Pith Number

pith:IJZGBBWB

pith:2021:IJZGBBWBK7GRZ76OZW2GLC3QWV

not attested not anchored not stored refs pending

Existence and nonexistence results of polyharmonic boundary value problems with supercritical growth

Abdellaziz Harrabi, Foued Mtiri, Wafa Mtaouaa

arxiv:2106.03920 v2 · 2021-06-07 · 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{IJZGBBWBK7GRZ76OZW2GLC3QWV}

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	2026-07-05T03:14:35.233286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42726086c157cd1cffcecdb4658b70b5511e2b78a0a5d7e75c70cd5c31d72ac3

Aliases

arxiv: 2106.03920 · arxiv_version: 2106.03920v2 · doi: 10.48550/arxiv.2106.03920 · pith_short_12: IJZGBBWBK7GR · pith_short_16: IJZGBBWBK7GRZ76O · pith_short_8: IJZGBBWB

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/IJZGBBWBK7GRZ76OZW2GLC3QWV \
  | 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: 42726086c157cd1cffcecdb4658b70b5511e2b78a0a5d7e75c70cd5c31d72ac3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62a8ffd9430a00abaed3c2ba8c86e5e0eb60b2618d989caf4f91b582019ae3ea",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-06-07T19:04:40Z",
    "title_canon_sha256": "eeebf099a91816f8c52cc03f8f2cd9cfbd2bbdd84acf41c64ec337aa5a791c96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.03920",
    "kind": "arxiv",
    "version": 2
  }
}