Pith Number

pith:TQ7HMPND

pith:2009:TQ7HMPNDP6Q4WUKBGRUZFTM4EX

not attested not anchored not stored refs pending

Interlacings for random walks on weighted graphs and the interchange process

A. B. Dieker

arxiv:0906.1716 v3 · 2009-06-09 · math.PR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQ7HMPNDP6Q4WUKBGRUZFTM4EX}

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	2026-05-18T04:18:15.414159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c3e763da37fa1cb5141346992cd9c25e3cea9d3be73ff9039a6ff54a1fe0af7

Aliases

arxiv: 0906.1716 · arxiv_version: 0906.1716v3 · doi: 10.48550/arxiv.0906.1716 · pith_short_12: TQ7HMPNDP6Q4 · pith_short_16: TQ7HMPNDP6Q4WUKB · pith_short_8: TQ7HMPND

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/TQ7HMPNDP6Q4WUKBGRUZFTM4EX \
  | 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: 9c3e763da37fa1cb5141346992cd9c25e3cea9d3be73ff9039a6ff54a1fe0af7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db3d47722e89ca69e55aa2c8d70779b34a082840b8fac28cf73da1676a820d28",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-06-09T18:57:54Z",
    "title_canon_sha256": "63513632d91c310e02116ac8d7ad4f788c6e74082b52cfebdbe3e8447be2679d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.1716",
    "kind": "arxiv",
    "version": 3
  }
}