Pith Number

pith:Q5A4ZG57

pith:2012:Q5A4ZG57TJRWSRN7XC4R4DDN6Z

not attested not anchored not stored refs pending

Alternating sign multibump solutions of nonlinear elliptic equations in expanding tubular domains

Filomena Pacella, Monica Clapp, Nils Ackermann

arxiv:1210.4229 v1 · 2012-10-16 · 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{Q5A4ZG57TJRWSRN7XC4R4DDN6Z}

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	2026-05-18T03:43:06.598606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8741cc9bbf9a636945bfb8b91e0c6df64c80751f5881649b727dc8d10f898db2

Aliases

arxiv: 1210.4229 · arxiv_version: 1210.4229v1 · doi: 10.48550/arxiv.1210.4229 · pith_short_12: Q5A4ZG57TJRW · pith_short_16: Q5A4ZG57TJRWSRN7 · pith_short_8: Q5A4ZG57

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/Q5A4ZG57TJRWSRN7XC4R4DDN6Z \
  | 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: 8741cc9bbf9a636945bfb8b91e0c6df64c80751f5881649b727dc8d10f898db2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3315f4ca4a6f940711540b17a6f2fab0aa3a93715d299e059ab1e71c55ef9ec8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-16T01:48:30Z",
    "title_canon_sha256": "4ac336bf5b0670aeed56d46e881b869e4c616c9338c94d3e7b4869a46c04a7e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4229",
    "kind": "arxiv",
    "version": 1
  }
}