Pith Number

pith:7ZPTRIQT

pith:2012:7ZPTRIQTTLXVXHRHB2YGUJL6FN

not attested not anchored not stored refs pending

Maximal multiplier on Stratified groups

Woocheol Choi

arxiv:1206.2817 v4 · 2012-06-13 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ZPTRIQTTLXVXHRHB2YGUJL6FN}

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	2026-05-18T03:30:42.086627Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe5f38a2139aef5b9e270eb06a257e2b42da041f967cf1226e47fdee75d3dd54

Aliases

arxiv: 1206.2817 · arxiv_version: 1206.2817v4 · doi: 10.48550/arxiv.1206.2817 · pith_short_12: 7ZPTRIQTTLXV · pith_short_16: 7ZPTRIQTTLXVXHRH · pith_short_8: 7ZPTRIQT

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/7ZPTRIQTTLXVXHRHB2YGUJL6FN \
  | 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: fe5f38a2139aef5b9e270eb06a257e2b42da041f967cf1226e47fdee75d3dd54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d7716522f8ab59152b0f67c4f5892a637d4877c08f7975369c856134746b7bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-13T14:27:20Z",
    "title_canon_sha256": "0aa1eeeb83d29ddec4db206ec4b8cf7f7a54996ae34e7baf313ba0c34340a2c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2817",
    "kind": "arxiv",
    "version": 4
  }
}