Pith Number

pith:WAZD5LEK

pith:2015:WAZD5LEK62EIMSDXLGSI3KMP6R

not attested not anchored not stored refs pending

On Brownian motion, simple paths, and loops

Artem Sapozhnikov, Daisuke Shiraishi

arxiv:1512.04864 v1 · 2015-12-15 · 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{WAZD5LEK62EIMSDXLGSI3KMP6R}

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	2026-05-18T01:24:15.246903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0323eac8af68886487759a48da98ff4474c8905e2a1b2dfdd16870566222276

Aliases

arxiv: 1512.04864 · arxiv_version: 1512.04864v1 · doi: 10.48550/arxiv.1512.04864 · pith_short_12: WAZD5LEK62EI · pith_short_16: WAZD5LEK62EIMSDX · pith_short_8: WAZD5LEK

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/WAZD5LEK62EIMSDXLGSI3KMP6R \
  | 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: b0323eac8af68886487759a48da98ff4474c8905e2a1b2dfdd16870566222276

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1bc15ea4055ccb48d4e80748446c8d0ae459c4877b92ee27de43bba465c5a3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-15T17:22:05Z",
    "title_canon_sha256": "bce3b938dea7b90ac9896127c68442801d31593d0e31b36850d4108b18b7d772"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04864",
    "kind": "arxiv",
    "version": 1
  }
}