Pith Number

pith:3B5PJEFU

pith:2025:3B5PJEFU6PNMRIVFD3MVN4LSO6

not attested not anchored not stored refs pending

Tilings of the sphere by congruent pentagons V: Edge combination $a^{4}b$ with rational angles

Erxiao Wang, Jinjin Liang, Wenchuan Hu, Yixi Liao

arxiv:2507.07038 v1 · 2025-07-09 · 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{3B5PJEFU6PNMRIVFD3MVN4LSO6}

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	2026-07-05T11:34:28.088929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d87af490b4f3dac8a2a51ed956f172779b83ec4e039211c74d9fdfd4da759a5c

Aliases

arxiv: 2507.07038 · arxiv_version: 2507.07038v1 · doi: 10.48550/arxiv.2507.07038 · pith_short_12: 3B5PJEFU6PNM · pith_short_16: 3B5PJEFU6PNMRIVF · pith_short_8: 3B5PJEFU

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/3B5PJEFU6PNMRIVFD3MVN4LSO6 \
  | 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: d87af490b4f3dac8a2a51ed956f172779b83ec4e039211c74d9fdfd4da759a5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a798a92d47b5f710d5571ec4f7b4334a8e5ad123193b80874aa9d29daa0afc2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-09T17:05:18Z",
    "title_canon_sha256": "b36ffec513377c6b4e25323b9025b1e125529be94bc0d2d66eea0569b166b5b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.07038",
    "kind": "arxiv",
    "version": 1
  }
}