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

Generated: 2026-06-15

Bridge
------
C <-> D
Name: Composite Closures to Boundary Absences / Constraints

Bridge meaning:
    Layer C — composite integer / neutral charge closures
    Layer D — boundary absences, non-observed cases, and empirical constraints

Central question:
    Does the boundary-absence layer continue the composite closure ladder,
    or does it act as a genuine boundary edge?

Why this bridge matters:
    C <-> D tests whether Layer D behaves as an ordinary extension of the
    composite closure layer or as a boundary-condition layer. Since Layer D
    is not an ordinary charge-state ladder, this bridge must be interpreted
    through Layer-D-safe encodings only.

Layer D Rule
------------
The CD bridge intentionally excludes:

    signed_charge
    absolute_charge

because Layer D contains boundary absences and constraints rather than
ordinary charge-state values. The valid CD encodings are:

    boundary_route_coordinate
    closure_class_code
    closure_state_code
    route_class_code

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
-----------
- CD_bridge_composite_to_boundary_ladder_boundary_route_coordinate.csv
- CD_bridge_composite_to_boundary_ladder_closure_class_code.csv
- CD_bridge_composite_to_boundary_ladder_closure_state_code.csv
- CD_bridge_composite_to_boundary_ladder_route_class_code.csv

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

    1. boundary_route_coordinate
    2. closure_class_code
    3. closure_state_code
    4. route_class_code

Executive Result
----------------
The C <-> D bridge is a fragmentation boundary with weakly persistent
boundary-state / boundary-route structure.

STRUC-PERC-I result:

    all four valid CD encodings -> HARD_FRAGMENTATION

STRUC-I result:

    boundary_route_coordinate -> Structural Boundary / Transitional Structure
    closure_class_code        -> Structural Boundary / Transitional Structure
    closure_state_code        -> Geometric Persistence / Weak Persistence
    route_class_code          -> Geometric Persistence / Weak Persistence

Compact result statement:

    Layer D breaks graph connectivity when attached to composite closures,
    but its coarse state and route-class encodings remain perturbatively
    stable. Thus Layer D acts as a boundary layer, not as a continuation
    of Layer C.

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

| Encoding | STRUC-PERC-I verdict | Giant ratio | Isolated | Isolated fraction | Tail dominance | STRUC-I regime | STRUC-I state | mean Aκ | min Aκ | mean rho | max rho | Interpretation |
|---|---:|---:|---:|---:|---:|---|---|---:|---:|---:|---:|---|
| boundary_route_coordinate | HARD_FRAGMENTATION | 0.875 | 1 | 0.125 | 0.998483316481 | Structural Boundary | Transitional Structure | 0.744238 | 0.679 | 0.942052 | 1.013375 | Fragments in STRUC-PERC-I and remains Structural Boundary in STRUC-I. The continuous boundary coordinate exposes the composite-to-absence break most strongly. |
| closure_class_code | HARD_FRAGMENTATION | 0.9 | 1 | 0.1 | 0.995449949444 | Structural Boundary | Transitional Structure | 0.745488 | 0.6755 | 0.941882 | 1.01225 | Fragments in STRUC-PERC-I and remains Structural Boundary in STRUC-I. Detailed closure taxonomy separates the boundary cases from composite closures rather than connecting them. |
| closure_state_code | HARD_FRAGMENTATION | 0.833333333333 | 1 | 0.166666666667 | 0.997472194135 | Geometric Persistence | Weak Persistence | 0.932038 | 0.908 | 0.81812 | 0.841167 | Fragments in STRUC-PERC-I but reaches Geometric Persistence / Weak Persistence in STRUC-I. The coarse state transition is perturbatively stable even though it is not graph-connected. |
| route_class_code | HARD_FRAGMENTATION | 0.857142857143 | 1 | 0.142857142857 | 0.996966632963 | Geometric Persistence | Weak Persistence | 0.933412 | 0.9085 | 0.820026 | 0.843 | Fragments in STRUC-PERC-I but reaches Geometric Persistence / Weak Persistence in STRUC-I. This is the strongest CD perturbation coordinate and marks a stable boundary-route identity. |

STRUC-PERC-I Findings
---------------------
The CD bridge shows complete graph fragmentation across all valid Layer-D-safe encodings:

- boundary_route_coordinate: HARD_FRAGMENTATION (giant ratio = 0.875, isolated = 1, isolated fraction = 0.125, kappa_connect = null, n = 8, tail dominance = 0.998483316481)
- closure_class_code: HARD_FRAGMENTATION (giant ratio = 0.9, isolated = 1, isolated fraction = 0.1, kappa_connect = null, n = 10, tail dominance = 0.995449949444)
- closure_state_code: HARD_FRAGMENTATION (giant ratio = 0.833333333333, isolated = 1, isolated fraction = 0.166666666667, kappa_connect = null, n = 6, tail dominance = 0.997472194135)
- route_class_code: HARD_FRAGMENTATION (giant ratio = 0.857142857143, isolated = 1, isolated fraction = 0.142857142857, kappa_connect = null, n = 7, tail dominance = 0.996966632963)

Interpretation:
    The direct composite-to-boundary bridge does not percolate. This confirms
    that Layer D is not simply a continuation of Layer C. Boundary absences
    and empirical constraints form a separating edge. The very high tail
    dominance values, approximately 0.995 to 0.998, indicate a strong
    boundary/tail separation rather than mild random fragmentation.

STRUC-I Findings
----------------
STRUC-I divides the CD bridge into two groups:

    coordinate / class encodings:
        boundary_route_coordinate -> Structural Boundary / Transitional Structure
        closure_class_code        -> Structural Boundary / Transitional Structure

    state / route encodings:
        closure_state_code -> Geometric Persistence / Weak Persistence
        route_class_code   -> Geometric Persistence / Weak Persistence

Strongest CD STRUC-I encoding:

    route_class_code
    mean Aκ = 0.933412
    min Aκ  = 0.9085
    mean rho = 0.820026
    max rho  = 0.843

Weakest CD STRUC-I encoding:

    boundary_route_coordinate
    mean Aκ = 0.744238
    min Aκ  = 0.679
    mean rho = 0.942052
    max rho  = 1.013375

Interpretation:
    CD is graph-fragmented, but not random. The coarse encodings that describe
    what kind of boundary relation a row has — closure_state_code and
    route_class_code — are weakly persistent. The detailed coordinate and
    class encodings remain transitional. This means the boundary is stable
    at the state/route level, not as a smooth coordinate continuation.

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

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

    Layer D alone:
        not applicable as an isolated STRUC-I ladder;
        Layer D is a boundary-condition / absence layer.

The CD bridge now adds:

    all valid CD graph encodings fragment in STRUC-PERC-I;
    state/route encodings become weakly persistent in STRUC-I.

This confirms that Layer D does not behave like a fourth ordinary layer.
It acts as a boundary edge attached to the composite closure system.

Relation to AB and BC
---------------------
Current Phase 2 bridge pattern:

    AB:
        value-fragmented
        route-connected
        absolute-charge weak persistence

    BC:
        signed-charge fragmented
        route / closure / magnitude connected
        all STRUC-I encodings transitional

    CD:
        all valid graph encodings fragmented
        state / route class weak persistence

Therefore:

    AB = magnitude-stable boundary interface
    BC = route-connected fractional-to-composite bridge
    CD = fragmentation boundary with stable boundary-state identity

This is a coherent Phase 2 chain. It separates the roles of the three
bridges rather than forcing them into one behavior.

Relation to ABCD Combined Result
--------------------------------
The full ABCD result showed route / closure connectivity despite signed-charge
fragmentation. The CD result explains why Layer D must be handled carefully:

    Layer D does not simply extend the composite closure ladder.
    It inserts a boundary edge.

The full ABCD system can therefore be read as a cross-layer route structure
that includes a terminal boundary marker, not as a smooth charge-value ladder.

UNNS Interpretation
-------------------
In the UNNS Substrate interpretation, the C <-> D bridge is the point where
composite closure meets non-observation, exclusion, or constraint.

The chamber results support the following reading:

    Boundary absences break graph connectivity.
    But boundary state and route identity remain perturbatively stable.

Thus Layer D acts as a boundary condition. It is not a failed ladder and not
a missing continuation of Layer C. It is the empirical edge of charge
externalization.

Key finding:

    The C <-> D bridge is a fragmentation boundary with weakly persistent
    boundary-state / boundary-route identity.

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

1. All valid C <-> D graph encodings fragment in STRUC-PERC-I.
2. The CD bridge has high tail dominance across all STRUC-PERC-I encodings.
3. boundary_route_coordinate and closure_class_code remain Structural Boundary / Transitional Structure in STRUC-I.
4. closure_state_code and route_class_code reach Geometric Persistence / Weak Persistence in STRUC-I.
5. Layer D acts as a boundary-condition layer, not an ordinary continuation of Layer C.
6. The composite-to-boundary interface is stable only at the state/route-class level.

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

1. A derivation of charge quantization.
2. A proof of confinement.
3. That Layer D is a physical particle layer.
4. That graph fragmentation is failure.
5. That weak persistence is full geometric stability.
6. That Layer D should be forced into signed_charge or absolute_charge ladders.

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

    graph-fragmented
    tail-dominated
    weakly persistent in state / route-class encodings

Do not repair CD fragmentation away. It is the signal.

Next bridge to run:

    A <-> B <-> C

Reason:
    ABC tests whether composite closure mediates the difficult A <-> B
    interface and whether the A-B-C route becomes more coherent than AB alone.

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

    charge_boundary_routing_i/
    └── outputs/
        └── reports/
            └── phase2_bridges/
                └── CD/
                    └── CD_bridge_chamber_comparison_report.txt

Supporting result files:

    results/struc_perc_i/phase2_bridges/CD/
        CD_STRUC_PERC_I_v2_5_0_batch_results.csv
        CD_STRUC_PERC_I_v2_5_0_batch_results.json

    results/struc_i/phase2_bridges/CD/
        CD_STRUC_I_v1_0_4_profiles.csv
        CD_STRUC_I_v1_0_4_results.json
