Pith Number

pith:CVCFNWME

pith:2005:CVCFNWMEWSYHDH42O7WQWMMWEQ

not attested not anchored not stored refs pending

Evolutionary Trees and the Ising Model on the Bethe Lattice: a Proof of Steel's Conjecture

Constantinos Daskalakis, Elchanan Mossel, Sebastien Roch

arxiv:math/0509575 v3 · 2005-09-23 · math.PR · cs.CE · cs.DS · math.CA · math.CO · math.ST · q-bio.PE · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CVCFNWMEWSYHDH42O7WQWMMWEQ}

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	2026-05-18T04:12:00.929270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

154456d984b4b0719f9a77ed0b319624301e4528b3d824c88f5cf34fe57eee77

Aliases

arxiv: math/0509575 · arxiv_version: math/0509575v3 · doi: 10.48550/arxiv.math/0509575 · pith_short_12: CVCFNWMEWSYH · pith_short_16: CVCFNWMEWSYHDH42 · pith_short_8: CVCFNWME

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/CVCFNWMEWSYHDH42O7WQWMMWEQ \
  | 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: 154456d984b4b0719f9a77ed0b319624301e4528b3d824c88f5cf34fe57eee77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f7b4e4f6f79089279d984e3db92f3bc721969f7615729c1e6ddf13930f5dc3b",
    "cross_cats_sorted": [
      "cs.CE",
      "cs.DS",
      "math.CA",
      "math.CO",
      "math.ST",
      "q-bio.PE",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2005-09-23T20:22:09Z",
    "title_canon_sha256": "18b863aee1864e0c42396d5ceb9f891bba3ce68828dcfc98e73feae54bea6241"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509575",
    "kind": "arxiv",
    "version": 3
  }
}