Pith Number

pith:LMWRF2F3

pith:2006:LMWRF2F3ZVIO2MQ652T37FUKBH

not attested not anchored not stored refs pending

The Colin de Verdi\`ere Graph Parameter for Threshold Graphs

Felix Goldberg, Hans Christianson

arxiv:math/0612720 v2 · 2006-12-22 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LMWRF2F3ZVIO2MQ652T37FUKBH}

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	2026-05-18T04:08:53.038586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b2d12e8bbcd50ed321eeea7bf968a09c4325b15c43f0c44a59f3ad770d1cc8c

Aliases

arxiv: math/0612720 · arxiv_version: math/0612720v2 · doi: 10.48550/arxiv.math/0612720 · pith_short_12: LMWRF2F3ZVIO · pith_short_16: LMWRF2F3ZVIO2MQ6 · pith_short_8: LMWRF2F3

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/LMWRF2F3ZVIO2MQ652T37FUKBH \
  | 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: 5b2d12e8bbcd50ed321eeea7bf968a09c4325b15c43f0c44a59f3ad770d1cc8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f64403369d18552aeb7f483c4694d2e4aa0fbdab882e47e5d4c51c1b8217728d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2006-12-22T19:23:06Z",
    "title_canon_sha256": "d161d4737b58762423c2269e4d6ddf0d3f00f8632aea610afdb3cd9bc3b02c6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612720",
    "kind": "arxiv",
    "version": 2
  }
}