Charge Boundary Routing I
Phase 3C — Constrained and Forbidden Transition Boundary Tests
PHASE3C_FORBIDDEN_BOUNDARY_chamber_comparison_report.txt

Generated: 2026-06-16


1. Purpose
----------
This report summarizes the Phase 3C chamber results for the Charge Boundary
Routing I program.

Phase 3C was designed as the negative / contrast test for the transition
sequence.

Earlier phases established the positive side:

    Phase 3:
        7 allowed seed transitions preserve route / closure structure.

    Phase 3B:
        38 expanded allowed transitions preserve route / closure structure,
        with route_transition_code and closure_transition_code reaching
        Geometric Persistence / Boundary-Stabilized.

Phase 3C asks the complementary question:

    What happens when allowed controls are mixed with forbidden,
    constrained, charge-violating, free-fractional, and route-incoherent
    transition candidates?

The core Phase 3C question is:

    Is charge balance alone sufficient, or can a transition conserve charge
    while failing the deeper route / closure admissibility test?


2. Executive Result
-------------------
Phase 3C produced a decisive refinement of the Charge Boundary Routing I
hypothesis.

The result is not simple graph fragmentation.

Instead:

    STRUC-PERC-I:
        the mixed Phase 3C corpus remains globally connected.

    STRUC-I:
        the mixed Phase 3C corpus loses route-transition admissibility.

This means:

    forbiddenness and constraint do not necessarily appear as graph
    disconnection;

    they appear as boundary pressure in perturbative route geometry.

The strongest Phase 3C finding is:

    Phase 3B allowed transitions:
        route_transition_code -> Geometric Persistence / Boundary-Stabilized
        mean Aκ ≈ 0.9851

    Phase 3C mixed allowed/forbidden/constrained corpus:
        route_transition_code -> Structural Boundary / Transitional Structure
        mean Aκ = 0.859238
        min Aκ  = 0.8140

Therefore:

    Charge balance is necessary but not sufficient.
    Boundary-route preservation is the structural discriminator of admissible
    transitions.


3. Corpus Design
----------------
Canonical corpus:

    data/canonical/
        phase3C_forbidden_constrained_transition_corpus.csv

Corpus size:

    48 rows
    71 columns

Group composition:

    Group A — allowed controls:
        12 rows

    Group B — charge-violating mocks:
        8 rows

    Group C — free-fractional externalization attempts:
        8 rows

    Group D — selection-rule violating comparison channels:
        8 rows

    Group E — route-incoherent charge-conserving mocks:
        8 rows

    Group F — constrained / upper-bounded boundary cases:
        4 rows

Charge-balance audit:

    Charge-balanced rows:
        40

    Charge-violating rows:
        8

This design deliberately separates two different forms of failure:

    1. direct charge-balance failure
       where Qi != Qf;

    2. route / closure failure despite charge balance
       where Qi = Qf but the route structure is forbidden, constrained, or
       deliberately incoherent.

The second class is the deeper UNNS test.


4. Group Definitions
--------------------
Group A — Allowed Controls
~~~~~~~~~~~~~~~~~~~~~~~~~~
Purpose:

    Preserve a representative subset of the Phase 3B allowed-transition
    interior.

Examples:

    neutron beta decay
    positive pion muonic decay
    negative muon decay
    W+ leptonic decay
    W- leptonic decay
    neutral pion two-photon decay
    positive kaon muonic decay
    selected baryon / meson decays

Expected role:

    Show the allowed-transition baseline inside the mixed Phase 3C corpus.


Group B — Charge-Violating Mocks
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Purpose:

    Introduce direct electric charge-balance violations.

Examples:

    neutron -> proton + neutrino
    electron -> neutrino + photon
    proton -> neutron + photon
    pi+ -> gamma + gamma
    W+ -> electron + neutrino

Expected role:

    Provide the obvious forbidden boundary:
        Qi != Qf


Group C — Free-Fractional Externalization Attempts
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Purpose:

    Test transitions that conserve total charge but attempt to externalize
    confined quark coordinates.

Examples:

    proton -> u + u + d
    neutron -> u + d + d
    pi+ -> u + anti_d
    K+ -> u + anti_s
    Delta++ -> u + u + u

Expected role:

    Test whether charge balance can pass while boundary-route admissibility
    fails due to attempted free fractional externalization.


Group D — Selection-Rule Violating Comparison Channels
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Purpose:

    Include transitions that may conserve electric charge but violate known
    non-charge selection structure.

Examples:

    proton -> positron + gamma
    neutron -> gamma + gamma
    mu- -> e- + gamma
    K+ -> pi+ + gamma
    pi0 -> neutrino + anti_neutrino

Expected role:

    Test whether non-charge selection failure becomes visible through route /
    closure geometry.


Group E — Route-Incoherent Charge-Conserving Mocks
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Purpose:

    Test the central UNNS distinction directly.

These rows conserve total charge but scramble or violate the expected route /
closure transition structure.

Examples:

    positron -> proton + anti_neutron
    photon -> proton + anti_proton
    W+ -> pi+ + neutron
    mu+ -> pi+ + gamma
    neutrino -> photon

Expected role:

    Determine whether charge balance alone is insufficient.


Group F — Constrained / Upper-Bounded Boundary Cases
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Purpose:

    Include physically constrained, searched, or unconfirmed boundary cases.

Examples:

    proton decay candidates
    mu -> e gamma
    upper-bounded rare or constrained channels

Expected role:

    Connect Phase 3C to Layer D boundary / absence logic.


5. STRUC-PERC-I Summary
-----------------------
STRUC-PERC-I result:

    Submitted ladders:
        43

    Completed ladders:
        42

    No-result ladders:
        1

    Completed ladders reaching FULL_PERCOLATION:
        42 / 42

    HARD_FRAGMENTATION:
        0

    Isolated nodes:
        0

    Tail dominance:
        0

No-result file:

    phase3C_ladder_allowed_control_flag.csv

Interpretation:

    The no-result control flag is not scientifically problematic. It is a
    low-information flag encoding and does not affect the Phase 3C conclusion.

Primary STRUC-PERC-I finding:

    The mixed allowed / forbidden / constrained Phase 3C corpus remains
    globally connected across all completed tested encodings.

This means:

    Phase 3C forbiddenness does not manifest as simple graph disconnection.

Instead, the corpus remains connected and must be evaluated by perturbative
admissibility.


6. STRUC-PERC-I Threshold Signals
---------------------------------
Although every completed STRUC-PERC-I ladder reached Full Percolation, not all
connected at the same threshold.

Most primary route / closure / status encodings connected immediately:

    kappa_connect ≈ 0.01

Examples:

    route_charge_consistency_code
    closure_charge_consistency_code
    allowed_vs_forbidden_code
    boundary_response_code
    route_transition_code
    closure_transition_code
    transition_class_code
    transition_status_code
    charge_balance_abs_error
    electric_charge_violation_flag
    selection_violation_flag
    route_incoherence_flag
    forbidden_flag

However, several boundary-pressure and free-fractional encodings required
larger connection thresholds:

    boundary_pressure_index:
        kappa_connect ≈ 0.5623

    free_fractional_externalization_flag:
        kappa_connect ≈ 0.7499

    fractional_external_count_delta:
        kappa_connect ≈ 0.7499

    final_fractional_external_count:
        kappa_connect ≈ 0.7499

Interpretation:

    Free-fractional externalization does not disconnect the graph, but it
    requires higher tolerance to connect. This is consistent with the
    interpretation that free-fractional externalization carries boundary
    pressure.


7. STRUC-I Summary
------------------
Total STRUC-I ladders parsed:

    43

Regime counts:

    Geometric Persistence:
        8

    Structural Boundary:
        35

State counts:

    Boundary-Stabilized:
        3

    Weak Persistence:
        5

    Transitional Structure:
        33

    Near-Critical:
        2

Primary STRUC-I finding:

    The mixed Phase 3C corpus remains percolatively connected, but most
    encodings fall to Structural Boundary / Transitional Structure.

Therefore:

    the Phase 3C boundary is not primarily a graph-connectivity boundary;
    it is an admissibility boundary.


8. Strongest STRUC-I Encodings
------------------------------
The strongest Phase 3C encodings were:

    closure_transition_code
        Regime / State:
            Geometric Persistence / Boundary-Stabilized
        mean Aκ:
            0.997850
        min Aκ:
            0.9950

    category_transition_code
        Regime / State:
            Geometric Persistence / Boundary-Stabilized
        mean Aκ:
            0.994462
        min Aκ:
            0.9890

    transition_family_code
        Regime / State:
            Geometric Persistence / Boundary-Stabilized
        mean Aκ:
            0.988050
        min Aκ:
            0.9810

Interpretation:

    Coarse classification structure remains stable in Phase 3C.

    The mixed corpus still has meaningful closure, category, and family
    organization.

Important nuance:

    Phase 3C does not destroy all structure.

    It preserves coarse classification while degrading route-transition
    admissibility.


9. Critical STRUC-I Contrast Encodings
--------------------------------------
The decisive Phase 3C signal appears in the route and boundary-pressure
encodings.

    route_transition_code
        Regime / State:
            Structural Boundary / Transitional Structure
        mean Aκ:
            0.859238
        min Aκ:
            0.8140

    transition_status_code
        Regime / State:
            Structural Boundary / Transitional Structure
        mean Aκ:
            0.885738
        min Aκ:
            0.8615

    boundary_pressure_index
        Regime / State:
            Structural Boundary / Transitional Structure
        mean Aκ:
            0.917750
        min Aκ:
            0.8760

Interpretation:

    The mixed forbidden / constrained corpus loses route-transition
    admissibility.

    Transition status and boundary-pressure structure also sit below the
    Geometric Persistence threshold.

This is the strongest evidence that Phase 3C has found the boundary side of
the transition program.


10. Phase 3B vs Phase 3C Comparison
-----------------------------------
Phase 3B allowed-transition corpus:

    route_transition_code
        Geometric Persistence / Boundary-Stabilized
        mean Aκ ≈ 0.9851

    closure_transition_code
        Geometric Persistence / Boundary-Stabilized
        mean Aκ ≈ 0.9839

Phase 3C mixed allowed/forbidden/constrained corpus:

    route_transition_code
        Structural Boundary / Transitional Structure
        mean Aκ = 0.859238

    closure_transition_code
        Geometric Persistence / Boundary-Stabilized
        mean Aκ = 0.997850

Key contrast:

    Allowed transitions stabilize both route and closure transition geometry.

    The mixed forbidden / constrained corpus preserves closure classification
    but collapses route-transition admissibility.

Therefore:

    closure labels remain classifiable;
    route transition admissibility is the sensitive boundary discriminator.

This is a stronger and more precise result than a simple claim that
"forbidden transitions fragment."


11. Allowed Controls vs Forbidden Boundary
------------------------------------------
Allowed controls were included to preserve the Phase 3B interior inside the
Phase 3C mixed corpus.

The mixed corpus did not fragment globally under STRUC-PERC-I. This means the
allowed and forbidden groups still belong to a connected transition space.

However, STRUC-I shows that the mixed space is not perturbatively stable in
route-transition geometry.

Interpretation:

    allowed and forbidden transition candidates can remain near one another
    in graph topology while separating under admissibility geometry.

This is directly aligned with the UNNS distinction between:

    connectivity

and

    admissibility.


12. Charge-Violating Mocks
--------------------------
Charge-violating mocks provide the baseline forbidden class.

They test cases where:

    Qi != Qf

Expected behavior:

    direct charge-balance failure.

STRUC-PERC-I result:

    the charge-balance encodings remained connected in the mixed corpus.

STRUC-I interpretation:

    charge-balance violation contributes to boundary pressure, but it is not
    the only source of Phase 3C instability.

This matters because Phase 3C is not merely rediscovering charge conservation.

The deeper result comes from charge-conserving but route-incoherent and
free-fractional cases.


13. Free-Fractional Externalization Attempts
--------------------------------------------
Free-fractional externalization attempts are central to the UNNS charge-routing
interpretation.

They test rows such as:

    proton -> u + u + d
    neutron -> u + d + d
    pi+ -> u + anti_d
    K+ -> u + anti_s

These conserve total charge but attempt to externalize confined fractional
coordinates.

STRUC-PERC-I threshold signal:

    free_fractional_externalization_flag
        FULL_PERCOLATION
        kappa_connect ≈ 0.7499

    fractional_external_count_delta
        FULL_PERCOLATION
        kappa_connect ≈ 0.7499

Interpretation:

    Free-fractional externalization does not break graph connectivity, but it
    requires a much higher tolerance to connect.

This is consistent with:

    fractional charge is a confined internal route coordinate;
    free fractional externalization belongs to the boundary side of the
    charge-routing system.


14. Route-Incoherent Charge-Conserving Mocks
--------------------------------------------
Route-incoherent charge-conserving mocks are the decisive Phase 3C test.

They ask:

    Can Qi = Qf hold while route / closure admissibility fails?

Examples include:

    positron -> proton + anti_neutron
    W+ -> pi+ + neutron
    mu+ -> pi+ + gamma
    neutrino -> photon

The combined Phase 3C result supports the expected answer:

    Yes.

The corpus remains connected, but route_transition_code falls to:

    Structural Boundary / Transitional Structure
    mean Aκ = 0.859238

Interpretation:

    Charge balance can pass while route-transition admissibility fails.

This supports the central manuscript claim:

    Charge conservation is necessary but not sufficient.


15. Constrained Boundary Cases
------------------------------
Constrained / upper-bounded cases connect Phase 3C to Layer D logic.

They include proton-decay candidates, charged-lepton flavor-violation cases,
and other boundary / search-based channels.

Their role is not to prove impossibility.

Their role is to populate the boundary side of the corpus with empirically
constrained or unconfirmed transition classes.

Interpretation:

    Constrained cases should be treated as boundary candidates, not as ordinary
    allowed-transition interior points.


16. Supported Claims
--------------------
Phase 3C supports the following claims:

1. The mixed allowed / forbidden / constrained transition corpus remains
   globally connected under STRUC-PERC-I.

2. Forbiddenness is not primarily expressed as simple graph fragmentation.

3. STRUC-I reveals the boundary: most Phase 3C encodings fall to Structural
   Boundary / Transitional Structure.

4. Coarse closure, category, and family structure remains stable.

5. Route-transition admissibility collapses relative to Phase 3B.

6. Free-fractional externalization carries elevated connection threshold /
   boundary pressure.

7. Charge-balanced but route-incoherent mocks support the claim that charge
   balance alone is insufficient.

8. Boundary-route preservation is a stronger discriminator than total charge
   balance alone.


17. Not Claimed
---------------
Phase 3C does not claim:

1. That all forbidden transitions are proven impossible.

2. That Standard Model selection rules are derived.

3. That U(1) charge conservation is derived.

4. That quark confinement is proven.

5. That categorical route codes are physical magnitudes.

6. That all possible forbidden or constrained transitions have been tested.

7. That Phase 3C replaces quantum field theory decay analysis.

Correct claim:

    Within the tested Phase 3C corpus, forbidden, constrained, free-fractional,
    and route-incoherent transition candidates remain graph-connected but
    degrade route-transition admissibility relative to the allowed Phase 3B
    corpus.


18. Manuscript Update Instructions
----------------------------------
Add a new results section after Phase 3B:

    11 Phase 3C Results:
       Forbidden and Constrained Transition Boundary Tests

Suggested subsections:

    11.1 Phase 3C corpus design
    11.2 STRUC-PERC-I: connected forbidden boundary corpus
    11.3 STRUC-I: route-transition admissibility collapse
    11.4 Free-fractional externalization threshold pressure
    11.5 Route-incoherent charge-conserving mocks
    11.6 Comparison with Phase 3B allowed transitions
    11.7 Phase 3C finding

Suggested manuscript finding:

    Phase 3C completes the allowed/forbidden contrast. Unlike Phase 3B, where
    allowed transitions make route_transition_code Boundary-Stabilized, the
    mixed Phase 3C corpus drives route_transition_code into Structural Boundary
    / Transitional Structure. The corpus remains percolatively connected, but
    loses route-transition admissibility. Forbiddenness therefore appears not
    as graph disconnection, but as boundary pressure in perturbative route
    geometry.

Update the final principle:

    Charge balance is necessary but not sufficient.
    Boundary-route preservation distinguishes admissible transitions from
    charge-balanced but structurally incoherent transformations.


19. Recommended Figures / Tables
--------------------------------
Recommended new table:

    Table 6 — Phase 3B vs Phase 3C comparison

Columns:

    Encoding
    Phase 3B regime / state
    Phase 3B mean Aκ
    Phase 3C regime / state
    Phase 3C mean Aκ
    Interpretation

Required rows:

    route_transition_code
    closure_transition_code
    category_transition_code
    transition_family_code
    boundary_pressure_index
    transition_status_code

Recommended new figure:

    Figure 7 — Allowed Interior vs Forbidden Boundary

Visual structure:

    Left:
        Phase 3B allowed transition space
        route_transition_code and closure_transition_code Boundary-Stabilized

    Right:
        Phase 3C mixed allowed/forbidden boundary space
        closure remains classifiable
        route_transition_code falls to Structural Boundary / Transitional

Caption idea:

    Phase 3C shows that the forbidden boundary is not a percolation break but
    an admissibility loss. Allowed transitions preserve route geometry; mixed
    forbidden and constrained transitions remain connected but lose
    route-transition persistence.


20. Final Phase 3C Interpretation
---------------------------------
Phase 3C strengthens, rather than weakens, the Charge Boundary Routing I
argument.

The expected result might have been simple fragmentation, but the actual result
is more informative:

    The mixed corpus remains connected.

    Coarse closure/category/family labels remain stable.

    Route-transition admissibility collapses.

This means the boundary is not a crude graph disconnection.

It is a perturbative admissibility boundary.

The final Phase 3C result is:

    Charge conservation is necessary but not sufficient.

    A transition may be charge-balanced and still fail the route / closure
    admissibility structure required of allowed transitions.

    Boundary-route preservation is therefore the structural discriminator of
    admissible transitions.


21. Final Report Statement
--------------------------
Phase 3C completes the allowed/forbidden contrast for Charge Boundary Routing I.

Phase 3B showed that allowed transitions stabilize route and closure transition
geometry.

Phase 3C shows that a mixed allowed/forbidden/constrained corpus remains
connected but loses route-transition admissibility.

The decisive observation is:

    closure_transition_code remains Boundary-Stabilized;
    route_transition_code collapses to Structural Boundary / Transitional
    Structure.

Thus:

    closure labels remain classifiable,
    but admissible route transition is lost.

This supports the refined final principle:

    Charge conservation is the visible projection.
    Boundary-route preservation is the structural invariant.
    Charge balance is necessary but not sufficient.
