Pith Number

pith:I3JAYAAF

pith:2013:I3JAYAAFM72NMZSJCCVUF2XECH

not attested not anchored not stored refs pending

A reduction of proof complexity to computational complexity for $AC^0[p]$ Frege systems

Jan Krajicek

arxiv:1311.2501 v4 · 2013-11-11 · math.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{I3JAYAAFM72NMZSJCCVUF2XECH}

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	2026-05-18T01:16:26.867665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46d20c000567f4d6664910ab42eae411d62350ce5353e53c116704cd5aed1365

Aliases

arxiv: 1311.2501 · arxiv_version: 1311.2501v4 · doi: 10.48550/arxiv.1311.2501 · pith_short_12: I3JAYAAFM72N · pith_short_16: I3JAYAAFM72NMZSJ · pith_short_8: I3JAYAAF

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/I3JAYAAFM72NMZSJCCVUF2XECH \
  | 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: 46d20c000567f4d6664910ab42eae411d62350ce5353e53c116704cd5aed1365

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c107140d8f4a34407e05ca0ef257655856ceaaa8dffc2a0ecf3320e0f78b142a",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2013-11-11T16:55:50Z",
    "title_canon_sha256": "3a7cb49aecb95d3aa47dc229d11dafebd381971c45b5634cf6c0f2dec1d96dde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2501",
    "kind": "arxiv",
    "version": 4
  }
}