Pith Number

pith:YP224XS7

pith:2016:YP224XS7DRDR5RVEVWWMX4SXED

not attested not anchored not stored refs pending

Boundaries of VP and VNP

Joshua A. Grochow, Ketan D. Mulmuley, Youming Qiao

arxiv:1605.02815 v1 · 2016-05-10 · cs.CC · math.AG · math.CO · 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{YP224XS7DRDR5RVEVWWMX4SXED}

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	2026-05-18T01:15:13.080990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3f5ae5e5f1c471ec6a4adaccbf25720f968d24a44329bcb4bb0a6161a593113

Aliases

arxiv: 1605.02815 · arxiv_version: 1605.02815v1 · doi: 10.48550/arxiv.1605.02815 · pith_short_12: YP224XS7DRDR · pith_short_16: YP224XS7DRDR5RVE · pith_short_8: YP224XS7

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/YP224XS7DRDR5RVEVWWMX4SXED \
  | 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: c3f5ae5e5f1c471ec6a4adaccbf25720f968d24a44329bcb4bb0a6161a593113

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a1915cb0623c020a1ad11b785c5b76a6feb58d66fc39a00deb8c528a70166a8",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2016-05-10T01:06:40Z",
    "title_canon_sha256": "dac85aebfa640572b5b9419e3af4f8deaa77e84b22ee9f5433c46aa79f6b84b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.02815",
    "kind": "arxiv",
    "version": 1
  }
}