Pith Number

pith:ZXOYAWA4

pith:2013:ZXOYAWA4QOKHPD6UPRUDWE43Y7

not attested not anchored not stored refs pending

Unifying and generalizing known lower bounds via geometric complexity theory

Joshua A. Grochow

arxiv:1304.6333 v1 · 2013-04-23 · 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{ZXOYAWA4QOKHPD6UPRUDWE43Y7}

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	2026-05-18T00:35:55.972790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cddd80581c8394778fd47c683b139bc7f22c25ce8122f175d9e7e1ddca0f8751

Aliases

arxiv: 1304.6333 · arxiv_version: 1304.6333v1 · doi: 10.48550/arxiv.1304.6333 · pith_short_12: ZXOYAWA4QOKH · pith_short_16: ZXOYAWA4QOKHPD6U · pith_short_8: ZXOYAWA4

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/ZXOYAWA4QOKHPD6UPRUDWE43Y7 \
  | 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: cddd80581c8394778fd47c683b139bc7f22c25ce8122f175d9e7e1ddca0f8751

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a17a5a408628e6f9e5bcc75fa1754a9954fb5800125296d0bdd812600d073d16",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2013-04-23T15:44:45Z",
    "title_canon_sha256": "1884c859b7f6365fc68bd6f49865aa2174da297f96c67f57d0831ca197438787"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.6333",
    "kind": "arxiv",
    "version": 1
  }
}