Pith Number

pith:CNQCF3TL

pith:2014:CNQCF3TLM2U7AHSXPAWU4IHNUJ

not attested not anchored not stored refs pending

Group ring elements with large spectral density

{\L}ukasz Grabowski

arxiv:1409.3212 v3 · 2014-09-10 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CNQCF3TLM2U7AHSXPAWU4IHNUJ}

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	2026-05-18T02:17:54.460975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

136022ee6b66a9f01e57782d4e20eda26fc2d490ca85dc0494d7833a65d2fa7b

Aliases

arxiv: 1409.3212 · arxiv_version: 1409.3212v3 · doi: 10.48550/arxiv.1409.3212 · pith_short_12: CNQCF3TLM2U7 · pith_short_16: CNQCF3TLM2U7AHSX · pith_short_8: CNQCF3TL

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/CNQCF3TLM2U7AHSXPAWU4IHNUJ \
  | 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: 136022ee6b66a9f01e57782d4e20eda26fc2d490ca85dc0494d7833a65d2fa7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4850ae47f6eb04622814f2517a83da7ab0f9236e11a72287cb35c5f989984485",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-09-10T19:50:41Z",
    "title_canon_sha256": "ff439b52e1bb4bd20921e24be6a3a7d654dfd7c6aa0efcb4996ff4e7a19096a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.3212",
    "kind": "arxiv",
    "version": 3
  }
}