Pith Number

pith:WX3URIBJ

pith:2005:WX3URIBJ4SN46FF7SUPM62B2CU

not attested not anchored not stored refs pending

A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood is Hard

S. Roch

arxiv:math/0504378 v2 · 2005-04-19 · math.PR · cs.CC · cs.CE · 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{WX3URIBJ4SN46FF7SUPM62B2CU}

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	2026-05-18T04:12:00.935947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5f748a029e49bcf14bf951ecf683a15273c95e07dea716c932cae5e2de3730c

Aliases

arxiv: math/0504378 · arxiv_version: math/0504378v2 · doi: 10.48550/arxiv.math/0504378 · pith_short_12: WX3URIBJ4SN4 · pith_short_16: WX3URIBJ4SN46FF7 · pith_short_8: WX3URIBJ

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/WX3URIBJ4SN46FF7SUPM62B2CU \
  | 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: b5f748a029e49bcf14bf951ecf683a15273c95e07dea716c932cae5e2de3730c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "370432be95c6958f032514688c438cde9604b8949d0f2d65a2b08d4d0ea345b6",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.CE",
      "math.ST",
      "q-bio.PE",
      "stat.TH"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-04-19T08:36:17Z",
    "title_canon_sha256": "c2e4f57a4affebbb663bfc8f02443d764b6ea2a6e196cc018a56acbda1a00a49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504378",
    "kind": "arxiv",
    "version": 2
  }
}