Pith Number

pith:2AM32GML

pith:2015:2AM32GMLU37YKYHUOYBAAI3F2N

not attested not anchored not stored refs pending

An $O(n^{0.4732})$ upper bound on the complexity of the GKS communication game

Mario Szegedy

arxiv:1506.06456 v1 · 2015-06-22 · 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{2AM32GMLU37YKYHUOYBAAI3F2N}

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	2026-05-18T01:41:45.173733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d019bd198ba6ff8560f47602002365d373854b1ac55b948c0b501debf89bf35a

Aliases

arxiv: 1506.06456 · arxiv_version: 1506.06456v1 · doi: 10.48550/arxiv.1506.06456 · pith_short_12: 2AM32GMLU37Y · pith_short_16: 2AM32GMLU37YKYHU · pith_short_8: 2AM32GML

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/2AM32GMLU37YKYHUOYBAAI3F2N \
  | 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: d019bd198ba6ff8560f47602002365d373854b1ac55b948c0b501debf89bf35a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9eb5aafc7d33c707baa2ecc36c5ddbf5f0603bf3f3f422307e0734409d7949b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-06-22T03:57:07Z",
    "title_canon_sha256": "af13e90c3c7882f736e807837da682b301f945ce3c2b0492f985729b2a469422"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.06456",
    "kind": "arxiv",
    "version": 1
  }
}