Pith Number

pith:WBWR4IME

pith:2012:WBWR4IMECVNVPQYCGKOOUJYRIR

not attested not anchored not stored refs pending

The Local-Global Principle for Integral Soddy Sphere Packings

Alex Kontorovich

arxiv:1208.5441 v2 · 2012-08-27 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WBWR4IMECVNVPQYCGKOOUJYRIR}

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.

Cited by

2 papers in Pith

Poissonian correlations of $\alpha n^d$ mod $1$

Receipt and verification

First computed	2026-05-18T00:42:19.021676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b06d1e2184155b57c302329cea2711446e62f645400e601c496a5db1d32f0089

Aliases

arxiv: 1208.5441 · arxiv_version: 1208.5441v2 · doi: 10.48550/arxiv.1208.5441 · pith_short_12: WBWR4IMECVNV · pith_short_16: WBWR4IMECVNVPQYC · pith_short_8: WBWR4IME

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/WBWR4IMECVNVPQYCGKOOUJYRIR \
  | 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: b06d1e2184155b57c302329cea2711446e62f645400e601c496a5db1d32f0089

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a21b5a2cfb4639252dc4ba82e3aa085e13e6199bc211be4be7caeaff11d8a4eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-27T16:48:06Z",
    "title_canon_sha256": "50833c24c4ef511502e2dfe873c6796080dd1ceabde0e81f3812a5f7ece2b869"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5441",
    "kind": "arxiv",
    "version": 2
  }
}