Pith Number

pith:4EHPBX6J

pith:2021:4EHPBX6JR5YZAWOOMMSEHGJG2L

not attested not anchored not stored refs pending

Existence and multiplicity of solutions for $m(x)-$polyharmonic elliptic Kirchhoff type equations without Ambrosetti-Rabinowitz conditions

Abdellaziz Harrabi, Mohamed Karim Hamdani

arxiv:2106.07705 v1 · 2021-06-14 · 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{4EHPBX6JR5YZAWOOMMSEHGJG2L}

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	2026-07-05T02:49:32.958433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e10ef0dfc98f719059ce6324439926d2fc6948a69f6d28b8a901ab7aeff49f82

Aliases

arxiv: 2106.07705 · arxiv_version: 2106.07705v1 · doi: 10.48550/arxiv.2106.07705 · pith_short_12: 4EHPBX6JR5YZ · pith_short_16: 4EHPBX6JR5YZAWOO · pith_short_8: 4EHPBX6J

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/4EHPBX6JR5YZAWOOMMSEHGJG2L \
  | 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: e10ef0dfc98f719059ce6324439926d2fc6948a69f6d28b8a901ab7aeff49f82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a491d8110c3888770cbf5ad5e45a68701865cf31e4f74ec850b704de11e3b4f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-06-14T18:51:47Z",
    "title_canon_sha256": "f6d3d93693ab2e347707cea5f8ad08eed7aa3b5d623977fe547010d1bdc93ff0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.07705",
    "kind": "arxiv",
    "version": 1
  }
}