Pith Number

pith:HGWEEL3Z

pith:2005:HGWEEL3ZVVGTAGTDTN2HMBR6IU

not attested not anchored not stored refs pending

Improved direct sum theorem in classical communication complexity

Rahul Jain

arxiv:cs/0504087 v3 · 2005-04-19 · cs.OH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HGWEEL3ZVVGTAGTDTN2HMBR6IU}

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	2026-07-04T14:25:01.673792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39ac422f79ad4d301a639b7476063e451795da53b9cdc7eb5cf51fcd52d33bff

Aliases

arxiv: cs/0504087 · arxiv_version: cs/0504087v3 · doi: 10.48550/arxiv.cs/0504087 · pith_short_12: HGWEEL3ZVVGT · pith_short_16: HGWEEL3ZVVGTAGTD · pith_short_8: HGWEEL3Z

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/HGWEEL3ZVVGTAGTDTN2HMBR6IU \
  | 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: 39ac422f79ad4d301a639b7476063e451795da53b9cdc7eb5cf51fcd52d33bff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8eb2bd85a9b90b7c336d04570816c0c074e2310134c6509345a88aa3fe6c3972",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "cs.OH",
    "submitted_at": "2005-04-19T21:53:09Z",
    "title_canon_sha256": "94f643674941221997594124f0028d949af5f6e0ecf2372c3fd774d9a613df04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cs/0504087",
    "kind": "arxiv",
    "version": 3
  }
}