Pith Number

pith:EONCAKGC

pith:2026:EONCAKGC5GBCHDUG6PC4SWCYTX

not attested not anchored not stored refs pending

Function-free Optimization via Comparison Oracles

Katya Scheinberg, Zikai Xiong

Introduces a comparison-oracle framework using preference level-set geometry to achieve near-optimal query complexity for normal direction estimation and descent-based optimization under regularity and convexity.

arxiv:2604.26867 v2 · 2026-04-29 · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EONCAKGC5GBCHDUG6PC4SWCYTX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

Under regularity of the preference relation in a d-dimensional Euclidean space, we estimate normal directions to accuracy ε using O(d log(d/ε)) comparisons, nearly matching a lower bound of Ω(d log(1/ε)). Under convexity, regularity, and a local growth condition on the regularity radius, the resulting normal direction descent method reaches an ε level-set optimality gap using at most Õ(d D²/ε²) comparisons over O(D²/ε²) normal direction estimation steps.

C2weakest assumption

The regularity of the preference relation together with convexity and the local growth condition on the regularity radius; these are invoked to derive the normal-direction estimation and descent complexity bounds but are not guaranteed to hold for arbitrary comparison oracles.

C3one line summary

Receipt and verification

First computed	2026-05-20T01:05:14.628029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

239a2028c2e982238e86f3c5c958589de2e413730389d3fb5b2a7f4f1004f000

Aliases

arxiv: 2604.26867 · arxiv_version: 2604.26867v2 · doi: 10.48550/arxiv.2604.26867 · pith_short_12: EONCAKGC5GBC · pith_short_16: EONCAKGC5GBCHDUG · pith_short_8: EONCAKGC

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/EONCAKGC5GBCHDUG6PC4SWCYTX \
  | 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: 239a2028c2e982238e86f3c5c958589de2e413730389d3fb5b2a7f4f1004f000

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb814d657d409a5a9d12c95406cfae2254fb7d31a2e03e586cb3cf3742a4efb4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-29T16:34:11Z",
    "title_canon_sha256": "8cc25123f57772b347fc61ae5be670b2ab4d2f3054e52b0d3bfdc2e5260d3aa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26867",
    "kind": "arxiv",
    "version": 2
  }
}