Pith Number

pith:TYRXUMHL

pith:2015:TYRXUMHLW5VJP76IDBRGTXBVXG

not attested not anchored not stored refs pending

Ball packings with high chromatic numbers from strongly regular graphs

Hao Chen

arxiv:1502.02070 v5 · 2015-02-06 · 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{TYRXUMHLW5VJP76IDBRGTXBVXG}

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	2026-05-18T00:07:56.295093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e237a30ebb76a97ffc8186269dc35b9a0188258bbf98eda3410bfa8125bb51b

Aliases

arxiv: 1502.02070 · arxiv_version: 1502.02070v5 · doi: 10.48550/arxiv.1502.02070 · pith_short_12: TYRXUMHLW5VJ · pith_short_16: TYRXUMHLW5VJP76I · pith_short_8: TYRXUMHL

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/TYRXUMHLW5VJP76IDBRGTXBVXG \
  | 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: 9e237a30ebb76a97ffc8186269dc35b9a0188258bbf98eda3410bfa8125bb51b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae557eaf7d4271ebe128f67de9bd9a87369e9b155e0f829e3bfc59add1b03c32",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-06T22:53:14Z",
    "title_canon_sha256": "ac5e3c721083635fac4c167835424e9b12cc892004b987acefb0ca1104ff17b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02070",
    "kind": "arxiv",
    "version": 5
  }
}