Pith Number

pith:NTKT7RFP

pith:2000:NTKT7RFPLULOWOQMTYFKWEDHHC

not attested not anchored not stored refs pending

Recurrence of Distributional Limits of Finite Planar Graphs

Itai Benjamini, Oded Schramm

arxiv:math/0011019 v4 · 2000-11-02 · math.PR · math-ph · math.CO · math.MG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NTKT7RFPLULOWOQMTYFKWEDHHC}

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	2026-07-04T15:28:55.278702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cd53fc4af5d16eb3a0c9e0aab106738825e8411717734eb6cbac073cf13baa4

Aliases

arxiv: math/0011019 · arxiv_version: math/0011019v4 · doi: 10.48550/arxiv.math/0011019 · pith_short_12: NTKT7RFPLULO · pith_short_16: NTKT7RFPLULOWOQM · pith_short_8: NTKT7RFP

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/NTKT7RFPLULOWOQMTYFKWEDHHC \
  | 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: 6cd53fc4af5d16eb3a0c9e0aab106738825e8411717734eb6cbac073cf13baa4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d29f1c14ccba49ee3878eeb3046cae2bcd3ad1a811cb31d6ca0c6daa5885448b",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MG",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2000-11-02T20:48:47Z",
    "title_canon_sha256": "f26c0ed930eba6d54b070b23817ef3d288648f8328384496ecff2e4b7f69cbb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0011019",
    "kind": "arxiv",
    "version": 4
  }
}