Pith Number

pith:E2RO66CS

pith:2017:E2RO66CSPX4U7VMS7NP5ROL5RZ

not attested not anchored not stored refs pending

Model-Theoretic Characterizations of Boolean and Arithmetic Circuit Classes of Small Depth

Anselm Haak, Arnaud Durand, Heribert Vollmer

arxiv:1710.01934 v2 · 2017-10-05 · 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{E2RO66CSPX4U7VMS7NP5ROL5RZ}

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	2026-05-18T00:33:34.370725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26a2ef78527df94fd592fb5fd8b97d8e55b1783af18100d3be9f595eccdf6649

Aliases

arxiv: 1710.01934 · arxiv_version: 1710.01934v2 · doi: 10.48550/arxiv.1710.01934 · pith_short_12: E2RO66CSPX4U · pith_short_16: E2RO66CSPX4U7VMS · pith_short_8: E2RO66CS

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/E2RO66CSPX4U7VMS7NP5ROL5RZ \
  | 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: 26a2ef78527df94fd592fb5fd8b97d8e55b1783af18100d3be9f595eccdf6649

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02c9c7d8162673c01173209724e51e223ae668f20cf23a90fba8fc19495ccd35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2017-10-05T09:23:29Z",
    "title_canon_sha256": "da7fd4a7eabdd8a35d374b71efef9a0d88c92b6eb094fd464ebac71945bd8e49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.01934",
    "kind": "arxiv",
    "version": 2
  }
}