Pith Number

pith:Z7JVCAFT

pith:2015:Z7JVCAFTXXHMW74LL2KF5OJ4XW

not attested not anchored not stored refs pending

Lower Bound for General Circuits Computing Clique Function

Weimin Chen

arxiv:1502.04650 v2 · 2015-02-16 · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z7JVCAFTXXHMW74LL2KF5OJ4XW}

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	2026-05-18T02:26:45.016635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfd35100b3bdcecb7f8b5e945eb93cbd97e88f9802961d890aec7862a9c06374

Aliases

arxiv: 1502.04650 · arxiv_version: 1502.04650v2 · doi: 10.48550/arxiv.1502.04650 · pith_short_12: Z7JVCAFTXXHM · pith_short_16: Z7JVCAFTXXHMW74L · pith_short_8: Z7JVCAFT

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/Z7JVCAFTXXHMW74LL2KF5OJ4XW \
  | 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: cfd35100b3bdcecb7f8b5e945eb93cbd97e88f9802961d890aec7862a9c06374

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca19c44a1c28c7e0c43bf69c5ad9e50edabc53504a9d56e7f66709fded900d93",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-02-16T17:58:08Z",
    "title_canon_sha256": "6f03dbbded2e314c2601f81353bb2c2f05b8b0f2efd29ebd11f8c7fa4e08eb77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.04650",
    "kind": "arxiv",
    "version": 2
  }
}