Pith Number

pith:OL47R4TL

pith:2025:OL47R4TLCMR5FJ6SYPURWKH4SE

not attested not anchored not stored refs pending

Sharp stability for critical points of the Sobolev inequality in the absence of bubbling

Gemei Liu, Yi Ru-Ya Zhang

arxiv:2503.02340 v2 · 2025-03-04 · 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{OL47R4TLCMR5FJ6SYPURWKH4SE}

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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

2 papers in Pith

Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$

On the anisotropic critical $p$-Laplace equation: classification, decomposition, and stability results

Receipt and verification

First computed	2026-07-05T10:29:35.412811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72f9f8f26b1323d2a7d2c3e91b28fc9122115f65b73d5bc1ff6e27d01c7be66c

Aliases

arxiv: 2503.02340 · arxiv_version: 2503.02340v2 · doi: 10.48550/arxiv.2503.02340 · pith_short_12: OL47R4TLCMR5 · pith_short_16: OL47R4TLCMR5FJ6S · pith_short_8: OL47R4TL

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/OL47R4TLCMR5FJ6SYPURWKH4SE \
  | 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: 72f9f8f26b1323d2a7d2c3e91b28fc9122115f65b73d5bc1ff6e27d01c7be66c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7248ff5ba5f1400ac6449ecd36b9155cac3630a9286483aac9f1c2f0876b0a07",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-03-04T07:02:49Z",
    "title_canon_sha256": "25b970c0bb0f435600b0fe049de33436b89c69c733affe605580696478f1adfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2503.02340",
    "kind": "arxiv",
    "version": 2
  }
}