Pith Number

pith:TXJPT57I

pith:2013:TXJPT57IK6MCWIRXICBEDC4LIT

not attested not anchored not stored refs pending

Complexity Hierarchies Beyond Elementary

Sylvain Schmitz

arxiv:1312.5686 v3 · 2013-12-19 · cs.CC · cs.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TXJPT57IK6MCWIRXICBEDC4LIT}

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	2026-05-18T01:21:20.029887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dd2f9f7e857982b22374082418b8b44ce0fc0259a540b04d4b0d950e5bf3bfc

Aliases

arxiv: 1312.5686 · arxiv_version: 1312.5686v3 · doi: 10.48550/arxiv.1312.5686 · pith_short_12: TXJPT57IK6MC · pith_short_16: TXJPT57IK6MCWIRX · pith_short_8: TXJPT57I

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/TXJPT57IK6MCWIRXICBEDC4LIT \
  | 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: 9dd2f9f7e857982b22374082418b8b44ce0fc0259a540b04d4b0d950e5bf3bfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44d94100f081d9162d10d3e3cbcde771f448477d10ac951928d869644825ea8f",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2013-12-19T18:30:18Z",
    "title_canon_sha256": "30c44a451926c53865021b56cc1ee98fcfe73ed61aa4a211c05c78c848d65758"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5686",
    "kind": "arxiv",
    "version": 3
  }
}