Pith Number

pith:GLMJPAT6

pith:2026:GLMJPAT6ISROQ2AKS2AVNRT2S6

not attested not anchored not stored refs pending

A parameterized family of balance indices for phylogenetic networks

Fran\c{c}ois Bienvenu, Hadrien Maffioli, Jean-Jil Duchamps

arxiv:2606.24562 v1 · 2026-06-23 · math.CO · math.PR · 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{GLMJPAT6ISROQ2AKS2AVNRT2S6}

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	2026-06-24T01:15:33.960075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32d897827e44a2e8680a968156c67a979ece68110f7d315227c72e2d0298d89a

Aliases

arxiv: 2606.24562 · arxiv_version: 2606.24562v1 · doi: 10.48550/arxiv.2606.24562 · pith_short_12: GLMJPAT6ISRO · pith_short_16: GLMJPAT6ISROQ2AK · pith_short_8: GLMJPAT6

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/GLMJPAT6ISROQ2AKS2AVNRT2S6 \
  | 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: 32d897827e44a2e8680a968156c67a979ece68110f7d315227c72e2d0298d89a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9ea2fd62660fcb19e1096a0eb3fbac080d225a922e5cabe197c16f89fd5b6ee",
    "cross_cats_sorted": [
      "math.PR",
      "q-bio.PE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-23T13:29:58Z",
    "title_canon_sha256": "084d3ed627837380150ac228ba4c4fa7fce52351f97eb87155d23b9e54e6cd18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24562",
    "kind": "arxiv",
    "version": 1
  }
}