Pith Number

pith:6BJ672R3

pith:2005:6BJ672R32OEYR3T7TTKFEEYKXU

not attested not anchored not stored refs pending

On two duality properties of random walks in random environment on the integer line

Didier Piau

arxiv:math/0510038 v1 · 2005-10-03 · 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{6BJ672R32OEYR3T7TTKFEEYKXU}

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	2026-05-18T01:05:23.025726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f053efea3bd38988ee7f9cd452130abd3eeb70e13bd31534ef78a8dc0d608bdd

Aliases

arxiv: math/0510038 · arxiv_version: math/0510038v1 · doi: 10.48550/arxiv.math/0510038 · pith_short_12: 6BJ672R32OEY · pith_short_16: 6BJ672R32OEYR3T7 · pith_short_8: 6BJ672R3

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/6BJ672R32OEYR3T7TTKFEEYKXU \
  | 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: f053efea3bd38988ee7f9cd452130abd3eeb70e13bd31534ef78a8dc0d608bdd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cee135b3bdba017297e70cf4cddb1371aa9ee72b32f92e6ac4c6b291ca82cf89",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-10-03T10:33:41Z",
    "title_canon_sha256": "1bc9c829beb0ce8e40eb5ada18303b38f8251d78ef227c5af9363361a39b7a84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0510038",
    "kind": "arxiv",
    "version": 1
  }
}