodingTheory/GuruswamiSudan/GuruswamiSudan.lean`**Verdict: Approved Checklist Verification:
Critical Misformalizations: Lean 4 / Mathlib Issues: Nitpicks:
📄 **Review for `ArkLib/Data/CodingTheory/ProximityGap/AHIV22.lean`**Verdict: Approved Checklist Verification:
(Other checklist items are safely out of scope for the modified Critical Misformalizations: Lean 4 / Mathlib Issues: Nitpicks:
📄 **Review for `ArkLib/Data/CodingTheory/ProximityGap/BCIKS20.lean`**Verdict: Approved Checklist Verification:
Critical Misformalizations: Lean 4 / Mathlib Issues: Nitpicks: 📄 **Review for `ArkLib/Data/CodingTheory/ProximityGap/DG25.lean`**Verdict: Needs Minor Revisions Checklist Verification:
(Note: The changes in this PR specifically abstract out the Critical Misformalizations: Lean 4 / Mathlib Issues:
Nitpicks:
📄 **Review for `ArkLib/Data/CodingTheory/ProximityGap/ListRecovery.lean`**Verdict: Changes Requested Checklist Verification:
Critical Misformalizations: Lean 4 / Mathlib Issues:
Nitpicks:
📄 **Review for `ArkLib/Data/Polynomial/Bivariate.lean`**Verdict: Changes Requested Checklist Verification:
Critical Misformalizations: Lean 4 / Mathlib Issues:
Nitpicks:
📄 **Review for `ArkLib/Data/Polynomial/Prelims.lean`**An analysis of the pull request reveals that while you successfully implemented the requested discriminant formula and removed Verdict: Changes Requested Checklist Verification:
Critical Misformalizations:
Lean 4 / Mathlib Issues:
Nitpicks:
📄 **Review for `ArkLib/Data/Polynomial/RationalFunctions.lean`**An excellent PR that tackles some of the heaviest algebraic machinery in the BCIKS20 paper. The formalization of the function field However, there is a critical logical flaw in how the Hensel lift coefficients are extracted via Verdict: Changes Requested Checklist Verification:
Critical Misformalizations:
Lean 4 / Mathlib Issues:
Nitpicks:
📄 **Review for `ArkLib/Data/Polynomial/RationalFunctionsInfrastructure.lean`**Verdict: Changes Requested Checklist Verification:
Critical Misformalizations:
Lean 4 / Mathlib Issues:
Nitpicks:
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/review External: Internal: Comments: |
Author
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I tried to fix the issue of vacuous error bounds and pushed the changes but cannot get the AI bot to trigger apparently. This definitely needs to be reviewed by coding theory experts |
Collaborator
Permission issue, sorry 😞 |
Collaborator
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/review External: Internal: Comments: |
🤖 AI Review (with external context)🤖 AI ReviewOverall Summary: 📄 **Review for `ArkLib.lean`**Analysis of The changes in
Logic and Correctness:
Misformalization Check:
Verdict: 📄 **Review for `ArkLib/Data/CodingTheory/BerlekampWelch/Sorries.lean`**Verdict: Correct The formalization in Analysis:
The implementation aligns with the expected behavior of a generic linear solver interface used in coding theory proofs (like those referenced in the context of Berlekamp-Welch where solution existence guarantees decoding). No off-by-one errors, type mismatches, or universe issues were found. The code compiles and the logic is sound. 📄 **Review for `ArkLib/Data/CodingTheory/GuruswamiSudan/GuruswamiSudan.lean`**Analysis of The file implements the Guruswami-Sudan list decoding algorithm for Reed-Solomon codes. The formalization includes the definition of the interpolation conditions (vanishing with multiplicity), the linear-algebraic existence of the interpolant, the factorization step (root finding), and bounds on the list size. 1. Definitions and Structures:
2. Interpolation (Existence):
3. Root Finding (Factorization):
4. Decoder Definition:
5. Parameter Choices:
6. List Size Bound:
Summary: Verdict: Correct. 📄 **Review for `ArkLib/Data/CodingTheory/ProximityGap/AHIV22.lean`**Verdict: Correct Feedback:
No issues found. 📄 **Review for `ArkLib/Data/CodingTheory/ProximityGap/BCIKS20.lean`**Verdict: Correct The formalization in Detailed Assessment:
The implementation is verified to be correct with respect to the supported subset of the external references. 📄 **Review for `ArkLib/Data/CodingTheory/ProximityGap/DG25.lean`**Analysis of The changes in this file involve a refactoring of the proofs for proximity gaps in the unique decoding regime for Reed-Solomon codes. Specifically, the direct derivation of the correlated agreement property (based on library lemmas like This refactoring essentially decouples the usage of the correlated agreement result from its proof, likely to improve modularity or avoid circular dependencies. The mathematical content of the assumption Review Checklist & Findings:
Conclusion: Verdict: 📄 **Review for `ArkLib/Data/CodingTheory/ProximityGap/ListRecovery.lean`**Analysis of The file Key Definitions and Lemmas:
Technical Assessment:
Conclusion: Verdict: Correct. 📄 **Review for `ArkLib/Data/Polynomial/Bivariate.lean`**Verdict: Correct Feedback:
No misformalization issues found. 📄 **Review for `ArkLib/Data/Polynomial/Prelims.lean`**The changes in
No misformalizations were found. ArkLib/Data/Polynomial/Prelims.lean -- No corrections needed.📄 **Review for `ArkLib/Data/Polynomial/RationalFunctions.lean`**Verdict: Incorrect Critical Issues:
Suggestions for Correction:
Minor Issue:
Correctness of Logic in 📄 **Review for `ArkLib/Data/Polynomial/RationalFunctionsInfrastructure.lean`**The formalization in The file defines the resultant of bivariate polynomials with respect to one variable (
The definitions align with standard algebraic geometry concepts and the specific usage in the referenced literature (treating bivariate polynomials as univariate polynomials over a polynomial ring). The proofs for index manipulation and summations involving the Sylvester matrix are detailed and correct. No issues found. |
… coefficient-by-coefficient recursive construction
Author
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@alexanderlhicks AI review required. I will leave the conflict resolution to you. |
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/review External: Internal: Comments: |
Collaborator
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running the somewhat improved review workflow whilst on the road to see if it picks up anything, should be able to do a final manual pass and look at resolving the merge conflicts once done with travel hopefully. It would be nice to avoid big PRs like this in the future, especially when many new declarations are added and a lot of code could be cleaned up. I'm not necessarily enthusiastic about merging this given it will require a bunch of tweaking things later on to organise the files better and hide some of the noise of intermediary lemmas generated by Aristotle (this also duplicates some proofs that are in other PRs and forks). |
eliasjudin
added a commit
to eliasjudin/ArkLib
that referenced
this pull request
Mar 3, 2026
Add `numberOfClosePts_eq_natCard` as a reusable helper in AHIV22 for converting `numberOfClosePts` to `Nat.card` in proximity-count arguments. Refs Verified-zkEVM#227 Refs Verified-zkEVM#298 Co-authored-by: Aristotle (Harmonic) <aristotle-harmonic@harmonic.fun>
Collaborator
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@FawadHa1der I'm just seeing you tagged me in this, sorry! Thanks for this and for listening to my talk. Would it be helpful to review the PR? cc @alexanderlhicks |
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Enabled by Codex 5.2. This is an attempt to provide all/majority of the proofs marked as sorry. For proximity gap related lemmas in BCIKS20.lean there have been some assumptions added which require proper review from the experts. @katyhr saw your talk on Coding Theory implementation recently, may be this helps in that regard.
@alexanderlhicks I know there is a refactor going on but I hope some of the proofs here are useful, and I open to doing smaller PRs for the proofs which are clean without any assumptions added.
@chung-thai-nguyen here another PR related to coding theory that you might want to review. I do hope some if not all the proofs are useful.
Please give any feedback or modifications necessary.
Thank you!