Pith Number

pith:PJT7XBO5

pith:2016:PJT7XBO5BKBFUN7WINHZILWIF5

not attested not anchored not stored refs pending

The sharp threshold for the Duarte model

B\'ela Bollob\'as, Hugo Duminil-Copin, Paul Smith, Robert Morris

arxiv:1603.05237 v2 · 2016-03-16 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PJT7XBO5BKBFUN7WINHZILWIF5}

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	2026-05-18T01:02:56.486298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a67fb85dd0a825a37f6434f942ec82f6ca1cd3bc291ce94029fe9d7b1ccd8d9

Aliases

arxiv: 1603.05237 · arxiv_version: 1603.05237v2 · doi: 10.48550/arxiv.1603.05237 · pith_short_12: PJT7XBO5BKBF · pith_short_16: PJT7XBO5BKBFUN7W · pith_short_8: PJT7XBO5

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/PJT7XBO5BKBFUN7WINHZILWIF5 \
  | 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: 7a67fb85dd0a825a37f6434f942ec82f6ca1cd3bc291ce94029fe9d7b1ccd8d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "548d4ed45093ee40813e872fe8be64c25d2787805cc9f085edac7e9a2cdc29be",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-03-16T19:50:40Z",
    "title_canon_sha256": "609bfb6a4192d3763b6fc2bb3a9f5eb569211b927f9392530bde73a4aa67b34f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.05237",
    "kind": "arxiv",
    "version": 2
  }
}