Pith Number

pith:YPKJRQ5O

pith:2011:YPKJRQ5OPFGWWO7YQUNL42O3YX

not attested not anchored not stored refs pending

Complete bipartite graphs whose topological symmetry groups are polyhedral

Blake Mellor

arxiv:1106.5797 v2 · 2011-06-28 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YPKJRQ5OPFGWWO7YQUNL42O3YX}

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	2026-05-18T02:30:40.707223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3d498c3ae794d6b3bf8851abe69dbc5c5d53a6011057e0b792ab91c4e15086d

Aliases

arxiv: 1106.5797 · arxiv_version: 1106.5797v2 · doi: 10.48550/arxiv.1106.5797 · pith_short_12: YPKJRQ5OPFGW · pith_short_16: YPKJRQ5OPFGWWO7Y · pith_short_8: YPKJRQ5O

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/YPKJRQ5OPFGWWO7YQUNL42O3YX \
  | 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: c3d498c3ae794d6b3bf8851abe69dbc5c5d53a6011057e0b792ab91c4e15086d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5515dcc8f404cab382370bc0658e49f0ad99246acc20a487958bda821e712fe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-06-28T20:37:56Z",
    "title_canon_sha256": "32e2cf6f4f3ea0633c4dc02c7ee76cd00a15504644fd5f065582f0926a39b591"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5797",
    "kind": "arxiv",
    "version": 2
  }
}