Pith Number

pith:6HTMCJXZ

pith:2026:6HTMCJXZ5ADEIGEXJ3HETGNJFM

not attested not anchored not stored refs pending

Critical $p$-Laplace equations with monotone coefficients: Liouville classification and a Schoen-type Harnack inequality

Yi Ru-Ya Zhang

arxiv:2608.09113 v1 · 2026-08-10 · math.AP · 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{6HTMCJXZ5ADEIGEXJ3HETGNJFM}

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	2026-08-11T02:21:49.578753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1e6c126f9e8064418974ece4999a92b27c26673c55c078b2a913ba368ecc4b1

Aliases

arxiv: 2608.09113 · arxiv_version: 2608.09113v1 · doi: 10.48550/arxiv.2608.09113 · pith_short_12: 6HTMCJXZ5ADE · pith_short_16: 6HTMCJXZ5ADEIGEX · pith_short_8: 6HTMCJXZ

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/6HTMCJXZ5ADEIGEXJ3HETGNJFM \
  | 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: f1e6c126f9e8064418974ece4999a92b27c26673c55c078b2a913ba368ecc4b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56f7838f179bd785b4fe379a3c64a7e8debea43709ccb02826ff87f6f263b0c8",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-10T04:38:55Z",
    "title_canon_sha256": "0a2d1b77e31caaac7de3913a15cf817e963f75df0d62bb0ea347ec166644defa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09113",
    "kind": "arxiv",
    "version": 1
  }
}