These diagrams provide structural reference for Paper 1 — The Coherence Operating Protocol (COP). The foundational paper is fully self‑contained in text form, but COP’s geometry benefits from visual representation. These diagrams map the lattice, states, operators, invariants, expression formats, and canonical sequences that define the COP substrate.
Corresponds to: Paper 1, Section 2 — The COP Lattice
Purpose: Shows the five independent dimensions that define COP’s coherence geometry.
+-----------------------------------------------------------+ | COP STRUCTURAL LATTICE | +-----------------------------------------------------------+ | 1. COHERENCE | Stable | Drifting | Collapsed | | 2. BOUNDARY | Implicit | Explicit | Permeable | Failing| | 3. RELATION | Aligned | Orthogonal | Coupled | Opposed| | 4. INTENT | I1 Clear | I2 Split | I3 Degrading | I4 Degraded | | 5. TIME | Ordered sequence t0 → t1 | +-----------------------------------------------------------+ Minimal independent set for coherence-preserving generativity.
Corresponds to: Paper 1, Section 3 — COP State Space
Purpose: Maps the six canonical COP states.
+----------------------+-----------------------------+ | STATE | DESCRIPTION | +----------------------+-----------------------------+ | S1 Inquiry | Stable, explicit boundary | | S2 Construction | Stable, aligned/coupled | | S3 Stabilizing Drift | Drifting, boundary tighten | | S4 Boundary Formation| Implicit → explicit | | S5 Pre‑Collapse | Drifting → collapse | | S6 Coherent Reframe | Stabilizing, new boundary | +----------------------+-----------------------------+
Corresponds to: Paper 1, Section 4 — State‑Primitive Compatibility
Purpose: Shows which primitives are admissible in each state.
+----------------------+-------------------------------------------+ | STATE | ALLOWED PRIMITIVES | DISALLOWED | +----------------------+-------------------------------------------+ | S1 | Inquiry, alignment | Construction, drift | | S2 | Construction, alignment | Opposition, drift | | S3 | Compression, boundary‑tighten | Expansion, construct | | S4 | Compression, sorting | Construct, expand | | S5 | None (overload) | All constructive ops | | S6 | Meta‑inquiry, compression | Construct, expand | +------------------------------------------------------------------+
Corresponds to: Paper 1, Section 5 — COP Operators
Purpose: Lists the ten operators that drive COP transitions.
+------+-----------------------+ | O1 | Boundary‑Tighten | | O2 | Boundary‑Reform | | O3 | Relation‑Align | | O4 | Relation‑Decouple | | O5 | Coherence‑Stabilize | | O6 | Intent‑Clarify | | O7 | Intent‑Constrain | | O8 | Drift‑Detect | | O9 | Collapse‑Guard | | O10 | Frame‑Form | +------+-----------------------+
Corresponds to: Paper 1, Section 6 — COP Invariants
Purpose: Shows the invariant constraints that govern admissible transitions.
+--------------------------------------------------------------+ | COP INVARIANTS (I1–I7) | +--------------------------------------------------------------+ | I1 No construction under degraded intent (I3/I4) | | I2 Reframe before collapse | | I3 No coupling increase in S5 | | I4 Boundary required for construction | | I5 Inquiry must not degrade coherence | | I6 Drift must trigger stabilization or reframe | | I7 Intent must always be classified (I1–I4) | +--------------------------------------------------------------+
Corresponds to: Paper 1, Section 7 — COP Expression Format
Purpose: Shows the atomic COP expression structure.
+---------------- COP-EXPR ----------------+ | S = Current State | | P = Active Primitives | | O = Operator Applied | | I = Invariant Status Vector | | TT = Transition Type | +------------------------------------------+ Transition Types: Stabilize | Reframe | Construct | Inquire | FormBoundary | Warning | None
Corresponds to: Paper 1, Section 8 — COP Sequence Format
Purpose: Shows how COP expressions form valid sequences.
Seq = [E1 → E2 → ... → En] Validity Conditions: • Adjacent states satisfy transition rules • No invariant remains FAIL • S5 must be followed by S6 • No construction under I3/I4 • Drift → Stabilize or Reframe
Corresponds to: Paper 1, Section 9 — Local Validity
Purpose: Shows the three local constraints between adjacent expressions.
+---------------------+
| Ek (current) |
+---------------------+
|
v
+---------------------+
| State Continuity |
| (TT → next state) |
+---------------------+
|
v
+---------------------+
| Invariant Monotonic |
| FAIL → WARN/OK |
+---------------------+
|
v
+---------------------+
| Intent Evolution |
| I1→I2→I3→I4 or back |
+---------------------+
Corresponds to: Paper 1, Section 10 — Global Validity
Purpose: Shows the global rules that govern entire COP sequences.
+-----------------------------------------------------------+ | GLOBAL VALIDITY RULES | +-----------------------------------------------------------+ | • No invariant remains FAIL | | • No construction under I3/I4 | | • S5 always followed by S6 | | • Drift always followed by Stabilize/Reframe | | • Boundaries never weakened during construction | | • Coupling never increased in S5 | | • Inquiry never induces drift | +-----------------------------------------------------------+
Corresponds to: Paper 1, Section 11 — Canonical Sequence Patterns
Purpose: Shows the four canonical COP trajectories.
S1 → S1 → S1 TT: Inquire / None
S1 → S4 → S2 → S2 TT: FormBoundary → Construct
S2 → S3 → S6 → S1/S2 TT: Stabilize → Reframe → Inquire/Construct
S2/S3 → S5 → S6 → S1/S3 TT: Warning → Reframe → Stabilize/Inquire