Pith Number

pith:NBWO6XA7

pith:2012:NBWO6XA7SP4QFFL2EG2RFSEIMS

not attested not anchored not stored refs pending

On growth in an abstract plane

H. A. Helfgott, Misha Rudnev, Nick Gill

arxiv:1212.5056 v1 · 2012-12-20 · 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{NBWO6XA7SP4QFFL2EG2RFSEIMS}

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	2026-05-18T03:38:04.018645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

686cef5c1f93f902957a21b512c8886484b6b37bea8e7fa9e67972e7955e5ce3

Aliases

arxiv: 1212.5056 · arxiv_version: 1212.5056v1 · doi: 10.48550/arxiv.1212.5056 · pith_short_12: NBWO6XA7SP4Q · pith_short_16: NBWO6XA7SP4QFFL2 · pith_short_8: NBWO6XA7

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/NBWO6XA7SP4QFFL2EG2RFSEIMS \
  | 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: 686cef5c1f93f902957a21b512c8886484b6b37bea8e7fa9e67972e7955e5ce3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0589f8b8ee35f79084200c361e202648e7ee6c14bc7ab95086e8a552fb977a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-20T14:37:25Z",
    "title_canon_sha256": "1aa1b69848d7c996cbd8abd9fe5c34747f10333970c3914156c3b7d36e15e797"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5056",
    "kind": "arxiv",
    "version": 1
  }
}