Pith Number

pith:6ATKP2LH

pith:2005:6ATKP2LH2DQZNGVRPTQLXGDK4I

not attested not anchored not stored refs pending

Normal approximations for descents and inversions of permutations of multisets

D. Viswanath, Mark Conger

arxiv:math/0508242 v2 · 2005-08-14 · 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{6ATKP2LH2DQZNGVRPTQLXGDK4I}

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	2026-05-18T02:44:07.379006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f026a7e967d0e1969ab17ce0bb986ae22f1463baaf2fb9789c68a2e65ff9d13d

Aliases

arxiv: math/0508242 · arxiv_version: math/0508242v2 · doi: 10.48550/arxiv.math/0508242 · pith_short_12: 6ATKP2LH2DQZ · pith_short_16: 6ATKP2LH2DQZNGVR · pith_short_8: 6ATKP2LH

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/6ATKP2LH2DQZNGVRPTQLXGDK4I \
  | 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: f026a7e967d0e1969ab17ce0bb986ae22f1463baaf2fb9789c68a2e65ff9d13d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c8b8ba838eb49859e52be338b960d4c32ceeaa2dedb36a32a98dff24ed61c60",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-08-14T18:55:52Z",
    "title_canon_sha256": "4c644afe4259478ae4b19cba3906efc1f4851aa07fd812248e92a0aa8db98531"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508242",
    "kind": "arxiv",
    "version": 2
  }
}