Pith Number

pith:YYS3664F

pith:2012:YYS3664FX72HFOQJH7CYGOIJSW

not attested not anchored not stored refs pending

Beurling's criterion and extremal metrics for Fuglede modulus

Matthew Badger

arxiv:1207.5277 v4 · 2012-07-23 · math.CA · 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{YYS3664FX72HFOQJH7CYGOIJSW}

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	2026-05-18T03:19:35.276088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c625bf7b85bff472ba093fc583390995bd80fef9c1917949456805272c8a1383

Aliases

arxiv: 1207.5277 · arxiv_version: 1207.5277v4 · doi: 10.48550/arxiv.1207.5277 · pith_short_12: YYS3664FX72H · pith_short_16: YYS3664FX72HFOQJ · pith_short_8: YYS3664F

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/YYS3664FX72HFOQJH7CYGOIJSW \
  | 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: c625bf7b85bff472ba093fc583390995bd80fef9c1917949456805272c8a1383

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "653e667132c44d1f119fd080f79463ed6476ee8387414b8583697a1ecb29d567",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-07-23T02:05:32Z",
    "title_canon_sha256": "7fb9bce30e05ec2051580b5434d1297845d813e792537faab3a46dbfa7de947c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5277",
    "kind": "arxiv",
    "version": 4
  }
}