Pith Number

pith:GJ2KGD3W

pith:2025:GJ2KGD3WY5SC4CHXHVVOVHQO5I

not attested not anchored not stored refs pending

A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications

Zhenyu Fan

arxiv:2509.01138 v1 · 2025-09-01 · 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{GJ2KGD3WY5SC4CHXHVVOVHQO5I}

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	2026-07-05T12:02:54.546250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3274a30f76c7642e08f73d6aea9e0eea0ba55ee66e2d69b2494bea4624610ced

Aliases

arxiv: 2509.01138 · arxiv_version: 2509.01138v1 · doi: 10.48550/arxiv.2509.01138 · pith_short_12: GJ2KGD3WY5SC · pith_short_16: GJ2KGD3WY5SC4CHX · pith_short_8: GJ2KGD3W

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/GJ2KGD3WY5SC4CHXHVVOVHQO5I \
  | 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: 3274a30f76c7642e08f73d6aea9e0eea0ba55ee66e2d69b2494bea4624610ced

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0bba8bb63d120181c4bb27e9cb6bf46085f68d7847424900e9862a63f90a7bba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-09-01T05:14:56Z",
    "title_canon_sha256": "62e1e833631358733648edd7cc5dd168941279c144d921659e83676cef761ced"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.01138",
    "kind": "arxiv",
    "version": 1
  }
}