Pith Number

pith:7HOEJ4GI

pith:2008:7HOEJ4GIVCDCG45DG4EKQ3OLC7

not attested not anchored not stored refs pending

Stochastic expansions and Hopf algebras

Anke Wiese, Simon J.A. Malham

arxiv:0805.2340 v2 · 2008-05-15 · math.PR · 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{7HOEJ4GIVCDCG45DG4EKQ3OLC7}

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	2026-05-18T02:15:52.742872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9dc44f0c8a8862373a33708a86dcb17f068334be2ec7e2d3d86d7392960f99f

Aliases

arxiv: 0805.2340 · arxiv_version: 0805.2340v2 · doi: 10.48550/arxiv.0805.2340 · pith_short_12: 7HOEJ4GIVCDC · pith_short_16: 7HOEJ4GIVCDCG45D · pith_short_8: 7HOEJ4GI

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/7HOEJ4GIVCDCG45DG4EKQ3OLC7 \
  | 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: f9dc44f0c8a8862373a33708a86dcb17f068334be2ec7e2d3d86d7392960f99f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9686f07d083313fe7f3f42fd7dff8622541ce25e6eca856e74e59b08ce424c9",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-05-15T15:48:53Z",
    "title_canon_sha256": "c952aad1535fd5e909510e5151606745377d96a56038f4848e5129971b8260f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0805.2340",
    "kind": "arxiv",
    "version": 2
  }
}