Pith Number

pith:CPIBOEU7

pith:2012:CPIBOEU766Q3PHVEFLJJXGHKM7

not attested not anchored not stored refs pending

A Proof of Fejes Toth's Conjecture on Sphere Packings with Kissing Number Twelve

Thomas C. Hales

arxiv:1209.6043 v1 · 2012-09-26 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CPIBOEU766Q3PHVEFLJJXGHKM7}

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	2026-05-18T03:44:45.596690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13d017129ff7a1b79ea42ad29b98ea67ebca52783501aec1cde00b5a3b79cb20

Aliases

arxiv: 1209.6043 · arxiv_version: 1209.6043v1 · doi: 10.48550/arxiv.1209.6043 · pith_short_12: CPIBOEU766Q3 · pith_short_16: CPIBOEU766Q3PHVE · pith_short_8: CPIBOEU7

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/CPIBOEU766Q3PHVEFLJJXGHKM7 \
  | 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: 13d017129ff7a1b79ea42ad29b98ea67ebca52783501aec1cde00b5a3b79cb20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce41f501fc5b8a342d342d65c502286d94228254f3168489755bf781615c70e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-09-26T19:35:50Z",
    "title_canon_sha256": "bd47428e5507f69c3a93b8fb969d5f1d717c25e5d80324d54dd8ad1589038921"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.6043",
    "kind": "arxiv",
    "version": 1
  }
}