Pith Number

pith:52GNSMJX

pith:2026:52GNSMJXZLQKU2UBXHKZ2ZXILQ

not attested not anchored not stored refs pending

Sharp Bounds on the Independence Number of Simplicial Spheres

Ethan X. Fang, Hailun Zheng, Jes\'us A. De Loera, Junwei Lu, Tingzhou Wei

arxiv:2608.05568 v1 · 2026-08-06 · 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{52GNSMJXZLQKU2UBXHKZ2ZXILQ}

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	2026-08-07T00:49:37.518018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee8cd93137cae0aa6a81b9d59d66e85c0827598d2b6d12e330bdb07444d6d354

Aliases

arxiv: 2608.05568 · arxiv_version: 2608.05568v1 · doi: 10.48550/arxiv.2608.05568 · pith_short_12: 52GNSMJXZLQK · pith_short_16: 52GNSMJXZLQKU2UB · pith_short_8: 52GNSMJX

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/52GNSMJXZLQKU2UBXHKZ2ZXILQ \
  | 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: ee8cd93137cae0aa6a81b9d59d66e85c0827598d2b6d12e330bdb07444d6d354

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cbd61488abed5abb2d51672f27ff2e8900b90664d26ef6405d4cafbc53eb9d38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-06T03:40:06Z",
    "title_canon_sha256": "0e078f40d1e7e8e9bf39e91ad2e0968c4f1394e1c96cc5480fffd640be067e09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.05568",
    "kind": "arxiv",
    "version": 1
  }
}