Pith Number

pith:ZDMR3EWR

pith:2011:ZDMR3EWRPBYJBOW7UGI3MYNZS4

not attested not anchored not stored refs pending

The blow-up and lifespan of solutions to systems of semilinear wave equation with critical exponents in high dimensions

Hiroyuki Takamura, Kyouhei Wakasa, Yuki Kurokawa

arxiv:1106.6221 v1 · 2011-06-30 · 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{ZDMR3EWRPBYJBOW7UGI3MYNZS4}

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	2026-05-18T02:53:54.400646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8d91d92d1787090badfa191b661b99706476bb3f997701d0b6573f2b9e6d799

Aliases

arxiv: 1106.6221 · arxiv_version: 1106.6221v1 · doi: 10.48550/arxiv.1106.6221 · pith_short_12: ZDMR3EWRPBYJ · pith_short_16: ZDMR3EWRPBYJBOW7 · pith_short_8: ZDMR3EWR

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/ZDMR3EWRPBYJBOW7UGI3MYNZS4 \
  | 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: c8d91d92d1787090badfa191b661b99706476bb3f997701d0b6573f2b9e6d799

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c40ca352034af4c2cf673fa70b7c7f70e03827003dad8c2104643cbe968cf36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-06-30T13:33:37Z",
    "title_canon_sha256": "0dd7825eb9bfb29782a81e9b93e025b5e2faa8d427601182e1358f0c6677f69f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.6221",
    "kind": "arxiv",
    "version": 1
  }
}