Pith Number

pith:MPUYS4X5

pith:2020:MPUYS4X5VOLC7HVR6JMIM4M5GJ

not attested not anchored not stored refs pending

On a $p(\cdot)$-biharmonic problem of Kirchhoff type involving critical growth

Ky Ho, Nguyen Thanh Chung

arxiv:2006.02410 v1 · 2020-06-03 · 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{MPUYS4X5VOLC7HVR6JMIM4M5GJ}

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	2026-07-05T01:07:46.492969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63e98972fdab962f9eb1f25886719d325d3d78e3a4eff795c5b048fd124cc96b

Aliases

arxiv: 2006.02410 · arxiv_version: 2006.02410v1 · doi: 10.48550/arxiv.2006.02410 · pith_short_12: MPUYS4X5VOLC · pith_short_16: MPUYS4X5VOLC7HVR · pith_short_8: MPUYS4X5

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/MPUYS4X5VOLC7HVR6JMIM4M5GJ \
  | 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: 63e98972fdab962f9eb1f25886719d325d3d78e3a4eff795c5b048fd124cc96b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8064ecc6f0b68b95d47051e8b55958a9146070722b84fc9e1b721f0362832e65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-06-03T17:36:47Z",
    "title_canon_sha256": "02d2320738adebfdee03eb49287f5e07a22ae98ebddc767c32b2cb61c3c7c48f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.02410",
    "kind": "arxiv",
    "version": 1
  }
}