Pith Number

pith:CNBUSFDR

pith:2019:CNBUSFDRXIDF2ZNDRI4TO2U5QN

not attested not anchored not stored refs pending

Bubbling of the prescribed $Q$-curvature equation on $4$-manifolds in the null case

Hong Zhang, Qu\^oc Anh Ng\^o

arxiv:1903.12054 v1 · 2019-03-28 · math.AP · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CNBUSFDRXIDF2ZNDRI4TO2U5QN}

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	2026-05-17T23:49:58.200664Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1343491471ba065d65a38a39376a9d83659896a514f8d6a9a39bd920a0ea64ba

Aliases

arxiv: 1903.12054 · arxiv_version: 1903.12054v1 · doi: 10.48550/arxiv.1903.12054 · pith_short_12: CNBUSFDRXIDF · pith_short_16: CNBUSFDRXIDF2ZND · pith_short_8: CNBUSFDR

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/CNBUSFDRXIDF2ZNDRI4TO2U5QN \
  | 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: 1343491471ba065d65a38a39376a9d83659896a514f8d6a9a39bd920a0ea64ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0108e772acf23eaba1cb15f6c0c101b72407ddc541c82cac77e1c9a6e763b45d",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-03-28T15:37:13Z",
    "title_canon_sha256": "3ffce54b5e039cf9fa0e2406cd3eca8cee391519d5470ad09b0d06e2be12d980"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.12054",
    "kind": "arxiv",
    "version": 1
  }
}