Pith Number

pith:GHTHKQE7

pith:2009:GHTHKQE73DRQTYTRXJ7MHG3HWG

not attested not anchored not stored refs pending

Proof of Aldous' spectral gap conjecture

Pietro Caputo, Thomas M. Liggett, Thomas Richthammer

arxiv:0906.1238 v4 · 2009-06-06 · 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{GHTHKQE73DRQTYTRXJ7MHG3HWG}

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	2026-05-18T02:13:28.580663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31e675409fd8e309e271ba7ec39b67b1bb1fe5cb53b4df02b8a125b8094c35ae

Aliases

arxiv: 0906.1238 · arxiv_version: 0906.1238v4 · doi: 10.48550/arxiv.0906.1238 · pith_short_12: GHTHKQE73DRQ · pith_short_16: GHTHKQE73DRQTYTR · pith_short_8: GHTHKQE7

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/GHTHKQE73DRQTYTRXJ7MHG3HWG \
  | 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: 31e675409fd8e309e271ba7ec39b67b1bb1fe5cb53b4df02b8a125b8094c35ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff333e1ded23c8e518216514fcc4a39d7a48e834ac1c2ced083ca21db8106e27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-06-06T01:01:37Z",
    "title_canon_sha256": "840fd75ece6a6205948032afc803ed75b7ef41ba374044ec35b3d7cbb3b7696f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.1238",
    "kind": "arxiv",
    "version": 4
  }
}