Pith Number

pith:MKVWXWCC

pith:2015:MKVWXWCCV66OVHIV5F7PHY6VF2

not attested not anchored not stored refs pending

Generic and non-generic behavior of solutions to the defocusing energy critical wave equation with potential in the radial case

Baoping Liu, Guixiang Xu, Hao Jia, Wilhelm Schlag

arxiv:1506.04763 v1 · 2015-06-15 · 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{MKVWXWCCV66OVHIV5F7PHY6VF2}

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	2026-05-18T01:48:05.942566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62ab6bd842afbcea9d15e97ef3e3d52eaa5e5519ae947e0f0a6c92e3da45492a

Aliases

arxiv: 1506.04763 · arxiv_version: 1506.04763v1 · doi: 10.48550/arxiv.1506.04763 · pith_short_12: MKVWXWCCV66O · pith_short_16: MKVWXWCCV66OVHIV · pith_short_8: MKVWXWCC

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/MKVWXWCCV66OVHIV5F7PHY6VF2 \
  | 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: 62ab6bd842afbcea9d15e97ef3e3d52eaa5e5519ae947e0f0a6c92e3da45492a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02f1c891ef6e2c7aa7a57b3d147e70abc9f832d52a3fae72c9b0bebc41bec590",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-06-15T20:09:17Z",
    "title_canon_sha256": "74677e4899a12ac4ac1a10f49fe4c61b61a8eae6b0237b2690664db13ff6be68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04763",
    "kind": "arxiv",
    "version": 1
  }
}