Pith Number

pith:RM5CDUYU

pith:2018:RM5CDUYUJK4RDMMHUOY4PS6P6R

not attested not anchored not stored refs pending

Counting Phylogenetic Networks with Few Reticulation Vertices: Tree-Child and Normal Networks

Bernhard Gittenberger, Marefatollah Mansouri, Michael Fuchs

arxiv:1803.11325 v3 · 2018-03-30 · 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{RM5CDUYUJK4RDMMHUOY4PS6P6R}

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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.

Cited by

1 paper in Pith

Counting Spinal Tree-Child Networks via Word Encodings and Generating Functions

Receipt and verification

First computed	2026-05-18T00:01:09.626607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b3a21d3144ab911b187a3b1c7cbcff44a7a3c878bbfdc12aaba34b04aeba24d

Aliases

arxiv: 1803.11325 · arxiv_version: 1803.11325v3 · doi: 10.48550/arxiv.1803.11325 · pith_short_12: RM5CDUYUJK4R · pith_short_16: RM5CDUYUJK4RDMMH · pith_short_8: RM5CDUYU

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/RM5CDUYUJK4RDMMHUOY4PS6P6R \
  | 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: 8b3a21d3144ab911b187a3b1c7cbcff44a7a3c878bbfdc12aaba34b04aeba24d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5b9107cfaf291692852e77b6f0627192d846eb69b7845ac7ce53ce1a185a5c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-03-30T03:18:19Z",
    "title_canon_sha256": "c9b9b02ac35e773386f3309910570f837f211968c251698404067fc7a0353da0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.11325",
    "kind": "arxiv",
    "version": 3
  }
}