Pith Number

pith:76GGGI2T

pith:2019:76GGGI2TTBLK5RBK2FA3SHRFZQ

not attested not anchored not stored refs pending

The average character degree and an improvement of the Ito-Michler theorem

Nguyen Ngoc Hung, Pham Huu Tiep

arxiv:1904.03574 v1 · 2019-04-07 · math.GR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{76GGGI2TTBLK5RBK2FA3SHRFZQ}

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	2026-05-17T23:49:12.952713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff8c6323539856aec42ad141b91e25cc230d287dc9af24f246a92b5226c25cf6

Aliases

arxiv: 1904.03574 · arxiv_version: 1904.03574v1 · doi: 10.48550/arxiv.1904.03574 · pith_short_12: 76GGGI2TTBLK · pith_short_16: 76GGGI2TTBLK5RBK · pith_short_8: 76GGGI2T

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/76GGGI2TTBLK5RBK2FA3SHRFZQ \
  | 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: ff8c6323539856aec42ad141b91e25cc230d287dc9af24f246a92b5226c25cf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6245370f3703785b652fc0eebcc6d1eb6297aa7ed56b67751ca2ecd23c7e2a24",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-04-07T03:08:39Z",
    "title_canon_sha256": "88a16ddc373b3ab1afc65da3050cf793930e50cf53488e3e64ab31c9d54f8bb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.03574",
    "kind": "arxiv",
    "version": 1
  }
}