Pith Number

pith:CQE5SBUL

pith:2015:CQE5SBULXHZAF6NADIG3JDG35P

not attested not anchored not stored refs pending

An average-case depth hierarchy theorem for Boolean circuits

Benjamin Rossman, Li-Yang Tan, Rocco A. Servedio

arxiv:1504.03398 v1 · 2015-04-14 · 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{CQE5SBULXHZAF6NADIG3JDG35P}

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	2026-05-18T02:18:52.299200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1409d9068bb9f202f9a01a0db48cdbebc1dc39727fb72644f936aa6b162332f9

Aliases

arxiv: 1504.03398 · arxiv_version: 1504.03398v1 · doi: 10.48550/arxiv.1504.03398 · pith_short_12: CQE5SBULXHZA · pith_short_16: CQE5SBULXHZAF6NA · pith_short_8: CQE5SBUL

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/CQE5SBULXHZAF6NADIG3JDG35P \
  | 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: 1409d9068bb9f202f9a01a0db48cdbebc1dc39727fb72644f936aa6b162332f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74d427ba916cffd3938d94e8f43b08104b64b10827af12fdedd7b369d4fa9a2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-04-14T01:44:39Z",
    "title_canon_sha256": "88b20b9354252ff7e73b5efb17593c3b64bbc929a0be12150950b2e2ac07ba84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03398",
    "kind": "arxiv",
    "version": 1
  }
}