Pith Number

pith:4KF5RVBP

pith:2010:4KF5RVBPBPBZYHLDHT4MI27ORB

not attested not anchored not stored refs pending

Smooth type II blow up solutions to the four dimensional energy critical wave equation

Matthieu Hillairet, Pierre Rapha\"el

arxiv:1010.1768 v1 · 2010-10-08 · 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{4KF5RVBPBPBZYHLDHT4MI27ORB}

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	2026-05-18T04:39:39.701742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e28bd8d42f0bc39c1d633cf8c46bee8867bca1bd3eafa95e65957c7ddb0f64b8

Aliases

arxiv: 1010.1768 · arxiv_version: 1010.1768v1 · doi: 10.48550/arxiv.1010.1768 · pith_short_12: 4KF5RVBPBPBZ · pith_short_16: 4KF5RVBPBPBZYHLD · pith_short_8: 4KF5RVBP

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/4KF5RVBPBPBZYHLDHT4MI27ORB \
  | 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: e28bd8d42f0bc39c1d633cf8c46bee8867bca1bd3eafa95e65957c7ddb0f64b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91baf7f45ce880ac39a2732670af15eb59d0251ca5a0ca7de14aeb6e4abdc1d3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-10-08T19:22:26Z",
    "title_canon_sha256": "71996e3d40544790eb2652e6d4d346751d3dff2dade308e03d567d4ab49a52c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1768",
    "kind": "arxiv",
    "version": 1
  }
}