Pith Number

pith:7WI7TVFX

pith:2018:7WI7TVFX6MZ22PT675JGZ655IK

not attested not anchored not stored refs pending

The effect on the spectral radius of r-graphs by grafting or contracting edges

An Chang, Wei Li

arxiv:1808.07189 v1 · 2018-08-22 · 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{7WI7TVFX6MZ22PT675JGZ655IK}

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	2026-05-18T00:07:29.658171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd91f9d4b7f333ad3e7eff526cfbbd428bd05a5014c8fb3e7efc0d8e5a6805ce

Aliases

arxiv: 1808.07189 · arxiv_version: 1808.07189v1 · doi: 10.48550/arxiv.1808.07189 · pith_short_12: 7WI7TVFX6MZ2 · pith_short_16: 7WI7TVFX6MZ22PT6 · pith_short_8: 7WI7TVFX

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/7WI7TVFX6MZ22PT675JGZ655IK \
  | 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: fd91f9d4b7f333ad3e7eff526cfbbd428bd05a5014c8fb3e7efc0d8e5a6805ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3376adf83d5b81c102def9339947e8adadd21056fdebec61ce3b53d94df621ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-08-22T02:29:45Z",
    "title_canon_sha256": "a4ad73b04afc73f60eaf577bc5ede1e88ca4b5682e285fc3672cd7d486dd00f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.07189",
    "kind": "arxiv",
    "version": 1
  }
}