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

Generated: 2026-06-15

Bridge
------
B <-> C <-> D
Name: Confined Fractional Coordinates to Composite Closures to Boundary Absences / Constraints

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

Central question:
    Does the B <-> C route-connected core survive when the boundary-absence
    layer is attached, or does Layer D terminate the route?

Why this bridge matters:
    BCD is the decisive test of whether the fractional-to-composite route
    becomes a larger boundary-aware structure or is cut off by Layer D.
    BC was route-connected. CD was a fragmentation boundary. BCD tests which
    behavior dominates when B, C, and D are combined.

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

    signed_charge
    absolute_charge

because Layer D contains boundary absences and empirical constraints rather
than ordinary charge-state values. The valid BCD 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
-----------
- BCD_bridge_fractional_composite_boundary_ladder_boundary_route_coordinate.csv
- BCD_bridge_fractional_composite_boundary_ladder_closure_class_code.csv
- BCD_bridge_fractional_composite_boundary_ladder_closure_state_code.csv
- BCD_bridge_fractional_composite_boundary_ladder_route_class_code.csv

Important STRUC-I Naming Note
-----------------------------
STRUC-I exported all four ladder names simply as 'BCD'.
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 B <-> C <-> D bridge is graph-fragmented and remains admissibility-
transitional under STRUC-I.

STRUC-PERC-I result:

    all four valid BCD encodings -> HARD_FRAGMENTATION

STRUC-I result:

    all four BCD encodings -> Structural Boundary / Transitional Structure

Compact result statement:

    Layer D terminates the B <-> C route. BCD is not a smooth extension of
    the BC route-connected core; it is BC plus a boundary wall.

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 | 0.777777777778 | 2 | 0.222222222222 | 0.998483316481 | Structural Boundary | Transitional Structure | 0.792875 | 0.7425 | 0.921878 | 0.9558 | Fragments most strongly in STRUC-PERC-I and is the weakest STRUC-I encoding. The continuous boundary route coordinate breaks under the terminal Layer-D attachment. |
| closure_class_code | HARD_FRAGMENTATION | 0.9 | 1 | 0.1 | 0.995449949444 | Structural Boundary | Transitional Structure | 0.797038 | 0.745 | 0.920344 | 0.95575 | Fragments in STRUC-PERC-I and remains Structural Boundary in STRUC-I. Detailed closure taxonomy does not repair the B-C route once Layer D is attached. |
| closure_state_code | HARD_FRAGMENTATION | 0.833333333333 | 1 | 0.166666666667 | 0.997472194135 | Structural Boundary | Transitional Structure | 0.919787 | 0.8975 | 0.867688 | 0.883917 | Fragments in STRUC-PERC-I but is one of the strongest STRUC-I encodings. State structure survives better than coordinate/class structure, but not enough for weak persistence. |
| route_class_code | HARD_FRAGMENTATION | 0.857142857143 | 1 | 0.142857142857 | 0.996966632963 | Structural Boundary | Transitional Structure | 0.921575 | 0.9005 | 0.868177 | 0.880458 | Fragments in STRUC-PERC-I but is the strongest STRUC-I encoding. Route-class identity is the most stable BCD perturbation coordinate, yet still transitional. |

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

- boundary_route_coordinate: HARD_FRAGMENTATION (giant ratio = 0.777777777778, isolated = 2, isolated fraction = 0.222222222222, kappa_connect = null, n = 9, 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:
    BC alone was route-connected. But when Layer D is attached, every valid
    BCD graph encoding fragments. The high tail-dominance values, approximately
    0.995 to 0.998, repeat the CD boundary signature. This is not mild noise.
    It is a terminal boundary separation.

STRUC-I Findings
----------------
STRUC-I classifies all four BCD bridge encodings as:

    Structural Boundary / Transitional Structure

Strongest BCD STRUC-I encoding:

    route_class_code
    mean Aκ = 0.921575
    min Aκ  = 0.9005
    mean rho = 0.868177
    max rho  = 0.880458

Very close second:

    closure_state_code
    mean Aκ = 0.919787
    min Aκ  = 0.8975
    mean rho = 0.867688
    max rho  = 0.883917

Weakest BCD STRUC-I encoding:

    boundary_route_coordinate
    mean Aκ = 0.792875
    min Aκ  = 0.7425
    mean rho = 0.921878
    max rho  = 0.9558

Interpretation:
    Route-class and closure-state encodings are the strongest perturbation
    coordinates, but unlike CD, they do not reach Geometric Persistence / Weak
    Persistence. Adding Layer B to the C-D boundary does not repair the
    boundary. It keeps the system transitional.

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

    signed_charge fragmented;
    route / closure / magnitude encodings percolated;
    all STRUC-I encodings remained Structural Boundary / Transitional Structure.

BCD now shows:

    all valid graph encodings fragment;
    all STRUC-I encodings remain Structural Boundary / Transitional Structure.

Therefore:

    Layer D terminates the B <-> C route rather than extending it.

BC is the route-connected core. BCD is that core after contact with the
boundary wall.

Relation to CD
--------------
CD showed:

    all valid graph encodings fragmented;
    closure_state_code and route_class_code reached Geometric Persistence / Weak Persistence.

BCD shows:

    all valid graph encodings fragmented;
    closure_state_code and route_class_code remain Structural Boundary / Transitional Structure.

Therefore:

    BCD is more severe than CD in STRUC-I. The boundary-state identity that
    weakly persisted in CD does not become weakly persistent in the larger
    B-C-D bridge.

Relation to AB and ABC
----------------------
AB showed a magnitude-stable boundary interface:

    signed_charge / absolute_charge fragmented in STRUC-PERC-I;
    absolute_charge reached Geometric Persistence / Weak Persistence in STRUC-I.

ABC showed composite-mediated selected-channel percolation:

    absolute_charge and closure / route-class encodings percolated;
    all STRUC-I encodings remained Structural Boundary / Transitional Structure.

BCD differs from both:

    no graph encoding percolates;
    no STRUC-I encoding reaches Weak Persistence.

Thus BCD is the clearest terminal-boundary bridge in Phase 2.

Current Phase 2 Pattern
-----------------------
So far:

    AB = magnitude-stable boundary interface
    BC = route-connected fractional-to-composite bridge
    CD = fragmentation boundary with stable boundary-state identity
    ABC = composite-mediated connectivity, still admissibility-transitional
    BCD = terminal boundary extension of BC, graph-fragmented and transitional

Compact:

    BC is the route-connected core.
    D is the terminal boundary.
    BCD is BC plus a boundary wall, not a smooth extension.

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

    signed_charge fragments
    route / closure encodings percolate

BCD explains the role of the boundary side of ABCD:

    Layer D does not join smoothly to the B-C route.
    It contributes terminal boundary pressure.

Therefore the full ABCD structure should be read as a cross-layer route
system that contains an internal route core and a terminal boundary marker.
It should not be read as one continuous charge-value ladder.

UNNS Interpretation
-------------------
In the UNNS Substrate interpretation, BCD tests whether confined fractional
coordinates and composite closures remain coherent after boundary absences
are attached.

The chamber results support the following reading:

    Boundary absences terminate the B-C route.
    Route-class and closure-state identity remain the best coordinates,
    but they stay below the weak-persistence threshold.
    The terminal boundary is structural, not accidental.

Key finding:

    The B <-> C <-> D bridge is graph-fragmented and admissibility-transitional;
    Layer D acts as a terminal boundary condition for the B-C route.

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

1. All valid BCD graph encodings fragment in STRUC-PERC-I.
2. The BCD bridge has high tail dominance across all STRUC-PERC-I encodings.
3. All BCD STRUC-I encodings remain Structural Boundary / Transitional Structure.
4. route_class_code is the strongest BCD perturbation coordinate.
5. boundary_route_coordinate is the weakest BCD perturbation coordinate.
6. Layer D terminates rather than extends the B-C route.

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

1. A derivation of charge quantization.
2. A proof of confinement.
3. That Layer D is an ordinary physical particle layer.
4. That graph fragmentation is a failed result.
5. That BCD alone explains the full ABCD result.
6. That signed_charge or absolute_charge should be forced into Layer-D ladders.

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

    graph-fragmented
    tail-dominated
    route/state strongest but still transitional
    terminal-boundary extension of BC

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

Next output to produce:

    Phase 2 bridge synthesis report

Reason:
    AB, BC, CD, ABC, and BCD are now all tested. The next step is to consolidate
    the bridge chain into one Phase 2 synthesis before deciding whether any
    additional control ladders are needed.

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

    charge_boundary_routing_i/
    └── outputs/
        └── reports/
            └── phase2_bridges/
                └── BCD/
                    └── BCD_bridge_chamber_comparison_report.txt

Supporting result files:

    results/struc_perc_i/phase2_bridges/BCD/
        BCD_STRUC_PERC_I_v2_5_0_batch_results.csv
        BCD_STRUC_PERC_I_v2_5_0_batch_results.json

    results/struc_i/phase2_bridges/BCD/
        BCD_STRUC_I_v1_0_4_profiles.csv
        BCD_STRUC_I_v1_0_4_results.json
