Pith Number

pith:V4HIAC7U

pith:2017:V4HIAC7UJFDVW2TR7A2ZBPDMVA

not attested not anchored not stored refs pending

A Nearly Optimal Lower Bound on the Approximate Degree of AC$^0$

Justin Thaler, Mark Bun

arxiv:1703.05784 v1 · 2017-03-16 · 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{V4HIAC7UJFDVW2TR7A2ZBPDMVA}

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	2026-05-18T00:48:32.104897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af0e800bf449475b6a71f83590bc6ca8314180f443398d399cab00b517b448fd

Aliases

arxiv: 1703.05784 · arxiv_version: 1703.05784v1 · doi: 10.48550/arxiv.1703.05784 · pith_short_12: V4HIAC7UJFDV · pith_short_16: V4HIAC7UJFDVW2TR · pith_short_8: V4HIAC7U

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/V4HIAC7UJFDVW2TR7A2ZBPDMVA \
  | 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: af0e800bf449475b6a71f83590bc6ca8314180f443398d399cab00b517b448fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c367ed0244e26a910f0728b488dd232806ce105871e0502b76ce141c261bc3c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2017-03-16T18:18:51Z",
    "title_canon_sha256": "bd142e77dcc3a01f10ee8c3e1a3b7721429366ed9798dfa984f23e63d036d481"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.05784",
    "kind": "arxiv",
    "version": 1
  }
}