Pith Number

pith:7V2DSHF3

pith:2015:7V2DSHF3BZHC7VAZGBLLCEKTE5

not attested not anchored not stored refs pending

Proof of the Ghahramani-Lau conjecture

Jan Pachl, Juris Stepr\=ans, Matthias Neufang, Viktor Losert

arxiv:1510.05412 v1 · 2015-10-19 · math.FA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7V2DSHF3BZHC7VAZGBLLCEKTE5}

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	2026-05-18T01:04:41.639738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd74391cbb0e4e2fd4193056b111532757ec0f40253bea2c2926c127cf78a532

Aliases

arxiv: 1510.05412 · arxiv_version: 1510.05412v1 · doi: 10.48550/arxiv.1510.05412 · pith_short_12: 7V2DSHF3BZHC · pith_short_16: 7V2DSHF3BZHC7VAZ · pith_short_8: 7V2DSHF3

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/7V2DSHF3BZHC7VAZGBLLCEKTE5 \
  | 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: fd74391cbb0e4e2fd4193056b111532757ec0f40253bea2c2926c127cf78a532

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbf9defd9cd396090cc96e0920c51ef77c43dc652430e18588074a020b24ce42",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-10-19T10:12:44Z",
    "title_canon_sha256": "34f94a191f1ab282bde9a2231134cfa73cfa44b2bccbffc1ce5f31cf8605f0c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05412",
    "kind": "arxiv",
    "version": 1
  }
}