Pith Number

pith:WXPPNPVI

pith:2011:WXPPNPVIOWT76PYSASKH6C5OEB

not attested not anchored not stored refs pending

The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions

Hiroyuki Takamura, Kyouhei Wakasa

arxiv:1103.2584 v1 · 2011-03-14 · 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{WXPPNPVIOWT76PYSASKH6C5OEB}

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	2026-05-18T04:19:04.258661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5def6bea875a7ff3f1204947f0bae205085e5ab9a27c3fc0b3b2e0d8c5af4c3

Aliases

arxiv: 1103.2584 · arxiv_version: 1103.2584v1 · doi: 10.48550/arxiv.1103.2584 · pith_short_12: WXPPNPVIOWT7 · pith_short_16: WXPPNPVIOWT76PYS · pith_short_8: WXPPNPVI

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/WXPPNPVIOWT76PYSASKH6C5OEB \
  | 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: b5def6bea875a7ff3f1204947f0bae205085e5ab9a27c3fc0b3b2e0d8c5af4c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d22cd1bbee6943510c7efe019c77d14bff2b8486ef63a014506c9b3e3817217",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-03-14T05:21:31Z",
    "title_canon_sha256": "65eca26e845e6de10188af7d8e29fcc9a2512bebbe681c165d1db160e6bbaf58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2584",
    "kind": "arxiv",
    "version": 1
  }
}