Pith Number

pith:UTBNG36I

pith:2020:UTBNG36IRTYBGAPDZPWYKDYRC4

not attested not anchored not stored refs pending

Graph minimization, focusing on the example of 5-chromatic unit-distance graphs in the plane

Jaan Parts

arxiv:2010.12665 v2 · 2020-10-23 · 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{UTBNG36IRTYBGAPDZPWYKDYRC4}

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.

Cited by

1 paper in Pith

A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane

Receipt and verification

First computed	2026-07-05T04:35:07.887117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4c2d36fc88cf01301e3cbed850f111705880b760543e16c5db5b739e99a3f4d

Aliases

arxiv: 2010.12665 · arxiv_version: 2010.12665v2 · doi: 10.48550/arxiv.2010.12665 · pith_short_12: UTBNG36IRTYB · pith_short_16: UTBNG36IRTYBGAPD · pith_short_8: UTBNG36I

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/UTBNG36IRTYBGAPDZPWYKDYRC4 \
  | 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: a4c2d36fc88cf01301e3cbed850f111705880b760543e16c5db5b739e99a3f4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8e029b92745fb8c8a53ee66d5c96958b96f43d65a1f207d14c69994709998ed",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-10-23T20:57:44Z",
    "title_canon_sha256": "f214a76f627afb1f6edf8ed8cc9f77b2793dffa40eb4c18e932898cb42609b65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.12665",
    "kind": "arxiv",
    "version": 2
  }
}