Pith Number

pith:RWGTDMFT

pith:2016:RWGTDMFTLL647QFGBUMMQT7GOV

not attested not anchored not stored refs pending

The sharp threshold for making squares

B\'ela Bollob\'as, Paul Balister, Robert Morris

arxiv:1608.03857 v1 · 2016-08-12 · math.NT · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RWGTDMFTLL647QFGBUMMQT7GOV}

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	2026-05-18T01:09:11.167202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d8d31b0b35afdcfc0a60d18c84fe67564fc9ddea3a3aa8eb8257ccf79e7b8fd

Aliases

arxiv: 1608.03857 · arxiv_version: 1608.03857v1 · doi: 10.48550/arxiv.1608.03857 · pith_short_12: RWGTDMFTLL64 · pith_short_16: RWGTDMFTLL647QFG · pith_short_8: RWGTDMFT

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/RWGTDMFTLL647QFGBUMMQT7GOV \
  | 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: 8d8d31b0b35afdcfc0a60d18c84fe67564fc9ddea3a3aa8eb8257ccf79e7b8fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f0cda8198d830c9a67cbd43d8ab57c470b012c76cec31f51db160de2933566d",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-08-12T17:43:02Z",
    "title_canon_sha256": "34e6a0d13e30cfa0c000771374c56c0ae94f1bd504c1efe15fc54ecb4356c596"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.03857",
    "kind": "arxiv",
    "version": 1
  }
}