Pith Number

pith:SI4X4UNY

pith:2019:SI4X4UNY33AF6OI4TLFXOA7QVK

not attested not anchored not stored refs pending

Quantum Lower Bounds for Approximate Counting via Laurent Polynomials

Justin Thaler, Robin Kothari, Scott Aaronson, William Kretschmer

arxiv:1904.08914 v3 · 2019-04-18 · quant-ph · 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{SI4X4UNY33AF6OI4TLFXOA7QVK}

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	2026-07-05T02:23:55.602834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92397e51b8dec05f391c9acb7703f0aab9a5e4988deb15de7fa43c221d654190

Aliases

arxiv: 1904.08914 · arxiv_version: 1904.08914v3 · doi: 10.48550/arxiv.1904.08914 · pith_short_12: SI4X4UNY33AF · pith_short_16: SI4X4UNY33AF6OI4 · pith_short_8: SI4X4UNY

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/SI4X4UNY33AF6OI4TLFXOA7QVK \
  | 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: 92397e51b8dec05f391c9acb7703f0aab9a5e4988deb15de7fa43c221d654190

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b46609714a5f1296fc78b6ddd46a7a743cca1d47697a003c7e3270415293af8",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2019-04-18T17:49:22Z",
    "title_canon_sha256": "03708d62561aad51149cee796440f5c13202090a3fc7b48ee3ff887ed1fbba0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.08914",
    "kind": "arxiv",
    "version": 3
  }
}