Pith Number

pith:GDDVQP77

pith:2020:GDDVQP77JWFNUSXQRI2JDR2VFK

not attested not anchored not stored refs pending

Liouville type theorems for stable solutions of elliptic system involving the Grushin operator

Foued Mtiri

arxiv:2012.11023 v1 · 2020-12-20 · 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{GDDVQP77JWFNUSXQRI2JDR2VFK}

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	2026-07-05T02:00:57.811161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30c7583fff4d8ada4af08a3491c7552ab563f9a0c73d605b5687fadd943b4ef0

Aliases

arxiv: 2012.11023 · arxiv_version: 2012.11023v1 · doi: 10.48550/arxiv.2012.11023 · pith_short_12: GDDVQP77JWFN · pith_short_16: GDDVQP77JWFNUSXQ · pith_short_8: GDDVQP77

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/GDDVQP77JWFNUSXQRI2JDR2VFK \
  | 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: 30c7583fff4d8ada4af08a3491c7552ab563f9a0c73d605b5687fadd943b4ef0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dee98b93e00fb88080f7bd0b83d37cc7f40774716c672546e5b7bee93f94287",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-12-20T21:05:31Z",
    "title_canon_sha256": "8eacbf7d8f398cf2653a0dacd1886b12408736ca168b54936d777683abd1aaa3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.11023",
    "kind": "arxiv",
    "version": 1
  }
}