The stated Nesterov accelerated-gradient iterates converge to a minimizer for every L-smooth convex objective with a minimizer
Intake record · four gates mapped · no audit gate has run
Current record status
What this docket currently establishes
Intake record · four gates mapped · no audit gate 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
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.
Scope of this docket
The audit 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 The withdrawn v1 side claim, infinite-dimensional extensions, FISTA, OGM, and other damping regimes are outside this docket.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
Evidence routes
- computational
- Planned: exact recurrence replay and independent algebraic derivation of the energy inequality.
- literature
- Planned: source comparison for the cited scalar convergence lemma.
- expert
- Planned: finite-dimensional convex-analysis review of the cluster-point and common-limit steps.
Findings and scope limits
No audit gate has run and no mathematical finding has been issued.
Version 2, not version 1 or an invented version 3, is the locked audit 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 audit target.
Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case.
Retrieved .
Version and record history
-
new docket
2025-10-27-nesterov-point-convergence
arXiv v2 locked and four audit gates mapped; no gate run
-
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.