Pith Number

pith:QKDGEO3Y

pith:2015:QKDGEO3YPZMXODJUE73GMAWREE

not attested not anchored not stored refs pending

Fuglede's conjecture holds in $\mathbb{Q}_p$

Aihua Fan, Lingmin Liao, Ruxi Shi, Shilei Fan

arxiv:1512.08904 v1 · 2015-12-30 · math.CA · math.FA · 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{QKDGEO3YPZMXODJUE73GMAWREE}

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	2026-05-18T01:23:34.537572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8286623b787e59770d3427f66602d12112444846b87790790f0c1903affd8e93

Aliases

arxiv: 1512.08904 · arxiv_version: 1512.08904v1 · doi: 10.48550/arxiv.1512.08904 · pith_short_12: QKDGEO3YPZMX · pith_short_16: QKDGEO3YPZMXODJU · pith_short_8: QKDGEO3Y

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/QKDGEO3YPZMXODJUE73GMAWREE \
  | 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: 8286623b787e59770d3427f66602d12112444846b87790790f0c1903affd8e93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94d987f9582069c751f99996338548812f3ad06e65462eac34ff2546fc022c56",
    "cross_cats_sorted": [
      "math.FA",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-30T10:39:39Z",
    "title_canon_sha256": "581387f536e6de1d649ac6108973346fadd44bafb85d67def48c92cce4056084"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08904",
    "kind": "arxiv",
    "version": 1
  }
}