Pith Number

pith:2Q5I4YCC

pith:2013:2Q5I4YCC4T2MSSNRFPDQDLUJ72

not attested not anchored not stored refs pending

The Apollonian structure of integer superharmonic matrices

Charles K. Smart, Lionel Levine, Wesley Pegden

arxiv:1309.3267 v4 · 2013-09-12 · math.AP · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2Q5I4YCC4T2MSSNRFPDQDLUJ72}

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	2026-05-18T00:40:16.653165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d43a8e6042e4f4c949b12bc701ae89fe9b2cc10afe67c424aab1fce6ef8225d9

Aliases

arxiv: 1309.3267 · arxiv_version: 1309.3267v4 · doi: 10.48550/arxiv.1309.3267 · pith_short_12: 2Q5I4YCC4T2M · pith_short_16: 2Q5I4YCC4T2MSSNR · pith_short_8: 2Q5I4YCC

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/2Q5I4YCC4T2MSSNRFPDQDLUJ72 \
  | 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: d43a8e6042e4f4c949b12bc701ae89fe9b2cc10afe67c424aab1fce6ef8225d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06cd6ae705132cdb4b2288a91adb7f1e3cfa9fff796430ab1bedf573711e74e0",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-09-12T19:58:01Z",
    "title_canon_sha256": "293edd04d957e311755e4763a3da474942659e9aa07decf78bc5701d30f79e37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3267",
    "kind": "arxiv",
    "version": 4
  }
}