Pith Number

pith:GWNREICI

pith:2026:GWNREICIPEVTVR4EA6Y53ZWFHH

not attested not anchored not stored refs pending

Fibrations, the First Betti Number, and Almost Nonnegative Ricci Curvature

Hongzhi Huang, Jikang Wang, Xian-Tao Huang, Xingyu Zhu

arxiv:2605.24380 v1 · 2026-05-23 · 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{GWNREICIPEVTVR4EA6Y53ZWFHH}

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	2026-05-26T01:03:02.833741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

359b122048792b3ac78407b1dde6c539ceb6e1ba94ac002d07976ed173771735

Aliases

arxiv: 2605.24380 · arxiv_version: 2605.24380v1 · doi: 10.48550/arxiv.2605.24380 · pith_short_12: GWNREICIPEVT · pith_short_16: GWNREICIPEVTVR4E · pith_short_8: GWNREICI

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/GWNREICIPEVTVR4EA6Y53ZWFHH \
  | 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: 359b122048792b3ac78407b1dde6c539ceb6e1ba94ac002d07976ed173771735

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d16555e1139a641abde4e531ac5946969950ca3b25fb51defb777dae52141cf7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-23T03:38:38Z",
    "title_canon_sha256": "d4f36d1d55d5ca12218216d8b3a6c83604f76435d5f12c978849396c8ee099e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.24380",
    "kind": "arxiv",
    "version": 1
  }
}