Pith Number

pith:Z5LETOOK

pith:2019:Z5LETOOKU3VZIZE3WYBWQLTHQT

not attested not anchored not stored refs pending

Hyperbolicity of coarse moduli spaces and isotriviality for certain families

Ya Deng

arxiv:1908.08372 v1 · 2019-08-22 · math.AG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z5LETOOKU3VZIZE3WYBWQLTHQT}

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	2026-07-04T23:59:12.208355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf5649b9caa6eb94649bb603682e6784d18688f27433d6415954d0361f0be9c1

Aliases

arxiv: 1908.08372 · arxiv_version: 1908.08372v1 · doi: 10.48550/arxiv.1908.08372 · pith_short_12: Z5LETOOKU3VZ · pith_short_16: Z5LETOOKU3VZIZE3 · pith_short_8: Z5LETOOK

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/Z5LETOOKU3VZIZE3WYBWQLTHQT \
  | 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: cf5649b9caa6eb94649bb603682e6784d18688f27433d6415954d0361f0be9c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e8a96129e1d397648c452654a74e4c6261e75f8a7197e7f133c92ae8be74340",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-08-22T13:41:20Z",
    "title_canon_sha256": "afa34fc105f68b4e049a8c2437c851c6fbce0144692063eb0a7b893fe116b3c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08372",
    "kind": "arxiv",
    "version": 1
  }
}