Pith Number

pith:PMR3PQK4

pith:2013:PMR3PQK4DFKKIVLAOE7SWWELIC

not attested not anchored not stored refs pending

Complexity Classes as Mathematical Axioms II

Michael H. Freedman, Shawn X. Cui, Zhenghan Wang

arxiv:1305.6076 v3 · 2013-05-26 · cs.CC · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PMR3PQK4DFKKIVLAOE7SWWELIC}

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	2026-05-18T01:11:41.532266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b23b7c15c1954a45560713f2b588b40a341b180a4349e276107a7fccdb89b6c

Aliases

arxiv: 1305.6076 · arxiv_version: 1305.6076v3 · doi: 10.48550/arxiv.1305.6076 · pith_short_12: PMR3PQK4DFKK · pith_short_16: PMR3PQK4DFKKIVLA · pith_short_8: PMR3PQK4

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/PMR3PQK4DFKKIVLAOE7SWWELIC \
  | 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: 7b23b7c15c1954a45560713f2b588b40a341b180a4349e276107a7fccdb89b6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e62738b3c25e7ec9e3c138ce95c025b861e2681ec88bd1220dd4fcd3084e0fd",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2013-05-26T23:16:42Z",
    "title_canon_sha256": "c173e2b9b6644c417b5d32c476aa57dc34ab59b30f5989bb67ba4a9e34275199"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6076",
    "kind": "arxiv",
    "version": 3
  }
}