Pith Number

pith:BTHWVPUK

pith:2014:BTHWVPUKZGGOPLTDL2CLWWVAWT

not attested not anchored not stored refs pending

The Random Transposition Dynamics on Random Regular Graphs and the Gaussian Free Field

Shirshendu Ganguly, Soumik Pal

arxiv:1409.7766 v2 · 2014-09-27 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BTHWVPUKZGGOPLTDL2CLWWVAWT}

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	2026-05-18T02:30:31.550375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ccf6abe8ac98ce7ae635e84bb5aa0b4d2a63c041b1a59073af0be011c7ae9a1

Aliases

arxiv: 1409.7766 · arxiv_version: 1409.7766v2 · doi: 10.48550/arxiv.1409.7766 · pith_short_12: BTHWVPUKZGGO · pith_short_16: BTHWVPUKZGGOPLTD · pith_short_8: BTHWVPUK

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/BTHWVPUKZGGOPLTDL2CLWWVAWT \
  | 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: 0ccf6abe8ac98ce7ae635e84bb5aa0b4d2a63c041b1a59073af0be011c7ae9a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd6dc4ea22969a138714df8f51855ec5e1566fec92dc172861eadd5dc7a87b58",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-09-27T05:35:29Z",
    "title_canon_sha256": "677c2d4a344a1243825ba28d9e60ed7bfb793e59aea2b75d9cb48e29e7993629"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.7766",
    "kind": "arxiv",
    "version": 2
  }
}