Pith Number

pith:IOZGMTOS

pith:2012:IOZGMTOSBMHZ2KNFFZ2HKIYGHJ

not attested not anchored not stored refs pending

An analytic approach to a weak non-Abelian Kneser-type theorem

Tom Sanders

arxiv:1212.0457 v1 · 2012-12-03 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IOZGMTOSBMHZ2KNFFZ2HKIYGHJ}

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	2026-05-18T03:39:17.442805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43b2664dd20b0f9d29a52e747523063a4a777372938cd468826fd12defa3c53c

Aliases

arxiv: 1212.0457 · arxiv_version: 1212.0457v1 · doi: 10.48550/arxiv.1212.0457 · pith_short_12: IOZGMTOSBMHZ · pith_short_16: IOZGMTOSBMHZ2KNF · pith_short_8: IOZGMTOS

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/IOZGMTOSBMHZ2KNFFZ2HKIYGHJ \
  | 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: 43b2664dd20b0f9d29a52e747523063a4a777372938cd468826fd12defa3c53c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a42e7cba959e1e7c40b9dc9511e2589091abb288470dfd08022b967e587ea251",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-12-03T17:28:52Z",
    "title_canon_sha256": "9a9791c62415ec46f2045193853dcfbfda4722679545f9004a4927072e591d68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0457",
    "kind": "arxiv",
    "version": 1
  }
}