Pith Number

pith:GR4KXIVS

pith:2025:GR4KXIVS3WYZTQCM5NB4MWXR6W

not attested not anchored not stored refs pending

Concentric bubbles concentrating in finite time for the energy critical wave maps equation

Jacek Jendrej, Joachim Krieger

arxiv:2501.08396 v1 · 2025-01-14 · 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{GR4KXIVS3WYZTQCM5NB4MWXR6W}

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

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

Receipt and verification

First computed	2026-07-05T10:01:02.160264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3478aba2b2ddb199c04ceb43c65af1f5a32d90fe026c159ddeb894aa39570653

Aliases

arxiv: 2501.08396 · arxiv_version: 2501.08396v1 · doi: 10.48550/arxiv.2501.08396 · pith_short_12: GR4KXIVS3WYZ · pith_short_16: GR4KXIVS3WYZTQCM · pith_short_8: GR4KXIVS

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/GR4KXIVS3WYZTQCM5NB4MWXR6W \
  | 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: 3478aba2b2ddb199c04ceb43c65af1f5a32d90fe026c159ddeb894aa39570653

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4a0d2a160b13140c7e26a711340dbbcf37e0ad9627f8f263a757823260ad13a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-01-14T19:26:58Z",
    "title_canon_sha256": "242d06cfa06a02ccbfb1412a3d6b2f8b9a2bb4a04f83908f338f46d6a9531f68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.08396",
    "kind": "arxiv",
    "version": 1
  }
}