Pith Number

pith:B23YWRAG

pith:2026:B23YWRAGBUV2USJEY3MUHVEZP4

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A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification

Atish Mitra, Pramita Bagchi, Sushovan Majhi, \v{Z}iga Virk

PLACE builds classifiers for point clouds and graphs from persistent-homology signatures using only training labels and closed-form rules.

arxiv:2605.02836 v2 · 2026-05-04 · cs.LG · math.AT

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Claims

C1strongest claim

PLACE is a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based excess-risk rate, a closed-form descriptor-selection rule, and a per-prediction certificate -- are derived from training labels alone, with no learned weights or held-out calibration.

C2weakest assumption

The derivations rely on a non-interference condition when summing Mitra-Virk coordinate functions over the landmark grid and on the existence of a structural distortion constant λ(ν) that can be maximized in closed form to produce the embedding weights.

C3one line summary

PLACE delivers a closed-form persistent-homology classifier for point clouds and graphs with explicit margin bounds, descriptor selection, and training-time certificates derived solely from labels.

Receipt and verification

First computed	2026-05-26T02:05:09.931904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0eb78b44060d2baa4924c6d943d4997f2bf8b3fcea4b35402a04e04489e565d1

Aliases

arxiv: 2605.02836 · arxiv_version: 2605.02836v2 · doi: 10.48550/arxiv.2605.02836 · pith_short_12: B23YWRAGBUV2 · pith_short_16: B23YWRAGBUV2USJE · pith_short_8: B23YWRAG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/B23YWRAGBUV2USJEY3MUHVEZP4 \
  | 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: 0eb78b44060d2baa4924c6d943d4997f2bf8b3fcea4b35402a04e04489e565d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66a14cac0122559eba6849d3a70840ac2ca146bd7c89dbd1f9e6821cbf794730",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-04T17:15:01Z",
    "title_canon_sha256": "f8d629b4018d695dd4d904ab26f2e8f6df923f60de80c310d2ee45f483b7876d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02836",
    "kind": "arxiv",
    "version": 2
  }
}