Pith Number

pith:UN6APCUH

pith:2019:UN6APCUHEZVKHBHCY4HO5GN3K5

not attested not anchored not stored refs pending

Liouville theorems on the upper half space

Lei Wang, Meijun Zhu

arxiv:1902.05187 v1 · 2019-02-14 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UN6APCUHEZVKHBHCY4HO5GN3K5}

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	2026-05-17T23:54:01.657986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a37c078a87266aa384e2c70eee99bb575b21baa05f49c9366018ebd42cccbb1b

Aliases

arxiv: 1902.05187 · arxiv_version: 1902.05187v1 · doi: 10.48550/arxiv.1902.05187 · pith_short_12: UN6APCUHEZVK · pith_short_16: UN6APCUHEZVKHBHC · pith_short_8: UN6APCUH

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/UN6APCUHEZVKHBHCY4HO5GN3K5 \
  | 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: a37c078a87266aa384e2c70eee99bb575b21baa05f49c9366018ebd42cccbb1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00ca999080afaf3381a2cc53ea45d77f2233de9e8205dd764a2d169792aad299",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-02-14T01:59:53Z",
    "title_canon_sha256": "f180abd34a8fd94f582fa9c70b82014c329828104a628e1ecdfbbcd6e9642c7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.05187",
    "kind": "arxiv",
    "version": 1
  }
}