Mathematical Foundation
The construction is grounded in the structure of mock modular forms:
- The holomorphic part is fully computable and locally observable.
- The completion requires non-holomorphic global data (the “shadow”).
- The holomorphic component does not canonically determine its completion.
This produces structured ambiguity:
- Multiple globally distinct objects share identical local observables.
- No canonical origin exists.
- Identity selection requires additional global data.
We formalize this phenomenon into a cryptographic hardness family called:
- MMIP – Mock Modular Identification Problems
Security is defined as the inability to collapse structured ambiguity under a Restricted Observables Model (ROM), even with polynomial-time quantum computation.
