Pith Number

pith:434FULTR

pith:2012:434FULTRYQAXPL6AKDJGMCTH2H

not attested not anchored not stored refs pending

Small ball probability, Inverse theorems, and applications

Hoi H. Nguyen, Van H. Vu

arxiv:1301.0019 v1 · 2012-12-31 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{434FULTRYQAXPL6AKDJGMCTH2H}

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	2026-05-18T03:37:28.567329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6f85a2e71c40177afc050d2660a67d1db48a536b597acb34b13a80af167ff1a

Aliases

arxiv: 1301.0019 · arxiv_version: 1301.0019v1 · doi: 10.48550/arxiv.1301.0019 · pith_short_12: 434FULTRYQAX · pith_short_16: 434FULTRYQAXPL6A · pith_short_8: 434FULTR

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/434FULTRYQAXPL6AKDJGMCTH2H \
  | 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: e6f85a2e71c40177afc050d2660a67d1db48a536b597acb34b13a80af167ff1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bc5e88fc6ecff242be98634b9c28245d16bf549de35bcfbca31bfd946047346",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-31T21:39:17Z",
    "title_canon_sha256": "a0232d57a5600b567ba690a46312adcd82ff1efa3f0569d488c77a8e9922852e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0019",
    "kind": "arxiv",
    "version": 1
  }
}