Charge Boundary Routing I
Phase 2 — A <-> B Bridge Chamber Comparison Report
AB_bridge_chamber_comparison_report.txt

Generated: 2026-06-15

Bridge
------
A <-> B
Name: External Primitive Closures to Confined Fractional Coordinates

Bridge meaning:
    Layer A — primitive external integer / neutral charge closures
    Layer B — confined fractional internal charge coordinates

Central question:
    Does the external primitive charge layer connect directly to the
    confined fractional coordinate layer, or does it require composite
    closure as a mediator?

Why this bridge matters:
    A <-> B is the difficult interface between ordinary external charge
    states and confined fractional coordinates. It tests whether free
    external charge and confined fractional charge share a direct charge-value
    ladder, or whether their relation is only coherent in route / closure
    coordinates.

Instruments
-----------
STRUC-PERC-I v2.5.0
    Role: full pairwise vulnerability graph / percolation / fragmentation screen.

STRUC-I v1.0.4
    Role: admissibility-pressure / perturbation-boundary screen.
    Inequality: inv(P_epsilon; L) <= nu(V_epsilon(L)).

Input Files
-----------
- AB_bridge_external_to_fractional_ladder_absolute_charge.csv
- AB_bridge_external_to_fractional_ladder_boundary_route_coordinate.csv
- AB_bridge_external_to_fractional_ladder_closure_class_code.csv
- AB_bridge_external_to_fractional_ladder_closure_state_code.csv
- AB_bridge_external_to_fractional_ladder_route_class_code.csv
- AB_bridge_external_to_fractional_ladder_signed_charge.csv

Important STRUC-I Naming Note
-----------------------------
STRUC-I exported all six ladder names simply as 'AB'.
Therefore, STRUC-I results are interpreted by the original upload order:

    1. absolute_charge
    2. boundary_route_coordinate
    3. closure_class_code
    4. closure_state_code
    5. route_class_code
    6. signed_charge

Executive Result
----------------
The A <-> B bridge fragments in charge-value topology but shows weak
persistence in absolute-charge perturbation geometry.

STRUC-PERC-I result:

    signed_charge / absolute_charge -> HARD_FRAGMENTATION
    route / closure encodings       -> FULL_PERCOLATION

STRUC-I result:

    absolute_charge -> Geometric Persistence / Weak Persistence
    all others      -> Structural Boundary / Transitional Structure

Compact result statement:

    The external-to-fractional bridge is not connected as a raw charge-value
    percolation graph, but its absolute-charge ladder is magnitude-stable
    under perturbation.

Combined Result Table
---------------------

| Encoding | STRUC-PERC-I verdict | Giant ratio | Isolated | kappa_connect | STRUC-I regime | STRUC-I state | mean Aκ | min Aκ | mean rho | max rho | Interpretation |
|---|---:|---:|---:|---:|---|---|---:|---:|---:|---:|---|
| absolute_charge | HARD_FRAGMENTATION | 0.75 | 1 | null | Geometric Persistence | Weak Persistence | 0.944375 | 0.9195 | 0.848233 | 0.877577 | Fragments in STRUC-PERC-I but reaches Geometric Persistence / Weak Persistence in STRUC-I. This is the strongest AB perturbation coordinate and indicates magnitude-stable boundary geometry. |
| boundary_route_coordinate | FULL_PERCOLATION | 1 | 0 | 2 | Structural Boundary | Transitional Structure | 0.902162 | 0.871 | 0.885804 | 0.907038 | Percolates in STRUC-PERC-I but remains Structural Boundary / Transitional Structure in STRUC-I. The explicit route coordinate connects the interface but still carries boundary pressure. |
| closure_class_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.903538 | 0.883 | 0.885907 | 0.903615 | Percolates in STRUC-PERC-I and remains transitional in STRUC-I. Closure taxonomy carries bridge connectivity, but not full perturbation persistence. |
| closure_state_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.838375 | 0.8095 | 0.923989 | 0.933962 | Percolates as a compact two-state bridge, but remains lower in A-kappa and higher in rho. It captures external-closed versus internal-fractional contrast as a pressure-sensitive boundary. |
| route_class_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.840113 | 0.8245 | 0.923897 | 0.931038 | Percolates as a compact route ladder but remains Structural Boundary. It behaves similarly to closure_state_code and marks the external-closure / confined-route split. |
| signed_charge | HARD_FRAGMENTATION | 0.666666666667 | 0 | null | Structural Boundary | Transitional Structure | 0.904763 | 0.875 | 0.847336 | 0.868409 | Fragments in STRUC-PERC-I but is not the weakest STRUC-I coordinate. It remains transitional, showing that signed charge does not connect the bridge topologically. |

STRUC-PERC-I Findings
---------------------
The AB bridge shows a charge-value versus route/closure split:

    signed_charge   -> HARD_FRAGMENTATION
    absolute_charge -> HARD_FRAGMENTATION
    boundary_route_coordinate -> FULL_PERCOLATION
    closure_class_code        -> FULL_PERCOLATION
    closure_state_code        -> FULL_PERCOLATION
    route_class_code          -> FULL_PERCOLATION

- absolute_charge: HARD_FRAGMENTATION (giant ratio = 0.75, isolated = 1, kappa_connect = null, n = 4)
- boundary_route_coordinate: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 2, n = 4)
- closure_class_code: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 0.01, n = 3)
- closure_state_code: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 0.01, n = 2)
- route_class_code: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 0.01, n = 2)
- signed_charge: HARD_FRAGMENTATION (giant ratio = 0.666666666667, isolated = 0, kappa_connect = null, n = 6)

Interpretation:
    The A <-> B interface does not form a connected raw charge-value graph.
    Both signed and absolute charge fragment under STRUC-PERC-I. However,
    the route and closure encodings fully percolate. This means that external
    primitive charge and confined fractional charge do not meet as a simple
    value ladder. They meet as a route / closure distinction.

STRUC-I Findings
----------------
STRUC-I classifies absolute_charge as:

    Geometric Persistence / Weak Persistence

and the remaining five encodings as:

    Structural Boundary / Transitional Structure

Strongest AB STRUC-I encoding:

    absolute_charge
    mean Aκ = 0.944375
    min Aκ  = 0.9195
    mean rho = 0.848233
    max rho  = 0.877577

Weakest AB STRUC-I encoding:

    closure_state_code
    mean Aκ = 0.838375
    min Aκ  = 0.8095
    mean rho = 0.923989
    max rho  = 0.933962

Interpretation:
    The AB bridge is subtle. STRUC-PERC-I says the charge-value topology
    fragments, but STRUC-I says the absolute-charge ladder has the strongest
    perturbation geometry and reaches Weak Persistence. Therefore the AB
    interface is not route-persistent in the same way as BC. It is a
    magnitude-stable boundary interface.

Relation to Phase 1
-------------------
Phase 1 showed:

    Layer A alone:
        signed_charge percolated and reached Geometric Persistence / Weak Persistence;
        route / closure encodings fragmented or remained transitional.

    Layer B alone:
        all encodings percolated in STRUC-PERC-I;
        all remained Structural Boundary / Transitional Structure in STRUC-I.

The AB bridge now adds:

    signed_charge and absolute_charge fragment as a bridge topology;
    route / closure encodings percolate as a bridge topology;
    absolute_charge becomes weakly persistent under perturbation.

This means AB is not simply Layer A plus Layer B. The interface itself
has a distinct signature: value-fragmented, route-connected, and
magnitude-stable under perturbation.

Relation to BC
--------------
BC showed:

    signed_charge fragments;
    route / closure / magnitude encodings percolate;
    all STRUC-I encodings remain Structural Boundary / Transitional Structure.

AB shows:

    signed_charge and absolute_charge fragment in STRUC-PERC-I;
    route / closure encodings percolate in STRUC-PERC-I;
    absolute_charge reaches Geometric Persistence / Weak Persistence in STRUC-I.

Therefore:

    BC is a route-connected but admissibility-transitional bridge.
    AB is a value-fragmented but magnitude-stable boundary interface.

This difference is scientifically useful. It suggests that the external
primitive layer and confined fractional layer do not join directly as a
simple route-core. Their direct interface is boundary-like, whereas the
fractional-to-composite bridge is the more natural route-core.

Relation to ABCD Combined Result
--------------------------------
The ABCD combined result showed:

    signed_charge fragments
    route / closure encodings percolate

AB partially matches this pattern:

    signed_charge fragments
    route / closure encodings percolate

But AB also adds a new feature:

    absolute_charge fragments in STRUC-PERC-I but weakly persists in STRUC-I.

This suggests that AB contributes a magnitude-stable boundary component to
the full ABCD structure, while BC likely supplies the central route connection.

UNNS Interpretation
-------------------
In the UNNS Substrate interpretation, the A <-> B bridge is the interface
between externalized charge closure and confined fractional coordinate.

The chamber results support the following reading:

    The A <-> B interface does not become coherent as a signed-charge or
    absolute-charge percolation graph.

    It becomes graph-connected only when represented through route and
    closure coordinates.

    Yet absolute charge remains the most stable perturbation coordinate.

Thus AB is not the main route-core. It is a boundary interface where magnitude
is perturbatively stable but topological charge-value connectivity fragments.

Key finding:

    The A <-> B bridge is a magnitude-stable boundary interface, not a simple
    charge-value connection between external and fractional regimes.

Supported Claims
----------------
Supported by this AB bridge test:

1. The A <-> B signed_charge encoding fragments in STRUC-PERC-I.
2. The A <-> B absolute_charge encoding fragments in STRUC-PERC-I.
3. The A <-> B route / closure encodings fully percolate in STRUC-PERC-I.
4. The A <-> B absolute_charge encoding reaches Geometric Persistence / Weak Persistence in STRUC-I.
5. All other A <-> B encodings remain Structural Boundary / Transitional Structure in STRUC-I.
6. The A <-> B interface is better interpreted as a boundary interface than as the main route-core.

Not Claimed
-----------
This result does not yet claim:

1. A derivation of charge quantization.
2. A proof of confinement.
3. That AB alone explains the full ABCD structure.
4. That weak persistence is equivalent to final geometric stability.
5. That charge magnitude alone is the complete physical explanation.

Operational Consequence
-----------------------
Keep AB as a separate bridge class:

    value-fragmented
    route-connected
    magnitude-stable under perturbation

Do not collapse AB into the BC interpretation. AB and BC have different
scientific roles.

Next bridge to run:

    C <-> D

Reason:
    C <-> D tests whether the composite closure layer changes sharply when
    boundary absences and constraints are attached.

File Placement
--------------
Save this report as:

    charge_boundary_routing_i/
    └── outputs/
        └── reports/
            └── phase2_bridges/
                └── AB/
                    └── AB_bridge_chamber_comparison_report.txt

Supporting result files:

    results/struc_perc_i/phase2_bridges/AB/
        AB_STRUC_PERC_I_v2_5_0_batch_results.csv
        AB_STRUC_PERC_I_v2_5_0_batch_results.json

    results/struc_i/phase2_bridges/AB/
        AB_STRUC_I_v1_0_4_profiles.csv
        AB_STRUC_I_v1_0_4_results.json
