Pith Number

pith:MRTUJWU6

pith:2026:MRTUJWU6UCTFFGZCD3WTFIM7JY

not attested not anchored not stored refs pending

Higher Regularity of Homogeneous Gradient Compositions for $p$-Laplace-Type Equations

Le Xuan Truong, Quoc Hung Nguyen

arxiv:2608.11586 v1 · 2026-08-12 · 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{MRTUJWU6UCTFFGZCD3WTFIM7JY}

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	2026-08-13T00:22:14.678243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

646744da9ea0a6529b221eed32a19f4e3bdeb0f22cd64aff73677bc67506663a

Aliases

arxiv: 2608.11586 · arxiv_version: 2608.11586v1 · doi: 10.48550/arxiv.2608.11586 · pith_short_12: MRTUJWU6UCTF · pith_short_16: MRTUJWU6UCTFFGZC · pith_short_8: MRTUJWU6

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/MRTUJWU6UCTFFGZCD3WTFIM7JY \
  | 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: 646744da9ea0a6529b221eed32a19f4e3bdeb0f22cd64aff73677bc67506663a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "022bb9ef80e278c355953882c9070a264d1fc4bcb8431fb92b606d838dd4dd74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-12T02:53:45Z",
    "title_canon_sha256": "db28a03f50f6dd0f5142532196f234c16e35b8b9d50c630557f3f4b52f0db52d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.11586",
    "kind": "arxiv",
    "version": 1
  }
}