Pith Number

pith:ENP5WI6C

pith:2009:ENP5WI6CK3XWQZB2UKWH4YWVDP

not attested not anchored not stored refs pending

Poisson asymptotics for random projections of points on a high-dimensional sphere

Itai Benjamini, Oded Schramm, Sasha Sodin

arxiv:0903.0107 v4 · 2009-02-28 · 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{ENP5WI6CK3XWQZB2UKWH4YWVDP}

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	2026-05-18T04:19:23.527798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

235fdb23c256ef68643aa2ac7e62d51bedb20262728e94677ae482d7b66c6fd5

Aliases

arxiv: 0903.0107 · arxiv_version: 0903.0107v4 · doi: 10.48550/arxiv.0903.0107 · pith_short_12: ENP5WI6CK3XW · pith_short_16: ENP5WI6CK3XWQZB2 · pith_short_8: ENP5WI6C

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/ENP5WI6CK3XWQZB2UKWH4YWVDP \
  | 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: 235fdb23c256ef68643aa2ac7e62d51bedb20262728e94677ae482d7b66c6fd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c14fb078bb4352120e769b3c8516ef3bde6d75e3d8d44338a80200f2a6633fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-02-28T20:49:09Z",
    "title_canon_sha256": "9a2f80d5eded2f75c1f28e489016f03f131eafadae795522d589a7ae91ebf39f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.0107",
    "kind": "arxiv",
    "version": 4
  }
}