Pith Number

pith:V3VQKHJG

pith:2008:V3VQKHJG4OK7BFXK532GE2Y6FO

not attested not anchored not stored refs pending

Higher Order Birkhoff Averages

Thomas Jordan, Todd Young, Vincent Naudot

arxiv:0806.3060 v2 · 2008-06-18 · math.DS · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V3VQKHJG4OK7BFXK532GE2Y6FO}

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	2026-05-18T04:07:18.078654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aeeb051d26e395f096eaeef4626b1e2b8048ac0e987dac503a7cdbf16c2810fb

Aliases

arxiv: 0806.3060 · arxiv_version: 0806.3060v2 · doi: 10.48550/arxiv.0806.3060 · pith_short_12: V3VQKHJG4OK7 · pith_short_16: V3VQKHJG4OK7BFXK · pith_short_8: V3VQKHJG

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/V3VQKHJG4OK7BFXK532GE2Y6FO \
  | 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: aeeb051d26e395f096eaeef4626b1e2b8048ac0e987dac503a7cdbf16c2810fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d7b60b52664414252ba78a308811372a1d03727cb4773ad327e3920b706987d",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2008-06-18T19:59:09Z",
    "title_canon_sha256": "fce6de1ada675a7905ddf7332800cc343b3dadad01ac77593d16d716d7319e48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.3060",
    "kind": "arxiv",
    "version": 2
  }
}