Pith Number

pith:7XS5BOLA

pith:2016:7XS5BOLAWV2A4TEYFHFXROQQPS

not attested not anchored not stored refs pending

Existence of multi-bump solutions to biharmonic operator with critical exponential growth in $\mathbb{R}^4$

Al\^annio B. N\'obrega, Denilson S. Pereira

arxiv:1603.05946 v1 · 2016-03-18 · 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{7XS5BOLAWV2A4TEYFHFXROQQPS}

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	2026-05-18T01:18:53.219420Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde5d0b960b5740e4c9829cb78ba107cb6462e637573d3006f1c897c38d2494f

Aliases

arxiv: 1603.05946 · arxiv_version: 1603.05946v1 · doi: 10.48550/arxiv.1603.05946 · pith_short_12: 7XS5BOLAWV2A · pith_short_16: 7XS5BOLAWV2A4TEY · pith_short_8: 7XS5BOLA

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/7XS5BOLAWV2A4TEYFHFXROQQPS \
  | 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: fde5d0b960b5740e4c9829cb78ba107cb6462e637573d3006f1c897c38d2494f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b35439c06cef70c3d0a312bad21fa6aa7e2d93061f286fefda14041d188533ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-03-18T18:02:16Z",
    "title_canon_sha256": "4d5bc4039b85e96764d791348256cca4af51018e18ffa32a804d55ecb8b34d05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.05946",
    "kind": "arxiv",
    "version": 1
  }
}