Pith Number

pith:I5DG64T3

pith:2016:I5DG64T3PC5SNGO3Z6B762367P

not attested not anchored not stored refs pending

A Liouville Theorem for a Class of Fractional Systems in $\mathbb{R}^n_+$

Jianming He, Lizhi Zhang, Mei Yu

arxiv:1611.09133 v2 · 2016-11-28 · 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{I5DG64T3PC5SNGO3Z6B762367P}

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	2026-05-18T00:52:13.675740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47466f727b78bb2699dbcf83ff6b7efbf5a58cd3d595a133e3f490d1d2513786

Aliases

arxiv: 1611.09133 · arxiv_version: 1611.09133v2 · doi: 10.48550/arxiv.1611.09133 · pith_short_12: I5DG64T3PC5S · pith_short_16: I5DG64T3PC5SNGO3 · pith_short_8: I5DG64T3

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/I5DG64T3PC5SNGO3Z6B762367P \
  | 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: 47466f727b78bb2699dbcf83ff6b7efbf5a58cd3d595a133e3f490d1d2513786

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ae34ee84a85114ab950db587e7f8e2ea19ebfaf94cbf28c0933273c7e2c2f3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-11-28T14:21:33Z",
    "title_canon_sha256": "5120d1b9badad7f37a2c2c9a29044e89c7ac789750fe39d9630f8bdbffb05812"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09133",
    "kind": "arxiv",
    "version": 2
  }
}