Pith Number

pith:BK4OLU7L

pith:2007:BK4OLU7LCBERMHO4BYQBEULF6F

not attested not anchored not stored refs pending

Projections, Entropy and Sumsets

B\'ela Bollob\'as, Paul Balister

arxiv:0711.1151 v1 · 2007-11-07 · math.CO · math.NT · 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{BK4OLU7LCBERMHO4BYQBEULF6F}

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	2026-05-18T00:53:16.152539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ab8e5d3eb1049161ddc0e20125165f15a716842268bed0231ca493ec66c30be

Aliases

arxiv: 0711.1151 · arxiv_version: 0711.1151v1 · doi: 10.48550/arxiv.0711.1151 · pith_short_12: BK4OLU7LCBER · pith_short_16: BK4OLU7LCBERMHO4 · pith_short_8: BK4OLU7L

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/BK4OLU7LCBERMHO4BYQBEULF6F \
  | 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: 0ab8e5d3eb1049161ddc0e20125165f15a716842268bed0231ca493ec66c30be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04d5ef09fe388378d85bf1fadce9da4abd772954ac6a7dd6a9ded9efe2b35632",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-11-07T20:15:50Z",
    "title_canon_sha256": "8be2579f583d04789ce6f5e51110ad4687808767c0db9d060397d84ac6dfb0d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.1151",
    "kind": "arxiv",
    "version": 1
  }
}