Pith Number

pith:JWKRM7XY

pith:2015:JWKRM7XYBGFHHCPEH3RQYRL3WZ

not attested not anchored not stored refs pending

Morse index and multiplicity of min-max minimal hypersurfaces

Andr\'e Neves, Fernando C. Marques

arxiv:1512.06460 v2 · 2015-12-20 · math.DG · 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{JWKRM7XYBGFHHCPEH3RQYRL3WZ}

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	2026-05-18T00:54:58.152087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d95167ef8098a7389e43ee30c457bb661d344dd1659cf7cb8443cc617d046fd

Aliases

arxiv: 1512.06460 · arxiv_version: 1512.06460v2 · doi: 10.48550/arxiv.1512.06460 · pith_short_12: JWKRM7XYBGFH · pith_short_16: JWKRM7XYBGFHHCPE · pith_short_8: JWKRM7XY

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/JWKRM7XYBGFHHCPEH3RQYRL3WZ \
  | 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: 4d95167ef8098a7389e43ee30c457bb661d344dd1659cf7cb8443cc617d046fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29334f3e248d70b0bb6f16f671045fd485541b2cfeeafac5b8e61251c4f15e7a",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-20T23:59:27Z",
    "title_canon_sha256": "9752e41276719464873181da8128fb87b0d9b611717778841b41156750e2b405"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06460",
    "kind": "arxiv",
    "version": 2
  }
}