Pith Number

pith:GPFFH4GW

pith:2013:GPFFH4GW3BOAOSJOQU7Q2XG43Z

not attested not anchored not stored refs pending

Yet another proof of the Morse index theorem

Alessandro Portaluri, Nils Waterstraat

arxiv:1312.5291 v2 · 2013-12-18 · math.DG · 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{GPFFH4GW3BOAOSJOQU7Q2XG43Z}

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	2026-05-18T01:28:15.041843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33ca53f0d6d85c07492e853f0d5cdcde5a71369bcbb211a7933907d133cf30c0

Aliases

arxiv: 1312.5291 · arxiv_version: 1312.5291v2 · doi: 10.48550/arxiv.1312.5291 · pith_short_12: GPFFH4GW3BOA · pith_short_16: GPFFH4GW3BOAOSJO · pith_short_8: GPFFH4GW

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/GPFFH4GW3BOAOSJOQU7Q2XG43Z \
  | 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: 33ca53f0d6d85c07492e853f0d5cdcde5a71369bcbb211a7933907d133cf30c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba297c7a971f3145fe66abbd5637be4afd69aa72250a103493b45542a997d9cb",
    "cross_cats_sorted": [
      "math.FA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-12-18T19:55:06Z",
    "title_canon_sha256": "75185140db6e32ed5e23798f9104445a2b505e99cfd8f249c57c29ec035c3a33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5291",
    "kind": "arxiv",
    "version": 2
  }
}