Pith Number

pith:45J2VUNL

pith:2013:45J2VUNLQCYMZCU2WZVFSX4LUS

not attested not anchored not stored refs pending

A Quantized Johnson Lindenstrauss Lemma: The Finding of Buffon's Needle

Laurent Jacques

arxiv:1309.1507 v6 · 2013-09-05 · cs.IT · cs.DS · math.IT · math.PR

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

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	2026-05-18T01:36:31.656923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e753aad1ab80b0cc8a9ab66a595f8ba4a21021fc72c1de7f2dc5e703c1eeb38b

Aliases

arxiv: 1309.1507 · arxiv_version: 1309.1507v6 · doi: 10.48550/arxiv.1309.1507 · pith_short_12: 45J2VUNLQCYM · pith_short_16: 45J2VUNLQCYMZCU2 · pith_short_8: 45J2VUNL

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/45J2VUNLQCYMZCU2WZVFSX4LUS \
  | 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: e753aad1ab80b0cc8a9ab66a595f8ba4a21021fc72c1de7f2dc5e703c1eeb38b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5124f06296798b3579d51949e719dce922a4a70ba83490728409b4c3b8b2d707",
    "cross_cats_sorted": [
      "cs.DS",
      "math.IT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2013-09-05T23:18:53Z",
    "title_canon_sha256": "a491f82880dd252eef33effa843d0e735246de4c9cdfaf62b859cc5b6c0afbe7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1507",
    "kind": "arxiv",
    "version": 6
  }
}