Pith Number

pith:T4MIC3DK

pith:2015:T4MIC3DKUVLGDNHPN5RJVIHZEX

not attested not anchored not stored refs pending

Random walk on unipotent matrix groups

Bob Hough, Persi Diaconis

arxiv:1512.06304 v4 · 2015-12-20 · math.PR · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T4MIC3DKUVLGDNHPN5RJVIHZEX}

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	2026-05-18T00:01:01.002181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f18816c6aa55661b4ef6f629aa0f925d0071740d6b9a7254c2eeba6167a5507

Aliases

arxiv: 1512.06304 · arxiv_version: 1512.06304v4 · doi: 10.48550/arxiv.1512.06304 · pith_short_12: T4MIC3DKUVLG · pith_short_16: T4MIC3DKUVLGDNHP · pith_short_8: T4MIC3DK

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/T4MIC3DKUVLGDNHPN5RJVIHZEX \
  | 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: 9f18816c6aa55661b4ef6f629aa0f925d0071740d6b9a7254c2eeba6167a5507

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e96d0abbee4e19b61e739b0ed79b2596d4bd952b25bf0f2328ca987e8d80883f",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-20T01:33:01Z",
    "title_canon_sha256": "a69005bdc7f455861267bb4fddaaa208b9dbd39bb956dfa63fe25dcb8756b8e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06304",
    "kind": "arxiv",
    "version": 4
  }
}