Pith Number

pith:WWHPXNR5

pith:2011:WWHPXNR53TGH4OEOXZYNQ3MKX6

not attested not anchored not stored refs pending

Inversion of signature for paths of bounded variation

Terry Lyons, Weijun Xu

arxiv:1112.0452 v1 · 2011-12-02 · math.CA · 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{WWHPXNR53TGH4OEOXZYNQ3MKX6}

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	2026-05-18T04:07:07.185379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b58efbb63ddccc7e388ebe70d86d8abfb89a97f6cbd230941d71da3f04416114

Aliases

arxiv: 1112.0452 · arxiv_version: 1112.0452v1 · doi: 10.48550/arxiv.1112.0452 · pith_short_12: WWHPXNR53TGH · pith_short_16: WWHPXNR53TGH4OEO · pith_short_8: WWHPXNR5

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/WWHPXNR53TGH4OEOXZYNQ3MKX6 \
  | 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: b58efbb63ddccc7e388ebe70d86d8abfb89a97f6cbd230941d71da3f04416114

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8b9739de71c0147207fdb095f003ff4125fcbff5b3f61babec5bceb57f3ddd9",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-12-02T12:52:34Z",
    "title_canon_sha256": "af30e63339ead2ceddfb082be11f4f30313c8127caf16d857336c6caed9439b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0452",
    "kind": "arxiv",
    "version": 1
  }
}