Pith Number

pith:CUIFJXQX

pith:2015:CUIFJXQXFJRM3CRCH26H4X66XG

not attested not anchored not stored refs pending

Graph Isomorphism and Circuit Size

Andrew Morgan, Cristopher Moore, Dieter van Melkebeek, Eric Allender, Joshua A. Grochow

arxiv:1511.08189 v2 · 2015-11-25 · 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{CUIFJXQXFJRM3CRCH26H4X66XG}

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	2026-05-18T00:19:42.929034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

151054de172a62cd8a223ebc7e5fdeb9a5c6b3c70fa722b3620db6949900a87a

Aliases

arxiv: 1511.08189 · arxiv_version: 1511.08189v2 · doi: 10.48550/arxiv.1511.08189 · pith_short_12: CUIFJXQXFJRM · pith_short_16: CUIFJXQXFJRM3CRC · pith_short_8: CUIFJXQX

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/CUIFJXQXFJRM3CRCH26H4X66XG \
  | 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: 151054de172a62cd8a223ebc7e5fdeb9a5c6b3c70fa722b3620db6949900a87a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41b498870e06d02ed50f81c556254bcf038f3a23d217992daab620a9c67de650",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-11-25T20:20:48Z",
    "title_canon_sha256": "4f2ce8f1e568591f0d16bea5e57c3fb23834acf0a5651a546708f8b0a8577d7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08189",
    "kind": "arxiv",
    "version": 2
  }
}