Pith Number

pith:A2QPZY3T

pith:2013:A2QPZY3T3JHOC6MRNFLZUQR3ES

not attested not anchored not stored refs pending

On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem

Alessandro Portaluri, Nils Waterstraat

arxiv:1301.1458 v3 · 2013-01-08 · math.AP · math.FA · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A2QPZY3T3JHOC6MRNFLZUQR3ES}

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	2026-05-18T03:11:24.032236Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06a0fce373da4ee1799169579a423b24b14b3a4477a2e47157d398bf9ff75a36

Aliases

arxiv: 1301.1458 · arxiv_version: 1301.1458v3 · doi: 10.48550/arxiv.1301.1458 · pith_short_12: A2QPZY3T3JHO · pith_short_16: A2QPZY3T3JHOC6MR · pith_short_8: A2QPZY3T

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/A2QPZY3T3JHOC6MRNFLZUQR3ES \
  | 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: 06a0fce373da4ee1799169579a423b24b14b3a4477a2e47157d398bf9ff75a36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f03af55c81fe095202d8b913bfad81a26b72499ca4379a1735e8f1c2991f15c4",
    "cross_cats_sorted": [
      "math.FA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-01-08T09:39:41Z",
    "title_canon_sha256": "2be85a73898be175c718e15211aabe82fdc60e3e5365eabda6d648a173b2d0bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1458",
    "kind": "arxiv",
    "version": 3
  }
}