Pith Number

pith:OL7XNF2Q

pith:2015:OL7XNF2QFW5ZCJP32IIR7NI3B7

not attested not anchored not stored refs pending

A formal proof of the Kepler conjecture

Alexey Solovyev, An Hoai Thi Ta, Cezary Kaliszyk, Dat Tat Dang, Diep Thi Trieu, Gertrud Bauer, Jason Rute, John Harrison, Josef Urban, Joseph Pleso, Ky Khac Vu, Mark Adams, Roland Zumkeller, Sean McLaughlin, Steven Obua, Thang Tat Nguyen, Thomas Hales, Tobias Nipkow, Trung Nam Tran, Truong Le Hoang, Truong Quang Nguyen, Victor Magron

arxiv:1501.02155 v1 · 2015-01-09 · math.MG · cs.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OL7XNF2QFW5ZCJP32IIR7NI3B7}

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	2026-05-18T02:29:44.745530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72ff7697502dbb9125fbd2111fb51b0fe0b5e1f85b2126bbc0c9dd7de9cb397f

Aliases

arxiv: 1501.02155 · arxiv_version: 1501.02155v1 · doi: 10.48550/arxiv.1501.02155 · pith_short_12: OL7XNF2QFW5Z · pith_short_16: OL7XNF2QFW5ZCJP3 · pith_short_8: OL7XNF2Q

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/OL7XNF2QFW5ZCJP32IIR7NI3B7 \
  | 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: 72ff7697502dbb9125fbd2111fb51b0fe0b5e1f85b2126bbc0c9dd7de9cb397f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cead7b9b6eb8ba76787ad9be8695245877b9adc59be24f7ea4c2bbcd5ffb9e2a",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-01-09T14:32:24Z",
    "title_canon_sha256": "732235cfb695e5242e1bf85da49c2430b4d4fc15ad73345b02a9e2fb088d4ed5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.02155",
    "kind": "arxiv",
    "version": 1
  }
}