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

Generated: 2026-06-15

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

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

Central question:
    Does composite closure mediate the difficult A <-> B interface and
    restore cross-layer route coherence?

Why this bridge matters:
    ABC tests whether adding composite closures to the external-to-fractional
    interface repairs the fragmentation seen in AB and creates a larger
    coherent route system across A, B, and C.

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
-----------
- ABC_bridge_external_fractional_composite_ladder_absolute_charge.csv
- ABC_bridge_external_fractional_composite_ladder_boundary_route_coordinate.csv
- ABC_bridge_external_fractional_composite_ladder_closure_class_code.csv
- ABC_bridge_external_fractional_composite_ladder_closure_state_code.csv
- ABC_bridge_external_fractional_composite_ladder_route_class_code.csv
- ABC_bridge_external_fractional_composite_ladder_signed_charge.csv

Important STRUC-I Naming Note
-----------------------------
STRUC-I exported all six ladder names simply as 'ABC'.
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 <-> C bridge restores selected percolation channels but remains
admissibility-transitional under STRUC-I.

STRUC-PERC-I result:

    absolute_charge    -> FULL_PERCOLATION
    closure_class_code -> FULL_PERCOLATION
    closure_state_code -> FULL_PERCOLATION
    route_class_code   -> FULL_PERCOLATION

    boundary_route_coordinate -> HARD_FRAGMENTATION
    signed_charge             -> HARD_FRAGMENTATION

STRUC-I result:

    all six encodings -> Structural Boundary / Transitional Structure

Compact result statement:

    Composite closure repairs some A-B connectivity, especially absolute
    charge and closure / route-class percolation, but ABC does not yet become
    a persistent geometric route. Signed charge remains fragmented.

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 | 0.867138 | 0.84 | 0.913112 | 0.932853 | Percolates in STRUC-PERC-I after C is added, repairing the AB absolute-charge fragmentation. However, it remains Structural Boundary / Transitional Structure in STRUC-I. |
| boundary_route_coordinate | HARD_FRAGMENTATION | 0.666666666667 | 0 | null | Structural Boundary | Transitional Structure | 0.874525 | 0.8475 | 0.905591 | 0.914941 | Fragments in STRUC-PERC-I but is the strongest ABC STRUC-I coordinate by mean A-kappa. This indicates a discontinuous but perturbatively favored route coordinate. |
| closure_class_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.87265 | 0.851 | 0.906369 | 0.916176 | Percolates in STRUC-PERC-I and is nearly the strongest STRUC-I encoding. Closure taxonomy is one of the best ABC mediating coordinates. |
| closure_state_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.802013 | 0.7835 | 0.945006 | 0.953333 | Percolates in STRUC-PERC-I but remains lower under STRUC-I. The coarse state ladder connects but does not dominate perturbation stability. |
| route_class_code | FULL_PERCOLATION | 1 | 0 | 0.01 | Structural Boundary | Transitional Structure | 0.866912 | 0.83 | 0.917506 | 0.934028 | Percolates in STRUC-PERC-I and remains transitional in STRUC-I. It preserves route-class connectivity but does not reach weak persistence. |
| signed_charge | HARD_FRAGMENTATION | 0.857142857143 | 1 | null | Structural Boundary | Transitional Structure | 0.660262 | 0.5875 | 0.976831 | 1.006393 | Fragments in STRUC-PERC-I and is the weakest STRUC-I encoding. Raw signed charge is not the ABC bridge coordinate. |

STRUC-PERC-I Findings
---------------------
The ABC bridge shows partial repair of AB fragmentation:

    absolute_charge now percolates.
    closure_class_code percolates.
    closure_state_code percolates.
    route_class_code percolates.
    signed_charge still fragments.
    boundary_route_coordinate also fragments.

- absolute_charge: FULL_PERCOLATION (giant ratio = 1, isolated = 0, kappa_connect = 1, n = 5)
- boundary_route_coordinate: HARD_FRAGMENTATION (giant ratio = 0.666666666667, isolated = 0, kappa_connect = null, n = 6)
- 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:
    Adding composite closures repairs the absolute-charge fragmentation seen
    in AB. It also preserves closure-class, closure-state, and route-class
    connectivity. However, raw signed charge still fragments, and the
    continuous boundary-route coordinate also fragments. Therefore ABC is
    not a smooth charge-value or smooth route-coordinate ladder. It is a
    mediated closure/class structure.

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

    Structural Boundary / Transitional Structure

Strongest ABC STRUC-I encoding:

    boundary_route_coordinate
    mean Aκ = 0.874525
    min Aκ  = 0.8475
    mean rho = 0.905591
    max rho  = 0.914941

Very close second:

    closure_class_code
    mean Aκ = 0.87265
    min Aκ  = 0.851
    mean rho = 0.906369
    max rho  = 0.916176

Weakest ABC STRUC-I encoding:

    signed_charge
    mean Aκ = 0.660262
    min Aκ  = 0.5875
    mean rho = 0.976831
    max rho  = 1.006393

Interpretation:
    ABC improves graph connectivity relative to AB, but STRUC-I keeps the
    larger A-B-C structure in the Structural Boundary regime. The strongest
    perturbation coordinate is boundary_route_coordinate, even though that
    same coordinate fragmented in STRUC-PERC-I. This means the route coordinate
    is not smoothly percolating, but it remains one of the most relevant
    perturbative coordinates in the full A-B-C bridge.

Relation to AB
--------------
AB showed:

    signed_charge / absolute_charge -> HARD_FRAGMENTATION
    route / closure encodings       -> FULL_PERCOLATION
    absolute_charge                 -> Geometric Persistence / Weak Persistence in STRUC-I

ABC now shows:

    absolute_charge -> FULL_PERCOLATION
    signed_charge   -> HARD_FRAGMENTATION
    all STRUC-I encodings -> Structural Boundary / Transitional Structure

Therefore:

    Adding C repairs absolute-charge connectivity in the percolation graph,
    but removes the weak-persistence status that absolute_charge had in AB.

This suggests that composite closure mediates connectivity, but the larger
three-layer structure remains under boundary pressure.

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

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

ABC partially resembles BC:

    signed_charge remains fragmented;
    absolute_charge and closure / route-class encodings percolate;
    all STRUC-I encodings remain Structural Boundary / Transitional Structure.

But ABC differs from BC because boundary_route_coordinate fragments in ABC.
This suggests that adding Layer A introduces a discontinuity into the continuous
route coordinate, even while closure/class encodings remain connected.

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

    all valid graph encodings fragment;
    closure_state_code and route_class_code become weakly persistent in STRUC-I.

ABC does not include Layer D, so it does not yet test the terminal boundary.
It tests mediation before the boundary-absence layer is attached.

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

ABC is therefore not the final persistent route. It is the mediated pre-boundary
structure connecting external primitive charge, fractional coordinates, and
composite closure.

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

    signed_charge fragments
    route / closure encodings percolate

ABC confirms part of this pattern:

    signed_charge fragments
    closure / route-class encodings percolate

but ABC does not yet include the boundary-absence layer. Therefore ABC should
be interpreted as the mediated closure structure before terminal boundary
conditions are attached.

UNNS Interpretation
-------------------
In the UNNS Substrate interpretation, ABC tests whether primitive external
charge, confined fractional charge, and composite closure can form a coherent
pre-boundary route.

The chamber results support the following reading:

    Composite closure mediates connectivity between A and B.
    The mediated structure is carried by absolute charge and closure/route
    class encodings, not by signed charge.
    The route remains admissibility-transitional under perturbation.

Key finding:

    The A <-> B <-> C bridge restores selected percolation channels but does
    not yet produce full geometric persistence.

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

1. Composite closure restores absolute-charge percolation across A <-> B <-> C.
2. signed_charge remains fragmented in the ABC bridge.
3. closure_class_code, closure_state_code, and route_class_code percolate in STRUC-PERC-I.
4. boundary_route_coordinate fragments in STRUC-PERC-I, despite being the strongest STRUC-I coordinate.
5. All ABC encodings remain Structural Boundary / Transitional Structure in STRUC-I.
6. ABC is a mediated pre-boundary route, not a final persistent structure.

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 A-B-C route.
4. That signed charge is the correct bridge coordinate.
5. That ABC alone explains the full ABCD structure.

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

    composite-mediated
    selected-channel percolating
    signed-charge fragmented
    admissibility-transitional

Next bridge to run:

    B <-> C <-> D

Reason:
    BCD tests whether the fractional-to-composite route acquires a terminal
    boundary edge when Layer D is attached.

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

    charge_boundary_routing_i/
    └── outputs/
        └── reports/
            └── phase2_bridges/
                └── ABC/
                    └── ABC_bridge_chamber_comparison_report.txt

Supporting result files:

    results/struc_perc_i/phase2_bridges/ABC/
        ABC_STRUC_PERC_I_v2_5_0_batch_results.csv
        ABC_STRUC_PERC_I_v2_5_0_batch_results.json

    results/struc_i/phase2_bridges/ABC/
        ABC_STRUC_I_v1_0_4_profiles.csv
        ABC_STRUC_I_v1_0_4_results.json
