Pith Number

pith:GKEAZPBI

pith:2026:GKEAZPBINH7T4UUPK6UIQXFMQX

not attested not anchored not stored refs pending

Polynomial iteration complexity of a path-following smoothing Newton method for symmetric cone programming

Rui-Jin Zhang, Ruoyu Diao, Xin-Wei Liu, Yu-Hong Dai

A path-following smoothing Newton method achieves polynomial iteration complexity O(sqrt(ν) ln(1/ε)) for symmetric cone programming.

arxiv:2604.04376 v2 · 2026-04-06 · math.OC

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\usepackage{pith}
\pithnumber{GKEAZPBINH7T4UUPK6UIQXFMQX}

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Record completeness

1 Bitcoin timestamp

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

the method is proven to achieve an iteration complexity of O( sqrt(nu) ln(1/eps) ), matching the best-known short-step bound for IPMs.

C2weakest assumption

The reduced SBAL function is self-concordant convex-concave, which extends the classical self-concordant theory beyond the convex setting and enables the central-path neighborhood analysis.

C3one line summary

A path-following smoothing Newton method for symmetric cone programming achieves O(sqrt(nu) ln(1/eps)) iteration complexity via a newly introduced self-concordant convex-concave reduced SBAL function that induces a central path.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:04:01.560425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32880cbc2869ff3e528f57a8885cac85ebcb2eb648a652492e0704e9216efd5d

Aliases

arxiv: 2604.04376 · arxiv_version: 2604.04376v2 · doi: 10.48550/arxiv.2604.04376 · pith_short_12: GKEAZPBINH7T · pith_short_16: GKEAZPBINH7T4UUP · pith_short_8: GKEAZPBI

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/GKEAZPBINH7T4UUPK6UIQXFMQX \
  | 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: 32880cbc2869ff3e528f57a8885cac85ebcb2eb648a652492e0704e9216efd5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e57297513aad4cdae67ab4b99c7237aae80dd5d54eb950a4a58efdea9d5715e4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-06T02:53:16Z",
    "title_canon_sha256": "130a9e5dcdef542bf1e413a10db3edaa36b10bd8b175b7c9caedbfad00c84749"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.04376",
    "kind": "arxiv",
    "version": 2
  }
}