Pith Number

pith:PSFJW5DM

pith:2026:PSFJW5DMPUPATXXCWAXPMC42FI

not attested not anchored not stored refs pending

Planar higher-rank trees have rank at most four

David Pask

arxiv:2606.05727 v1 · 2026-06-04 · math.CT · math.CO · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PSFJW5DMPUPATXXCWAXPMC42FI}

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	2026-06-05T01:15:00.857849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c8a9b746c7d1e09dee2b02ef60b9a2a1dee960f7753093d35c0ac3462bff583

Aliases

arxiv: 2606.05727 · arxiv_version: 2606.05727v1 · doi: 10.48550/arxiv.2606.05727 · pith_short_12: PSFJW5DMPUPA · pith_short_16: PSFJW5DMPUPATXXC · pith_short_8: PSFJW5DM

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/PSFJW5DMPUPATXXCWAXPMC42FI \
  | 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: 7c8a9b746c7d1e09dee2b02ef60b9a2a1dee960f7753093d35c0ac3462bff583

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdc4fc7ad3891be953a07a6a370b17d3dc60229e62c3c570ec527defd6485eff",
    "cross_cats_sorted": [
      "math.CO",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-06-04T05:36:44Z",
    "title_canon_sha256": "8fec2e64604e9d0ac936fc422bedb130f8c2ff405e315bcd512d4207ca821347"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.05727",
    "kind": "arxiv",
    "version": 1
  }
}