Pith Number

pith:DBEI55QC

pith:2020:DBEI55QC7RWIMP7SPB2P577FGN

not attested not anchored not stored refs pending

A near-optimal direct-sum theorem for communication complexity

Rahul Jain

arxiv:2008.07188 v3 · 2020-08-17 · 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{DBEI55QC7RWIMP7SPB2P577FGN}

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	2026-07-05T01:32:46.640440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18488ef602fc6c863ff27874feffe53342ee2c1f4c8f1e727356a990e2caeed3

Aliases

arxiv: 2008.07188 · arxiv_version: 2008.07188v3 · doi: 10.48550/arxiv.2008.07188 · pith_short_12: DBEI55QC7RWI · pith_short_16: DBEI55QC7RWIMP7S · pith_short_8: DBEI55QC

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/DBEI55QC7RWIMP7SPB2P577FGN \
  | 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: 18488ef602fc6c863ff27874feffe53342ee2c1f4c8f1e727356a990e2caeed3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af3274c32c245d4bd59a0a626379c3705f9381a7c5a1fa548dad930cb41736e1",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2020-08-17T10:04:08Z",
    "title_canon_sha256": "1004f3ee00bda0c0e333018ddcea0d3efbe36f2290463df2d5d31868006e30ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2008.07188",
    "kind": "arxiv",
    "version": 3
  }
}