Pith Number

pith:TOLOISFB

pith:2025:TOLOISFBLCI7ZN3J7HNBYXTOD2

not attested not anchored not stored refs pending

Multi-bubble solutions for the Brezis-Nirenberg problem in four dimensions

Angela Pistoia, Giuseppe Mario Rago, Giusi Vaira

arxiv:2505.24387 v1 · 2025-05-30 · 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{TOLOISFBLCI7ZN3J7HNBYXTOD2}

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

Sharp quantitative stability estimates for the Brezis-Nirenberg problem

Receipt and verification

First computed	2026-07-05T11:12:48.147153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b96e448a15891fcb769f9da1c5e6e1ea04d4a510f1b8d536eb08eb1641d80d8

Aliases

arxiv: 2505.24387 · arxiv_version: 2505.24387v1 · doi: 10.48550/arxiv.2505.24387 · pith_short_12: TOLOISFBLCI7 · pith_short_16: TOLOISFBLCI7ZN3J · pith_short_8: TOLOISFB

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/TOLOISFBLCI7ZN3J7HNBYXTOD2 \
  | 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: 9b96e448a15891fcb769f9da1c5e6e1ea04d4a510f1b8d536eb08eb1641d80d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09ee118d4cdb6d2b7137752f7878feb0a90bf0382647ba2e55d14f77e378bfe8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-05-30T09:18:04Z",
    "title_canon_sha256": "0e78283f52407a14f377643f8752cb10d471d08f58cc30e630926c1cc2f5aec8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.24387",
    "kind": "arxiv",
    "version": 1
  }
}