Pith Number

pith:3VN3J7CM

pith:2015:3VN3J7CMWBBNUEIMH2Z775WIKE

not attested not anchored not stored refs pending

Concentration-compactness and universal profiles for the non-radial energy critical wave equation

Carlos Kenig, Frank Merle, Thomas Duyckaerts

arxiv:1510.01750 v1 · 2015-10-06 · 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{3VN3J7CMWBBNUEIMH2Z775WIKE}

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	2026-05-18T01:30:50.471899Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd5bb4fc4cb042da110c3eb3fff6c8511d2900dbf104e78b3340ab6fb57ec385

Aliases

arxiv: 1510.01750 · arxiv_version: 1510.01750v1 · doi: 10.48550/arxiv.1510.01750 · pith_short_12: 3VN3J7CMWBBN · pith_short_16: 3VN3J7CMWBBNUEIM · pith_short_8: 3VN3J7CM

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/3VN3J7CMWBBNUEIMH2Z775WIKE \
  | 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: dd5bb4fc4cb042da110c3eb3fff6c8511d2900dbf104e78b3340ab6fb57ec385

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e84acb2c50c2e2c0b3d609571bd5dbc1af4fe837581ae449689de9463e851e01",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-06T20:18:43Z",
    "title_canon_sha256": "f414fc5061a5819cd1a149d98c8cc38fbdb24a923b3c82a0f0072dbc8eee6515"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01750",
    "kind": "arxiv",
    "version": 1
  }
}