Pith Number

pith:AWA64TUE

pith:2025:AWA64TUEJEOK5L2JNBH7HPCYQG

not attested not anchored not stored refs pending

Entropy and Learning of Lipschitz Functions under Log-Concave Measures

Boaz Klartag, Pierre Bizeul

arxiv:2509.10355 v1 · 2025-09-12 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AWA64TUEJEOK5L2JNBH7HPCYQG}

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	2026-07-05T12:11:08.305500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0581ee4e84491caeaf49684ff3bc58818286673e2d463a28e2c433592176e3db

Aliases

arxiv: 2509.10355 · arxiv_version: 2509.10355v1 · doi: 10.48550/arxiv.2509.10355 · pith_short_12: AWA64TUEJEOK · pith_short_16: AWA64TUEJEOK5L2J · pith_short_8: AWA64TUE

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/AWA64TUEJEOK5L2JNBH7HPCYQG \
  | 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: 0581ee4e84491caeaf49684ff3bc58818286673e2d463a28e2c433592176e3db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95d32b3a2cb3e5e8a103de80d1def03440b467291078de429a549453bd98dbd6",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-09-12T15:43:13Z",
    "title_canon_sha256": "9d63bb7b975fcee51cf88423592c8b282cd0567dd8afacac8c57fc3c29b4a3cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.10355",
    "kind": "arxiv",
    "version": 1
  }
}