Pith Number

pith:MB7SWAWF

pith:2012:MB7SWAWFGNQS2BKI7QWFY5WK5P

not attested not anchored not stored refs pending

Classification of radial solutions of the focusing, energy-critical wave equation

Carlos Kenig, Frank Merle, Thomas Duyckaerts

arxiv:1204.0031 v1 · 2012-03-30 · 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{MB7SWAWFGNQS2BKI7QWFY5WK5P}

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	2026-05-18T03:58:50.561694Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

607f2b02c533612d0548fc2c5c76caebccc80bfccc0cb7fb7cbb6996a88edf3b

Aliases

arxiv: 1204.0031 · arxiv_version: 1204.0031v1 · doi: 10.48550/arxiv.1204.0031 · pith_short_12: MB7SWAWFGNQS · pith_short_16: MB7SWAWFGNQS2BKI · pith_short_8: MB7SWAWF

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/MB7SWAWFGNQS2BKI7QWFY5WK5P \
  | 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: 607f2b02c533612d0548fc2c5c76caebccc80bfccc0cb7fb7cbb6996a88edf3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac96b2fc31a878c1e09bd82e87bef4f5fc61cfabf0dcf06fc66fd27fb58f5c0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-03-30T21:33:03Z",
    "title_canon_sha256": "4533b7555eb002400681e9cd069e5b71f0e162ad2049461bd6a1795baad4b9ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0031",
    "kind": "arxiv",
    "version": 1
  }
}