Pith Number

pith:JWPRGBXT

pith:2025:JWPRGBXT5OWOP7WYEG2KD2LGL4

not attested not anchored not stored refs pending

The stability of independence polynomials of complete bipartite graphs

Bo Ning, Guo Chen, Jianhua Tu

arxiv:2505.24381 v1 · 2025-05-30 · 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{JWPRGBXT5OWOP7WYEG2KD2LGL4}

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	2026-07-05T11:12:48.034158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d9f1306f3ebace7fed821b4a1e9665f212946f361a85ff4194dadefa6b2202a

Aliases

arxiv: 2505.24381 · arxiv_version: 2505.24381v1 · doi: 10.48550/arxiv.2505.24381 · pith_short_12: JWPRGBXT5OWO · pith_short_16: JWPRGBXT5OWOP7WY · pith_short_8: JWPRGBXT

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/JWPRGBXT5OWOP7WYEG2KD2LGL4 \
  | 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: 4d9f1306f3ebace7fed821b4a1e9665f212946f361a85ff4194dadefa6b2202a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31750074cfdb090b75e58a0a765001a4c1cbc5d546035f0d86930d853c2bca5d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-30T09:10:28Z",
    "title_canon_sha256": "c9b611ee50d79629cc5758a14d62257e7e6c0f573b70b060f0a443978382a216"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.24381",
    "kind": "arxiv",
    "version": 1
  }
}