Pith Number

pith:XL3U74OB

pith:2012:XL3U74OBAFXW4OJLDP7NM2KQ7Q

not attested not anchored not stored refs pending

On randomness reduction in the Johnson-Lindenstrauss lemma

Pawe{\l} Wolff

arxiv:1202.5500 v2 · 2012-02-24 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XL3U74OBAFXW4OJLDP7NM2KQ7Q}

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	2026-05-18T03:41:20.286328Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

baf74ff1c1016f6e392b1bfed66950fc12bc11f9a3703ab785f4111de60bd0b2

Aliases

arxiv: 1202.5500 · arxiv_version: 1202.5500v2 · doi: 10.48550/arxiv.1202.5500 · pith_short_12: XL3U74OBAFXW · pith_short_16: XL3U74OBAFXW4OJL · pith_short_8: XL3U74OB

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/XL3U74OBAFXW4OJLDP7NM2KQ7Q \
  | 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: baf74ff1c1016f6e392b1bfed66950fc12bc11f9a3703ab785f4111de60bd0b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f908312f7b8251914f790826dccd88c75ef7fe1d21102f8f6a4cfdb72d0ad5fb",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-02-24T16:54:10Z",
    "title_canon_sha256": "2fd0bd7a80d7c4b38bd84fd94d03d6b6d82cb60639353672847d6ee96c988ad2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5500",
    "kind": "arxiv",
    "version": 2
  }
}