Pith Number

pith:APTSZZ6D

pith:2025:APTSZZ6DVJHD5P5I2ZV3JXHHMQ

not attested not anchored not stored refs pending

Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay

Shuli Chen

arxiv:2508.04173 v2 · 2025-08-06 · 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{APTSZZ6DVJHD5P5I2ZV3JXHHMQ}

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

Linking at Infinity and Scalar Curvature Decay on Non-Compact Manifolds

Receipt and verification

First computed	2026-07-05T12:00:28.694674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03e72ce7c3aa4e3ebfa8d66bb4dce7640cec887c3236a2aa9c14ff8e85cbb51b

Aliases

arxiv: 2508.04173 · arxiv_version: 2508.04173v2 · doi: 10.48550/arxiv.2508.04173 · pith_short_12: APTSZZ6DVJHD · pith_short_16: APTSZZ6DVJHD5P5I · pith_short_8: APTSZZ6D

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/APTSZZ6DVJHD5P5I2ZV3JXHHMQ \
  | 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: 03e72ce7c3aa4e3ebfa8d66bb4dce7640cec887c3236a2aa9c14ff8e85cbb51b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6442e22c7030ae0b1e8dcfe711eefff849d486b839d95202352675dd4b937fa7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-08-06T07:58:32Z",
    "title_canon_sha256": "7c498efd6067a577c867788dc83fc4c1a3426866ff0229972090c5ab90ce0518"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.04173",
    "kind": "arxiv",
    "version": 2
  }
}