Pith Number

pith:CCUMJSCR

pith:2025:CCUMJSCRRN5O4HFLZEH25JVRJZ

not attested not anchored not stored refs pending

Kurdyka-\L ojasiewicz exponent via square transformation

Wenqing Ouyang

arxiv:2506.10110 v2 · 2025-06-11 · 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{CCUMJSCRRN5O4HFLZEH25JVRJZ}

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.

Receipt and verification

First computed	2026-07-05T11:20:56.716869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10a8c4c8518b7aee1cabc90faea6b14e535b392efebdc01727edee9b209dc736

Aliases

arxiv: 2506.10110 · arxiv_version: 2506.10110v2 · doi: 10.48550/arxiv.2506.10110 · pith_short_12: CCUMJSCRRN5O · pith_short_16: CCUMJSCRRN5O4HFL · pith_short_8: CCUMJSCR

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/CCUMJSCRRN5O4HFLZEH25JVRJZ \
  | 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: 10a8c4c8518b7aee1cabc90faea6b14e535b392efebdc01727edee9b209dc736

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09dd5986a4a7a8c28feb660549f3a6d25257f9e7a55176f418424ed876972e63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-06-11T18:49:46Z",
    "title_canon_sha256": "20165fa9d9ec943e1e49f699bd1ef1872a8b020d9899319e14d832edd48ff3f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.10110",
    "kind": "arxiv",
    "version": 2
  }
}