Pith Number

pith:QSSIROKZ

pith:2004:QSSIROKZI65AHCKPPPBRZZZZ7T

not attested not anchored not stored refs pending

The hyperbolic geometry of random transpositions

Nathana\"el Berestycki

arxiv:math/0411011 v3 · 2004-10-31 · 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{QSSIROKZI65AHCKPPPBRZZZZ7T}

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	2026-05-18T01:08:51.502330Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84a488b95947ba03894f7bc31ce739fcdd921476cb0bc6e0d3ea103dc53633cc

Aliases

arxiv: math/0411011 · arxiv_version: math/0411011v3 · doi: 10.48550/arxiv.math/0411011 · pith_short_12: QSSIROKZI65A · pith_short_16: QSSIROKZI65AHCKP · pith_short_8: QSSIROKZ

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/QSSIROKZI65AHCKPPPBRZZZZ7T \
  | 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: 84a488b95947ba03894f7bc31ce739fcdd921476cb0bc6e0d3ea103dc53633cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c6903aa10c46d47549fb34b81fbc952055b461d815d22f6ea45582f5b235886",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-10-31T15:59:46Z",
    "title_canon_sha256": "92a21dbc4637614801aeb071726817948ca91a5dd166cbc8ffa12b8e2e45ed93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411011",
    "kind": "arxiv",
    "version": 3
  }
}