Pith Number

pith:W7ZQHDH5

pith:2023:W7ZQHDH5NVYHZPUOPRL4YNXDA2

not attested not anchored not stored refs pending

$L^{2}$-Hodge theory on Complete Almost K\"{a}hler Manifolds and the Hopf Conjecture

Pan Zhang, Qiang Tan, Teng Huang

arxiv:2302.14032 v4 · 2023-01-28 · 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{W7ZQHDH5NVYHZPUOPRL4YNXDA2}

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	2026-05-29T00:04:12.139900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7f3038cfd6d707cbe8e7c57cc36e306b18f64fb2faa25d7e2cb6c1c513b06ef

Aliases

arxiv: 2302.14032 · arxiv_version: 2302.14032v4 · doi: 10.48550/arxiv.2302.14032 · pith_short_12: W7ZQHDH5NVYH · pith_short_16: W7ZQHDH5NVYHZPUO · pith_short_8: W7ZQHDH5

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/W7ZQHDH5NVYHZPUOPRL4YNXDA2 \
  | 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: b7f3038cfd6d707cbe8e7c57cc36e306b18f64fb2faa25d7e2cb6c1c513b06ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7f3b1e93ea1f54019481b6cbf121d383ebbb0e924fbc5e18aa09bbd1dbf530c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2023-01-28T06:52:02Z",
    "title_canon_sha256": "839d070165868ab963d15f85773edfe69ba9672528f0915f856949a008fa8362"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2302.14032",
    "kind": "arxiv",
    "version": 4
  }
}