Unified Operator Grammar v1.1

With Drift‑Correction Rules#

Summary#

Version 1.1 extends the v1.0 grammar with drift‑correction operators, reconstruction windows, and cross‑module propagation constraints.

1. Core Types (unchanged)#

Triad#

$$T = (s,c,u),\quad s+c+u=1$$

Asymmetry#

$$A(T)=0.01$$

Extended State#

$$S = (T, X)$$

where $$X$$ is:

• blueprint $$M$$
• substrate $$S_i$$
• environment $$E$$

2. Operators (unchanged)#

Continuity Operator#

$$O(T) = (T, A(T))$$

Replication Operator#

$$\mathcal{R}(T,M) = (T,M)$$

Transport Operator#

$$\mathcal{T}(T,S_1 \to S_2) = (T,S_2)$$

CT Operator#

$$\mathcal{C}(T,E) = (T,E')$$

3. Drift‑Correction Rules (new)#

3.1 Deviation Metric#

$$D(T) = |T - T^*|$$

3.2 Correction Operator#

$$C_\lambda(T) = N((1-\lambda)T + \lambda T^*)$$

3.3 Drift‑Corrected Transform#

$$F^\# = C_\lambda \circ F$$

3.4 Legality#

A transform is legal if:

• $$A(F(T)) > 0$$
  or

$$A(F^\#(T)) > 0$$

4. Reconstruction Windows (new)#

Definition#

$$W = [1-\delta, 1]$$

Allowed operations#

• drift‑correction
• environment alignment
• substrate stabilization

5. Cross‑Module Propagation Constraints#

• All operators must preserve:
  • triad
  • asymmetry
  • continuity
• Reconstruction windows may not overlap across modules
• Drift‑correction is allowed only:
  • inside transporter windows
  • inside CT windows
  • optionally inside replicator windows

Claim#

Operator Grammar v1.1 introduces drift‑correction and reconstruction rules, completing the continuity‑safe operator system across all three goals.