Appendix D: Topological Deficits and Manifold Integrity

D.1 Three Interpretations of "Debits"

Extending the topological deficit analysis:

Energetic Deficits: Regions where conserved quantities drain, causing PDE blow-up

Topological Deficits: Holes or non-compact intrusions in solution manifolds

Dual-Layered Ravines: Simultaneous energetic drains and topological gaps

Theorem D.1 (Debit Injectivity):

A manifold maintains injective integrity if all deficits are locally compact and energy-bounded.

D.2 Applications to Blockchain and Relational Systems

Topological deficits correspond to:

Blockchain: Network partitions, consensus failures

Relational: Trust violations, communication gaps

Quantum: Decoherence, measurement collapse