Pith Number

pith:PTUNH6L6

pith:2010:PTUNH6L66NHWUTSLVDLH5B6CT3

not attested not anchored not stored refs pending

Semilinear equations, the $\gamma_k$ function, and generalized Gauduchon metrics

Damin Wu, Jixiang Fu, Zhizhang Wang

arxiv:1010.2013 v2 · 2010-10-11 · 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{PTUNH6L66NHWUTSLVDLH5B6CT3}

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	2026-05-18T04:26:55.544835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ce8d3f97ef34f6a4e4ba8d67e87c29ecaea2a56df37778451f4618a8cc8b136

Aliases

arxiv: 1010.2013 · arxiv_version: 1010.2013v2 · doi: 10.48550/arxiv.1010.2013 · pith_short_12: PTUNH6L66NHW · pith_short_16: PTUNH6L66NHWUTSL · pith_short_8: PTUNH6L6

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/PTUNH6L66NHWUTSLVDLH5B6CT3 \
  | 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: 7ce8d3f97ef34f6a4e4ba8d67e87c29ecaea2a56df37778451f4618a8cc8b136

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e96f4be8941cfcf17c5fbe107e1cae8f349d1b560ccf5ff77b4691476b54725f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-10-11T06:43:27Z",
    "title_canon_sha256": "cf3cdb07b1db1275804c1342eb48b4938f9e4aa5ae8fa94c0ee1139508d6a10d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2013",
    "kind": "arxiv",
    "version": 2
  }
}