debt_forces_unique_future
plain-language theorem explainer
Any integer debt accumulated in an unclosed 8-tick window fixes a unique future integer contribution that cancels it exactly to zero. Researchers modeling mock theta functions as unresolved phase debt in Recognition Science cite this to guarantee that phantom light projections remain unambiguous. The argument is a direct one-line application of the shadow uniqueness lemma.
Claim. For any integer debt $d$, there exists a unique integer future contribution $f$ such that $d + f = 0$.
background
In the MockThetaPhantom module, mock theta functions are interpreted as unclosed 8-tick windows that carry a balance debt equal to the accumulated sum of registered events. The future is the set of uncommitted later ticks that must supply the compensating contribution to close the window. The upstream shadow_is_unique theorem states that the shadow (required future compensation) is uniquely determined by the debt: given accumulated sum $s$, there is exactly one value $t$ such that $s + t = 0$ (equivalently, the shadow is always the negation of the sum).
proof idea
This is a term-mode proof consisting of a single direct application of the shadow_is_unique lemma to the currentDebt parameter.
why it matters
The theorem secures uniqueness of debt resolution in the RamanujanBridge treatment of mock theta functions, confirming that the phantom magnitude constraining an unclosed window is always unambiguous. It supports the module's core claim that Zwegers' shadow corresponds to Phantom Light restoring symmetry once the future balance arrives. The result aligns with the eight-tick octave structure and the uniqueness properties in the forcing chain, though it has no downstream citations yet.
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