DATASET A — ALPHA APPLICATION V2 RESULT
Cosmological Boundary Routing
Classical Friedmann Singular Approach

STATUS

DATASET A DIRECT AND ALPHA STAGES: COMPLETE

DATASET

Dataset:
A_classical_friedmann

Trajectory role:
Matched classical Friedmann contraction approaching the small-a numerical singular cutoff.

Validated trajectory:
generated_trajectory/validated/
classical_friedmann_approach_validated.csv

Trajectory direction:
contraction

Branch convention:
H < 0

Numerical cutoff:
a = 1e-8

DIRECT PRELIMINARY STRUCTURAL RESULT

Scalar ladder:

q_A(a) = ln(E(a))

where:

E(a) = |H(a)| / H0

Sorted ladder size:
4001 elements

Gap count:
4000

STRUC-PERC-I RESULT

Input:
classical_friedmann_response_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 = 4000 / 4000 gaps
Isolated vertices = 0
kappa_connect = 0.0133352143
Final components = 1
Downsampling = no
Approximate mode = no
Tail dominance = 0

Interpretation:

The sorted Dataset A ln(E) ladder forms one fully connected vulnerability structure across the tested kappa range.

STRUC-I RESULT

Input:
classical_friedmann_response_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 = 4001
subsampled = false

Result:

Regime = Geometric Persistence
State = Stable Structure
mean A_kappa = 1.000000
minimum A_kappa = 1.000000
A_kappa at kappa = 1 = 1.000000
mean structural pressure rho = 0.041570
maximum structural pressure rho = 0.290260
rho at kappa = 1 = 0.290260

Interpretation:

Every tested perturbation satisfied:

inv(P_epsilon; L) <= nu(V_epsilon(L))

throughout the complete tested kappa range.

ALPHA APPLICATION V2

Script:

canonical/alpha/tools/
a_classical_friedmann_alpha_apply_v2.py

Alpha range:

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

ACTIVE RESPONSE CHANNELS

ln(E) gap response          weight 0.35
total-density response      weight 0.30
curvature response          weight 0.20
composition response        weight 0.15

The provisional margin channel is retained for diagnosis only.

It does not contribute to:

- structural_response
- phase_persistence_score
- instability_flag
- collapse_onset_radius

NORMALIZATION STATUS

Active-channel normalization:
PASS

Active scale review needed:
NO

Review status:
comparable_active_channels

Margin diagnostic warning:
YES

The margin warning does not invalidate the accepted active-channel vector because the provisional margin is excluded from the structural-response calculation.

ACCEPTED 5D VECTOR

mean_GR:
0.244474571041

var_GR:
0.022290080269

anisotropic_persistence:
0.172874406964

admissibility_persistence:
0.992619047619

collapse_onset_radius:
0.45

collapse_observed:
yes

GRID OUTCOME

Valid rows:
83,380

Instability rows:
620

Total rows:
84,000

Admissibility persistence:
0.992619047619

Stable alpha basin:

0.60 <= alpha <= 1.40

Instability occurs only at:

alpha = 0.50
alpha = 0.55
alpha = 1.45
alpha = 1.50

Instability onset:

|alpha - 1| = 0.45

The unstable rows are confined to matter- and Lambda-dominated intervals.

No radiation-era instability rows were found.

INTERPRETATION OF COLLAPSE ONSET

The reported collapse_onset_radius = 0.45 is an alpha-deformation threshold within the selected structural representation.

It must not be interpreted as direct evidence of a physical cosmological singularity.

The remaining instability is driven mainly by the composition-shift channel in intervals where the relative matter and Lambda fractions redistribute rapidly.

REPRESENTATION DEGENERACY WITH DATASET C

Dataset A and Dataset C produce the same direct sorted ln(E) ladder because both use:

- the same Planck parameter anchor;
- the same scale-factor samples;
- the same Friedmann magnitude E(a);
- the same scalar mapping q = ln(E).

Their direct STRUC-PERC-I results are therefore identical.

Their STRUC-I results differ only by expected Monte Carlo variation.

The Dataset A alpha-v2 vector is also numerically identical to Dataset C because the active feature definitions use magnitude-only interval responses:

- |Delta ln(E)|
- |Delta ln(rho_total)|
- |Delta curvature|
- composition-shift magnitude

Although Dataset A preserves:

- contraction order;
- negative signed H;
- increasing density toward the cutoff;
- increasing curvature toward the cutoff;
- decreasing provisional margin;

those directional quantities do not currently enter the accepted 5D metrics.

SCIENTIFIC CONCLUSION

Dataset A is structurally stable and highly admissible under the current sorted-ladder and magnitude-only alpha representations.

However, these representations do not distinguish classical contraction from observational expansion when the same scalar magnitudes are used.

This establishes a methodological result:

set geometry is not trajectory orientation

and:

magnitude-only deformation is not directional dynamics

The accepted Dataset A result must therefore be preserved as evidence of representation degeneracy, not altered merely to force separation from Dataset C.

ACCEPTED STATUS

Dataset A trajectory generation:
PASS

Dataset A trajectory validation:
PASS

Direct STRUC-PERC-I:
PASS

Direct STRUC-I:
PASS

Alpha application v2:
COMPLETE

Active-channel normalization:
PASS

Margin isolation:
PASS

Direction metadata preservation:
PASS

Direction-sensitive discrimination:
NOT ACHIEVED

5D vector:
VALID, PRELIMINARY, DEGENERATE WITH DATASET C

INTERPRETIVE LIMITS

This result does not establish:

- that the universe physically followed the modeled contraction;
- that a singularity was directly observed;
- singularity removal;
- cosmological boundary routing;
- a final shared A/B/C boundary margin;
- directional equivalence between contraction and expansion.

NEXT STEP

Proceed to Dataset B:

B_lqc_bounce

Dataset B must preserve:

contracting branch
→ finite bounce
→ expanding branch

After Dataset B is generated and validated, construct an orientation-sensitive A/B/C bridge using signed flow quantities rather than modifying the accepted Dataset A and Dataset C direct results.
