Pith Number

pith:7KU7JD7W

pith:2010:7KU7JD7WZPRVKT5UELDDXSE6ZX

not attested not anchored not stored refs pending

Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function

Adam J. Harper

arxiv:1012.0210 v2 · 2010-12-01 · math.PR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7KU7JD7WZPRVKT5UELDDXSE6ZX}

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	2026-05-18T03:32:57.487613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

faa9f48ff6cbe3554fb422c63bc89ecde04ed0fd931979ec52ea2956185cd8f8

Aliases

arxiv: 1012.0210 · arxiv_version: 1012.0210v2 · doi: 10.48550/arxiv.1012.0210 · pith_short_12: 7KU7JD7WZPRV · pith_short_16: 7KU7JD7WZPRVKT5U · pith_short_8: 7KU7JD7W

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/7KU7JD7WZPRVKT5UELDDXSE6ZX \
  | 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: faa9f48ff6cbe3554fb422c63bc89ecde04ed0fd931979ec52ea2956185cd8f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42d8e7e4fb45c90717fbdf907e23f230439c7efb14a4c1f22a19391853a9003d",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-01T14:59:45Z",
    "title_canon_sha256": "cf3d7cafa0072d084060dbc714d762518682615340e56634ce9269ef68fb9cf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0210",
    "kind": "arxiv",
    "version": 2
  }
}