Pith Number

pith:A6GMHNTO

pith:2012:A6GMHNTO2TL6YRKN4VXTWKK4HB

not attested not anchored not stored refs pending

Approximate (Abelian) groups

Tom Sanders

arxiv:1212.0456 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{A6GMHNTO2TL6YRKN4VXTWKK4HB}

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	2026-05-18T00:01:44.207023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

078cc3b66ed4d7ec454de56f3b295c3848141977fb74fd4b41fc6f8ac3651e68

Aliases

arxiv: 1212.0456 · arxiv_version: 1212.0456v1 · doi: 10.48550/arxiv.1212.0456 · pith_short_12: A6GMHNTO2TL6 · pith_short_16: A6GMHNTO2TL6YRKN · pith_short_8: A6GMHNTO

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/A6GMHNTO2TL6YRKN4VXTWKK4HB \
  | 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: 078cc3b66ed4d7ec454de56f3b295c3848141977fb74fd4b41fc6f8ac3651e68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dddd27b96d4c3c02d6627352dba94723027e463bd8c0d48159313e21efa45ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-12-03T17:25:53Z",
    "title_canon_sha256": "94158e40449cb00f34811b85af23cea923fad6adf5059507671ec4530fac1ab1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0456",
    "kind": "arxiv",
    "version": 1
  }
}