Pith Number

pith:EHUN63EV

pith:2013:EHUN63EVYTF2LFVELS4WXGWRBI

not attested not anchored not stored refs pending

Hardness Amplification and the Approximate Degree of Constant-Depth Circuits

Justin Thaler, Mark Bun

arxiv:1311.1616 v4 · 2013-11-07 · cs.CC

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EHUN63EVYTF2LFVELS4WXGWRBI}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T02:53:07.808805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21e8df6c95c4cba596a45cb96b9ad10a04bf75c10df7925cb930f2ab5d00597d

Aliases

arxiv: 1311.1616 · arxiv_version: 1311.1616v4 · doi: 10.48550/arxiv.1311.1616 · pith_short_12: EHUN63EVYTF2 · pith_short_16: EHUN63EVYTF2LFVE · pith_short_8: EHUN63EV

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/EHUN63EVYTF2LFVELS4WXGWRBI \
  | 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: 21e8df6c95c4cba596a45cb96b9ad10a04bf75c10df7925cb930f2ab5d00597d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7eb980820879591145129b32b6272d6517d40cd77d19c40fba63ea88a734fb35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2013-11-07T09:26:48Z",
    "title_canon_sha256": "28f142c18c0767d3b94992ec00c0f1b5167e6b184e2b18dc08cd7bf069c1b39f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1616",
    "kind": "arxiv",
    "version": 4
  }
}