Pith Number

pith:WRP7IUFO

pith:2012:WRP7IUFOAIZ7F4ZZYYCHP3VF2M

not attested not anchored not stored refs pending

A non-abelian analogue of Whitney's 2-isomorphism theorem

Eric Katz

arxiv:1208.1994 v2 · 2012-08-09 · 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{WRP7IUFOAIZ7F4ZZYYCHP3VF2M}

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	2026-05-18T03:45:55.003837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b45ff450ae0233f2f339c60477eea5d312716b2916c9cfa21950fca0a03c8d95

Aliases

arxiv: 1208.1994 · arxiv_version: 1208.1994v2 · doi: 10.48550/arxiv.1208.1994 · pith_short_12: WRP7IUFOAIZ7 · pith_short_16: WRP7IUFOAIZ7F4ZZ · pith_short_8: WRP7IUFO

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/WRP7IUFOAIZ7F4ZZYYCHP3VF2M \
  | 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: b45ff450ae0233f2f339c60477eea5d312716b2916c9cfa21950fca0a03c8d95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "369c30f84305a3812fc6f493a84a2b227d36ea1c36b2c7f2900c29c4faa5ce33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-09T18:37:10Z",
    "title_canon_sha256": "7c096e3a4ea143d49ab19299b1dde501fae50a2a6ab9624dd09f9dfe70b89189"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1994",
    "kind": "arxiv",
    "version": 2
  }
}