Pith Number

pith:ZXMK4WUX

pith:2026:ZXMK4WUX3R6W3ACK6XSTUHCC33

not attested not anchored not stored refs pending

TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection

Ali Zia, Farid Hazratian, Hien Duy Nguyen

Source embeddings encode global, local, and topological signals that identify which checkpoints will remain accurate under distribution shift.

arxiv:2605.08870 v2 · 2026-05-09 · cs.LG · math.AT · math.DG

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\usepackage{pith}
\pithnumber{ZXMK4WUX3R6W3ACK6XSTUHCC33}

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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.

Claims

C1strongest claim

source representations contain measurable global--local--topological evidence of robustness, supporting practical checkpoint selection before deployment under distribution shift.

C2weakest assumption

That the self-supervised objective, which enforces invariance under approximately geometry-preserving embedding views, selects for actual OOD robustness rather than some other incidental property of the source embeddings.

C3one line summary

TopoGeoScore combines a torsion-inspired Laplacian log-determinant, Ollivier-Ricci curvature, and higher-order topological summaries from source embeddings, with weights learned via self-supervised invariance to geometry-preserving views, to rank checkpoints by expected OOD robustness.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-29T02:05:46.296990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdd8ae5a97dc7d6d804af5e53a1c42ded0a46480d56a78f22d8ca897ff1a0b87

Aliases

arxiv: 2605.08870 · arxiv_version: 2605.08870v2 · doi: 10.48550/arxiv.2605.08870 · pith_short_12: ZXMK4WUX3R6W · pith_short_16: ZXMK4WUX3R6W3ACK · pith_short_8: ZXMK4WUX

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/ZXMK4WUX3R6W3ACK6XSTUHCC33 \
  | 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: cdd8ae5a97dc7d6d804af5e53a1c42ded0a46480d56a78f22d8ca897ff1a0b87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b3b6524769358d1c8a3259369bda9a130bc1a4e42099f2365d238262ad0d4d0",
    "cross_cats_sorted": [
      "math.AT",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-09T10:46:47Z",
    "title_canon_sha256": "a64837122d93dce45e620c9930bb984590b687d599abb94a8decd31bc1f30fda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08870",
    "kind": "arxiv",
    "version": 2
  }
}