COSMOLOGICAL BOUNDARY ROUTING SYNTHESIS
UNNS Substrate
Consolidated A–B–C Structural Result

STATUS

PROGRAM STAGE:
COMPLETE FOR DATASETS A, B, AND C

DIRECT STRUCTURAL ANALYSIS:
COMPLETE

ALPHA-DEFORMATION ANALYSIS:
COMPLETE

ORIENTATION-SENSITIVE A–B–C BRIDGE:
COMPLETE

SHARED DIMENSIONLESS ROUTE COORDINATE:
ACHIEVED

BRANCH-RESOLVED DATASET B INTERPRETATION:
ACHIEVED

FINAL UNIVERSAL PHYSICAL DISTANCE ON THE ADMISSIBILITY MANIFOLD:
NOT YET FROZEN

FINAL CANONICAL UNNS MARGIN:
NOT YET FROZEN


1. PURPOSE

This synthesis consolidates the complete Cosmological Boundary Routing experiment.

The experiment was designed to test whether singularity removal can be represented structurally as a boundary-routing mechanism rather than merely as the deletion of a divergent point.

Three matched cosmological trajectories were constructed and analyzed:

Dataset A:
classical Friedmann contraction toward a small-scale terminal boundary;

Dataset B:
effective loop-quantum-cosmology contraction, finite bounce, and expansion;

Dataset C:
Planck-anchored Lambda-CDM expansion.

The central question was:

Does a non-singular cosmological trajectory preserve admissibility by reaching a finite turning surface and continuing onto another branch, in a way structurally distinguishable from terminal classical collapse and ordinary classical recession?


2. DATASET ARCHITECTURE

DATASET A — CLASSICAL FRIEDMANN APPROACH

Physical role:
classical contraction toward a -> 0.

Validated trajectory:
A_classical_friedmann/generated_trajectory/validated/
classical_friedmann_approach_validated.csv

Route class:
terminal_boundary_approach

Shared route coordinate:
-1 -> 0


DATASET B — EFFECTIVE LQC BOUNCE

Physical role:
contraction -> exact finite bounce -> expansion.

Validated trajectory:
B_lqc_bounce/generated_trajectory/validated/
lqc_bounce_trajectory_validated_v2_2.csv

Direction-preserving structural path:
B_lqc_bounce/canonical/ladder/
lqc_bounce_response_path_preliminary.csv

Route class:
finite_turning_surface_route

Shared route coordinate:
-1 -> 0 -> +1


DATASET C — PLANCK-ANCHORED EXPANSION

Physical role:
classical Lambda-CDM-compatible expansion.

Validated trajectory:
C_planck_lcdm/generated_trajectory/validated/
planck_lcdm_trajectory_validated.csv

Route class:
boundary_recession_expansion

Shared route coordinate:
0 -> +1


3. DATASET B VALIDATED BOUNCE

The accepted Dataset B generator is version 2.2.

It uses the effective equation:

H^2 = H0^2 * rho_rel * (1 - rho_rel / rho_c_rel)

with:

rho_c = 0.41 * rho_Planck

The accepted trajectory contains:

4001 rows

2000 contraction rows

1 exact bounce row

2000 post-bounce expansion rows

At the exact bounce:

a_bounce = 2.46836418015e-32

H = 0

rho / rho_c = 1

lqc_correction_factor = 0

E_lqc = 0

The branch time from the bounce to a = 1 is:

13.7989388794 Gyr

The corresponding extracted Planck age reference is:

13.79731 Gyr

The difference is approximately:

0.001629 Gyr

The accepted hybrid grid resolves both:

the quantum-corrected near-bounce region;

the outer classical cosmological region.

The exact bounce, density bound, positive minimum scale factor, branch orientation, finite curvature representation, and time integration all pass validation.


4. DIRECT SCALAR STRUCTURE

The direct ladder layer tests magnitude geometry without path orientation.

Datasets A and C use matched classical response ladders.

Dataset B uses the finite post-bounce expansion branch only because:

ln(E_lqc)

is undefined at the exact bounce;

including both contraction and expansion would duplicate the same magnitude values in reverse order and create artificial zero gaps.


5. STRUC-PERC-I RESULTS

DATASET A

Verdict:
FULL_PERCOLATION

kappa_connect:
approximately 0.013335

Final giant ratio:
1.000000


DATASET B

Verdict:
FULL_PERCOLATION

kappa_connect:
0.100000

Final giant ratio:
1.000000

Initial giant ratio at kappa = 0.01:
approximately 0.533


DATASET C

Verdict:
FULL_PERCOLATION

kappa_connect:
approximately 0.013335

Final giant ratio:
1.000000


DIRECT CONNECTIVITY INTERPRETATION

All three ladders eventually form one connected structure.

Dataset B, however, requires a substantially larger vulnerability scale to become fully connected.

The relative threshold is approximately:

kappa_connect(B) / kappa_connect(A,C) ~= 7.5

Therefore Dataset B is not disconnected or inadmissible.

It is structurally broader, less immediately connected, and carries a more extended gap hierarchy.


6. STRUC-I RESULTS

DATASET A

Regime:
Geometric Persistence

State:
Stable Structure

mean A_kappa:
1.000000

mean structural pressure rho:
approximately 0.0416


DATASET B

Regime:
Geometric Persistence

State:
Weak Persistence

mean A_kappa:
1.000000

minimum A_kappa:
1.000000

A_kappa at kappa = 1:
1.000000

mean structural pressure rho:
0.306052

maximum structural pressure rho:
0.636336

rho at kappa = 1:
0.450930


DATASET C

Regime:
Geometric Persistence

State:
Stable Structure

mean A_kappa:
1.000000

mean structural pressure rho:
approximately 0.0416


DIRECT PRESSURE INTERPRETATION

All three remain admissible throughout the tested structural range.

Dataset B is nevertheless much more pressured than A and C.

Thus the bounce trajectory is not structurally forbidden.

It occupies a shallower and more vulnerable admissible regime.


7. ALPHA-DEFORMATION RESULTS

DATASETS A AND C

Accepted alpha convention:
v2 active-channel treatment

Admissibility persistence:
approximately 0.992619

The accepted magnitude-based alpha results for A and C are nearly degenerate.

That degeneracy is not a contradiction.

It occurs because the direct and alpha layers discard path orientation.


DATASET B

Accepted script:
b_lqc_bounce_alpha_apply_v2_2.py

Input:
full direction-preserving bounce path

Bounce-safe coordinate:

q_B = asinh(H_signed / H0)

Alpha range:

0.50 <= alpha <= 1.50

Alpha points:
21

Base intervals:
4000

Grid rows:
84,000

Accepted normalization:

five structural regions;

Q90 regional scales;

dedicated bounce-crossing scales;

bounded normalized responses;

response cap = 5.

Active response weights:

signed-flow response:
0.35

density response:
0.30

curvature response:
0.20

composition response:
0.15

The provisional margin channel remains diagnostic-only.


8. DATASET B ACCEPTED ALPHA VECTOR

mean_GR:
0.259626302909

var_GR:
0.041445769350

anisotropic_persistence:
0.001170567290

admissibility_persistence:
0.988309523810

collapse_onset_radius:
0.05

collapse_observed:
yes

Valid grid rows:
83,018

Unstable grid rows:
982

Total grid rows:
84,000


9. LOCATION OF DATASET B INSTABILITY

All unstable rows are confined to the symmetric near-bounce regions:

contraction_near_bounce:
491

expansion_near_bounce:
491

bounce_crossing:
0

contraction_outer:
0

expansion_outer:
0

The exact bounce-crossing intervals remain admissible across the full alpha grid.

The outer contraction and expansion regions also remain admissible.

The affected shell lies approximately within:

0.03 <= rho / rho_c <= 0.82

The first localized instability appears at:

|alpha - 1| = 0.05

This is a first-local-instability coordinate.

It is not a statement that the full trajectory globally collapses under a five-percent deformation.

The correct interpretation is:

The exact turning surface remains admissible, while the surrounding quantum-transition shell is locally deformation sensitive.


10. WHY A AND C REQUIRED AN ORIENTATION-SENSITIVE BRIDGE

The direct scalar ladders and magnitude-only alpha vectors made A and C appear nearly identical.

That representation erased the distinction between:

contraction toward a boundary;

expansion away from a boundary.

Bridge v1.1 restores:

signed Delta ln(a);

signed H flow;

signed density flow;

signed curvature flow;

signed provisional-margin flow;

branch identity;

route phase;

turning-surface identity.


11. SHARED DIMENSIONLESS ROUTE COORDINATE

Bridge v1.1 replaces heterogeneous distance variables with one path-intrinsic coordinate derived from cumulative:

|Delta ln(a)|

The convention is:

Dataset A:
-1 at the outer contraction endpoint;
0 at the terminal endpoint.

Dataset B:
-1 at the outer contraction endpoint;
0 at the exact bounce;
+1 at the outer expansion endpoint.

Dataset C:
0 at the early small-scale endpoint;
+1 at the late expansion endpoint.

This gives the common route topologies:

A:
-1 -> 0

B:
-1 -> 0 -> +1

C:
0 -> +1


12. NORMALIZED SIGNED FLOWS

Bridge v1.1 uses dataset-specific Q90 absolute interval scales:

normalized flow =
raw flow / (Q90(|raw flow|) + |raw flow|)

The normalized values are:

dimensionless;

sign preserving;

bounded within [-1,1];

resistant to dimensional endpoint domination.

They compare direction and relative within-path response.

They do not compare absolute physical amplitudes between different cosmological models.


13. DATASET A ROUTE SIGNATURE

Route class:
terminal_boundary_approach

Route coordinate:
-1 -> 0

Mean normalized signed Delta ln(a):
-0.500000

Mean normalized signed H flow:
-0.100772

Mean normalized signed density flow:
+0.462724

Mean normalized signed curvature flow:
+0.480638

Mean normalized signed margin flow:
-0.092779

Margin-decreasing fraction:
0.538

Interpretation:

Dataset A contracts.

Density increases.

Curvature increases.

The provisional margin decreases.

The path approaches a terminal small-scale boundary.


14. DATASET C ROUTE SIGNATURE

Route class:
boundary_recession_expansion

Route coordinate:
0 -> +1

Mean normalized signed Delta ln(a):
+0.500000

Mean normalized signed H flow:
-0.100772

Mean normalized signed density flow:
-0.462724

Mean normalized signed curvature flow:
-0.480638

Mean normalized signed margin flow:
+0.092779

Margin-increasing fraction:
0.538

Interpretation:

Dataset C expands.

Density decreases.

Curvature decreases.

The provisional margin increases.

The path recedes from the early small-scale boundary regime.


15. A–C DIRECTIONAL SEPARATION

Datasets A and C are opposite orientations of the same magnitude geometry.

Their signed route signatures reverse:

A:
Delta ln(a) negative;
density flow positive;
curvature flow positive;
margin flow negative.

C:
Delta ln(a) positive;
density flow negative;
curvature flow negative;
margin flow positive.

Therefore the apparent A–C degeneracy in direct scalar geometry is resolved.

They are not the same trajectory.

They are oppositely oriented realizations of matched magnitude structure.


16. DATASET B BRANCH-RESOLVED ROUTING

The full-path signed means for Dataset B nearly cancel because the pre-bounce and post-bounce branches are symmetric.

That cancellation is not loss of structure.

It is the signature of route reversal.

The accepted interpretation is branch resolved.


B PRE-BOUNCE APPROACH

Intervals:
1999

Route coordinate:
-1 -> 0

Mean normalized signed Delta ln(a):
-0.304527

Mean normalized signed H flow:
+0.058775

Mean normalized signed density flow:
+0.298770

Mean normalized signed curvature flow:
approximately -0.000075

Mean normalized signed margin flow:
-0.100246

Margin-decreasing fraction:
approximately 0.097049

Interpretation:

The LQC contraction branch approaches the finite turning surface.

Scale factor decreases.

Density increases.

The provisional margin decreases.


B TURNING SURFACE

Intervals:
2

Route coordinate:
approximately 0

Turning-crossing intervals:
2

Mean normalized signed Delta ln(a):
approximately 0

Mean normalized signed density flow:
0

Mean normalized signed curvature flow:
0

Mean normalized signed margin flow:
0

Interpretation:

The exact finite turning surface joins the contraction and expansion branches without a terminal path break.

The route changes orientation at coordinate zero.


B POST-BOUNCE RECESSION

Intervals:
1999

Route coordinate:
0 -> +1

Mean normalized signed Delta ln(a):
+0.304527

Mean normalized signed H flow:
+0.058775

Mean normalized signed density flow:
-0.298770

Mean normalized signed curvature flow:
approximately +0.000075

Mean normalized signed margin flow:
+0.100246

Margin-increasing fraction:
approximately 0.097049

Interpretation:

The LQC expansion branch recedes from the turning surface.

Scale factor increases.

Density decreases.

The provisional margin increases.


17. DATASET B ROUTING SYMMETRY

The pre-bounce and post-bounce signatures have opposite signs and closely matched magnitudes.

This is the expected route pattern:

approach
-> finite turning surface
-> recession

The exact turning surface itself remains admissible.

The deformation-sensitive region is a shell around the bounce, not the bounce point itself.


18. CONSOLIDATED COMPARISON

Layer:
Physical route

A:
Classical contraction

B:
Finite LQC bounce

C:
Planck-compatible expansion


Layer:
Route coordinate

A:
-1 -> 0

B:
-1 -> 0 -> +1

C:
0 -> +1


Layer:
Route class

A:
Terminal approach

B:
Finite turning-surface routing

C:
Boundary recession


Layer:
Direct connectivity

A:
Full percolation

B:
Full percolation

C:
Full percolation


Layer:
kappa_connect

A:
approximately 0.013335

B:
0.100000

C:
approximately 0.013335


Layer:
STRUC-I state

A:
Stable Structure

B:
Weak Persistence

C:
Stable Structure


Layer:
Mean structural pressure

A:
approximately 0.0416

B:
0.306052

C:
approximately 0.0416


Layer:
Alpha admissibility persistence

A:
approximately 0.992619

B:
0.988309523810

C:
approximately 0.992619


Layer:
Local sensitivity

A:
extreme-alpha region

B:
symmetric near-bounce shell

C:
extreme-alpha region


Layer:
Exact turning point

A:
none

B:
admissible

C:
none


Layer:
Signed density flow

A:
positive

B:
positive then negative

C:
negative


Layer:
Signed provisional-margin flow

A:
negative

B:
negative then positive

C:
positive


19. PRINCIPAL FINDING

The combined experiment distinguishes three structurally different cosmological routes.

Dataset A approaches a terminal boundary.

Dataset C recedes from an early boundary regime.

Dataset B approaches a finite turning surface, remains admissible through the route change, and continues onto the opposite branch.

The result can be stated as follows:

The classical contracting and expanding solutions are opposite orientations of matched magnitude geometry, whereas the effective LQC solution has a different route topology: it reaches a finite admissible turning locus and continues through structural reversal.


20. WHAT THE THREE STRUCTURAL LAYERS SHOW

CONNECTIVITY GEOMETRY

All three trajectories remain connected.

Dataset B requires a much larger kappa to achieve full percolation.

Therefore B is structurally broader and less immediately connected.


STRUCTURAL PRESSURE

All three remain admissible.

Dataset B carries much higher structural pressure and is classified as Weak Persistence rather than Stable Structure.

Therefore B lies closer to the structural boundary while remaining inside admissibility.


ALPHA-DEFORMATION GEOMETRY

A and C remain broadly stable under matched magnitude-based deformation.

B remains globally admissible but contains a narrow, symmetric near-bounce sensitivity shell.

The exact turning surface is not the unstable component.


ROUTE TOPOLOGY

A terminates.

C recedes.

B reverses and continues.

This is the decisive distinction that magnitude-only analysis could not reveal.


21. COSMOLOGICAL BOUNDARY ROUTING INTERPRETATION

The combined result supports the following UNNS framing:

A cosmological singularity-avoiding correction can be represented not merely as removal of a divergent endpoint, but as a change in admissible route topology.

In the classical contracting case, the trajectory moves toward terminal boundary approach.

In the effective LQC case, the trajectory reaches a finite turning locus, preserves admissibility through the route change, and continues into expansion.

The structure is therefore routed rather than destroyed.

This is the operational meaning of Cosmological Boundary Routing in the present experiment.


22. WHAT HAS BEEN ESTABLISHED

The following results are computationally established within the selected models and conventions:

A and C are directionally distinct despite magnitude degeneracy.

Dataset B contains a finite exact bounce with H = 0 and rho / rho_c = 1.

The exact bounce remains admissible across the tested alpha grid.

Dataset B remains fully connected and globally admissible.

Dataset B carries higher structural pressure than A and C.

Dataset B exhibits a symmetric near-bounce sensitivity shell.

Bridge v1.1 separates terminal approach, finite route reversal, and boundary recession in one common dimensionless route coordinate.

Branch-resolved profiles preserve the non-cancelling structure of Dataset B.


23. WHAT HAS NOT YET BEEN ESTABLISHED

The present experiment does not by itself establish:

that loop quantum cosmology is the correct theory of the early universe;

that a cosmological bounce occurred in nature;

direct observational confirmation of singularity removal;

a universal metric distance on the admissibility manifold;

a final canonical UNNS boundary margin;

a unique deformation normalization independent of the fixed Q90 and response-cap choices;

a model-independent proof that all non-singular cosmologies route through the same structural mechanism.


24. METHODOLOGICAL FIXED POINTS

The following conventions must remain fixed in matched reruns:

Dataset B effective equation;

rho_c convention;

hybrid trajectory grid;

exact bounce identification;

Q90 regional alpha normalization;

response cap = 5;

first-local-instability criterion;

shared cumulative |Delta ln(a)| route coordinate;

dataset-specific Q90 signed-flow normalization;

branch-resolved Dataset B interpretation.


25. REPRODUCIBILITY ARTIFACTS

DATASET A

Validated trajectory:
A_classical_friedmann/generated_trajectory/validated/
classical_friedmann_approach_validated.csv

Preliminary ladder:
A_classical_friedmann/canonical/ladder/

Direct structural outputs:
A_classical_friedmann/canonical/struc_perc/

Alpha outputs:
A_classical_friedmann/canonical/alpha/


DATASET B

Validated trajectory:
B_lqc_bounce/generated_trajectory/validated/
lqc_bounce_trajectory_validated_v2_2.csv

Preliminary full path:
B_lqc_bounce/canonical/ladder/
lqc_bounce_response_path_preliminary.csv

Direct ladder:
B_lqc_bounce/canonical/ladder/
lqc_bounce_expansion_ladder_preliminary_struc_i.csv

Direct structural outputs:
B_lqc_bounce/canonical/struc_perc/

Alpha outputs:
B_lqc_bounce/canonical/alpha/

Accepted result record:
B_lqc_bounce/canonical/alpha/
DATASET_B_ALPHA_V2_2_RESULT.txt


DATASET C

Validated trajectory:
C_planck_lcdm/generated_trajectory/validated/
planck_lcdm_trajectory_validated.csv

Direct structural outputs:
C_planck_lcdm/canonical/struc_perc/

Alpha outputs:
C_planck_lcdm/canonical/alpha/


A–B–C BRIDGE

Bridge generator:
ABC_bridge/tools/
build_orientation_sensitive_abc_bridge_v1_1.py

Route-profile generator:
ABC_bridge/tools/
build_abc_route_profiles_v1_1.py

Bridge interval dataset:
ABC_bridge/outputs/
ABC_orientation_sensitive_bridge_v1_1.csv

Bridge summary:
ABC_bridge/outputs/
ABC_orientation_sensitive_bridge_summary_v1_1.csv

Phase summary:
ABC_bridge/outputs/
ABC_orientation_sensitive_phase_summary_v1_1.csv

Route profile:
ABC_bridge/outputs/
ABC_orientation_sensitive_route_profile_v1_1.csv

Bridge result record:
ABC_bridge/outputs/
ABC_BRIDGE_V1_1_RESULT.txt


26. FINAL PROGRAM STATUS

Dataset A trajectory:
COMPLETE

Dataset A direct structure:
COMPLETE

Dataset A alpha:
COMPLETE

Dataset B trajectory:
COMPLETE

Dataset B validation:
COMPLETE

Dataset B direct structure:
COMPLETE

Dataset B alpha:
COMPLETE

Dataset C trajectory:
COMPLETE

Dataset C direct structure:
COMPLETE

Dataset C alpha:
COMPLETE

A–B–C Bridge v1.1:
COMPLETE

Route profile:
COMPLETE

Phase summary:
COMPLETE

Consolidated Cosmological Boundary Routing synthesis:
COMPLETE


27. FINAL SYNTHESIS STATEMENT

The experiment has moved the Cosmological Boundary Routing hypothesis from a verbal analogy to a reproducible structural test.

Across matched cosmological trajectories:

the classical contraction approaches a terminal boundary;

the classical expansion recedes from the corresponding early boundary regime;

the effective LQC trajectory reaches a finite admissible turning surface, reverses route orientation, and continues into expansion.

The bounce is not represented as structural disappearance.

It is represented as admissible route continuation through a finite turning locus.

That is the central result of the Cosmological Boundary Routing program at this stage.


28. NEXT RESEARCH STEP

The next research step should not be another local conversion.

It should be one of the following two coordinated outputs:

1. a formal technical manuscript presenting the model construction, direct structural results, alpha analysis, route topology, limits, and falsifiable extensions;

2. a unns.tech research article supported by the complete technical dossier and interactive route-profile visualizations.

Before either publication path, the following final audit should be performed:

verify every numerical value against the stored CSV and JSON outputs;

freeze all accepted script versions;

archive rejected normalization runs separately;

record software dependencies and execution commands;

create publication-quality route-profile figures;

state clearly that the route coordinate is path intrinsic rather than a physical manifold metric.
