Pith Number

pith:UX5IUXSF

pith:2016:UX5IUXSFCJZICVRZGDZQO5SOYF

not attested not anchored not stored refs pending

A conceptual breakthrough in sphere packing

Henry Cohn

arxiv:1611.01685 v1 · 2016-11-05 · math.MG · 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{UX5IUXSFCJZICVRZGDZQO5SOYF}

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	2026-05-18T00:47:26.654747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5fa8a5e45127281563930f307764ec170084a5132e3af1a11826c22c9878343

Aliases

arxiv: 1611.01685 · arxiv_version: 1611.01685v1 · doi: 10.48550/arxiv.1611.01685 · pith_short_12: UX5IUXSFCJZI · pith_short_16: UX5IUXSFCJZICVRZ · pith_short_8: UX5IUXSF

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/UX5IUXSFCJZICVRZGDZQO5SOYF \
  | 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: a5fa8a5e45127281563930f307764ec170084a5132e3af1a11826c22c9878343

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b970327d4c88bf8d954888d2fb5d0bb9bf588a81b3fbe8db9b524de489f794a",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-11-05T18:16:28Z",
    "title_canon_sha256": "743d0c06f2c08e16089f1b55fef9de05af5468d6f22eae0ca1e181926c466a4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.01685",
    "kind": "arxiv",
    "version": 1
  }
}