Pith Number

pith:XA6KTJ2Y

pith:2013:XA6KTJ2YV5IX57VGBDG2NDTBTX

not attested not anchored not stored refs pending

Unseparated pairs and fixed points in random permutations

Persi Diaconis, Ron Graham, Steven N. Evans

arxiv:1308.5459 v2 · 2013-08-25 · 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{XA6KTJ2YV5IX57VGBDG2NDTBTX}

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	2026-05-18T02:53:08.139928Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b83ca9a758af517efea608cda68e619df2d8c0b126731cc1c670bbeaa3ebb9df

Aliases

arxiv: 1308.5459 · arxiv_version: 1308.5459v2 · doi: 10.48550/arxiv.1308.5459 · pith_short_12: XA6KTJ2YV5IX · pith_short_16: XA6KTJ2YV5IX57VG · pith_short_8: XA6KTJ2Y

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/XA6KTJ2YV5IX57VGBDG2NDTBTX \
  | 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: b83ca9a758af517efea608cda68e619df2d8c0b126731cc1c670bbeaa3ebb9df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "490e0035619b6fc97ee2342eab824a76ace75156d3d82a29eb9c3cc63fcde79c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-08-25T22:40:52Z",
    "title_canon_sha256": "9449dd8d01cb1c65bec937c1f847e9f27f50306bcb3688bd47755d1c50de1e3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.5459",
    "kind": "arxiv",
    "version": 2
  }
}