Pith Number

pith:4Z365G4E

pith:2025:4Z365G4EFEK35ZGJQA65D2RJ5Z

not attested not anchored not stored refs pending

Hyper-Catalan and Geode Recurrences and Three Conjectures of Wildberger

Dean Rubine

arxiv:2507.04552 v1 · 2025-07-06 · 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{4Z365G4EFEK35ZGJQA65D2RJ5Z}

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.

Cited by

1 paper in Pith

Ordered trees and the Geode

Receipt and verification

First computed	2026-07-05T11:32:49.746789Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e677ee9b842915bee4c9803dd1ea29ee6f831d687b09ce11a2f82bbc107347f9

Aliases

arxiv: 2507.04552 · arxiv_version: 2507.04552v1 · doi: 10.48550/arxiv.2507.04552 · pith_short_12: 4Z365G4EFEK3 · pith_short_16: 4Z365G4EFEK35ZGJ · pith_short_8: 4Z365G4E

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/4Z365G4EFEK35ZGJQA65D2RJ5Z \
  | 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: e677ee9b842915bee4c9803dd1ea29ee6f831d687b09ce11a2f82bbc107347f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a62426ef4ee34dab19abcbd1fb9fe84d8bb50e5bfed1fbfc7f32546781a88fc1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-06T22:03:56Z",
    "title_canon_sha256": "5ecebb2e462c3729fa4fc8d954275c984a7b81c87e47fbb2c371c0cfef62cd57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.04552",
    "kind": "arxiv",
    "version": 1
  }
}