Pith Number

pith:CJLGRFV3

pith:2026:CJLGRFV3KC7B6Y2JO2YWACXWVS

not attested not anchored not stored refs pending

Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality

Bao Yu, Yang Zhou

arxiv:2607.21429 v1 · 2026-07-23 · 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{CJLGRFV3KC7B6Y2JO2YWACXWVS}

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	2026-07-24T01:24:31.958348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12566896bb50be1f634976b1600af6acbc208f7c5271a3a8b17fd10f70dba3d2

Aliases

arxiv: 2607.21429 · arxiv_version: 2607.21429v1 · doi: 10.48550/arxiv.2607.21429 · pith_short_12: CJLGRFV3KC7B · pith_short_16: CJLGRFV3KC7B6Y2J · pith_short_8: CJLGRFV3

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/CJLGRFV3KC7B6Y2JO2YWACXWVS \
  | 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: 12566896bb50be1f634976b1600af6acbc208f7c5271a3a8b17fd10f70dba3d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b235a83765a42705388b9b7ca5ed05c7faf9593bd1ea1767c4c41ac8bd6fc44",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-23T15:31:39Z",
    "title_canon_sha256": "255d82517604c890cf4e466ad51aa55542f2899fd110c99f333cc1d760ce4968"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21429",
    "kind": "arxiv",
    "version": 1
  }
}