Pith Number

pith:ZG7DRUBG

pith:2015:ZG7DRUBGIXIZAB6GCW33R2FONG

not attested not anchored not stored refs pending

Harnack inequality for degenerate and singular operators of $p$-Laplacian type on Riemannian manifolds

Soojung Kim

arxiv:1503.09032 v1 · 2015-03-31 · 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{ZG7DRUBGIXIZAB6GCW33R2FONG}

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	2026-05-18T02:19:51.580345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9be38d02645d19007c615b7b8e8ae6997186b13b98c4ad3042cd0db4a57b4f0

Aliases

arxiv: 1503.09032 · arxiv_version: 1503.09032v1 · doi: 10.48550/arxiv.1503.09032 · pith_short_12: ZG7DRUBGIXIZ · pith_short_16: ZG7DRUBGIXIZAB6G · pith_short_8: ZG7DRUBG

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/ZG7DRUBGIXIZAB6GCW33R2FONG \
  | 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: c9be38d02645d19007c615b7b8e8ae6997186b13b98c4ad3042cd0db4a57b4f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8165f0b094daeb69ba72b1b887d48a4382149ae9ac5fd821f2835068774656c4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-31T13:05:03Z",
    "title_canon_sha256": "2768ccd6b67d8bb8831725f4739dae2b76ebfa7807408b2931ef5355d7cdbdb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.09032",
    "kind": "arxiv",
    "version": 1
  }
}