Pith Number

pith:2QXWO4UX

pith:2015:2QXWO4UXFJECS7BH4FDWJ37GLT

not attested not anchored not stored refs pending

Bounds on the speed of type II blow-up for the energy critical wave equation in the radial case

Jacek Jendrej

arxiv:1509.03331 v1 · 2015-09-10 · 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{2QXWO4UXFJECS7BH4FDWJ37GLT}

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	2026-05-18T01:09:36.446958Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d42f6772972a48297c27e14764efe65cd6fcb151f58d673ec4111bc07326c2bd

Aliases

arxiv: 1509.03331 · arxiv_version: 1509.03331v1 · doi: 10.48550/arxiv.1509.03331 · pith_short_12: 2QXWO4UXFJEC · pith_short_16: 2QXWO4UXFJECS7BH · pith_short_8: 2QXWO4UX

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/2QXWO4UXFJECS7BH4FDWJ37GLT \
  | 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: d42f6772972a48297c27e14764efe65cd6fcb151f58d673ec4111bc07326c2bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91eb41ef66d59583b216ede287891d1cf3c25a496ed9eba7e19885aef86062e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-10T20:42:21Z",
    "title_canon_sha256": "c92ef0d03f652f97f714d2e4ce5ba47fa96b6ba0d466c38d0dc21d8292a8f6ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03331",
    "kind": "arxiv",
    "version": 1
  }
}