Pith Number

pith:CX27BUYQ

pith:2026:CX27BUYQX57QL4VSZEWCHEU5NY

not attested not anchored not stored refs pending

Construction of multi-bubble solutions for the energy-critical wave equation in dimension four

Jacek Jendrej, Jingyuan Gu, Lifeng Zhao

arxiv:2606.04449 v1 · 2026-06-03 · 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{CX27BUYQX57QL4VSZEWCHEU5NY}

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	2026-06-04T01:09:08.581630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15f5f0d310bf7f05f2b2c92c23929d6e161ee51070d8b3898f37dadb3219e403

Aliases

arxiv: 2606.04449 · arxiv_version: 2606.04449v1 · doi: 10.48550/arxiv.2606.04449 · pith_short_12: CX27BUYQX57Q · pith_short_16: CX27BUYQX57QL4VS · pith_short_8: CX27BUYQ

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/CX27BUYQX57QL4VSZEWCHEU5NY \
  | 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: 15f5f0d310bf7f05f2b2c92c23929d6e161ee51070d8b3898f37dadb3219e403

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b84eab7d6eef39bb9e43b75bf4308adb3705c40102b145d8c72f3e186f6d4196",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-03T04:51:52Z",
    "title_canon_sha256": "4d6a042355f621f852536f9b850845d9a99a58c99c33c18a41ccf1988e18b5ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.04449",
    "kind": "arxiv",
    "version": 1
  }
}