Pith Number

pith:WM24KAE5

pith:2025:WM24KAE546ZAMDLUDWYPKQMNT7

not attested not anchored not stored refs pending

Sharp quantitative stability estimates for the Brezis-Nirenberg problem

Haixia Chen, Juncheng Wei, Seunghyeok Kim

arxiv:2506.07602 v1 · 2025-06-09 · 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{WM24KAE546ZAMDLUDWYPKQMNT7}

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	2026-07-05T11:18:30.183492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b335c5009de7b2060d741db0f5418d9fc377b7ea748c54e562656fce823b8f1a

Aliases

arxiv: 2506.07602 · arxiv_version: 2506.07602v1 · doi: 10.48550/arxiv.2506.07602 · pith_short_12: WM24KAE546ZA · pith_short_16: WM24KAE546ZAMDLU · pith_short_8: WM24KAE5

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/WM24KAE546ZAMDLUDWYPKQMNT7 \
  | 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: b335c5009de7b2060d741db0f5418d9fc377b7ea748c54e562656fce823b8f1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32e286e33c59efd9153d518ece0c22e66e8eb0335648f54c71b68234b661fe41",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-09T10:01:59Z",
    "title_canon_sha256": "ebec6d4325d80041d89e41558827ce8f53e1c38708ec73beee5ec885ba501d6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07602",
    "kind": "arxiv",
    "version": 1
  }
}