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Cohesion Dynamics (CD)

E-W1 — Internal Consistency Bounds on Tolerance Window W

E-W1 derives rigorous upper and lower bounds on the tolerance window WW from self-consistency requirements within Cohesion Dynamics. We demonstrate that quantum-capable substrates (DCC-QM) can exist only when WW lies within a non-empty interval [Wmin⁡,Wmax⁡][W_{\min}, W_{\max}], and that any WW outside this range breaks the quantum recovery established in the B-series.

Key Results:

  • Mode stability requirements (B3) impose lower bound Wmin⁡W_{\min}; coherence preservation constraints (M4, B1) impose upper bound Wmax⁡W_{\max}
  • Proof that interval is non-empty, establishing first internal consistency constraint on WW
  • If derivation had yielded Wmin⁡>Wmax⁡W_{\min} > W_{\max}, it would have constituted falsification of CD
  • Successful demonstration of non-empty interval is first decisive test of programme viability

Epistemic Role: This is an empirical-theoretical investigation establishing existence and bounds through analytical derivation. Does not provide numerical value for WW, does not assume W=ℏW = \hbar, introduces no new axioms or mechanisms. Serves as foundation for subsequent empirical recovery strategies (E-W2, E-W3).

Paper ID: CD-E-W1 | Series: E-series (Empirical Narrowing) | Status: Draft | Dependencies: A, M4, B1, B3, B5; informed by R-DCC