Pith Number

pith:UT6QEOTB

pith:2026:UT6QEOTBK5UWUFIOCEN4OCMCZT

not attested not anchored not stored refs pending

Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five

Chencheng Zhang, Jacek Jendrej, Lifeng Zhao

arxiv:2605.27994 v1 · 2026-05-27 · 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{UT6QEOTBK5UWUFIOCEN4OCMCZT}

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	2026-05-28T01:04:55.490053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4fd023a6157696a150e111bc70982cce3ae1063953b59bbc98cc841671835de

Aliases

arxiv: 2605.27994 · arxiv_version: 2605.27994v1 · doi: 10.48550/arxiv.2605.27994 · pith_short_12: UT6QEOTBK5UW · pith_short_16: UT6QEOTBK5UWUFIO · pith_short_8: UT6QEOTB

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/UT6QEOTBK5UWUFIOCEN4OCMCZT \
  | 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: a4fd023a6157696a150e111bc70982cce3ae1063953b59bbc98cc841671835de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7115c33a131d9fcab69ad49a60121160cb0e970d1796c7fa32a2fcfeb15837f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-27T05:35:16Z",
    "title_canon_sha256": "0aeec636e8574a791ad97c5f1fba73fb43664019ff24c8d6b29aa6554e540e36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.27994",
    "kind": "arxiv",
    "version": 1
  }
}