Pith Number

pith:DVEO4JYD

pith:2012:DVEO4JYDVZKT4EXAE3TL2FGYYD

not attested not anchored not stored refs pending

A strong direct product theorem in terms of the smooth rectangle bound

Penghui Yao, Rahul Jain

arxiv:1209.0263 v3 · 2012-09-03 · 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{DVEO4JYDVZKT4EXAE3TL2FGYYD}

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	2026-05-18T03:33:13.917621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d48ee2703ae553e12e026e6bd14d8c0d8e905c0b8d21ce676b9eb2b110a4844

Aliases

arxiv: 1209.0263 · arxiv_version: 1209.0263v3 · doi: 10.48550/arxiv.1209.0263 · pith_short_12: DVEO4JYDVZKT · pith_short_16: DVEO4JYDVZKT4EXA · pith_short_8: DVEO4JYD

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/DVEO4JYDVZKT4EXAE3TL2FGYYD \
  | 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: 1d48ee2703ae553e12e026e6bd14d8c0d8e905c0b8d21ce676b9eb2b110a4844

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dff943be3acf0769d5d9839bb56b95d4cfafb15629e823ba93725d1bede6dc1d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2012-09-03T08:02:29Z",
    "title_canon_sha256": "056b767f94f5ba83075a6ab18323fca902d41a05ae67e7cf5e5001a1c7105159"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0263",
    "kind": "arxiv",
    "version": 3
  }
}