The stated Nesterov accelerated-gradient iterates converge to a minimizer for every L-smooth convex objective with a minimizer
Queued record · four gates mapped · no examination route has run
Current record status
What this docket currently establishes
Queued record · four gates mapped · no examination route has run. This docket identifies what has been checked and what remains open. It does not validate or reject the manuscript's headline claim beyond the explicitly stated scope.
- Claim
- The stated Nesterov accelerated-gradient iterates converge to a minimizer for every L-smooth convex objective with a minimizer
- Source version
- arXiv 2510.23513v2 · arXiv v2
- Source SHA-256
31dafeda57a8b0f933fbadefe20d32543ca36ea176292dfaf240d179f3b273f0- Source locked
- Last material update
- Next open step
- Independently derive the recurrence equivalence and discrete energy inequality under the exact tₖ hypotheses
- Machine-readable record
- JSON record · Atom change feed
One-minute summary
The locked v2 manuscript claims point convergence of the Nesterov iterates, not merely convergence of objective values. Four load-bearing gates are mapped from the recurrence and energy inequality through the unique-cluster-point argument. No gate has run.
For non-specialists
Why this matters
A nontechnical reading of the claim and its possible consequences. These are implications to consider, not findings of this docket.
In plain English
The manuscript studies a specified accelerated optimization method and claims that its sequence of proposed answers converges to an actual minimizer. This is stronger than showing only that the objective values approach the best possible value.
If the claim holds
If the argument holds under its stated assumptions, it would establish point convergence for that particular method and parameter schedule in the specified finite-dimensional setting. It would not automatically extend to other accelerated methods or settings.
Potential concerns
The conclusion rests on an exact recurrence, an energy inequality, boundedness, and a final argument that rules out multiple limiting points. No part of that chain has yet been examined in this docket.
If it does not hold up
If a step fails, weaker conclusions may still be possible, but this manuscript would not have established convergence of the iterates themselves under the stated conditions.
Scope of this docket
The examination target is Theorem 3.5 in arXiv v2 under its stated finite-dimensional assumptions. The withdrawn v1 side claim, infinite-dimensional extensions, FISTA, OGM, and other damping regimes are outside this docket.
Claim and dependency map
Recurrence equivalence and discrete energy inequality
Depends on: locked v2 assumptions
Boundedness of the auxiliary and NAG sequences
Depends on: G1
Scalar convergence bridge and all tₖ hypotheses
Depends on: G2
Unique cluster point and common xₖ,yₖ limit
Depends on: G3
Examination routes
- computational
- Queued · updated 2026-08-26
Planned: exact recurrence replay and independent algebraic derivation of the energy inequality. - literature
- Queued · updated 2026-08-26
Planned: source comparison for the cited scalar convergence lemma. - expert
- Queued · updated 2026-08-26
Planned: finite-dimensional convex-analysis review of the cluster-point and common-limit steps.
Findings and scope limits
No examination route has run and no mathematical finding has been issued.
Version 2, not version 1 or an invented version 3, is the locked examination target.
Open Steps—where expert eyes are needed
Does the stated recurrence yield the one-step energy inequality under exactly the manuscript's tₖ condition?
Every later boundedness and convergence step depends on this first algebraic gate.
Source record and provenance
Seventeen-page v2 source. The withdrawn v1 argument for r∈[1,3) is preserved only as source lineage and is not the examination target.
Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case.
Retrieved .
- Preservation
- The source is pinned to arXiv v2. No separate public Wayback snapshot was found in the read-only availability check.
- Record provenance
- Claim map and route plan prepared by Material Shift from the recorded source; no mathematical finding or external review is recorded.
- Author contact
- No author outreach, correspondence, response, or author approval is recorded for this docket. Contact the record steward.
Version and record history
-
record provenance
2025-10-27-nesterov-point-convergence
Record classified as queued; source preservation, route provenance, and author-contact state published
-
new docket
2025-10-27-nesterov-point-convergence
arXiv v2 locked and four examination gates mapped; no gate run
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source updated
2025-10-27-nesterov-point-convergence
v2 published; the withdrawn v1 r∈[1,3) route retained as lineage only
Statuses describe evidence collected for a defined scope. They are not peer-review decisions, publication recommendations, or certificates of mathematical truth.