Pith Number

pith:24WSKJAG

pith:2012:24WSKJAGWMNVTTBV7J4YSTKGU4

not attested not anchored not stored refs pending

Testing quantum expanders is co-QMA-complete

Adam D. Bookatz, Pawel Wocjan, Stephen P. Jordan, Yi-Kai Liu

arxiv:1210.0787 v2 · 2012-10-02 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{24WSKJAGWMNVTTBV7J4YSTKGU4}

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	2026-05-18T03:22:05.995147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d72d252406b31b59cc35fa79894d46a73e386ba2a7acfc51fcd21e263515a65a

Aliases

arxiv: 1210.0787 · arxiv_version: 1210.0787v2 · doi: 10.48550/arxiv.1210.0787 · pith_short_12: 24WSKJAGWMNV · pith_short_16: 24WSKJAGWMNVTTBV · pith_short_8: 24WSKJAG

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/24WSKJAGWMNVTTBV7J4YSTKGU4 \
  | 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: d72d252406b31b59cc35fa79894d46a73e386ba2a7acfc51fcd21e263515a65a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "106da1d206a10c6054a92b25f9d1eacbe32b09377e1981b7502ac2d6594f4d4e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2012-10-02T14:46:20Z",
    "title_canon_sha256": "3d84df21d04f12b1af21854904e6b5df70748a3ee1b4f6e4da6603040fee3157"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0787",
    "kind": "arxiv",
    "version": 2
  }
}