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

Generated: 2026-06-15

Bridge
------
B <-> C
Name: Confined Fractional Coordinates to Composite Closures

Bridge meaning:
    Layer B — confined fractional internal charge coordinates
    Layer C — composite integer / neutral charge closures

Central question:
    Do fractional quark charge coordinates route coherently into integer
    or neutral composite closures?

Why this bridge matters:
    B <-> C is the central physical bridge of Charge Boundary Routing I.
    It tests whether the transition from confined fractional charge to
    composite closure is organized by raw charge value or by route / closure
    structure.

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
-----------
- BC_bridge_fractional_to_composite_ladder_absolute_charge.csv
- BC_bridge_fractional_to_composite_ladder_boundary_route_coordinate.csv
- BC_bridge_fractional_to_composite_ladder_closure_class_code.csv
- BC_bridge_fractional_to_composite_ladder_closure_state_code.csv
- BC_bridge_fractional_to_composite_ladder_route_class_code.csv
- BC_bridge_fractional_to_composite_ladder_signed_charge.csv

Important STRUC-I Naming Note
-----------------------------
STRUC-I exported all six ladder names simply as 'BC'.
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 B <-> C bridge is route-connected but admissibility-transitional.

STRUC-PERC-I result:

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

STRUC-I result:

    all six encodings -> Structural Boundary / Transitional Structure

Compact result statement:

    The fractional-to-composite bridge is not organized by raw signed charge.
    It is organized by route / closure / magnitude structure, but remains
    under admissibility boundary pressure.

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 | FULL_PERCOLATION | 1 | 0 | 1 | Structural Boundary | Transitional Structure | 0.918812 | 0.896 | 0.85266 | 0.8869 | Strongest BC STRUC-I encoding. Magnitude-based bridge structure is connected and has the best A-kappa / rho profile, but it still remains Structural Boundary / Transitional Structure. |
| boundary_route_coordinate | FULL_PERCOLATION | 1 | 0 | 0.749894209332 | Structural Boundary | Transitional Structure | 0.782687 | 0.743 | 0.938605 | 0.9546 | Percolates in STRUC-PERC-I but remains boundary-pressured in STRUC-I. This is the explicit route-coordinate bridge between fractional and composite layers. |
| closure_class_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.782925 | 0.7345 | 0.93864 | 0.95895 | Percolates cleanly in STRUC-PERC-I and remains transitional in STRUC-I. This confirms that closure taxonomy carries the bridge, but not as standalone persistence. |
| closure_state_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.86015 | 0.8425 | 0.9088 | 0.918273 | Percolates with a compact state ladder and performs better than raw route coordinate under STRUC-I. It encodes the internal-to-closed transition in a moderate-pressure form. |
| route_class_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.859087 | 0.8425 | 0.909645 | 0.919864 | Percolates with a compact route ladder and behaves similarly to closure_state_code under STRUC-I. It supports bridge connectivity while remaining transitional. |
| signed_charge | HARD_FRAGMENTATION | 0.857142857143 | 1 | null | Structural Boundary | Transitional Structure | 0.684375 | 0.6045 | 0.961057 | 1.009857 | Only encoding that fragments in STRUC-PERC-I and weakest in STRUC-I. Raw signed charge is the wrong coordinate for the fractional-to-composite bridge. |

STRUC-PERC-I Findings
---------------------
The BC bridge shows a one-versus-five split:

    signed_charge -> HARD_FRAGMENTATION
    all other tested encodings -> FULL_PERCOLATION

- absolute_charge: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 1, n = 5)
- boundary_route_coordinate: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 0.749894209332, n = 5)
- closure_class_code: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 0.01, n = 5)
- closure_state_code: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 0.01, n = 3)
- route_class_code: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 0.01, n = 3)
- signed_charge: HARD_FRAGMENTATION (giant ratio = 0.857142857143, isolated = 1, kappa_connect = null, n = 7)

Interpretation:
    Raw signed charge fragments across the fractional-to-composite bridge.
    The bridge becomes connected only when represented through absolute charge,
    boundary route coordinate, closure class, closure state, or route class.
    This is the first direct Phase 2 evidence that the B <-> C transition is
    a routing phenomenon, not a simple signed-charge ladder.

STRUC-I Findings
----------------
STRUC-I classifies all six BC bridge encodings as:

    Structural Boundary / Transitional Structure

This means the B <-> C bridge is connected, but remains pressure-sensitive.

Strongest BC STRUC-I encoding:

    absolute_charge
    mean Aκ = 0.918812
    min Aκ  = 0.896
    mean rho = 0.85266
    max rho  = 0.8869

Weakest BC STRUC-I encoding:

    signed_charge
    mean Aκ = 0.684375
    min Aκ  = 0.6045
    mean rho = 0.961057
    max rho  = 1.009857

Interpretation:
    Absolute charge is the strongest BC bridge coordinate under STRUC-I.
    Signed charge is the weakest and also the only STRUC-PERC-I fragmentation case.
    This reinforces the conclusion that raw signed charge does not carry the
    fractional-to-composite route. The bridge is carried by route / closure /
    magnitude structure.

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

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

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

The BC bridge now adds:

    signed_charge fragments at the bridge,
    route / closure / magnitude encodings percolate at the bridge,
    all remain transitional under STRUC-I.

This is sharper than either isolated layer alone. It shows that the transition
between B and C exposes the difference between charge-value representation
and charge-route representation.

Relation to ABCD Combined Result
--------------------------------
The BC bridge resembles the ABCD combined pattern:

    ABCD combined:
        signed_charge fragments
        route / closure encodings percolate

    B <-> C bridge:
        signed_charge fragments
        route / closure encodings percolate

This is important because it suggests that the B <-> C bridge may be the
structural core of the full ABCD charge-boundary route.

However, STRUC-I still keeps the bridge transitional, so the result should
not be overstated as final persistence. It is connected but still boundary-
pressured.

UNNS Interpretation
-------------------
In the UNNS Substrate interpretation, the B <-> C bridge is the first direct
test of:

    confined fractional coordinate -> composite external closure

The chamber results support the following reading:

    Fractional charge does not become coherent as raw signed charge.
    It becomes coherent when interpreted as a route into composite closure.

Thus the bridge is not a charge-value identity. It is a routing transition.

Key finding:

    The B <-> C bridge is the first confirmed route-connected bridge of
    Charge Boundary Routing I, but it remains a Structural Boundary under
    perturbation.

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

1. The B <-> C bridge fully percolates in absolute_charge, boundary_route_coordinate,
   closure_class_code, closure_state_code, and route_class_code.
2. The B <-> C signed_charge encoding fragments in STRUC-PERC-I.
3. All BC encodings remain Structural Boundary / Transitional Structure in STRUC-I.
4. Absolute charge is the strongest BC STRUC-I encoding.
5. Signed charge is the weakest BC STRUC-I encoding.
6. The fractional-to-composite bridge is better represented as route / closure
   structure than as raw signed charge.

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

1. A derivation of charge quantization.
2. A proof of confinement.
3. Full geometric persistence of the B <-> C bridge.
4. That B <-> C alone explains all ABCD behavior.
5. That percolation alone is equivalent to a physical law.

Operational Consequence
-----------------------
The B <-> C bridge should be retained as a primary candidate for the
structural core of Charge Boundary Routing I.

Next bridge to run:

    A <-> B

Reason:
    A <-> B tests whether the external primitive charge layer connects directly
    to the confined fractional coordinate layer, or whether composite closure
    is required as a mediator.

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

    charge_boundary_routing_i/
    └── outputs/
        └── reports/
            └── phase2_bridges/
                └── BC/
                    └── BC_bridge_chamber_comparison_report.txt

Supporting result files:

    results/struc_perc_i/phase2_bridges/BC/
        BC_STRUC_PERC_I_v2_5_0_batch_results.csv
        BC_STRUC_PERC_I_v2_5_0_batch_results.json

    results/struc_i/phase2_bridges/BC/
        BC_STRUC_I_v1_0_4_profiles.csv
        BC_STRUC_I_v1_0_4_results.json
