# ALPHA_APPLICATION_INDEX.txt
# STELLAR_BOUNDARY_DYNAMICS_I
# Phase B — Alpha Application / Deformation-Grid Construction

PHASE:
B_supernova_light_curves

STAGE:
alpha_application

PURPOSE:
Apply α-deformation to Phase B supernova light-curve structures after they have
passed STRUC-PERC-I numeric ladder evaluation.

This stage tests whether the observed post-collapse brightness-response ladders
remain structurally coherent under controlled deformation of their compact
phase-local features.

PIPELINE POSITION:
OSC raw JSON
→ Phase B light-curve ladder CSV
→ STRUC_PERC_I canonical input CSV
→ STRUC-PERC-I numeric ladder TXT
→ STRUC-PERC-I batch result
→ α-application / deformation grid
→ 5D structural vector
→ cross-object comparison

INPUTS:
../struc_perc_i/canonical_inputs/B_SN1987A_struc_perc_input.csv
../struc_perc_i/canonical_inputs/B_SN1993J_struc_perc_input.csv
../struc_perc_i/canonical_inputs/B_SN1999em_struc_perc_input.csv
../struc_perc_i/canonical_inputs/B_SN2011dh_struc_perc_input.csv
../struc_perc_i/canonical_inputs/B_SN2012aw_struc_perc_input.csv
../struc_perc_i/canonical_inputs/B_SN2013ej_struc_perc_input.csv

REFERENCE RESULTS:
../struc_perc_i/struc_perc_batch_results.csv
../struc_perc_i/struc_perc_batch_results.json
../struc_perc_i/summaries/B_STRUC_PERC_I_RESULTS_INTERPRETATION.txt

INPUT_STATUS:
All six Phase B pilot numeric ladders returned FULL_PERCOLATION under
STRUC-PERC-I v2.5.0.

OBJECTS:
B_SN1987A
B_SN1993J
B_SN1999em
B_SN2011dh
B_SN2012aw
B_SN2013ej

STRUCTURAL FEATURES TO DEFORM:
gap
duration_days
mag_range
mean_slope
mean_curvature
phase order
band-local persistence

PRIMARY α-DEFORMATION IDEA:
For each compact STRUC_PERC_I canonical input, perturb phase-local structural
features over an α-grid and evaluate whether the object preserves a coherent
deformation response.

The goal is not to re-run raw photometry. The goal is to test stability of the
compact structural representation already obtained from the light-curve ladder.

DEFORMATION TARGETS:
1. Gap deformation:
   gap_alpha = gap × α

2. Duration deformation:
   duration_alpha = duration_days × α

3. Slope deformation:
   mean_slope_alpha = mean_slope × α

4. Curvature deformation:
   mean_curvature_alpha = mean_curvature × α

5. Combined structural score:
   A derived phase-local deformation score combining gap, duration, slope, and
   curvature into a comparable response coordinate.

RECOMMENDED FIRST α GRID:
α_min = 0.50
α_max = 1.50
α_points = 21

Recommended values:
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50

OUTPUT STRUCTURE:
alpha_application/
  ALPHA_APPLICATION_INDEX.txt

  grids/
    B_SN1987A_alpha_grid.csv
    B_SN1993J_alpha_grid.csv
    B_SN1999em_alpha_grid.csv
    B_SN2011dh_alpha_grid.csv
    B_SN2012aw_alpha_grid.csv
    B_SN2013ej_alpha_grid.csv

  vectors/
    B_SN1987A_5d_vector.csv
    B_SN1993J_5d_vector.csv
    B_SN1999em_5d_vector.csv
    B_SN2011dh_5d_vector.csv
    B_SN2012aw_5d_vector.csv
    B_SN2013ej_5d_vector.csv

  summaries/
    B_ALPHA_APPLICATION_SUMMARY.csv
    B_5D_VECTOR_SUMMARY.csv
    B_ALPHA_APPLICATION_INTERPRETATION.txt

EXPECTED GRID COLUMNS:
object_id
object_name
supernova_type
band
phase_name
stage_index
alpha
gap_alpha
duration_alpha
slope_alpha
curvature_alpha
structural_response
gap_response_norm
duration_response_norm
slope_response_norm
curvature_response_norm
phase_persistence_score
boundary_role
support_regime_proxy
alpha_status

EXPECTED 5D VECTOR COLUMNS:
object_id
object_name
mean_GR
var_GR
anisotropic_persistence
admissibility_persistence
collapse_onset_radius
kappa_connect_reference
tail_dominance_reference
notes

5D VECTOR DEFINITIONS FOR PHASE B:

mean_GR:
Mean normalized gap response over α and phase-local rows.

var_GR:
Variance of normalized gap response over α and phase-local rows.

anisotropic_persistence:
Degree to which deformation response differs across bands and phases while
remaining structurally coherent.

admissibility_persistence:
Fraction of α-grid rows that remain valid and non-collapsed under the chosen
response thresholds.

collapse_onset_radius:
First α distance from α = 1.0 at which the object shows deformation instability.
If no instability is detected in the tested grid, record the maximum tested
radius and mark as no collapse observed.

INTERPRETATION RULE:
α-application does not claim new astrophysical mechanisms. It tests structural
stability of the observable post-collapse light-curve ladder representation.

UNNS ROLE:
This stage asks whether a real observed boundary-response trajectory remains
inside a coherent admissible deformation basin after controlled perturbation.

In UNNS language:

Φ:
The phase-ladder geometry is perturbed.

Ψ:
The gap/slope/curvature response is tracked as a structural coherence signal.

τ:
Persistence under α-deformation is interpreted as continuity of the
post-boundary relaxation trajectory.

SPECIAL ATTENTION:
SN 2012aw should be watched carefully because STRUC-PERC-I returned
FULL_PERCOLATION but required κ_connect ≈ 4.4 and showed tailDominance ≈ 0.329.
It is not a failure case, but it is the strongest deformation-sensitivity
candidate in the first pilot set.

NEXT SCRIPT:
../tools/b_alpha_apply.py

SCRIPT ROLE:
Read:
../struc_perc_i/canonical_inputs/*.csv

Write:
grids/*.csv
vectors/*.csv
summaries/*.csv

STATUS:
Directory initialized.
Ready for b_alpha_apply.py creation.
