Pith Number

pith:EKMZ32D2

pith:2015:EKMZ32D2QFKIATU3VSJCU4XGZ4

not attested not anchored not stored refs pending

Some old and new problems in combinatorial geometry I: Around Borsuk's problem

Gil Kalai

arxiv:1505.04952 v1 · 2015-05-19 · math.CO · cs.CG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EKMZ32D2QFKIATU3VSJCU4XGZ4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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.

Cited by

1 paper in Pith

The Grasshopper Problem on the Sphere

Receipt and verification

First computed	2026-05-18T02:05:22.682281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22999de87a8154804e9bac922a72e6cf2bb3c572c484293c962fa7ae073197e1

Aliases

arxiv: 1505.04952 · arxiv_version: 1505.04952v1 · doi: 10.48550/arxiv.1505.04952 · pith_short_12: EKMZ32D2QFKI · pith_short_16: EKMZ32D2QFKIATU3 · pith_short_8: EKMZ32D2

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/EKMZ32D2QFKIATU3VSJCU4XGZ4 \
  | 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: 22999de87a8154804e9bac922a72e6cf2bb3c572c484293c962fa7ae073197e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "631840fc8f648cd2d8fbe615708e50f762a2cc27d48ae9f0f6527f4d4b912b3b",
    "cross_cats_sorted": [
      "cs.CG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-19T10:49:42Z",
    "title_canon_sha256": "3b4b4bdc2a43070de03d06e348fd25b70045bbaf2225f1f094351dc94304d6ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04952",
    "kind": "arxiv",
    "version": 1
  }
}