Pith Number

pith:J6OUKN24

pith:2026:J6OUKN24TFOV3COTVXN7IG6ZEZ

not attested not anchored not stored refs pending

Sheaf-Laplacian Obstruction and Projection Hardness for Cross-Modal Compatibility on a Modality-Independent Site

Tibor Sloboda

Cross-modal representations fail to align either because no simple global projection works or because local projections cannot be made consistent without large parameter changes.

arxiv:2604.07632 v2 · 2026-04-08 · cs.LG · cs.AI

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Claims

C1strongest claim

This separates two distinct failure modes: hardness failure, where no low-complexity global projection exists, and obstruction failure, where local projections exist but cannot be made globally consistent over the semantic neighborhood graph without large parameter variation. We link the sheaf spectral gap to stability of global alignment, derive bounds relating obstruction energy to excess global-map error under mild Lipschitz assumptions.

C2weakest assumption

The core object is a modality-independent neighborhood site on sample indices, equipped with a cellular sheaf of finite-dimensional real inner-product spaces, which is assumed to exist and support the defined projection families and Laplacian constructions.

C3one line summary

A cellular sheaf framework on a modality-independent site defines projection hardness and sheaf-Laplacian obstruction as distinct measures of cross-modal incompatibility, separating global mapping complexity from local consistency failures.

Receipt and verification

First computed	2026-07-28T01:22:33.284715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f9d45375c995d5d89d3addbf41bd92669c9c0b36c6c885bfe8907aae7e3be1c

Aliases

arxiv: 2604.07632 · arxiv_version: 2604.07632v2 · doi: 10.48550/arxiv.2604.07632 · pith_short_12: J6OUKN24TFOV · pith_short_16: J6OUKN24TFOV3COT · pith_short_8: J6OUKN24

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/J6OUKN24TFOV3COTVXN7IG6ZEZ \
  | 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: 4f9d45375c995d5d89d3addbf41bd92669c9c0b36c6c885bfe8907aae7e3be1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8027b51f5902e112c63cb53d43822e5697ddaca993b4f32a04af829e2d86cfc3",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-08T22:20:25Z",
    "title_canon_sha256": "bb1885b53ad71d3a68fd0f610201d4e0a0b21dcd71fea88a4578b4bf22bbfe96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.07632",
    "kind": "arxiv",
    "version": 2
  }
}