What does this research mean for the field?

Clifford sheaves over a manifold with a cometric degenerating to corank one on a hypersurface maintain constant rank by acquiring a canonical square-zero ideal over the degeneracy, enabling stable extensions of structures such as the Schwarzschild singularity. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

To resolve the apparent contradiction where Clifford sheaf fibre dimensions cannot jump over a hypersurface of metric corank-one degeneration despite transport principle requirements.

September 14, 2026Open Access

Transport Papers T04. Clifford Sheaves over Degenerate Metrics

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Authors

LBLeon Butler

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Implication

Mathematical analysis demonstrates Clifford sheaf completion across degenerate metric hypersurfaces, suggesting stable extensions to Schwarzschild singularities.

Key Points

To resolve the apparent contradiction where Clifford sheaf fibre dimensions cannot jump over a hypersurface of metric corank-one degeneration despite transport principle requirements.
Analyzed degeneration sheaves and ambient sheaves over a smooth manifold with a cometric degenerating tamely on a hypersurface.
Constructed completions using radical lines, exceptional algebras on normal cones, and Kasner blow-up weights.
Verified all 296 computational identities via exact rational arithmetic using custom Python verification scripts.
Demonstrated that degeneration sheaves maintain a constant rank of 2^n, acquiring a canonical square-zero ideal over the hypersurface, while ambient sheaves hold rank 2^(n+2).
Established a conservation law proving no completion standard is nondegenerate on both sides, causing degeneracy to manifest on a displaced shadow wall under iteration.
Applied the framework to the Schwarzschild singularity via Kasner-weighting, establishing it as a boundary-tame wall receiving the unique rain-bounded completion without shadow walls.

Cite This Study

Leon Butler (2026) studied this question.

synapsesocial.com/papers/6aa7b3aa0926e14a848b2c77 https://doi.org/10.5281/zenodo.22721670

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Implication

Mathematical analysis demonstrates Clifford sheaf completion across degenerate metric hypersurfaces, suggesting stable extensions to Schwarzschild singularities.

Transport Papers T04. Clifford Sheaves over Degenerate Metrics

Discussion

Member takes

Implication

Key Points

Cite This Study

Transport Papers T04. Clifford Sheaves over Degenerate Metrics

Discussion

Member takes

Implication

Key Points

Cite This Study

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