Pith Number

pith:L7YTNKVQ

pith:2026:L7YTNKVQJPVNLRMC7YLBRH7YLB

not attested not anchored not stored refs pending

Exact Enumeration of Phylogenetic Networks: The Tree-Child, Reticulation-Visible and Orchard Hierarchy

Josep Batle

arxiv:2606.24325 v1 · 2026-06-23 · math.CO · q-bio.PE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L7YTNKVQJPVNLRMC7YLBRH7YLB}

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	2026-06-24T01:14:50.036862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ff136aab04bead5c582fe16189ff858687fa6ab3ff5e9c2fe035ad002815756

Aliases

arxiv: 2606.24325 · arxiv_version: 2606.24325v1 · doi: 10.48550/arxiv.2606.24325 · pith_short_12: L7YTNKVQJPVN · pith_short_16: L7YTNKVQJPVNLRMC · pith_short_8: L7YTNKVQ

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/L7YTNKVQJPVNLRMC7YLBRH7YLB \
  | 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: 5ff136aab04bead5c582fe16189ff858687fa6ab3ff5e9c2fe035ad002815756

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57b205deadad7e97a207f573235ebd4e9c53cd93cdff5be20a0255dd3115f89b",
    "cross_cats_sorted": [
      "q-bio.PE"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-23T09:02:23Z",
    "title_canon_sha256": "322426c7e04e0a0c02f38b3a90d75b979f7a601728fd6229ea4e80cfc0ce9ccc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24325",
    "kind": "arxiv",
    "version": 1
  }
}