These diagrams provide structural reference for Paper 4 — Cross‑Architecture Generative Synthesis (CAGS). The foundational paper is fully self‑contained in text form, but cross‑architecture synthesis benefits from visual representation. These diagrams map the synthesis preconditions, CAP/CAS/CAF hierarchy, operator dynamics, invariants, binding patterns, trajectories, and manifold topology.
Corresponds to: Paper 4, Section 2 — Preconditions
Purpose: Shows the seven structural requirements for synthesis.
+-----------------------------------------------------------+ | CROSS‑ARCHITECTURE SYNTHESIS PRECONDITIONS | +-----------------------------------------------------------+ | 1. COP‑valid expressions in all architectures | | 2. USI‑valid units across architectures | | 3. Stable symbolic anchors | | 4. Compatible binding vectors | | 5. Resolution‑level compatibility | | 6. Interface compatibility | | 7. Cross‑architecture load below threshold | +-----------------------------------------------------------+ Synthesis is disallowed if any precondition fails.
Corresponds to: Paper 4, Section 3 — Synthesis Objects
Purpose: Shows the three cross‑architecture generative object types.
+----------------------+
| Cross‑Architecture |
| Pair (CAP) |
+----------------------+
|
v
+----------------------+
| Cross‑Architecture |
| Structure (CAS) |
+----------------------+
|
v
+----------------------+
| Cross‑Architecture |
| Field (CAF) |
+----------------------+
Corresponds to: Paper 4, Section 4 — Synthesis Operators
Purpose: Lists the ten operators that act across architectures.
+------+---------------------------+ | S1 | Align | | S2 | Bridge | | S3 | Couple | | S4 | Decouple | | S5 | Lift | | S6 | Compress | | S7 | Expand | | S8 | Constrain | | S9 | Reframe | | S10 | Stabilize | +------+---------------------------+
Corresponds to: Paper 4, Section 5 — Operator Dynamics
Purpose: Shows how operators transform CAPs and CASs.
S1 Align → Align anchors across architectures S2 Bridge → Form CAP (bind units across architectures) S3 Couple → Create generative dependency S4 Decouple → Remove dependency to prevent overload S5 Lift → Raise CAP/CAS to higher resolution level S6 Compress → Reduce resolution to maintain stability S7 Expand → Increase generative scope S8 Constrain → Limit propagation S9 Reframe → Reconfigure after drift or overload S10 Stabilize → Restore coherence across architectures
Corresponds to: Paper 4, Section 6 — Invariants
Purpose: Shows the seven invariants that constrain synthesis.
+--------------------------------------------------------------+ | CROSS‑ARCHITECTURE INVARIANTS | +--------------------------------------------------------------+ | 1. No synthesis under degraded intent | | 2. No cross‑architecture binding that increases drift | | 3. No resolution expansion without anchor compatibility | | 4. No synthesis chain exceeding load threshold | | 5. No opposed binding vectors across architectures | | 6. No unresolved collapse in any architecture | | 7. No propagation of boundary failure | +--------------------------------------------------------------+
Corresponds to: Paper 4, Section 7 — Cross‑Architecture Binding
Purpose: Shows allowed and disallowed cross‑architecture binds.
+-----------------------------+------------------------------+ | BINDING TYPE | STATUS | +-----------------------------+------------------------------+ | Aligned Cross‑Bind | Allowed | | Orthogonal Cross‑Bind | Allowed | | Constrained Cross‑Bind | Allowed | | Lifted Cross‑Bind | Allowed | | Meta Cross‑Bind | Allowed | | Opposed Cross‑Bind | DISALLOWED | +------------------------------------------------------------+ Binding Requirements: • Compatible anchors • Non‑collapsing resolution signatures • Compatible interface markers • No invariant FAIL in any architecture
Corresponds to: Paper 4, Section 8 — Composition
Purpose: Shows how CAPs combine into CASs.
CAP1 ----\
+----> CAS ----> CAF
CAP2 ----/
Composition Requirements:
• Stable binding sequences
• No drift propagation
• No boundary inversion
• No relational collapse
• No resolution collapse
• No cross‑architecture overload
Corresponds to: Paper 4, Section 9 — Canonical Patterns
Purpose: Shows the five stable synthesis trajectories.
A ↔ B Stable CAP formation.
A → B A → C B ⟂ C Forms stable triad across architectures.
CAP → Lift → Higher‑Resolution CAS
A → B → C Expansion limited by load threshold.
A → B Collapse detected in B Reframe applied Structure restored.
Corresponds to: Paper 4, Section 13 — Synthesis Trajectories
Purpose: Shows the cross‑architecture analog of generative trajectories.
T = [CAP1 → CAP2 → ... → CAPn] Trajectory Validity: • Preconditions satisfied at each step • No collapse without reframe • No drift propagation • No boundary violation • No relational inversion • No resolution‑level collapse
Corresponds to: Paper 4, Section 14 — Manifold Topology
Purpose: Shows the global topology of cross‑architecture synthesis.
+-----------------------------------------------------------+ | CROSS‑ARCHITECTURE MANIFOLD TOPOLOGY | +-----------------------------------------------------------+ | Nodes: CAPs | | Edges: Cross‑Binding Vectors | | Surfaces: CASs | | Volumes: Cross‑Architecture Fields | | Gradients: Coherence Levels | | Contours: Boundary Configurations | | Flows: Synthesis Trajectories | +-----------------------------------------------------------+ Topology Constraints: 1. No closed loops with unresolved drift 2. No surfaces with boundary inversion 3. No volumes exceeding load threshold 4. No gradients reversing direction 5. No flows crossing incompatible resolution levels