DATASET B — ALPHA APPLICATION V2.2 RESULT
Cosmological Boundary Routing
Effective LQC Contraction–Bounce–Expansion

STATUS

DATASET B DIRECT AND ALPHA STAGES: COMPLETE

DATASET

Dataset:
B_lqc_bounce

Trajectory role:
Effective loop-quantum-cosmology contraction–bounce–expansion path.

Validated trajectory:
generated_trajectory/validated/
lqc_bounce_trajectory_validated_v2_2.csv

Full direction-preserving path:
canonical/ladder/
lqc_bounce_response_path_preliminary.csv

Trajectory structure:

contraction
→ exact finite bounce
→ expansion

Exact bounce:

a_bounce = 2.46836418015e-32
H = 0
rho/rho_c = 1
lqc_correction_factor = 0
E_lqc = 0

DIRECT PRELIMINARY STRUCTURAL RESULT

Direct scalar coordinate:

q_B(a) = ln(E_lqc(a))

The direct scalar ladder uses only the finite post-bounce expansion branch.

The exact bounce row is excluded from this ladder because ln(0) is undefined.

The contraction branch is also excluded from the sorted direct ladder to avoid duplicating the same |H| values in reverse order and creating artificial zero gaps.

Finite expansion ladder size:
2000 elements

STRUC-PERC-I RESULT

Input:
lqc_bounce_expansion_ladder_preliminary_struc_i.csv

Settings:

Domain adapter = Generic
kappa points = 17
kappa minimum = 0.01
kappa maximum = 1.0

Result:

Verdict = FULL_PERCOLATION
Giant ratio = 1.000000
Final chain size = 1999 / 1999 gaps
Final components = 1
Isolated vertices = 0
kappa_connect = 0.100000
kappa_star = none
Tail dominance = 0
Outliers = 0
Downsampling = no
Approximate mode = no

Initial giant ratio at kappa = 0.01:
approximately 0.533

Interpretation:

The finite LQC expansion ladder is ultimately fully connected, but it requires a substantially larger vulnerability scale to assemble into one connected structure than Datasets A and C.

Relative connectivity threshold:

kappa_connect(B) / kappa_connect(A,C)
approximately 7.5

This indicates a broader and less immediately connected gap hierarchy.

STRUC-I RESULT

Input:
lqc_bounce_expansion_ladder_preliminary_struc_i.csv

Settings:

Maximum ladder size = 5000
Monte Carlo runs = 2000
kappa steps = 40
kappa minimum = 0.01
kappa maximum = 1.0

Full-ladder status:

n = 2000
subsampled = false

Result:

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

Interpretation:

The finite LQC expansion branch remains admissible across the complete tested kappa range.

However, its structural pressure is substantially higher than for Datasets A and C.

The direct result therefore indicates:

- preserved admissibility;
- weaker persistence;
- higher structural pressure;
- a broader gap hierarchy;
- delayed full connectivity.

ALPHA APPLICATION V2.2

Script:

canonical/alpha/tools/
b_lqc_bounce_alpha_apply_v2_2.py

Input:

canonical/ladder/
lqc_bounce_response_path_preliminary.csv

The alpha stage uses the full direction-preserving path:

contraction
→ exact bounce
→ expansion

BOUNCE-SAFE RESPONSE COORDINATE

q_B = asinh(H_signed / H0)

This coordinate:

- remains finite at H = 0;
- preserves contraction and expansion signs;
- passes continuously through the exact bounce;
- avoids replacing the bounce with an arbitrary epsilon.

ALPHA GRID

alpha minimum = 0.50
alpha maximum = 1.50
alpha points = 21
alpha radius = |alpha - 1|

Trajectory rows:
4001

Base intervals:
4000

Grid rows:
84,000

Bounce-crossing intervals:
2

ACTIVE RESPONSE CHANNELS

signed-flow response       weight 0.35
total-density response     weight 0.30
curvature response         weight 0.20
composition response       weight 0.15

The provisional margin response is diagnostic-only.

It does not contribute to:

- structural_response;
- phase_persistence_score;
- instability_flag;
- collapse_onset_radius.

NORMALIZATION METHOD

Version 2.2 uses:

- five structural regions;
- Q90 regional scales;
- dedicated bounce-crossing scales;
- bounded normalized responses;
- response cap = 5.

Structural regions:

1. contraction_outer
2. contraction_near_bounce
3. bounce_crossing
4. expansion_near_bounce
5. expansion_outer

Scale quantile:

Q90

Response cap:

5

NORMALIZATION STATUS

Active-channel normalization:
PASS

Active scale review needed:
NO

Review status:
comparable_active_channels

Margin diagnostic warning:
NO

Mean normalized responses:

signed-flow response:
0.259626

density response:
0.240791

curvature response:
0.115114

composition response:
0.115764

margin response:
0.363301

Relative to signed flow:

density / flow:
0.927

curvature / flow:
0.443

composition / flow:
0.446

margin / flow:
1.399

The active channels are therefore comparable under the accepted v2.2 treatment.

ACCEPTED PRELIMINARY 5D 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

GRID OUTCOME

Valid rows:
83,018

Instability rows:
982

Total rows:
84,000

Admissibility persistence:
0.988309523810

Unstable rows are confined to:

contraction_near_bounce:
491

expansion_near_bounce:
491

bounce_crossing:
0

contraction_outer:
0

expansion_outer:
0

The instability distribution is symmetric across the contracting and expanding near-bounce shells.

EXACT BOUNCE RESULT

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

No unstable row occurs in the bounce_crossing region.

Therefore, the accepted result does not indicate failure of the exact turning point.

It indicates localized sensitivity in the surrounding quantum-transition shell.

LOCAL INSTABILITY ONSET

The first unstable rows appear at:

|alpha - 1| = 0.05

At alpha = 0.95 and alpha = 1.05, only a small subset of intervals is unstable.

The reported collapse_onset_radius is therefore a strict first-local-instability coordinate.

It must not be interpreted as global trajectory collapse under a five-percent deformation.

Correct interpretation:

The first localized near-bounce sensitivity appears at a deformation radius of 0.05, while approximately 98.83 percent of the full alpha grid remains admissible.

The affected shell lies approximately within:

0.03 <= rho/rho_c <= 0.82

The instability is driven mainly by bounded density and curvature responses.

Composition is no longer a pathological normalization driver.

SCIENTIFIC INTERPRETATION

Dataset B preserves global admissibility through the exact bounce.

The outer contraction and expansion regions remain fully admissible across the tested alpha range.

The exact turning-point intervals also remain admissible.

Only the surrounding near-bounce quantum-transition region develops localized deformation sensitivity.

This supports the following structural interpretation:

The effective LQC trajectory does not terminate at the classical singular boundary.

Instead, it reaches a finite turning surface, remains admissible through the route change, and continues into expansion.

The quantum-transition neighborhood behaves as a narrow sensitivity shell rather than a forbidden terminal collapse.

RELATION TO DATASETS A AND C

Datasets A and C:

- direct state = Stable Structure;
- direct mean rho approximately 0.0416;
- kappa_connect approximately 0.013335;
- alpha admissibility persistence approximately 0.992619;
- magnitude-only representation;
- A and C remain degenerate under the present direct and alpha metrics.

Dataset B:

- direct state = Weak Persistence;
- direct mean rho = 0.306052;
- kappa_connect = 0.100000;
- alpha admissibility persistence = 0.988309523810;
- full signed bounce path;
- localized near-bounce sensitivity;
- exact bounce crossing remains admissible.

Thus Dataset B is structurally distinct from A and C:

- it is more weakly connected at small kappa;
- it carries higher structural pressure;
- it remains globally admissible;
- it routes through a finite turning surface;
- its sensitivity is localized around, but not at, the exact bounce.

ACCEPTED STATUS

Dataset B trajectory generation v2.2:
PASS

Dataset B trajectory validation:
PASS

Exact bounce condition:
PASS

Direct STRUC-PERC-I:
PASS

Direct STRUC-I:
PASS

Alpha application v2.2:
COMPLETE

Bounce-safe signed coordinate:
PASS

Five-region classification:
PASS

Q90 regional normalization:
PASS

Dedicated bounce-crossing scales:
PASS

Bounded response treatment:
PASS

Active-channel comparability:
PASS

5D vector:
ACCEPTED, PRELIMINARY

INTERPRETIVE LIMITS

This result does not 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 final canonical UNNS boundary-distance coordinate;
- a final A/B/C boundary-routing conclusion.

The reported onset radius depends on the fixed methodological choices:

- Q90 regional scale;
- response cap = 5;
- first-local-instability criterion;
- five-region decomposition.

Those settings must remain fixed for any matched rerun or comparison.

PROVISIONAL MARGIN STATUS

boundary_margin_candidate remains diagnostic-only.

At the exact bounce, the provisional margin reaches zero because the density-to-bounce component is defined as:

1 - rho/rho_c

This zero marks the effective turning surface in the present diagnostic construction.

It must not yet be interpreted as the final canonical UNNS margin.

NEXT STEP

Construct the orientation-sensitive A/B/C bridge.

The bridge must compare:

Dataset A:
classical contraction toward terminal boundary approach

Dataset B:
finite contraction–bounce–expansion route

Dataset C:
Planck-compatible expansion away from the early boundary regime

The bridge must retain signed path information, including:

- signed H flow;
- signed Delta ln(a);
- signed density flow;
- signed curvature flow;
- margin-flow direction;
- distance to turning or boundary surface;
- branch identity;
- rho/rho_c for Dataset B;
- x_bounce_distance for Dataset B.

The immediate next artifact is:

ABC_bridge/tools/
build_orientation_sensitive_abc_bridge.py
