Pith Number

pith:VPJODAGL

pith:2020:VPJODAGL7NNRD2XMIAMMRCVYBJ

not attested not anchored not stored refs pending

The Life and Mathematical Legacy of Thomas M. Liggett

Alexander E. Holroyd, Amber L. Puha, David Aldous, Paul Jung, Pietro Caputo, Rick Durrett

arxiv:2008.03137 v1 · 2020-08-07 · 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{VPJODAGL7NNRD2XMIAMMRCVYBJ}

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.

Cited by

1 paper in Pith

Aldous-type Spectral Gaps in Generalized Symmetric Groups

Receipt and verification

First computed	2026-07-05T01:25:31.118949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd2e180cbfb5b11eaec4018c88ab80a4b9d48aa08460b97862e10ec37e881f4

Aliases

arxiv: 2008.03137 · arxiv_version: 2008.03137v1 · doi: 10.48550/arxiv.2008.03137 · pith_short_12: VPJODAGL7NNR · pith_short_16: VPJODAGL7NNRD2XM · pith_short_8: VPJODAGL

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/VPJODAGL7NNRD2XMIAMMRCVYBJ \
  | 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: abd2e180cbfb5b11eaec4018c88ab80a4b9d48aa08460b97862e10ec37e881f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfb4bd4454b85f8e8499cb6e4d98d20fe8c206644f97df38e89c294a53dbee49",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-08-07T12:58:02Z",
    "title_canon_sha256": "fbeaf9a70c3829684fa39f924739b52c39a66bc066487f2686b7bd8d0eb21240"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2008.03137",
    "kind": "arxiv",
    "version": 1
  }
}