Pith Number

pith:PJCFWERI

pith:2025:PJCFWERIQ2663YRB62T62FWNTG

not attested not anchored not stored refs pending

Gradient Shrinking Ricci Solitons and Modified Sectional Curvature

Ernani Ribeiro Jr, Hosea Wondo, Xiaodong Cao

arxiv:2509.20669 v3 · 2025-09-25 · 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{PJCFWERIQ2663YRB62T62FWNTG}

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	2026-07-28T00:21:32.442898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a445b122886bdede221f6a7ed16cd9986b715f4384914a410f84cd92263065e

Aliases

arxiv: 2509.20669 · arxiv_version: 2509.20669v3 · doi: 10.48550/arxiv.2509.20669 · pith_short_12: PJCFWERIQ266 · pith_short_16: PJCFWERIQ2663YRB · pith_short_8: PJCFWERI

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/PJCFWERIQ2663YRB62T62FWNTG \
  | 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: 7a445b122886bdede221f6a7ed16cd9986b715f4384914a410f84cd92263065e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2ce7f07ce8e193082f88e7e2e1bcc05c39206e2d4735fbca7337a156b1ade10",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-09-25T02:04:43Z",
    "title_canon_sha256": "d8a6d47b95d64f1c942218c561af581e6ff0c22d3a8b11deacf8b2d59cb77aa1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.20669",
    "kind": "arxiv",
    "version": 3
  }
}