Pith Number

pith:SRJ42SMV

pith:2016:SRJ42SMVQIC7UMIHSCM6OSZBP7

not attested not anchored not stored refs pending

Proof Complexity Lower Bounds from Algebraic Circuit Complexity

Amir Shpilka, Avi Wigderson, Iddo Tzameret, Michael A. Forbes

arxiv:1606.05050 v1 · 2016-06-16 · cs.CC · cs.LO · math.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{SRJ42SMVQIC7UMIHSCM6OSZBP7}

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	2026-05-18T01:12:22.125843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9453cd49958205fa31079099e74b217fe7aede0692dd2b419cf50d9f23ad59e3

Aliases

arxiv: 1606.05050 · arxiv_version: 1606.05050v1 · doi: 10.48550/arxiv.1606.05050 · pith_short_12: SRJ42SMVQIC7 · pith_short_16: SRJ42SMVQIC7UMIH · pith_short_8: SRJ42SMV

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/SRJ42SMVQIC7UMIHSCM6OSZBP7 \
  | 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: 9453cd49958205fa31079099e74b217fe7aede0692dd2b419cf50d9f23ad59e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5e38ceb4562ae83ab0bfdabe3251fe625dd10a5fdcbb487d07e4d7f24546f9e",
    "cross_cats_sorted": [
      "cs.LO",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2016-06-16T05:01:58Z",
    "title_canon_sha256": "080981f2010e855803e552e1d61a4adafaf4513a86408e60181f2fe544f82380"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.05050",
    "kind": "arxiv",
    "version": 1
  }
}