Pith Number

pith:5O5QBPFZ

pith:2005:5O5QBPFZ7CMKJLU45DUG2G3VCG

not attested not anchored not stored refs pending

Theories for TC0 and Other Small Complexity Classes

Phuong Nguyen, Stephen Cook

arxiv:cs/0505013 v4 · 2005-05-05 · cs.LO · 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{5O5QBPFZ7CMKJLU45DUG2G3VCG}

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	2026-05-18T00:53:03.503072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebbb00bcb9f898a4ae9ce8e86d1b7511bbf7714c55a06fdd2fbdbd6ac4108c3f

Aliases

arxiv: cs/0505013 · arxiv_version: cs/0505013v4 · doi: 10.48550/arxiv.cs/0505013 · pith_short_12: 5O5QBPFZ7CMK · pith_short_16: 5O5QBPFZ7CMKJLU4 · pith_short_8: 5O5QBPFZ

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/5O5QBPFZ7CMKJLU45DUG2G3VCG \
  | 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: ebbb00bcb9f898a4ae9ce8e86d1b7511bbf7714c55a06fdd2fbdbd6ac4108c3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12c4fdfe9bb96f034a075467faec259165ef869612236e7eaf64d868b2840d9b",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "",
    "primary_cat": "cs.LO",
    "submitted_at": "2005-05-05T22:17:01Z",
    "title_canon_sha256": "a97b634225f482819ae246343d1eb822b151e5be19338c8b94752c0f518c5fdf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cs/0505013",
    "kind": "arxiv",
    "version": 4
  }
}