Pith Number

pith:4HUYRNUL

pith:2016:4HUYRNULJ2426NI6ED4EFMR5WZ

not attested not anchored not stored refs pending

Vanishing theorems of the basic harmonic forms on a complete foliated Riemannian manifold

Huili Liu, Seoung Dal Jung

arxiv:1606.08934 v1 · 2016-06-29 · 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{4HUYRNULJ2426NI6ED4EFMR5WZ}

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	2026-05-18T01:11:42.041405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1e988b68b4eb9af351e20f842b23db645658eb63acf47e1aaa151f108de59f9

Aliases

arxiv: 1606.08934 · arxiv_version: 1606.08934v1 · doi: 10.48550/arxiv.1606.08934 · pith_short_12: 4HUYRNULJ242 · pith_short_16: 4HUYRNULJ2426NI6 · pith_short_8: 4HUYRNUL

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/4HUYRNULJ2426NI6ED4EFMR5WZ \
  | 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: e1e988b68b4eb9af351e20f842b23db645658eb63acf47e1aaa151f108de59f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe2918cecca03d6381d5c4962e9c1678b9280c6e76fccf599ad3699e86460d71",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-06-29T02:21:12Z",
    "title_canon_sha256": "5aa42d9bcfefa6526d45629f1fb8b26c2319b2d3c4e50f86a5e4345ded717cce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08934",
    "kind": "arxiv",
    "version": 1
  }
}