Pith Number

pith:7D3XMU2T

pith:2019:7D3XMU2TEMXYB47SLDO5J2FFBD

not attested not anchored not stored refs pending

On the minimum value of the Colless index and the bifurcating trees that achieve it

Francesc Rossell\'o, Kristina Wicke, Lina Herbst, Mareike Fischer, Tom\'as M. Coronado

arxiv:1907.05064 v2 · 2019-07-11 · q-bio.PE · cs.DM · 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{7D3XMU2TEMXYB47SLDO5J2FFBD}

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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.

Receipt and verification

First computed	2026-07-05T00:40:56.852536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8f7765353232f80f3f258ddd4e8a508f3d8aacd37aad12bb84c08ad9cc71808

Aliases

arxiv: 1907.05064 · arxiv_version: 1907.05064v2 · doi: 10.48550/arxiv.1907.05064 · pith_short_12: 7D3XMU2TEMXY · pith_short_16: 7D3XMU2TEMXYB47S · pith_short_8: 7D3XMU2T

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/7D3XMU2TEMXYB47SLDO5J2FFBD \
  | 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: f8f7765353232f80f3f258ddd4e8a508f3d8aacd37aad12bb84c08ad9cc71808

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0382ddcf5a79e1d3af879b24fa21960fd1525844f4110b571f6a402eb0dfd441",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-bio.PE",
    "submitted_at": "2019-07-11T09:07:29Z",
    "title_canon_sha256": "112688eacd651c886fb0317cf0a983f5d3eb81f6aef9adb6778587457574dbc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.05064",
    "kind": "arxiv",
    "version": 2
  }
}