Pith Number

pith:VQZRBLW5

pith:2019:VQZRBLW57ZALCR2VHHE3PFN4EV

not attested not anchored not stored refs pending

Plurisuperharmonicity of reciprocal energy function on Teichmuller space and Weil-Petersson metrics

Genkai Zhang, Inkang Kim, Xueyuan Wan

arxiv:1901.05048 v1 · 2019-01-15 · 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{VQZRBLW57ZALCR2VHHE3PFN4EV}

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	2026-05-17T23:56:12.120017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac3310aeddfe40b1475539c9b795bc25708a5c8a583953d1d0e972b39b2b905f

Aliases

arxiv: 1901.05048 · arxiv_version: 1901.05048v1 · doi: 10.48550/arxiv.1901.05048 · pith_short_12: VQZRBLW57ZAL · pith_short_16: VQZRBLW57ZALCR2V · pith_short_8: VQZRBLW5

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/VQZRBLW57ZALCR2VHHE3PFN4EV \
  | 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: ac3310aeddfe40b1475539c9b795bc25708a5c8a583953d1d0e972b39b2b905f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6dbd0ce286a80dfadaa55c7d585493cbf60537e752a70a2266c86e734d8f194",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-01-15T21:26:02Z",
    "title_canon_sha256": "6028b7894b4a9122bc52531d9c1c1f729b97f14e989995022a6de3555c394550"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.05048",
    "kind": "arxiv",
    "version": 1
  }
}