Pith Number

pith:XLFU4ZG2

pith:2008:XLFU4ZG2NITLSFSMQ7YALIXLK5

not attested not anchored not stored refs pending

On the spectral gap of the Kac walk and other binary collision processes

Pietro Caputo

arxiv:0807.3415 v1 · 2008-07-22 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XLFU4ZG2NITLSFSMQ7YALIXLK5}

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	2026-05-18T04:39:59.750295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bacb4e64da6a26b9164c87f005a2eb5771e4d4b667740a076309a33fc1a458e9

Aliases

arxiv: 0807.3415 · arxiv_version: 0807.3415v1 · doi: 10.48550/arxiv.0807.3415 · pith_short_12: XLFU4ZG2NITL · pith_short_16: XLFU4ZG2NITLSFSM · pith_short_8: XLFU4ZG2

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/XLFU4ZG2NITLSFSMQ7YALIXLK5 \
  | 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: bacb4e64da6a26b9164c87f005a2eb5771e4d4b667740a076309a33fc1a458e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac4ac0796b01a401fa21e2de2f7328112e154cf4e965169694eff99e9f906581",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-07-22T08:39:40Z",
    "title_canon_sha256": "6965160b851d8d12b6ce5c4e4f389065befa301281729c153439a5b4fa676250"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.3415",
    "kind": "arxiv",
    "version": 1
  }
}