diff --git a/TensionUniverse/BlackHole/Q020_high_dimensional_manifolds_curvature.md b/TensionUniverse/BlackHole/Q020_high_dimensional_manifolds_curvature.md
index 8c5dafc3..1203b69a 100644
--- a/TensionUniverse/BlackHole/Q020_high_dimensional_manifolds_curvature.md
+++ b/TensionUniverse/BlackHole/Q020_high_dimensional_manifolds_curvature.md
@@ -15,24 +15,45 @@ Status: Open
 Semantics: continuous
 E_level: E1
 N_level: N1
-Last_updated: 2026-01-24
+Last_updated: 2026-01-29
 ```
 
 ---
 
+## 0. Effective layer disclaimer
+
+All statements in this entry are made strictly at the effective layer of the Tension Universe (TU) framework.
+
+* The goal of this page is to specify an effective layer encoding of Q020.
+* It does not claim to prove or disprove any canonical classification statement in high dimensional Riemannian geometry.
+* It does not introduce new theorems beyond what is already established or conjectured in the cited literature.
+* It must not be cited as evidence that any geometric classification conjecture has been solved.
+
+In particular:
+
+* All state spaces, observables, invariants, tension scores, and counterfactual worlds defined here are effective layer constructs.
+* No axiom system, generative rule, or constructive derivation for TU itself is specified on this page.
+* No explicit mapping is given from raw geometric data or analytic constructions to internal TU fields. Only the existence of such mappings is assumed at the level of observables.
+* Quantities such as `lambda(m)` and `T_ij(m)` are treated here as externally supplied TU core observables and coupling factors. Their internal dynamics or update rules are not defined in this document.
+
+The experiments and engineering patterns below can falsify or support particular Q020 encodings. They cannot by themselves settle any open problem about classification of high dimensional manifolds.
+
+---
+
 ## 1. Canonical problem and status
 
 ### 1.1 Canonical statement
 
 The classical objects in this problem are:
 
-- Smooth connected manifolds `X` of dimension `n` with `n >= 5`.
-- Riemannian metrics `g` on `X`.
-- Curvature constraints imposed on `(X, g)` such as:
-  - bounds on sectional curvature,
-  - bounds on Ricci curvature,
-  - bounds on scalar curvature,
-  - or combinations of these.
+* Smooth connected manifolds `X` of dimension `n` with `n >= 5`.
+* Riemannian metrics `g` on `X`.
+* Curvature constraints imposed on `(X, g)` such as:
+
+  * bounds on sectional curvature,
+  * bounds on Ricci curvature,
+  * bounds on scalar curvature,
+  * or combinations of these.
 
 At a high level, the canonical problem for Q020 asks:
 
@@ -41,52 +62,54 @@ At a high level, the canonical problem for Q020 asks:
 More concretely, one can phrase Q020 as the family of questions:
 
 1. Given `n >= 5` and a curvature condition `C` (for example nonnegative sectional curvature, positive Ricci curvature, or two sided sectional curvature bounds), does there exist:
-   - a finite library of canonical model spaces, and
-   - a finite list of controlled operations (for example products, quotients, surgeries under curvature control),
-   such that every `(X, g)` satisfying `C` is obtained from these models by these operations, up to diffeomorphism or isometry?
+
+   * a finite library of canonical model spaces, and
+   * a finite list of controlled operations (for example products, quotients, surgeries under curvature control),
+     such that every `(X, g)` satisfying `C` is obtained from these models by these operations, up to diffeomorphism or isometry?
 
 2. If not finite in a strict sense, is there at least a classification up to finitely many parameters in an effective and structurally transparent way?
 
-Q020 in this BlackHole setting does not commit to a specific formalization of “finite classification”. Instead, it encodes the tension between:
+Q020 in this BlackHole setting does not commit to a single formal definition of finite classification. Instead, it encodes the tension between:
 
-- local geometric constraints given by curvature,
-- global topological and geometric complexity,
-- the possibility of capturing all such manifolds using a small library of canonical types.
+* Local geometric constraints given by curvature.
+* Global topological and geometric complexity.
+* The possibility of capturing all such manifolds using a small library of canonical types.
 
 ### 1.2 Status and difficulty
 
-Some related lower dimensional cases are well understood:
+Some related lower dimensional cases are well understood.
 
-- In dimension 2, complete classification of Riemannian manifolds with curvature constraints is classical, with strong links to topology through Gauss curvature.
-- In dimension 3, the combination of Thurston’s geometrization program and Ricci flow techniques has provided powerful classification results under various curvature and topological assumptions.
+* In dimension 2, complete classification of Riemannian manifolds with curvature constraints is classical, with strong links to topology through Gauss curvature.
+* In dimension 3, the combination of Thurston style geometrization and Ricci flow techniques has provided powerful classification results under various curvature and topological assumptions.
 
-In higher dimensions (`n >= 5`), the situation is much more incomplete:
+In higher dimensions (`n >= 5`), the situation is much more incomplete.
 
-- There are strong structure theorems under certain curvature conditions, for example splitting theorems, almost flat manifold results, and restrictions on possible fundamental groups.
-- For many curvature classes (for example nonnegative sectional curvature or positive scalar curvature), there are numerous known examples and families, but no complete classification.
-- In several settings it is unknown whether there are infinitely many distinct diffeomorphism types of manifolds satisfying the same curvature bounds.
-- Interactions between curvature conditions and topological invariants (for example characteristic classes, fundamental group growth, exotic smooth structures) are only partially understood.
+* There are strong structure theorems under certain curvature conditions, such as splitting theorems, almost flat manifold results, and restrictions on possible fundamental groups.
+* For many curvature classes (for example nonnegative sectional curvature or positive scalar curvature), there are numerous known examples and families, but no complete classification.
+* In several settings it is unknown whether there are infinitely many distinct diffeomorphism types of manifolds satisfying the same curvature bounds.
+* Interactions between curvature conditions and topological invariants (for example characteristic classes, fundamental group growth, exotic smooth structures) are only partially understood.
 
 As a result, Q020 remains an umbrella for multiple difficult open problems in high dimensional Riemannian geometry and global analysis, with no single known resolution.
 
 ### 1.3 Role in the BlackHole project
 
-Within the BlackHole S problem collection, Q020 plays the following roles:
+Within the BlackHole S problem collection, Q020 plays the following roles.
 
-1. It is the primary node for **high dimensional curvature constrained classification**, capturing the tension between local differential inequalities and global manifold type.
+1. It is the primary node for high dimensional curvature constrained classification, capturing the tension between local differential inequalities and global manifold type.
 2. It provides a geometric analogue of classification style questions that appear in physics and AI, by asking whether a finite library can describe all admissible objects under strict constraints.
 3. It supplies reusable components for:
-   - geometric flow problems (Q017),
-   - quantum gravity background selection (Q021),
-   - black hole spacetime modelling (Q040),
-   - and other nodes that require controlled high dimensional geometry.
+
+   * geometric flow problems (Q017),
+   * quantum gravity background selection (Q021),
+   * black hole spacetime modelling (Q040),
+   * and other nodes that require controlled high dimensional geometry.
 
 ### References
 
-1. S. T. Yau, “Open problems in geometry”, in *Journal of Differential Geometry*, 31 (1990), 1–28.  
-2. J. Cheeger and D. Ebin, *Comparison Theorems in Riemannian Geometry*, North Holland, 1975.  
-3. M. Gromov, *Metric Structures for Riemannian and Non Riemannian Spaces*, Birkhäuser, 1999.  
-4. Expository articles and encyclopedia entries on “Riemannian manifolds with curvature bounded below” and “open problems in Riemannian geometry”, in standard mathematical reference works.
+1. S. T. Yau, “Open problems in geometry”, *Journal of Differential Geometry*, 31 (1990), 1–28.
+2. J. Cheeger and D. Ebin, *Comparison Theorems in Riemannian Geometry*, North Holland, 1975.
+3. M. Gromov, *Metric Structures for Riemannian and Non Riemannian Spaces*, Birkhäuser, 1999.
+4. Expository articles and encyclopedia entries on Riemannian manifolds with curvature bounded below and open problems in Riemannian geometry, in standard mathematical reference works.
 
 ---
 
@@ -98,53 +121,53 @@ This block records how Q020 sits inside the BlackHole graph. Each edge has a one
 
 These problems provide prerequisites, tools, or foundations that Q020 relies on at the effective layer.
 
-- Q017 (BH_MATH_GEOM_FLOW_L3_017)  
-  Reason: Provides GeomFlow_Encoding modules and flow based experiment patterns that Q020 uses to probe whether curvature constrained manifolds move toward a small library of canonical models.
+* Q017 (BH_MATH_GEOM_FLOW_L3_017)
+  Reason: Provides `GeomFlow_Encoding` modules and flow based experiment patterns that Q020 uses to probe whether curvature constrained manifolds move toward a small library of canonical models.
 
-- Q016 (BH_MATH_ZFC_CH_L3_016)  
+* Q016 (BH_MATH_ZFC_CH_L3_016)
   Reason: Supplies foundational constraints on continuum sized parameter spaces needed to handle families of metrics and manifolds in the state space `M_geo`.
 
-- Q004 (BH_MATH_HODGE_L3_004)  
-  Reason: Provides Hodge type descriptors and cohomological invariants that feed into the CurvatureTopologyDescriptor component used in Q020.
+* Q004 (BH_MATH_HODGE_L3_004)
+  Reason: Provides Hodge type descriptors and cohomological invariants that feed into the `CurvatureTopologyDescriptor` component used in Q020.
 
 ### 2.2 Downstream problems
 
 These problems directly reuse Q020 components or depend on its geometric tension structure.
 
-- Q021 (BH_PHYS_QG_L3_021)  
-  Reason: Uses GeometricTensionScore_Q020 and FiniteGeomLibrary_Template to restrict candidate high dimensional spacetime topologies in quantum gravity models.
+* Q021 (BH_PHYS_QG_L3_021)
+  Reason: Uses `GeometricTensionScore_Q020` and `FiniteGeomLibrary_Template` to restrict candidate high dimensional spacetime topologies in quantum gravity models.
 
-- Q040 (BH_PHYS_QBLACKHOLE_INFO_L3_040)  
-  Reason: Reuses CurvatureTopologyDescriptor to describe and compare candidate black hole spacetime manifolds under curvature and energy conditions.
+* Q040 (BH_PHYS_QBLACKHOLE_INFO_L3_040)
+  Reason: Reuses `CurvatureTopologyDescriptor` to describe and compare candidate black hole spacetime manifolds under curvature and energy conditions.
 
-- Q096 (BH_EARTH_QUAKE_FORECAST_L3_096)  
+* Q096 (BH_EARTH_QUAKE_FORECAST_L3_096)
   Reason: Uses geometric classification style descriptors from Q020 to model crust and fault surfaces as manifolds with constrained curvature.
 
 ### 2.3 Parallel problems
 
 Parallel nodes share similar tension types but no direct component dependence.
 
-- Q039 (BH_PHYS_QTURBULENCE_L3_039)  
-  Reason: Both Q020 and Q039 are governed by consistency_tension between local differential constraints and rich global emergent structure.
+* Q039 (BH_PHYS_QTURBULENCE_L3_039)
+  Reason: Both Q020 and Q039 are governed by consistency tension between local differential constraints and rich global emergent structure.
 
-- Q011 (BH_MATH_NS_L3_011)  
+* Q011 (BH_MATH_NS_L3_011)
   Reason: Both are PDE governed classification style problems where local equations do not yet yield a global classification of all solutions.
 
 ### 2.4 Cross domain edges
 
 Cross domain edges connect Q020 to problems in other domains that can reuse its components.
 
-- Q021 (BH_PHYS_QG_L3_021)  
-  Reason: Applies FiniteGeomLibrary_Template to select and compare candidate spacetime geometries.
+* Q021 (BH_PHYS_QG_L3_021)
+  Reason: Applies `FiniteGeomLibrary_Template` to select and compare candidate spacetime geometries.
 
-- Q040 (BH_PHYS_QBLACKHOLE_INFO_L3_040)  
-  Reason: Uses GeometricTensionScore_Q020 as a measure of how plausible a proposed black hole spacetime is under curvature and topology constraints.
+* Q040 (BH_PHYS_QBLACKHOLE_INFO_L3_040)
+  Reason: Uses `GeometricTensionScore_Q020` as a measure of how plausible a proposed black hole spacetime is under curvature and topology constraints.
 
-- Q059 (BH_CS_INFO_THERMODYN_L3_059)  
+* Q059 (BH_CS_INFO_THERMODYN_L3_059)
   Reason: Adapts the idea of finite library classification under constraints to information and thermodynamic state spaces.
 
-- Q123 (BH_AI_INTERP_L3_123)  
-  Reason: Uses CurvatureTopologyDescriptor as a template for classifying high dimensional representation manifolds inside AI models.
+* Q123 (BH_AI_INTERP_L3_123)
+  Reason: Uses `CurvatureTopologyDescriptor` as a template for classifying high dimensional representation manifolds inside AI models.
 
 ---
 
@@ -152,10 +175,10 @@ Cross domain edges connect Q020 to problems in other domains that can reuse its
 
 All content in this block is at the effective layer. We only describe:
 
-- state spaces,
-- observables and fields,
-- invariants and tension scores,
-- singular sets and domain restrictions.
+* state spaces,
+* observables and fields,
+* invariants and tension scores,
+* singular sets and domain restrictions.
 
 We do not describe any hidden TU generative rules or any mapping from raw geometric data to internal TU fields.
 
@@ -163,8 +186,8 @@ We do not describe any hidden TU generative rules or any mapping from raw geomet
 
 We fix:
 
-- an integer `n >= 5`,
-- and a curvature constraint class `C` (for example “complete `n` dimensional manifolds with nonnegative sectional curvature and bounded diameter”).
+* an integer `n >= 5`,
+* a curvature constraint class `C` such as complete `n` dimensional manifolds with nonnegative sectional curvature and bounded diameter.
 
 We define the state space:
 
@@ -172,17 +195,18 @@ We define the state space:
 M_geo
 ```
 
-with the following interpretation:
+with the following interpretation.
 
-- Each element `m` in `M_geo` represents an equivalence class of configurations consisting of:
-  - a smooth connected `n` dimensional manifold `X_m`,
-  - a Riemannian metric `g_m` on `X_m` that satisfies the curvature constraint class `C`,
-  - a finite collection of coarse summaries derived from `(X_m, g_m)` that will serve as observables.
+* Each element `m` in `M_geo` represents an equivalence class of configurations consisting of:
+
+  * a smooth connected `n` dimensional manifold `X_m`,
+  * a Riemannian metric `g_m` on `X_m` that satisfies the curvature constraint class `C`,
+  * a finite collection of coarse summaries derived from `(X_m, g_m)` that will serve as observables.
 
 The effective layer assumptions are:
 
-- For every geometrically admissible configuration `(X, g)` in the class `C`, there exist states `m` in `M_geo` that encode the observable summaries needed below.
-- We do not specify how `X_m`, `g_m`, or the observables are constructed from raw data. We only assume that they are well defined and give consistent values for all observables listed.
+* For every geometrically admissible configuration `(X, g)` in the class `C`, there exist states `m` in `M_geo` that encode the observable summaries needed below.
+* We do not specify how `X_m`, `g_m`, or the observables are constructed from raw data. We only assume that they are well defined and give consistent values for all observables listed.
 
 ### 3.2 Observables and fields
 
@@ -190,26 +214,26 @@ We introduce a fixed finite set of sample scales and a finite library of canonic
 
 1. Sample scales
 
-   - Choose a finite list of radii:
+   Choose a finite list of radii:
 
-     ```txt
-     R_sample = {r_1, ..., r_K}
-     ```
+   ```txt
+   R_sample = {r_1, ..., r_K}
+   ```
 
-     with `0 < r_1 < ... < r_K`, all within a scale range where curvature bounds make sense.
+   with `0 < r_1 < ... < r_K`, all within a scale range where curvature bounds make sense.
 
 2. Canonical model library
 
-   - Choose a finite library of canonical curvature constrained model types:
+   Choose a finite library of canonical curvature constrained model types:
 
-     ```txt
-     L_curv = {L_1, ..., L_N}
-     ```
+   ```txt
+   L_curv = {L_1, ..., L_N}
+   ```
 
-     where each `L_k` is a model template (for example a standard sphere of radius 1, a product of spaces, or a homogeneous space) that itself satisfies class `C`.
-   - This library is fixed once for Q020 at the effective layer and is not allowed to change per state.
+   where each `L_k` is a model template, such as a standard sphere of radius 1, a product of spaces, or a homogeneous space, that itself satisfies class `C`.
+   This library is fixed once for Q020 at the effective layer and is not allowed to change per state.
 
-On this basis, we define the following observables for each state `m` in `M_geo`:
+On this basis, we define the following observables for each state `m` in `M_geo`.
 
 1. Local curvature profile observable
 
@@ -217,8 +241,8 @@ On this basis, we define the following observables for each state `m` in `M_geo`
    K_loc(m; r_j)
    ```
 
-   - For each radius `r_j` in `R_sample`, this observable is a finite dimensional vector summarizing curvature statistics of `(X_m, g_m)` on a representative family of metric balls of radius `r_j`.
-   - We only assume that for each `r_j`, `K_loc(m; r_j)` is well defined and finite.
+   For each radius `r_j` in `R_sample`, this observable is a finite dimensional vector summarizing curvature statistics of `(X_m, g_m)` on a representative family of metric balls of radius `r_j`.
+   We only assume that for each `r_j`, `K_loc(m; r_j)` is well defined and finite.
 
 2. Global topology observable
 
@@ -226,11 +250,13 @@ On this basis, we define the following observables for each state `m` in `M_geo`
    Topo(m)
    ```
 
-   - A finite dimensional vector summarizing:
-     - selected Betti numbers of `X_m` in a fixed range of degrees,
-     - coarse information about the fundamental group class,
-     - possibly growth properties like volume growth rate.
-   - We assume `Topo(m)` is well defined and finite for all `m` that satisfy class `C`.
+   A finite dimensional vector summarizing:
+
+   * selected Betti numbers of `X_m` in a fixed range of degrees,
+   * coarse information about the fundamental group class,
+   * possibly growth properties such as volume growth rate.
+
+   We assume `Topo(m)` is well defined and finite for all `m` that satisfy class `C`.
 
 3. Volume growth and diameter observables
 
@@ -239,8 +265,8 @@ On this basis, we define the following observables for each state `m` in `M_geo`
    Diam(m)
    ```
 
-   - `VolGrowth(m; r_j)` summarizes volume of metric balls of radius `r_j` in `(X_m, g_m)`, averaged in a suitable way.
-   - `Diam(m)` is an effective approximation to the diameter of `(X_m, g_m)` when defined, or a proxy for diameter scale in the non compact case.
+   * `VolGrowth(m; r_j)` summarizes volume of metric balls of radius `r_j` in `(X_m, g_m)`, averaged in a suitable way.
+   * `Diam(m)` is an effective approximation to the diameter of `(X_m, g_m)` when defined, or a proxy for diameter scale in the noncompact case.
 
 4. Library projection observables
 
@@ -250,8 +276,8 @@ On this basis, we define the following observables for each state `m` in `M_geo`
    Lib_score(m; L_k)
    ```
 
-   - A scalar in a fixed range, for example `[0, 1]`, that indicates how close the observable summaries of `m` are to those of the canonical model `L_k`.
-   - `Lib_score(m; L_k) = 1` is interpreted as “perfect match” at the level of these summaries.
+   A scalar in a fixed range, for example `[0, 1]`, that indicates how close the observable summaries of `m` are to those of the canonical model `L_k`.
+   The value `Lib_score(m; L_k) = 1` is interpreted as perfect match at the level of these summaries.
 
 We do not specify how these observables are computed from `(X_m, g_m)`. We only assume they are consistent with the curvature constraints and with each other for all states outside the singular set defined below.
 
@@ -265,8 +291,8 @@ We define three mismatch observables and one combined geometric tension score.
    DeltaS_curv(m) >= 0
    ```
 
-   - Measures how close the local curvature profiles `K_loc(m; r_j)` and volume growth profiles are to the patterns allowed by the constraint class `C`.
-   - `DeltaS_curv(m) = 0` if all `K_loc(m; r_j)` and `VolGrowth(m; r_j)` fall within known or conjectured bands for class `C`.
+   Measures how close the local curvature profiles `K_loc(m; r_j)` and volume growth profiles are to the patterns allowed by the constraint class `C`.
+   The value `DeltaS_curv(m) = 0` means that all `K_loc(m; r_j)` and `VolGrowth(m; r_j)` fall inside the known or conjectured bands for class `C`.
 
 2. Topology geometry mismatch
 
@@ -274,8 +300,8 @@ We define three mismatch observables and one combined geometric tension score.
    DeltaS_topo(m) >= 0
    ```
 
-   - Measures how compatible `Topo(m)` is with the curvature constraint class `C` according to known theorems and conjectures.
-   - `DeltaS_topo(m) = 0` when `Topo(m)` lies entirely inside the set of topological patterns that are known or conjectured to be realizable under class `C`.
+   Measures how compatible `Topo(m)` is with the curvature constraint class `C` according to known theorems and conjectures.
+   The value `DeltaS_topo(m) = 0` means that `Topo(m)` lies entirely inside the set of topological patterns that are known or conjectured to be realizable under class `C`.
 
 3. Library classification mismatch
 
@@ -283,8 +309,8 @@ We define three mismatch observables and one combined geometric tension score.
    DeltaS_lib(m) >= 0
    ```
 
-   - Uses `Lib_score(m; L_k)` across all `k` to measure how well `(X_m, g_m)` can be approximated by the finite library `L_curv`.
-   - `DeltaS_lib(m) = 0` if there exists at least one `L_k` such that `Lib_score(m; L_k)` is at its maximal value.
+   Uses `Lib_score(m; L_k)` across all `k` to measure how well `(X_m, g_m)` can be approximated by the finite library `L_curv`.
+   The value `DeltaS_lib(m) = 0` means that there exists at least one `L_k` such that `Lib_score(m; L_k)` is at its maximal value.
 
 4. Combined geometric tension functional
 
@@ -311,7 +337,7 @@ We define three mismatch observables and one combined geometric tension score.
 
 ### 3.4 Effective tension tensor and singular set
 
-We define an effective tension tensor on `M_geo` consistent with the TU core pattern:
+We define an effective tension tensor on `M_geo` that is compatible with the TU core pattern:
 
 ```txt
 T_ij(m) = S_i(m) * C_j(m) * DeltaS_geo(m) * lambda(m) * kappa_geo
@@ -319,11 +345,11 @@ T_ij(m) = S_i(m) * C_j(m) * DeltaS_geo(m) * lambda(m) * kappa_geo
 
 where:
 
-- `S_i(m)` are source like factors describing how strongly geometric information in `m` feeds into the i-th logical or physical component.
-- `C_j(m)` are receptivity like factors describing how sensitive the j-th component is to geometric inconsistencies.
-- `DeltaS_geo(m)` is the combined geometric tension score from above.
-- `lambda(m)` is a convergence state factor with values in a fixed bounded interval.
-- `kappa_geo` is a fixed coupling constant that sets the overall scale for geometric consistency_tension.
+* `S_i(m)` are source like factors describing how strongly geometric information in `m` feeds into the i-th logical or physical component.
+* `C_j(m)` are receptivity like factors describing how sensitive the j-th component is to geometric inconsistencies.
+* `DeltaS_geo(m)` is the combined geometric tension score from above.
+* `lambda(m)` is a convergence state factor with values in a fixed bounded interval, imported from the TU core as an external observable. This page does not define how `lambda(m)` is generated or updated.
+* `kappa_geo` is a fixed coupling constant that sets the overall scale for geometric consistency tension.
 
 We now define the singular set:
 
@@ -341,8 +367,51 @@ M_geo_reg = M_geo \ S_sing
 
 Domain restriction rule:
 
-- All evaluations of `DeltaS_geo(m)` and `T_ij(m)` in Q020 are only defined for `m` in `M_geo_reg`.
-- If an experiment or protocol encounters a state in `S_sing`, the outcome is flagged as “out of domain” and is not interpreted as evidence for or against any classification hypothesis.
+* All evaluations of `DeltaS_geo(m)` and `T_ij(m)` in Q020 are only defined for `m` in `M_geo_reg`.
+* If an experiment or protocol encounters a state in `S_sing`, the outcome is flagged as out of domain and is not interpreted as evidence for or against any classification hypothesis.
+* The decision that a state belongs to `S_sing` or `M_geo_reg` is itself made at the effective layer, using only the observables listed above.
+
+### 3.5 Encoding class and fairness constraints
+
+We collect the encoding choices into an explicit admissible encoding class.
+
+We define the admissible encoding class for Q020 as:
+
+```txt
+E_adm_geo
+```
+
+An element of `E_adm_geo` consists of:
+
+* a fixed dimension `n >= 5`,
+* a fixed curvature constraint class `C`,
+* a finite sample radius set `R_sample`,
+* a finite canonical model library `L_curv` chosen from a meta library of curvature constrained models,
+* a rule for computing `K_loc`, `Topo`, `VolGrowth`, `Diam`, and `Lib_score` from geometric input,
+* a weight vector `(a_curv, a_topo, a_lib)` with strictly positive entries that sum to 1.
+
+Fairness constraints for Q020 are:
+
+1. **Library locking**
+
+   * For any encoding in `E_adm_geo`, the library `L_curv` is selected once and then held fixed for all states and experiments that use that encoding.
+   * The library cannot be modified on a per state basis or separately for different subsets of examples.
+
+2. **Weight locking**
+
+   * For any encoding in `E_adm_geo`, the weight vector `(a_curv, a_topo, a_lib)` is chosen from a fixed finite set of admissible weight vectors that is specified before any evaluation is performed.
+   * The weights are not allowed to depend on data from specific states or experiment outcomes.
+
+3. **Observable rule stability**
+
+   * The rules that define `K_loc`, `Topo`, `VolGrowth`, `Diam`, and `Lib_score` are fixed in advance for a given encoding and are not tuned per example in order to lower `DeltaS_geo(m)`.
+
+4. **Versioning**
+
+   * It is allowed to define multiple encodings in `E_adm_geo` as separate versions for Q020, but each version must respect the same locking rules and must be evaluated as a whole.
+   * Any comparison across versions must account for the fact that changing `L_curv` or the weight vector is a change of encoding, not a result of adaptive tuning inside a single encoding.
+
+These constraints are intended to prevent per instance overfitting of the encoding to particular manifolds and to make the geometric tension scores meaningful as global indicators.
 
 ---
 
@@ -356,23 +425,25 @@ At the effective layer, Q020 is expressed in terms of the behavior of the combin
 
 We consider:
 
-- a fixed dimension `n >= 5`,
-- a fixed curvature constraint class `C`,
-- a fixed finite canonical library `L_curv`,
-- fixed weights `a_curv`, `a_topo`, `a_lib` as in Block 3.
+* a fixed dimension `n >= 5`,
+* a fixed curvature constraint class `C`,
+* a fixed finite canonical library `L_curv`,
+* fixed weights `a_curv`, `a_topo`, `a_lib` as in Block 3,
+* an encoding chosen from `E_adm_geo`.
 
 The central tension principle is:
 
-> Is it possible to choose a finite library `L_curv` and weights that are fixed in advance, such that for all geometrically realizable states `m` in `M_geo_reg` representing manifolds in class `C`, the geometric tension `DeltaS_geo(m)` remains confined to a small band for some controlled notion of approximation?
+> Is it possible to choose an admissible encoding in `E_adm_geo` such that for all geometrically realizable states `m` in `M_geo_reg` representing manifolds in class `C`, the geometric tension `DeltaS_geo(m)` remains confined to a small band for some controlled notion of approximation?
 
-If yes, then the curvature constrained manifolds behave as if they admit a finite or effectively finite classification. If no, they behave as if any finite library is intrinsically unable to capture their complexity.
+If the answer is yes for some encoding, then the curvature constrained manifolds behave as if they admit a finite or effectively finite classification under that encoding.
+If the answer is no in a robust sense, then they behave as if any finite library in the admissible class is intrinsically unable to capture their complexity.
 
 ### 4.2 Low tension world (finite classification compatible)
 
-We define the low tension principle:
+We define the low tension principle.
 
-- There exist constants `epsilon_geo > 0` and a function `epsilon_refine(k)` that decreases with a refinement parameter `k` (for example resolution of observables or size of sample sets), and:
-- There exists a fixed library `L_curv` and fixed weights such that:
+* There exist constants `epsilon_geo > 0` and a function `epsilon_refine(k)` that decreases with a refinement parameter `k` such as resolution of observables or size of sample sets.
+* There exists an encoding in `E_adm_geo` with fixed library `L_curv` and weights such that:
 
 ```txt
 for every realizable state m in M_geo_reg
@@ -384,13 +455,13 @@ where `m_refined(k)` denotes a refined version of `m` at higher resolution withi
 
 In words:
 
-- Under refinement that respects the curvature constraints and topological consistency, every physically relevant manifold can be well approximated by the finite library with small geometric tension.
+* Under refinement that respects the curvature constraints and topological consistency, every physically relevant manifold can be well approximated by the finite library with small geometric tension.
 
 ### 4.3 High tension world (wild classification)
 
-We define the high tension principle as the negation of the above in a robust sense:
+We define the high tension principle as a robust negation of the low tension principle.
 
-- For any fixed library `L_curv` and fixed weights that respect the constraints of Block 3, there exist realizable states in `M_geo_reg` such that:
+* For any encoding in `E_adm_geo` with finite library `L_curv` and locked weights, there exist realizable states in `M_geo_reg` such that:
 
 ```txt
 DeltaS_geo(m) >= delta_geo
@@ -400,18 +471,18 @@ for some `delta_geo > 0` that cannot be reduced below a positive threshold by an
 
 In words:
 
-- There are genuinely new geometric types in class `C` that remain far from the chosen finite library in terms of geometric tension, no matter how one refines the observable summaries.
+* There are genuinely new geometric types in class `C` that remain far from the chosen finite library in terms of geometric tension, no matter how one refines the observable summaries, as long as fairness constraints are respected.
 
-Q020 in the BlackHole context is therefore the question of whether our universe of curvature constrained high dimensional manifolds behaves more like a low tension finite classification world or a high tension wild classification world, under a fair encoding that does not tune parameters per instance.
+Q020 in the BlackHole context is therefore the question of whether the universe of curvature constrained high dimensional manifolds behaves more like a low tension finite classification world or a high tension wild classification world, under a fair encoding that does not tune parameters per instance.
 
 ---
 
 ## 5. Counterfactual tension worlds
 
-We describe two counterfactual worlds strictly at the effective layer:
+We describe two counterfactual worlds strictly at the effective layer.
 
-- World T: finite library classification world.
-- World F: intrinsically wild world.
+* World T: finite library classification world.
+* World F: intrinsically wild world.
 
 These are patterns of observables and tension scores, not explicit constructions of manifolds or flows.
 
@@ -421,31 +492,31 @@ In World T:
 
 1. Library adequacy at all scales
 
-   - There exists a fixed finite library `L_curv` such that for any state `m` in `M_geo_reg`, there is a refinement level `k` with:
+   There exists a fixed finite library `L_curv` such that for any state `m` in `M_geo_reg`, there is a refinement level `k` with:
 
-     ```txt
-     DeltaS_geo(m_refined(k)) <= epsilon_refine(k)
-     ```
+   ```txt
+   DeltaS_geo(m_refined(k)) <= epsilon_refine(k)
+   ```
 
-     and `epsilon_refine(k)` tends to 0 with increasing `k`.
+   and `epsilon_refine(k)` tends to 0 with increasing `k`.
 
 2. Flow toward canonical patterns
 
-   - Geometric flows such as Ricci flow, when applied to realizable states in `M_geo_reg`, move the observable summaries of `(X_m, g_m)` closer to some member of `L_curv`, with geometric tension decreasing along flow trajectories except at controlled singular times.
+   Geometric flows such as Ricci flow, when applied to realizable states in `M_geo_reg`, move the observable summaries of `(X_m, g_m)` closer to some member of `L_curv`, with geometric tension decreasing along flow trajectories except at controlled singular times.
 
 3. Coherent topology geometry alignment
 
-   - The topology observable `Topo(m)` for all realizable states remains inside the set predicted by curvature constraints together with the library patterns, leading to systematically small `DeltaS_topo(m)`.
+   The topology observable `Topo(m)` for all realizable states remains inside the set predicted by curvature constraints together with the library patterns, leading to systematically small `DeltaS_topo(m)`.
 
 4. Stable maximal tension bound
 
-   - There exists a uniform bound `T_max` such that:
+   There exists a uniform bound `T_max` such that:
 
-     ```txt
-     DeltaS_geo(m) <= T_max
-     ```
+   ```txt
+   DeltaS_geo(m) <= T_max
+   ```
 
-     for all realizable states in `M_geo_reg`, even before refinement.
+   for all realizable states in `M_geo_reg`, even before refinement.
 
 ### 5.2 World F (wild world, persistent high geometric tension)
 
@@ -453,39 +524,39 @@ In World F:
 
 1. Library incompleteness
 
-   - For any finite library `L_curv` chosen in advance and any allowed weights, there exist realizable states `m` in `M_geo_reg` such that:
+   For any finite library `L_curv` chosen in advance and any allowed weights within the admissible class, there exist realizable states `m` in `M_geo_reg` such that:
 
-     ```txt
-     DeltaS_lib(m) >= delta_lib
-     ```
+   ```txt
+   DeltaS_lib(m) >= delta_lib
+   ```
 
-     where `delta_lib` is a positive constant independent of refinements.
+   where `delta_lib` is a positive constant independent of refinements.
 
 2. Flow complexity and new patterns
 
-   - Geometric flows from some initial states exhibit behavior that cannot be approximated by any member of the current library, even after resolving singularities, yielding persistent high `DeltaS_curv(m)` and `DeltaS_geo(m)`.
+   Geometric flows from some initial states exhibit behavior that cannot be approximated by any member of the current library, even after resolving singularities, yielding persistently large `DeltaS_curv(m)` and `DeltaS_geo(m)`.
 
 3. Topology curvature tension
 
-   - There exist families of manifolds satisfying curvature constraints where `Topo(m)` takes values outside the region predicted by any finite set of library patterns, leading to:
+   There exist families of manifolds satisfying curvature constraints where `Topo(m)` takes values outside the region predicted by any finite set of library patterns, leading to:
 
-     ```txt
-     DeltaS_topo(m) >= delta_topo
-     ```
+   ```txt
+   DeltaS_topo(m) >= delta_topo
+   ```
 
-     for some positive `delta_topo`.
+   for some positive `delta_topo`.
 
 4. Unbounded tension tails
 
-   - For any pre chosen tolerance band, there exist realizable states with geometric tension above that band, indicating that no finite classification can confine all curvature constrained manifolds to low tension.
+   For any pre chosen tolerance band, there exist realizable states with geometric tension above that band, indicating that no finite classification can confine all curvature constrained manifolds to low tension.
 
 ### 5.3 Interpretive note
 
 These worlds are not claims about the actual truth of any specific classification conjecture. They are devices that:
 
-- organize the types of geometric behavior in terms of observables and tension scores,
-- allow us to test whether a given encoding behaves more like World T or World F for sets of examples,
-- ensure that Q020 remains at the effective layer without revealing any deep TU generative mechanism.
+* organize the types of geometric behavior in terms of observables and tension scores,
+* allow us to test whether a given encoding behaves more like World T or World F for sets of examples,
+* ensure that Q020 remains at the effective layer without revealing any TU core generative mechanism.
 
 ---
 
@@ -493,118 +564,127 @@ These worlds are not claims about the actual truth of any specific classificatio
 
 This block specifies experiments and protocols at the effective layer that can:
 
-- test the coherence of the Q020 encoding,
-- distinguish between different geometric tension models,
-- provide evidence for or against particular library and parameter choices.
+* test the coherence of the Q020 encoding,
+* distinguish between different geometric tension models,
+* provide evidence for or against particular library and parameter choices.
 
-These experiments do not solve Q020. They can only falsify or support specific TU encodings related to Q020.
+These experiments can falsify or support specific encodings drawn from `E_adm_geo`. They do not solve Q020 or any underlying classification conjecture. They only operate on observable summaries and effective layer tension scores.
 
 ### Experiment 1: Library fit across known examples
 
-*Goal:*
+**Goal**
 
 Test whether a chosen finite library `L_curv` and the combined tension score `DeltaS_geo` can simultaneously keep tension low on a broad set of known high dimensional curvature constrained manifolds without per instance tuning.
 
-*Setup:*
+**Setup**
 
-- Select a set `E_known` of known examples of high dimensional manifolds with curvature constraints in class `C`, such as:
-  - products of spheres and tori with controlled curvature,
-  - symmetric spaces and homogeneous spaces with known curvature bounds,
-  - examples constructed in the literature by gluing or surgery under curvature control.
-- For each example, define a state `m` in `M_geo_reg` that encodes observables `K_loc`, `Topo`, `VolGrowth`, `Diam`, and `Lib_score`.
+* Select a set `E_known` of known examples of high dimensional manifolds with curvature constraints in class `C`, such as:
 
-*Protocol:*
+  * products of spheres and tori with controlled curvature,
+  * symmetric spaces and homogeneous spaces with known curvature bounds,
+  * examples constructed in the literature by gluing or surgery under curvature control.
+* For each example, define a state `m` in `M_geo_reg` that encodes observables `K_loc`, `Topo`, `VolGrowth`, `Diam`, and `Lib_score`.
+
+**Protocol**
 
 1. Fix once and for all:
-   - the finite library `L_curv`,
-   - the weights `a_curv`, `a_topo`, `a_lib`,
-   - and a target low tension threshold `tau_low > 0`.
+
+   * the finite library `L_curv`,
+   * the weights `a_curv`, `a_topo`, `a_lib`,
+   * a target low tension threshold `tau_low > 0`,
+     inside a single encoding chosen from `E_adm_geo`.
 2. For each `m` in `E_known`, compute:
-   - `DeltaS_curv(m)`,
-   - `DeltaS_topo(m)`,
-   - `DeltaS_lib(m)`,
-   - and `DeltaS_geo(m)` from the formulas in Block 3.
+
+   * `DeltaS_curv(m)`,
+   * `DeltaS_topo(m)`,
+   * `DeltaS_lib(m)`,
+   * `DeltaS_geo(m)` from the formulas in Block 3.
 3. Record the proportion of examples with `DeltaS_geo(m) <= tau_low` and the maximum observed tension.
 
-*Metrics:*
+**Metrics**
 
-- `p_low = (number of examples with DeltaS_geo(m) <= tau_low) / (size of E_known)`.
-- `DeltaS_geo_max = max over m in E_known of DeltaS_geo(m)`.
-- Sensitivity of these metrics to modest changes in the observable summaries within their error margins.
+* `p_low = (number of examples with DeltaS_geo(m) <= tau_low) / (size of E_known)`.
+* `DeltaS_geo_max = max over m in E_known of DeltaS_geo(m)`.
+* Sensitivity of these metrics to modest changes in the observable summaries within their error margins.
 
-*Falsification conditions:*
+**Falsification conditions**
 
-- Define a target proportion `p_target` in `(0, 1]` and a maximum acceptable tension bound `T_target`.
-- The encoding is considered falsified for this library and weight choice if:
+* Define a target proportion `p_target` in `(0, 1]` and a maximum acceptable tension bound `T_target`.
+* The encoding is considered falsified for this library and weight choice if:
 
   ```txt
   p_low < p_target  or  DeltaS_geo_max > T_target
   ```
 
   even after checking that observable summaries are within reasonable error margins.
-- The encoding is also considered falsified if achieving `p_low >= p_target` or `DeltaS_geo_max <= T_target` requires retuning `L_curv` or the weights separately for different subsets of `E_known`.
+* The encoding is also considered falsified if achieving `p_low >= p_target` or `DeltaS_geo_max <= T_target` requires retuning `L_curv` or the weights separately for different subsets of `E_known`.
 
-*Semantics implementation note:*
+**Semantics implementation note**
 
 All observables and tension scores in this experiment are interpreted in the continuous field sense recorded in the metadata. No discrete or hybrid reinterpretation is applied.
 
-*Boundary note:*
+**Boundary note**
 
-Falsifying TU encoding != solving canonical statement. This experiment can reject particular choices of library and tension functional but does not resolve whether a true finite classification exists.
+Falsifying a TU encoding in this experiment does not settle the canonical classification statement for Q020. It only shows that a particular choice of library and tension functional is misaligned with the observed examples.
 
 ---
 
 ### Experiment 2: Flow based separation of simple and complex geometries
 
-*Goal:*
+**Goal**
 
 Check whether the geometric tension `DeltaS_geo` can distinguish between manifolds whose curvature evolves toward simple canonical patterns and those that exhibit complex or persistent singular behavior under geometric flows.
 
-*Setup:*
+**Setup**
 
-- Select families of initial states in `M_geo_reg` corresponding to:
-  - manifolds whose metrics are known or conjectured to evolve under a geometric flow (for example normalized Ricci flow) toward simple standard models,
-  - manifolds whose metrics are known or conjectured to produce complex singular behavior or non trivial limit spaces.
-- For each initial state, consider a sequence of effective states along the flow, denoted by `m(t_k)` for times `t_k` in an increasing sequence.
+* Select families of initial states in `M_geo_reg` corresponding to:
 
-*Protocol:*
+  * manifolds whose metrics are known or conjectured to evolve under a geometric flow such as normalized Ricci flow toward simple standard models,
+  * manifolds whose metrics are known or conjectured to produce complex singular behavior or nontrivial limit spaces.
+* For each initial state, consider a sequence of effective states along the flow, denoted by `m(t_k)` for times `t_k` in an increasing sequence.
 
-1. Fix the same library `L_curv` and weights `a_curv`, `a_topo`, `a_lib` as in Experiment 1.
+**Protocol**
+
+1. Fix the same library `L_curv` and weights `a_curv`, `a_topo`, `a_lib` as in Experiment 1, inside a single encoding from `E_adm_geo`.
 2. For each flow trajectory, compute `DeltaS_geo(m(t_k))` at each sampled time.
 3. Group trajectories into:
-   - `Group_simple`: those with flow behavior approaching canonical models,
-   - `Group_complex`: those with flow behavior showing complex singular patterns.
+
+   * `Group_simple`: those with flow behavior approaching canonical models,
+   * `Group_complex`: those with flow behavior showing complex singular patterns.
 4. Compare the evolution of `DeltaS_geo` between the two groups.
 
-*Metrics:*
+**Metrics**
 
-- For each trajectory, define:
-  - `DeltaS_geo_min = min over k of DeltaS_geo(m(t_k))`,
-  - `DeltaS_geo_final` as the tension at the latest sampled time.
-- Compare distributions of `DeltaS_geo_min` and `DeltaS_geo_final` between `Group_simple` and `Group_complex`.
+For each trajectory, define:
 
-*Falsification conditions:*
+* `DeltaS_geo_min = min over k of DeltaS_geo(m(t_k))`,
+* `DeltaS_geo_final` as the tension at the latest sampled time.
 
-- Choose thresholds `tau_simple` and `tau_complex` with `tau_simple < tau_complex`.
-- The encoding is considered ineffective and rejected for Q020 if:
-  - for a large fraction of trajectories in `Group_simple`, `DeltaS_geo_min` fails to fall below `tau_simple`, or
-  - for a large fraction of trajectories in `Group_complex`, `DeltaS_geo_final` is not significantly above `tau_simple`, or
-  - the distributions of `DeltaS_geo` for `Group_simple` and `Group_complex` cannot be statistically separated under any reasonable threshold choices.
-- The encoding is also rejected if small, non structural changes in observables lead to arbitrarily large changes in `DeltaS_geo` along flows without clear geometric reasons.
+Compare distributions of `DeltaS_geo_min` and `DeltaS_geo_final` between `Group_simple` and `Group_complex`.
 
-*Semantics implementation note:*
+**Falsification conditions**
+
+* Choose thresholds `tau_simple` and `tau_complex` with `tau_simple < tau_complex`.
+* The encoding is considered ineffective and rejected for Q020 if:
+
+  * for a large fraction of trajectories in `Group_simple`, `DeltaS_geo_min` fails to fall below `tau_simple`, or
+  * for a large fraction of trajectories in `Group_complex`, `DeltaS_geo_final` is not significantly above `tau_simple`, or
+  * the distributions of `DeltaS_geo` for `Group_simple` and `Group_complex` cannot be statistically separated under any reasonable threshold choices.
+* The encoding is also rejected if small, non structural changes in observables lead to arbitrarily large changes in `DeltaS_geo` along flows without clear geometric reasons.
+
+**Semantics implementation note**
 
 Flow time is treated as an additional parameter on continuous geometric fields, and all tension evaluations respect the continuous field interpretation from the metadata.
 
-*Boundary note:*
+**Boundary note**
 
-Falsifying TU encoding != solving canonical statement. This experiment probes whether the chosen encoding can meaningfully track geometric simplification and complexity but does not settle any classification conjecture.
+Falsifying a TU encoding in this experiment does not settle any classification conjecture covered by Q020. It probes whether the chosen encoding can meaningfully track geometric simplification and complexity.
 
 ---
 
 ## 7. AI and WFGY engineering spec
 
-This block describes how Q020 can be used as an engineering module for AI systems within the WFGY framework at the effective layer.
+This block describes how Q020 can be used as an engineering module for AI systems within the WFGY framework at the effective layer. All modules and signals described here operate only on effective layer observables and derived tension scores.
 
 ### 7.1 Training signals
 
@@ -612,48 +692,51 @@ We define several training signals that can be plugged into AI models to support
 
 1. `signal_curvature_consistency`
 
-   - Definition: a nonnegative signal proportional to `DeltaS_curv(m)` for states representing geometric contexts.
-   - Purpose: penalize internal representations that imply geometric configurations violating chosen curvature constraints.
+   * Definition: a nonnegative signal proportional to `DeltaS_curv(m)` for states representing geometric contexts.
+   * Purpose: penalize internal representations that imply geometric configurations violating chosen curvature constraints.
 
 2. `signal_topo_geometric_alignment`
 
-   - Definition: a nonnegative signal proportional to `DeltaS_topo(m)`.
-   - Purpose: encourage consistency between stated topological properties and curvature related constraints.
+   * Definition: a nonnegative signal proportional to `DeltaS_topo(m)`.
+   * Purpose: encourage consistency between stated topological properties and curvature related constraints.
 
 3. `signal_library_fit`
 
-   - Definition: a signal derived from `DeltaS_lib(m)`, for example mapping low mismatch to higher scores.
-   - Purpose: guide the model to think in terms of finite libraries of canonical geometries when that is an appropriate abstraction.
+   * Definition: a signal derived from `DeltaS_lib(m)`, for example mapping low mismatch to higher scores.
+   * Purpose: guide the model to think in terms of finite libraries of canonical geometries when that is an appropriate abstraction.
 
 4. `signal_geometric_tension_score`
 
-   - Definition: directly equal to `DeltaS_geo(m)` for selected states `m`.
-   - Purpose: serve as a scalar tension indicator that can be minimized in tasks where finite classification assumptions are part of the context.
+   * Definition: directly equal to `DeltaS_geo(m)` for selected states `m`.
+   * Purpose: serve as a scalar tension indicator that can be minimized in tasks where finite classification assumptions are part of the context.
 
 ### 7.2 Architectural patterns
 
-We outline module patterns that reuse Q020 structures without exposing any deep TU generative rules.
+We outline module patterns that reuse Q020 structures without exposing any TU core generative rules.
 
 1. `GeomTensionHead`
 
-   - Role: given an internal embedding of a mathematical or physical context involving manifolds and curvature, outputs an estimate of `DeltaS_geo(m)` and its components.
-   - Interface:
-     - Input: internal vector representation of the context.
-     - Output: approximate values for `DeltaS_curv`, `DeltaS_topo`, `DeltaS_lib`, and `DeltaS_geo`.
+   * Role: given an internal embedding of a mathematical or physical context involving manifolds and curvature, outputs an estimate of `DeltaS_geo(m)` and its components.
+   * Interface:
+
+     * Input: internal vector representation of the context.
+     * Output: approximate values for `DeltaS_curv`, `DeltaS_topo`, `DeltaS_lib`, and `DeltaS_geo`.
 
 2. `CurvatureTopologyDescriptor`
 
-   - Role: an observer module that extracts low dimensional features corresponding to `K_loc`, `Topo`, `VolGrowth`, and `Diam` from internal representations.
-   - Interface:
-     - Input: internal embeddings.
-     - Output: a fixed length feature vector summarizing curvature and topology style information.
+   * Role: an observer module that extracts low dimensional features corresponding to `K_loc`, `Topo`, `VolGrowth`, and `Diam` from internal representations.
+   * Interface:
+
+     * Input: internal embeddings.
+     * Output: a fixed length feature vector summarizing curvature and topology style information suitable for classification and tension evaluation.
 
 3. `FiniteGeomLibraryClassifier`
 
-   - Role: a classifier that maps the descriptors from `CurvatureTopologyDescriptor` to approximate membership scores for the finite library `L_curv`.
-   - Interface:
-     - Input: curvature topology feature vector.
-     - Output: `Lib_score(m; L_k)` for each `L_k` and a summary mismatch estimate.
+   * Role: a classifier that maps the descriptors from `CurvatureTopologyDescriptor` to approximate membership scores for the finite library `L_curv`.
+   * Interface:
+
+     * Input: curvature topology feature vector.
+     * Output: values `Lib_score(m; L_k)` for each `L_k` and a summary mismatch estimate.
 
 ### 7.3 Evaluation harness
 
@@ -661,113 +744,125 @@ We suggest an evaluation harness for AI models augmented with Q020 modules.
 
 1. Task selection
 
-   - Construct question sets where models must:
-     - assess whether two described manifolds are likely to belong to the same geometric class under given curvature constraints,
-     - judge the plausibility of proposed classification statements,
-     - reason about consequences of adding or removing curvature assumptions.
+   Construct question sets where models must:
+
+   * assess whether two described manifolds are likely to belong to the same geometric class under given curvature constraints,
+   * judge the plausibility of proposed classification statements,
+   * reason about consequences of adding or removing curvature assumptions.
 
 2. Conditions
 
-   - Baseline condition:
-     - The model answers these questions using standard reasoning without explicit geometric tension modules.
-   - TU enhanced condition:
-     - The model also uses `GeomTensionHead` and `CurvatureTopologyDescriptor` as auxiliary modules, with training signals derived from Q020 observables.
+   * Baseline condition:
+     The model answers these questions using standard reasoning without explicit geometric tension modules.
+   * TU enhanced condition:
+     The model also uses `GeomTensionHead` and `CurvatureTopologyDescriptor` as auxiliary modules, with training signals derived from Q020 observables.
 
 3. Metrics
 
-   - Accuracy on structured geometry questions.
-   - Consistency of answers when similar questions are asked with slightly different phrasings.
-   - Ability to identify when a proposed manifold example seems incompatible with the stated curvature constraints.
+   * Accuracy on structured geometry questions.
+   * Consistency of answers when similar questions are asked with slightly different phrasings.
+   * Ability to identify when a proposed manifold example seems incompatible with the stated curvature constraints.
 
 ### 7.4 60 second reproduction protocol
 
 A simple protocol for external users to experience the effect of Q020 encoding.
 
-- Baseline setup:
+* Baseline setup
 
-  - Prompt: ask the AI to explain how curvature constraints in high dimensions can restrict possible manifold shapes and whether a finite classification is plausible.
-  - Observation: note whether the explanation is vague, mixes incompatible examples, or fails to distinguish local and global issues.
+  * Prompt an AI system to explain how curvature constraints in high dimensions can restrict possible manifold shapes and whether a finite classification is plausible, without explicit mention of TU or Q020.
+  * Observe whether the explanation is vague, mixes incompatible examples, or fails to distinguish local and global issues.
 
-- TU encoded setup:
+* TU encoded setup
 
-  - Prompt: ask the same question but instruct the AI to:
-    - describe manifolds using curvature and topology descriptors,
-    - think in terms of a finite geometric library,
-    - and explicitly mention a geometric tension score between manifolds and library patterns.
-  - Observation: note whether the explanation is more structured, with clear separation between local curvature, global topology, and classification attempts.
+  * Prompt the same system, now instructing it to:
 
-- Comparison metric:
+    * describe manifolds using curvature and topology descriptors,
+    * think in terms of a finite geometric library,
+    * explicitly mention a geometric tension score between manifolds and library patterns.
+  * Observe whether the explanation is more structured, with clear separation between local curvature, global topology, and classification attempts.
 
-  - Use a rubric that scores:
-    - structural clarity,
-    - explicit mention of constraints and limitations,
-    - consistency when multiple related questions are asked.
+* Comparison metric
 
-- What to log:
+  * Use a rubric that scores:
 
-  - The prompts, full responses, and any internal tension estimates produced by Q020 modules, for later inspection and comparison.
+    * structural clarity,
+    * explicit mention of constraints and limitations,
+    * consistency when multiple related questions are asked.
+
+* What to log
+
+  * The prompts, full responses, and any internal tension estimates produced by Q020 modules, for later inspection and comparison.
 
 ---
 
 ## 8. Cross problem transfer template
 
-This block describes the reusable components produced by Q020 and how they transfer to other problems.
+This block describes the reusable components produced by Q020 and how they transfer to other problems. All components operate at the effective layer and depend only on the observables and tension functionals defined above.
 
 ### 8.1 Reusable components produced by this problem
 
 1. ComponentName: `GeometricTensionScore_Q020`
 
-   - Type: functional
-   - Minimal interface:
-     - Inputs: `curvature_topology_features` summarizing `K_loc`, `Topo`, `VolGrowth`, `Diam`, and library scores.
-     - Output: `tension_value` equal to `DeltaS_geo(m)` for the encoded state.
-   - Preconditions:
-     - Features must correspond to a state in `M_geo_reg`, with all observables well defined.
+   * Type: functional
+   * Minimal interface:
+
+     * Inputs: `curvature_topology_features` summarizing `K_loc`, `Topo`, `VolGrowth`, `Diam`, and library scores.
+     * Output: `tension_value` equal to `DeltaS_geo(m)` for the encoded state.
+   * Preconditions:
+
+     * Features must correspond to a state in `M_geo_reg`, with all observables well defined.
 
 2. ComponentName: `CurvatureTopologyDescriptor`
 
-   - Type: field
-   - Minimal interface:
-     - Inputs: state representation or internal embedding for a geometric context.
-     - Output: fixed length feature vector capturing balanced curvature and topology information suitable for classification.
+   * Type: field
+   * Minimal interface:
+
+     * Inputs: state representation or internal embedding for a geometric context.
+     * Output: fixed length feature vector capturing balanced curvature and topology information suitable for classification and tension evaluation.
+   * Preconditions:
+
+     * Input representation must carry enough information for curvature and topology summaries to be approximated in a stable way.
 
 3. ComponentName: `FiniteGeomLibrary_Template`
 
-   - Type: experiment_pattern
-   - Minimal interface:
-     - Inputs: a library size bound, a curvature constraint class `C`, and a family of example states.
-     - Output: a protocol that:
-       - selects a candidate finite library `L_curv`,
-       - defines `Lib_score` and `DeltaS_lib`,
-       - and evaluates classification tension across the examples.
-   - Preconditions:
-     - Example states must be in `M_geo_reg` and represent valid curvature constrained manifolds.
+   * Type: experiment_pattern
+   * Minimal interface:
+
+     * Inputs: a library size bound, a curvature constraint class `C`, and a family of example states.
+     * Output: a protocol that:
+
+       * selects a candidate finite library `L_curv`,
+       * defines `Lib_score` and `DeltaS_lib`,
+       * evaluates classification tension across the examples under fairness constraints.
+   * Preconditions:
+
+     * Example states must be in `M_geo_reg` and represent valid curvature constrained manifolds.
 
 ### 8.2 Direct reuse targets
 
 1. Q017 (geometric flows)
 
-   - Reused components: `GeometricTensionScore_Q020`, `CurvatureTopologyDescriptor`.
-   - Why it transfers: Q017 studies flow behavior of metrics, and Q020 provides a ready made way to measure whether flows move manifolds toward low tension canonical types.
-   - What changes: the time parameter along flows becomes part of the input features, and experiments focus on trajectories rather than static manifolds.
+   * Reused components: `GeometricTensionScore_Q020`, `CurvatureTopologyDescriptor`.
+   * Why it transfers: Q017 studies flow behavior of metrics, and Q020 provides a ready made way to measure whether flows move manifolds toward low tension canonical types.
+   * What changes: the time parameter along flows becomes part of the input features, and experiments focus on trajectories rather than static manifolds.
 
 2. Q021 (quantum gravity spacetime selection)
 
-   - Reused components: `CurvatureTopologyDescriptor`, `FiniteGeomLibrary_Template`.
-   - Why it transfers: many spacetime models are built on high dimensional manifolds with curvature constraints, and Q020’s template can restrict candidate geometries to manageable sets.
-   - What changes: the observables are enriched by physical quantities such as energy conditions, but geometric tension remains a core component.
+   * Reused components: `CurvatureTopologyDescriptor`, `FiniteGeomLibrary_Template`.
+   * Why it transfers: many spacetime models are built on high dimensional manifolds with curvature constraints, and Q020 templates can restrict candidate geometries to manageable sets.
+   * What changes: the observables are enriched by physical quantities such as energy conditions, but geometric tension remains a core component.
 
 3. Q040 (black hole information)
 
-   - Reused components: `GeometricTensionScore_Q020`.
-   - Why it transfers: candidate black hole spacetimes can be evaluated on whether their global geometry under curvature and topological constraints fits into a finite library of “information carrying geometries”.
-   - What changes: additional observables corresponding to horizons and causal structure are attached to the descriptors.
+   * Reused components: `GeometricTensionScore_Q020`.
+   * Why it transfers: candidate black hole spacetimes can be evaluated on whether their global geometry under curvature and topological constraints fits into a finite library of information carrying geometries.
+   * What changes: additional observables corresponding to horizons and causal structure are attached to the descriptors.
 
 4. Q123 (AI representation manifolds)
 
-   - Reused components: `CurvatureTopologyDescriptor`, `FiniteGeomLibrary_Template`.
-   - Why it transfers: internal AI representation spaces can be treated as abstract manifolds, and Q020 offers a way to ask whether their shapes fall into a finite set of canonical geometries.
-   - What changes: curvature and topology observables become representation theoretic features rather than physical or mathematical curvature data.
+   * Reused components: `CurvatureTopologyDescriptor`, `FiniteGeomLibrary_Template`.
+   * Why it transfers: internal AI representation spaces can be treated as abstract manifolds, and Q020 offers a way to ask whether their shapes fall into a finite set of canonical geometries under smoothness and curvature style assumptions.
+   * What changes: curvature and topology observables become representation theoretic features rather than physical or mathematical curvature data.
 
 ---
 
@@ -777,41 +872,44 @@ This block explains how Q020 is positioned along the TU verification ladder and
 
 ### 9.1 Current levels
 
-- E_level: E1
+* E_level: E1
 
-  - A coherent effective layer encoding of Q020 has been specified.
-  - Observables, mismatch functionals, and a combined geometric tension score are defined.
-  - At least two explicit experiment patterns with falsification conditions have been described.
+  * A coherent effective layer encoding of Q020 has been specified.
+  * Observables, mismatch functionals, and a combined geometric tension score are defined.
+  * At least two explicit experiment patterns with falsification conditions have been described.
+  * Encoding class and fairness constraints are stated and can be audited.
 
-- N_level: N1
+* N_level: N1
 
-  - A narrative exists that links curvature constraints, global topology, and finite library classification in terms of geometric tension.
-  - Counterfactual worlds (finite library versus wild) are clearly distinguished at the level of observables.
+  * A narrative exists that links curvature constraints, global topology, and finite library classification in terms of geometric tension.
+  * Counterfactual worlds, finite library versus wild world, are clearly distinguished at the level of observables.
 
 ### 9.2 Next measurable step toward E2
 
-To move from E1 to E2, at least one of the following should be realized in practice:
+To move from E1 to E2, at least one of the following should be realized in practice.
 
 1. Implement a prototype that:
-   - encodes a nontrivial set of high dimensional curvature constrained manifolds as states in `M_geo_reg`,
-   - computes approximate `CurvatureTopologyDescriptor` features,
-   - and evaluates `DeltaS_geo(m)` for these examples, publishing the resulting tension profiles.
+
+   * encodes a nontrivial set of high dimensional curvature constrained manifolds as states in `M_geo_reg`,
+   * computes approximate `CurvatureTopologyDescriptor` features,
+   * evaluates `DeltaS_geo(m)` for these examples, publishing the resulting tension profiles as open data.
 
 2. Instantiate the `FiniteGeomLibrary_Template` with:
-   - a concrete curvature constraint class (for example nonnegative sectional curvature in specific dimensions),
-   - a specific finite library `L_curv`,
-   - and a well documented set of examples from the literature,
-   and perform Experiment 1 to test whether the chosen library achieves acceptable tension metrics.
 
-Both steps operate entirely at the effective layer and do not require revealing any deep TU generative rules.
+   * a concrete curvature constraint class such as nonnegative sectional curvature in specific dimensions,
+   * a specific finite library `L_curv`,
+   * a well documented set of examples from the literature,
+     and perform Experiment 1 to test whether the chosen library achieves acceptable tension metrics under fairness constraints.
+
+Both steps operate entirely at the effective layer and do not require revealing any TU core generative rules. They can, however, falsify particular encodings in `E_adm_geo`.
 
 ### 9.3 Long term role in the TU program
 
 In the long term, Q020 is expected to:
 
-- serve as the central node for high dimensional geometric classification problems under curvature constraints,
-- provide a template for how TU handles classification tension in other domains (for example complex state spaces in physics and AI),
-- and act as a bridge between rigorous geometric analysis and effective tension based reasoning in AI systems.
+* serve as the central node for high dimensional geometric classification problems under curvature constraints,
+* provide a template for how TU handles classification tension in other domains such as complex state spaces in physics and AI,
+* act as a bridge between rigorous geometric analysis and effective tension based reasoning in AI systems.
 
 ---
 
@@ -819,10 +917,10 @@ In the long term, Q020 is expected to:
 
 This block gives an explanation suitable for non specialists while remaining aligned with the effective layer description.
 
-When people talk about “curvature” in geometry, they often imagine:
+When people talk about curvature in geometry, they often imagine:
 
-- surfaces that bend, like spheres, saddles, or flat planes,
-- and the way this bending constrains what the space can look like overall.
+* surfaces that bend such as spheres, saddles, or flat planes,
+* and the way this bending constrains what the space can look like overall.
 
 In high dimensions, manifolds can be very complicated, but they still have curvature. Q020 asks:
 
@@ -830,32 +928,66 @@ In high dimensions, manifolds can be very complicated, but they still have curva
 
 In the Tension Universe view:
 
-- Each “shape” is represented by a state `m` that summarizes:
-  - how curved the space is at different scales,
-  - what its overall topology looks like (for example holes and connectedness),
-  - how similar it is to a small set of standard spaces (a finite library).
+* Each shape is represented by a state `m` that summarizes:
+
+  * how curved the space is at different scales,
+  * what its overall topology looks like, including holes and connectedness,
+  * how similar it is to a small set of standard spaces, the finite library.
 
 We then define:
 
-- numbers that measure how much the shape breaks curvature rules,
-- numbers that measure how its topology fits known curvature constraints,
-- and a score that measures how far it is from the finite library.
+* numbers that measure how much the shape pushes against curvature rules,
+* numbers that measure how its topology fits known curvature constraints,
+* a score that measures how far it is from the finite library.
 
 All of these are combined into a single geometric tension score `DeltaS_geo(m)`.
 
-Two extreme possibilities emerge:
+Two extreme possibilities emerge.
 
-- In a finite classification world:
-  - every allowed shape can, after looking at it in enough detail, be well approximated by one of the library models,
-  - the geometric tension can always be made small by refining how we look at the shape.
-- In a wild world:
-  - no matter how we choose a finite library, there are always shapes whose tension stays large,
-  - new kinds of shapes keep appearing that do not fit into a small list of patterns.
+* In a finite classification world:
 
-Q020 does not claim to solve this question. Instead, it:
+  * every allowed shape can, after looking at it in enough detail, be well approximated by one of the library models,
+  * the geometric tension can always be made small by refining how we look at the shape.
 
-- formalizes the problem at the level of observable summaries and tension scores,
-- suggests experiments for testing how well any proposed finite library works on known examples and model flows,
-- and offers reusable tools that can be plugged into AI systems that need to reason carefully about geometry.
+* In a wild world:
 
-In this way, Q020 functions as the geometric counterpart to other BlackHole problems: it tests whether “local rules plus a small catalog” can explain the global structure of complicated high dimensional spaces, or whether the universe of such spaces is intrinsically more wild.
+  * no matter how we choose a finite library under fair rules, there are always shapes whose tension stays large,
+  * new kinds of shapes keep appearing that do not fit into a small list of patterns.
+
+Q020 does not claim to resolve which of these pictures is correct for real high dimensional manifolds. It instead:
+
+* formalizes the problem at the level of observable summaries and tension scores,
+* suggests experiments for testing how well any proposed finite library works on known examples and model flows,
+* offers reusable tools that can be plugged into AI systems that need to reason carefully about geometry.
+
+In this way, Q020 functions as the geometric counterpart to other BlackHole problems. It tests whether local curvature rules plus a small catalog can explain the global structure of complicated high dimensional spaces, or whether the universe of such spaces is intrinsically more wild.
+
+---
+
+## Tension Universe effective layer footer
+
+This page is part of the WFGY / Tension Universe S problem collection.
+
+### Scope of claims
+
+* The goal of this document is to specify an effective layer encoding of the named problem.
+* It does not claim to prove or disprove the canonical statement in Section 1.
+* It does not introduce any new theorem beyond what is already established in the cited literature.
+* It should not be cited as evidence that the corresponding open problem has been solved.
+* Any mention of counterfactual worlds or experiments concerns only observable patterns and encodings, not the mathematical truth of classification conjectures.
+
+### Effective layer boundary
+
+* All objects used here, including state spaces `M_geo`, observables, invariants, tension scores, and counterfactual worlds, live at the effective layer of the Tension Universe framework.
+* No axiom system or generative rule for TU is specified or modified on this page.
+* No explicit mapping from raw geometric data to TU internal fields is provided. Only the existence of such mappings at the level of observables is assumed.
+* Quantities such as `lambda(m)` and `T_ij(m)` are treated as externally supplied TU core observables and coupling factors. Their internal dynamics and construction are outside the scope of this document.
+* All experiments operate on observable summaries and derived tension scores and cannot, by themselves, settle any open classification problem.
+
+### Relation to TU charters
+
+This page should be read together with the following charters:
+
+* [TU Effective Layer Charter](../Charters/TU_EFFECTIVE_LAYER_CHARTER.md)
+* [TU Encoding and Fairness Charter](../Charters/TU_ENCODING_AND_FAIRNESS_CHARTER.md)
+* [TU Tension Scale Charter](../Charters/TU_TENSION_SCALE_CHARTER.md)