Pith Number

pith:J73TCOF2

pith:2014:J73TCOF2N2YBAVZIADSUEW3UWY

not attested not anchored not stored refs pending

Measurable Chromatic Number of Spheres

Greg Malen

arxiv:1412.2091 v1 · 2014-12-05 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J73TCOF2N2YBAVZIADSUEW3UWY}

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	2026-05-18T02:32:05.386938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ff73138ba6eb010572800e5425b74b61343e13eba73f71f06a2afc3ff59ce11

Aliases

arxiv: 1412.2091 · arxiv_version: 1412.2091v1 · doi: 10.48550/arxiv.1412.2091 · pith_short_12: J73TCOF2N2YB · pith_short_16: J73TCOF2N2YBAVZI · pith_short_8: J73TCOF2

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/J73TCOF2N2YBAVZIADSUEW3UWY \
  | 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: 4ff73138ba6eb010572800e5425b74b61343e13eba73f71f06a2afc3ff59ce11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7abe8bac9f8fd33cffe368966e0d5ab45f7dcb52457c688798f4320f0bc37281",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-12-05T18:24:01Z",
    "title_canon_sha256": "5c04383aa95552a1edc7375cc45714e0ebb868771dc91c255c0a16b796b627a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2091",
    "kind": "arxiv",
    "version": 1
  }
}