Pith Number

pith:RTZQNDX7

pith:2010:RTZQNDX74PYUVDNURRBQHD326U

not attested not anchored not stored refs pending

A strong direct product theorem for two-way public coin communication complexity

Rahul Jain

arxiv:1010.0846 v2 · 2010-10-05 · cs.CC · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RTZQNDX74PYUVDNURRBQHD326U}

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	2026-05-18T04:34:45.758035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cf3068effe3f14a8db48c43038f7af53d7812906ebc1af9754eab3e74512388

Aliases

arxiv: 1010.0846 · arxiv_version: 1010.0846v2 · doi: 10.48550/arxiv.1010.0846 · pith_short_12: RTZQNDX74PYU · pith_short_16: RTZQNDX74PYUVDNU · pith_short_8: RTZQNDX7

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/RTZQNDX74PYUVDNURRBQHD326U \
  | 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: 8cf3068effe3f14a8db48c43038f7af53d7812906ebc1af9754eab3e74512388

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e79010d1d634936d58683a74d3c51e9d489f22c435ec0e81f75423c8ef878fb",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2010-10-05T11:38:19Z",
    "title_canon_sha256": "5a3c63beab7a8c8c1c94bc70567e10f51752a118cda7655ec6ad0f67e3867096"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0846",
    "kind": "arxiv",
    "version": 2
  }
}