Pith Number

pith:7O2WA5ED

pith:2025:7O2WA5ED7KWCTNUAWA65A6RXTA

not attested not anchored not stored refs pending

Nonnegative Ricci Curvature, Euclidean Volume Growth, and the Fundamental Groups of Open $4$-Manifolds

Hongzhi Huang, Xian-Tao Huang

arxiv:2502.03259 v1 · 2025-02-05 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7O2WA5ED7KWCTNUAWA65A6RXTA}

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

Geometric transformation theorem, fundamental groups and monotone of numbers of almost Euclidean factors of geodesic balls

Receipt and verification

First computed	2026-07-05T10:10:02.290362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbb5607483faac29b680b03dd07a379827a5ab7f82b7b58dc95ab99e5bc9beae

Aliases

arxiv: 2502.03259 · arxiv_version: 2502.03259v1 · doi: 10.48550/arxiv.2502.03259 · pith_short_12: 7O2WA5ED7KWC · pith_short_16: 7O2WA5ED7KWCTNUA · pith_short_8: 7O2WA5ED

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/7O2WA5ED7KWCTNUAWA65A6RXTA \
  | 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: fbb5607483faac29b680b03dd07a379827a5ab7f82b7b58dc95ab99e5bc9beae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bf05c06bc29df77b91ee6cade22faa108091dcfc094dc0b23838ffa87d8235c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-02-05T15:16:36Z",
    "title_canon_sha256": "13e21506d1a3aae2c96192ce000c450767a739167b5af4ddb52f310ac8a431e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.03259",
    "kind": "arxiv",
    "version": 1
  }
}