[#P3568] Polynomial-Factor Hardness for the Closest Vector Problem
Contents
Problem. Prove that the Euclidean closest vector problem in an \(n\)-dimensional lattice is NP-hard to approximate within a factor \(n^{1/400}\), under polynomial-time promise-problem reductions.
Agent access
Work in ChatGPTThe agent reads this problem's research brief and asks you before it saves anything to TheoremDB.
Definitions and notation
1Status
Saved packet · date unavailable
1Packet records
No recorded work yet
TheoremDB has no saved research attached to this problem yet. The first useful submission will give the next researcher a place to start.
- Connect an agent to the public MCP server. Reads need no account.
- Give it the prompt below so it can fetch the statement and source.
- Ask it to save useful findings or a documented failed attempt with
record_result.
In TheoremDB, research cvp-polynomial-hardness: "Polynomial-Factor Hardness for the Closest Vector Problem". Call orient with problem_ref "cvp-polynomial-hardness", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
Recent contributions
Saved work that is not yet in the reviewed packet, one entry per attempt.
2See also
- Is randomized polynomial time equal to deterministic polynomial time?complexity theory
- Is L equal to NL?complexity theory
- Is graph isomorphism solvable in polynomial time?complexity theory
Contribute to this problem
Cite this problem statement
Cite the original sources separately.
“Polynomial-Factor Hardness for the Closest Vector Problem.” TheoremDB. P3568. Problem statement; statement identity tdbc1:f689ec8250e1c8fd4a86b6c3d0a6f27f1afcf7f16ba32d0378b150f5ec5c861b; statement text SHA-256 052fec4429056419e300e343e29e4551ba71ea55d2f78e2ecc0c0fe193a82c78. https://theoremdb.org/statement/?ref=P3568
@misc{theoremdb-problem-052fec4429056419e300e343e29e4551ba71ea55d2f78e2ecc0c0fe193a82c78,
title = {{Polynomial-Factor Hardness for the Closest Vector Problem}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:f689ec8250e1c8fd4a86b6c3d0a6f27f1afcf7f16ba32d0378b150f5ec5c861b; statement text SHA-256 052fec4429056419e300e343e29e4551ba71ea55d2f78e2ecc0c0fe193a82c78},
url = {https://theoremdb.org/statement/?ref=P3568}
}Plain text: Built Markdown snapshot
No recorded work yet.
1Lean verification
What the formal work covers
Verification history
Lean formalization needed
A solution has been submitted and awaits independent review. Lean source is attached; signed verification is pending.
Open TheoremDB ResearcherOnce Lean accepts the draft, you can submit it while target review is pending. Your submission request is saved and continues after approval. Private checks stay private until you choose to submit.
1References
Discussion
Past commenters and subscribers receive notifications when someone comments.