Pith Number

pith:X4KG4BGH

pith:2011:X4KG4BGHT3EPM3OLMNPLAH4ZZP

not attested not anchored not stored refs pending

An analogue of Gromov's waist theorem for coloring the cube

Roman Karasev

arxiv:1109.1078 v2 · 2011-09-06 · math.CO · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X4KG4BGHT3EPM3OLMNPLAH4ZZP}

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	2026-05-18T03:15:21.246598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf146e04c79ec8f66dcb635eb01f99cbdd2b0e8ac9c68d3fd89ce3711ae6ffa4

Aliases

arxiv: 1109.1078 · arxiv_version: 1109.1078v2 · doi: 10.48550/arxiv.1109.1078 · pith_short_12: X4KG4BGHT3EP · pith_short_16: X4KG4BGHT3EPM3OL · pith_short_8: X4KG4BGH

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/X4KG4BGHT3EPM3OLMNPLAH4ZZP \
  | 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: bf146e04c79ec8f66dcb635eb01f99cbdd2b0e8ac9c68d3fd89ce3711ae6ffa4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05e43b1a6cca721add52c3de6529b55158487057dcbc31ee91c5791b4591a4dd",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-09-06T06:14:35Z",
    "title_canon_sha256": "d372f3a97390bf72341e9d45a026c9f5936cc36bd0f468dcce46cbfc978f300e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1078",
    "kind": "arxiv",
    "version": 2
  }
}