Pith Number

pith:WRN3CNAK

pith:2014:WRN3CNAKYAYOLTN4JZHVRPUIWG

not attested not anchored not stored refs pending

A Morse-Smale index theorem for indefinite elliptic systems and bifurcation

Alessandro Portaluri, Nils Waterstraat

arxiv:1408.1419 v2 · 2014-08-06 · math.AP · math.DG · math.DS · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WRN3CNAKYAYOLTN4JZHVRPUIWG}

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	2026-05-18T01:28:14.852612Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b45bb1340ac030e5cdbc4e4f58be88b1912083214b8f2a882a84b16343827cec

Aliases

arxiv: 1408.1419 · arxiv_version: 1408.1419v2 · doi: 10.48550/arxiv.1408.1419 · pith_short_12: WRN3CNAKYAYO · pith_short_16: WRN3CNAKYAYOLTN4 · pith_short_8: WRN3CNAK

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/WRN3CNAKYAYOLTN4JZHVRPUIWG \
  | 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: b45bb1340ac030e5cdbc4e4f58be88b1912083214b8f2a882a84b16343827cec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12c63a2e694a397c2ebee15891f228d6881731003ba5b186efbde35724f7762d",
    "cross_cats_sorted": [
      "math.DG",
      "math.DS",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-08-06T20:51:55Z",
    "title_canon_sha256": "61c8831ca1ba2741b78f6ad752992db62274fb9e9c7663bdcecc2983fcdc24b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.1419",
    "kind": "arxiv",
    "version": 2
  }
}