Pith Number

pith:4YUDM7PC

pith:2010:4YUDM7PCZG4AKDUHU5FFUM24DF

not attested not anchored not stored refs pending

A simpler proof of the Boros-F\"uredi-B\'ar\'any-Pach-Gromov theorem

R.N. Karasev

arxiv:1012.5890 v2 · 2010-12-29 · math.CO · 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{4YUDM7PCZG4AKDUHU5FFUM24DF}

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	2026-05-18T03:37:53.439844Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e628367de2c9b8050e87a74a5a335c196f208a8e9a44045f56b5721cec3f765d

Aliases

arxiv: 1012.5890 · arxiv_version: 1012.5890v2 · doi: 10.48550/arxiv.1012.5890 · pith_short_12: 4YUDM7PCZG4A · pith_short_16: 4YUDM7PCZG4AKDUH · pith_short_8: 4YUDM7PC

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/4YUDM7PCZG4AKDUHU5FFUM24DF \
  | 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: e628367de2c9b8050e87a74a5a335c196f208a8e9a44045f56b5721cec3f765d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "855c18c3d4bf0e0838b1e38a04e142c2e76a5fa93b0a98218a8a3d5a699da9f1",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-29T08:56:58Z",
    "title_canon_sha256": "6d1a28e75fe4dcccb9b430518ef37f7cb2adbef3044cd2babf443ed0218b82a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5890",
    "kind": "arxiv",
    "version": 2
  }
}