Pith Number

pith:P7OWKNQB

pith:2026:P7OWKNQBJFZU5LED6RA6BSVLHM

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Notes on obstructions in the hyperbolic Clifford algebra bundle structure

E. Notte-Cuello, J. M. Hoff da Silva

Hyperbolic Clifford algebra bundles allow spinor structures to be defined without topological obstructions.

arxiv:2605.16558 v1 · 2026-05-15 · math-ph · hep-th · math.MP

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\pithnumber{P7OWKNQBJFZU5LED6RA6BSVLHM}

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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

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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

unlike classical tangent bundle cases, the hyperbolic frame bundle admits lifting without any topological obstruction. This leads to the possibility of always defining spinor structures in hyperbolic Clifford bundles.

C2weakest assumption

The particularities arising from the Whitney sum in the hyperbolic setting eliminate the topological obstructions to lifting that exist in classical tangent bundle cases, based on a general analysis of obstruction classes.

C3one line summary

Hyperbolic Clifford algebra bundles admit frame bundle lifts without topological obstructions, enabling consistent spinor structures unlike classical tangent bundles.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] W. Greub and H. R. Petry,On the lifting of structure groups, in Differential Geometrical Methods in Mathematical Physics, II, Lecture Notes in Mathematics, Springer, New York (1978) 1978

[2] H. Osborn,Vector Bundles, Vol. I, Academic Press, New York (1982) 1982

[3] R. Geroch,Spinor structure of space-times in General Relativity I, J. Math. Phys. 9, 1739–1744 (1968) 1968

[4] R. Geroch,Spinor structure of space-times in General Relativity II, J. Math. Phys. 11, 343–348 (1970) 1970

[5] W. Greub, S. Halperin, and J. Van Stone,Connections, Curvature and Cohomology, Academic Press, New York (1973) 1973

Receipt and verification

First computed	2026-05-20T00:02:29.059471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fdd65360149734eac83f441e0caab3b19e9eefd5822fd08be679f2984c93a52

Aliases

arxiv: 2605.16558 · arxiv_version: 2605.16558v1 · doi: 10.48550/arxiv.2605.16558 · pith_short_12: P7OWKNQBJFZU · pith_short_16: P7OWKNQBJFZU5LED · pith_short_8: P7OWKNQB

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/P7OWKNQBJFZU5LED6RA6BSVLHM \
  | 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: 7fdd65360149734eac83f441e0caab3b19e9eefd5822fd08be679f2984c93a52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81ef63c60a702a097e5639a5e6aa1035e057fcbab83afbd3d1d7d8582df0e5aa",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-15T19:00:06Z",
    "title_canon_sha256": "2ab2df5f9f84707eeb836174297ca808f298c1aa28eecd0ccc21de51015b779a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16558",
    "kind": "arxiv",
    "version": 1
  }
}