Pith Number

pith:6HA45TRX

pith:2015:6HA45TRXPNBKRMKETMGBBRVUFT

not attested not anchored not stored refs pending

Existence of solutions for a higher order Kirchhoff type problem with exponential critical growth

Liang Zhao, Ning Zhang

arxiv:1507.05280 v1 · 2015-07-19 · 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{6HA45TRXPNBKRMKETMGBBRVUFT}

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	2026-05-18T01:36:37.329281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1c1cece377b42a8b1449b0c10c6b42ccbc5f3f08ce883506c6ea078c788f5d9

Aliases

arxiv: 1507.05280 · arxiv_version: 1507.05280v1 · doi: 10.48550/arxiv.1507.05280 · pith_short_12: 6HA45TRXPNBK · pith_short_16: 6HA45TRXPNBKRMKE · pith_short_8: 6HA45TRX

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/6HA45TRXPNBKRMKETMGBBRVUFT \
  | 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: f1c1cece377b42a8b1449b0c10c6b42ccbc5f3f08ce883506c6ea078c788f5d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dc9c64d85bfb04a4e8877542d1d8c76416748d84b8add862900b61dd89b0aa5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-19T12:33:44Z",
    "title_canon_sha256": "a18f5aa6611bd85cc7c4fa47daa34c3f3c29064ecd512f6ba69aa1e2c2962c8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05280",
    "kind": "arxiv",
    "version": 1
  }
}