Pith Number

pith:4MH5T47T

pith:2014:4MH5T47TJN2SG5EWYX5E2WPIT7

not attested not anchored not stored refs pending

Spectral radius minus average degree: a better bound

Felix Goldberg

arxiv:1407.4285 v1 · 2014-07-16 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MH5T47TJN2SG5EWYX5E2WPIT7}

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	2026-05-18T02:47:30.751330Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e30fd9f3f34b75237496c5fa4d59e89fe3e60350afb0253e5b224696c95afc31

Aliases

arxiv: 1407.4285 · arxiv_version: 1407.4285v1 · doi: 10.48550/arxiv.1407.4285 · pith_short_12: 4MH5T47TJN2S · pith_short_16: 4MH5T47TJN2SG5EW · pith_short_8: 4MH5T47T

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/4MH5T47TJN2SG5EWYX5E2WPIT7 \
  | 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: e30fd9f3f34b75237496c5fa4d59e89fe3e60350afb0253e5b224696c95afc31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6470120dc15f6e9ae3d57c6449375c685f48a35af7ba2165a08456aa0ee92f95",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-07-16T12:44:34Z",
    "title_canon_sha256": "ed28005831de57fbc15989c82f9869381d6b8513e781af41cf7f6541f3bdac0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.4285",
    "kind": "arxiv",
    "version": 1
  }
}