Pith Number

pith:N3JVJMDW

pith:2026:N3JVJMDW7GAA4QD7VCF6DGNVLH

not attested not anchored not stored refs pending

A refined blow-up analysis of the Brezis-Nirenberg equation and its application: The one-bubble case for $N\geq4$

Juncheng Wei, Rui He, Xiangqing Liu, Yuanze Wu

arxiv:2607.11132 v1 · 2026-07-13 · 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{N3JVJMDW7GAA4QD7VCF6DGNVLH}

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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.

Receipt and verification

First computed	2026-07-14T01:22:18.121384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ed354b076f9800e407fa88be199b559d12cf3a2c9a41041d6abecbbbf138a6b

Aliases

arxiv: 2607.11132 · arxiv_version: 2607.11132v1 · doi: 10.48550/arxiv.2607.11132 · pith_short_12: N3JVJMDW7GAA · pith_short_16: N3JVJMDW7GAA4QD7 · pith_short_8: N3JVJMDW

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/N3JVJMDW7GAA4QD7VCF6DGNVLH \
  | 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: 6ed354b076f9800e407fa88be199b559d12cf3a2c9a41041d6abecbbbf138a6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7c04ef7232a02953db3de5f507332e7052924623b8dd6ffeff8b16f8e99246b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-13T06:11:59Z",
    "title_canon_sha256": "47eb229aebd5f3c2d1bb31213544977c754c05e5a58e30b2ce9c8700dff713cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.11132",
    "kind": "arxiv",
    "version": 1
  }
}