Pith Number

pith:3PQETJJL

pith:2026:3PQETJJLCXFKNZIDTD2N4J6GSB

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The Topological Dual of a Dataset: A Logic-to-Topology Encoding for AlphaGeometry-Style Data

Anthony Bordg

A logic-to-topology encoder transforms datasets into topological duals to reveal structural invariants preserved in neural latent spaces under input changes.

arxiv:2604.18050 v2 · 2026-04-20 · cs.AI · cs.LO

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\usepackage{pith}
\pithnumber{3PQETJJLCXFKNZIDTD2N4J6GSB}

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4 Citations open

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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.

Claims

C1strongest claim

By leveraging the Logic of Observation, we utilize the duality between provability in observable theories and topologies to propose a logic-to-topology encoder for the input space. We introduce the concept of the 'topological dual of a dataset', a transformation that bridges formal logic, topology, and neural processing.

C2weakest assumption

That the duality between provability in observable theories and topologies can be turned into a practical encoder that actually reveals structural invariants in a neural model's latent space under input transformations, rather than remaining a high-level analogy.

C3one line summary

The topological dual of a dataset is introduced as a transformation that encodes logical structures into topological ones to expose invariants in neural latent spaces for AlphaGeometry-style reasoning.

Receipt and verification

First computed	2026-06-09T01:05:17.524338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbe049a52b15caa6e50398f4de27c69055f1c92ae26027d545f081d80694f1f1

Aliases

arxiv: 2604.18050 · arxiv_version: 2604.18050v2 · doi: 10.48550/arxiv.2604.18050 · pith_short_12: 3PQETJJLCXFK · pith_short_16: 3PQETJJLCXFKNZID · pith_short_8: 3PQETJJL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3PQETJJLCXFKNZIDTD2N4J6GSB \
  | 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: dbe049a52b15caa6e50398f4de27c69055f1c92ae26027d545f081d80694f1f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b43521376b806c4e7e9c9ff26737eac36cc1e58014c9b374f2ed6d07ab3cafda",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-04-20T10:18:08Z",
    "title_canon_sha256": "ad97023ed8feb34b6812f9f478821d167a12cdf13ef74d426f2c99261989ec76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18050",
    "kind": "arxiv",
    "version": 2
  }
}