Pith Number

pith:W56HBIAP

pith:2004:W56HBIAPRWDBTW3XI3LURWZ7I4

not attested not anchored not stored refs pending

Combinatorics of random processes and sections of convex bodies

Mark Rudelson, Roman Vershynin

arxiv:math/0404192 v1 · 2004-04-08 · math.FA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W56HBIAPRWDBTW3XI3LURWZ7I4}

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	2026-05-18T00:54:09.298790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b77c70a00f8d8619db7746d748db3f47171426ee7292f003288e2b35da84cfc8

Aliases

arxiv: math/0404192 · arxiv_version: math/0404192v1 · doi: 10.48550/arxiv.math/0404192 · pith_short_12: W56HBIAPRWDB · pith_short_16: W56HBIAPRWDBTW3X · pith_short_8: W56HBIAP

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/W56HBIAPRWDBTW3XI3LURWZ7I4 \
  | 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: b77c70a00f8d8619db7746d748db3f47171426ee7292f003288e2b35da84cfc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "405dc35803228c0d6c0143c8c9aafb7f17d44cfb73f9666b2830bfe1566f44a6",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2004-04-08T19:25:33Z",
    "title_canon_sha256": "a5e4269cb65405d955b9c1d45d5181facaa203d4eb98a29ad854f3bc2e35b1f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0404192",
    "kind": "arxiv",
    "version": 1
  }
}