Pith Number

pith:HCWW72JH

pith:2026:HCWW72JHZ333WSZL3ZUM3DXLSO

not attested not anchored not stored refs pending

The Grimmer--Shu--Wang Certificate and the Drori--Teboulle Minimax Constant-Stepsize Bound for $N\ge 3$

Lixing Zhang

For every number of steps N at least 3, positive vectors exist that satisfy the equations of the strengthened low-rank certificate for the worst-case analysis of gradient descent with constant stepsize.

arxiv:2605.11421 v2 · 2026-05-12 · math.OC

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\usepackage{pith}
\pithnumber{HCWW72JHZ333WSZL3ZUM3DXLSO}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove, for every horizon N >= 3, the existence of the strengthened low-rank performance-estimation certificate proposed by Grimmer, Shu, and Wang for the Drori-Teboulle minimax nonnegative constant-stepsize problem for gradient descent.

C2weakest assumption

The GSW certificate equations admit positive vectors a, b, c, d satisfying all residual equations, shown via a reduced residual system, simplex existence argument, terminal residual completion identity, and tail-square convolution argument proving cumulative margins.

C3one line summary

The Grimmer-Shu-Wang low-rank PEP certificate exists for every horizon N >= 3 and establishes the exact Drori-Teboulle minimax nonnegative constant-stepsize bound for gradient descent.

Receipt and verification

First computed	2026-05-27T01:05:56.842816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38ad6fe927cef7bb4b2bde68cd8eeb9393135667eb5224e677aedbc7dc2d86b5

Aliases

arxiv: 2605.11421 · arxiv_version: 2605.11421v2 · doi: 10.48550/arxiv.2605.11421 · pith_short_12: HCWW72JHZ333 · pith_short_16: HCWW72JHZ333WSZL · pith_short_8: HCWW72JH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HCWW72JHZ333WSZL3ZUM3DXLSO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 38ad6fe927cef7bb4b2bde68cd8eeb9393135667eb5224e677aedbc7dc2d86b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0de5901a44cec94acee269fee3f46d39edaf9993ed16f53e6ababcf1b3aaaab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-12T02:15:33Z",
    "title_canon_sha256": "d25c8abb5414025428bfad464683c89ad2bbdcec9c4834152d518fff27d5e31b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11421",
    "kind": "arxiv",
    "version": 2
  }
}