Pith Number

pith:OSY3FZ7Z

pith:2019:OSY3FZ7ZSKEAIKQGFZKZSKQYNQ

not attested not anchored not stored refs pending

Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5

Jacek Jendrej, Yvan Martel

arxiv:1907.06885 v1 · 2019-07-16 · 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{OSY3FZ7ZSKEAIKQGFZKZSKQYNQ}

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	2026-05-17T23:40:28.802884Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74b1b2e7f99288042a062e55992a186c1e58573d4159f1f55ce2f3b8c37a7731

Aliases

arxiv: 1907.06885 · arxiv_version: 1907.06885v1 · doi: 10.48550/arxiv.1907.06885 · pith_short_12: OSY3FZ7ZSKEA · pith_short_16: OSY3FZ7ZSKEAIKQG · pith_short_8: OSY3FZ7Z

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/OSY3FZ7ZSKEAIKQGFZKZSKQYNQ \
  | 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: 74b1b2e7f99288042a062e55992a186c1e58573d4159f1f55ce2f3b8c37a7731

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8db771db716304cc616e50b072ec1da3863c1e99eaf6314638d1ef09d3dac392",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-07-16T08:13:47Z",
    "title_canon_sha256": "afcffccf4e7a5ac2a79c73b6887bd28ac6a7099da6f33c1a46a54752cbacd31d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.06885",
    "kind": "arxiv",
    "version": 1
  }
}