Pith Number

pith:F6563OKX

pith:2025:F6563OKXFHHVSIBJDOOV44WHKJ

not attested not anchored not stored refs pending

Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application

Wen-Qi Li, Zhikai Zhang

arxiv:2505.19113 v1 · 2025-05-25 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F6563OKXFHHVSIBJDOOV44WHKJ}

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	2026-07-05T11:09:25.097562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fbbedb95729cf5920291b9d5e72c7526479af8b72a4d8253529dae3876add38

Aliases

arxiv: 2505.19113 · arxiv_version: 2505.19113v1 · doi: 10.48550/arxiv.2505.19113 · pith_short_12: F6563OKXFHHV · pith_short_16: F6563OKXFHHVSIBJ · pith_short_8: F6563OKX

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/F6563OKXFHHVSIBJDOOV44WHKJ \
  | 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: 2fbbedb95729cf5920291b9d5e72c7526479af8b72a4d8253529dae3876add38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faac079d61de1e2024b813e9168f286734eeef979637fbc7edca4e93b515a333",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-05-25T12:13:52Z",
    "title_canon_sha256": "315ae5041c32f0c28cf45be297ec1012dd9a736aaa43d4c8a0aee0c7f988f42a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.19113",
    "kind": "arxiv",
    "version": 1
  }
}