Pith Number

pith:BKUZ7ZP4

pith:1998:BKUZ7ZP4FOOZ6PRSVJGXLVVC3Q

not attested not anchored not stored refs pending

A counterexample to the "hot spots" conjecture

Krzysztof Burdzy, Wendelin Werner

arxiv:math/9803030 v2 · 1998-03-10 · math.PR · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BKUZ7ZP4FOOZ6PRSVJGXLVVC3Q}

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	2026-07-04T14:40:28.364940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0aa99fe5fc2b9d9f3e32aa4d75d6a2dc0f5bb5d1684562cbf177808d462cdf38

Aliases

arxiv: math/9803030 · arxiv_version: math/9803030v2 · doi: 10.48550/arxiv.math/9803030 · pith_short_12: BKUZ7ZP4FOOZ · pith_short_16: BKUZ7ZP4FOOZ6PRS · pith_short_8: BKUZ7ZP4

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/BKUZ7ZP4FOOZ6PRSVJGXLVVC3Q \
  | 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: 0aa99fe5fc2b9d9f3e32aa4d75d6a2dc0f5bb5d1684562cbf177808d462cdf38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23d2c8e95ec364f1eb9d006076034041625db36938c37e02d67d06db374c6680",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1998-03-10T00:13:04Z",
    "title_canon_sha256": "556265c3027de972df81589333be2fa3d1d5d21927e4d8f8edd27bee98979b12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9803030",
    "kind": "arxiv",
    "version": 2
  }
}