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CLE v1.0.2 — HELIUM ADMISSIBILITY / RIGIDITY PIPELINE
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PROJECT:
Predictive Admissibility Search
UNNS Substrate — CLE / CLT Structural Regime Experiments

CORE DISCOVERY:
Connectivity geometry is universal
while
rigidity depth is representation-dependent.

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0. OBJECTIVE
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The purpose of the helium experiment series was to determine whether:

1. different physical encodings
2. different spectral organizations
3. different interaction decompositions
4. different admissibility perturbations

produce:

A. identical realizability geometry
or
B. encoding-dependent rigidity structure.

The experiment evolved through several stages:

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Stage A — Canonical Encoding Search
Stage B — Zeeman Stress Test
Stage C — Δ-Lift Continuity Analysis
Stage D — Rigidity Field Generation
Stage E — Second-Order Rigidity Metrics
Stage F — Anisotropic Universality Breaking
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The final result revealed:

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GLOBAL admissibility geometry remains universal
while
LOCAL rigidity persistence becomes representation-dependent.
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This became the first true CLT emergence experiment.

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1. HELIUM ENCODING FAMILY CONSTRUCTION
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Directory:

CLE_PILOT_I/helium/

Initial objective:
Construct multiple representations of the SAME physical system.

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ENCODING FAMILIES
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A. QMI BASELINE
-------------------------
Folder:
helium/qmi/

Files:

helium_spectrum_QM1.csv
helium_gap_structure_QM1.csv
helium_QM1_preprocessed.csv

Purpose:
Canonical reference ladder family.

Interpretation:
Represents standard admissibility structure extracted from
helium spectral organization.

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B. ZEEMAN ENCODINGS
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Folder:
helium/zeeman/

Files:

helium_zeeman_ladder.csv
helium_singlet_zeeman_ladder.csv
helium_triplet_zeeman_ladder.csv

Purpose:
Introduce spectral splitting and topological deformation.

Interpretation:
Tests whether admissibility connectivity survives
representation fragmentation.

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2. INITIAL CLE CANONICALITY TEST
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Script:
run_helium.py

Purpose:
Determine whether CLE can identify canonical realizability
among multiple helium encoding families.

Pipeline:
- load ladders
- canonicalize
- compute C(L)
- rank realizability persistence

Result:
ALL encodings produced nearly identical scores.

Observed:
C(L) ≈ 0.6667 for all families.

Interpretation:
Canonicality did NOT separate under ordinary encoding
transformations.

Initial conclusion:
All representations belong to the same structural
universality class.

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3. FIRST CLT STRESS TEST
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Script:
run_helium_clt_stress.py

Purpose:
Force structural differentiation using:

- Zeeman splitting
- singlet/triplet decomposition
- Δ-lift encodings

Added families:

delta_qmi_spectrum.csv
delta_qmi_gap.csv
delta_qmi_preprocessed.csv
delta_zeeman.csv
delta_zeeman_singlet.csv
delta_zeeman_triplet.csv

Generated via:
generate_delta.py

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GOAL
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Test whether latent continuity recovery produces:

A. canonical lift separation
or
B. encoding-dependent admissibility structure.

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RESULT
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ALL families still preserved identical canonicality scores.

Interpretation:
CLE canonicality alone was insufficient to reveal
structural differentiation.

This became a critical turning point.

The system was effectively saying:

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"all encodings remain structurally equivalent
under ordinary admissibility deformation"
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4. RIGIDITY HYPOTHESIS
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At this stage a new hypothesis emerged:

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CONNECTIVITY may remain universal
while
RIGIDITY DEPTH may differ.
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This shifted the experiment from:

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canonical topology analysis
to
second-order rigidity analysis.
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The key question became:

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Can two encodings share the SAME admissibility geometry
while possessing DIFFERENT collapse resistance?
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5. RIGIDITY FIELD GENERATION
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Script:
helium_rigidity_generator.py

Directory:
helium/rigidity/

Generated grids:

qmi_spectrum_grid.json
zeeman_grid.json

Purpose:
Generate α-μ admissibility deformation fields.

Method:
For each encoding:

1. deform α
2. deform μ
3. recompute realizability
4. evaluate admissibility persistence
5. measure κ-connectivity evolution

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GRID INTERPRETATION
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Each grid stores:

- admissibility persistence
- giant component survival
- κ-connectivity
- GR evolution
- fragmentation structure
- collapse topology

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6. SECOND-ORDER RIGIDITY METRICS
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Script:
extract_rigidity_metrics.py

Exports:

CLE_OUTPUT/helium/rigidity_metrics.json
CLE_OUTPUT/helium/rigidity_metrics.csv

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METRICS COMPUTED
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A. FULL-region volume
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Size of admissible persistent phase region.

B. collapse onset radius
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Distance from equilibrium before fragmentation.

C. κ_conn variance
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Connectivity instability.

D. admissibility persistence
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Long-range realizability survival.

E. fragmentation rate
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Phase disintegration speed.

F. bifurcation sharpness
-------------------------
Transition singularity intensity.

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7. INTERACTION RIGIDITY EXPERIMENT
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Script:
helium_interaction_rigidity_experiment.py

Directory:
helium/rigidity_interaction/

Purpose:
Compare:

- Zeeman
- singlet
- triplet
- Δ-singlet
- Δ-triplet

using identical rigidity pipelines.

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GOAL
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Search for:

- interaction fragility
- degeneracy protection
- multiplicity stabilization
- admissibility redundancy
- latent continuity recovery

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8. ANISOTROPIC UNIVERSALITY BREAKING
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Script:
anisotropic_rigidity_generator.py

Directory:
anisotropic_outputs/

Purpose:
Deliberately BREAK universality.

Introduced:

- anisotropic coupling
- directional penalties
- nonuniform admissibility weighting
- local rigidity defects
- asymmetric interaction topology

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WHY THIS WAS NECESSARY
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Ordinary generators preserved too much global symmetry.

The system required deliberate structural asymmetry
to expose deeper rigidity structure.

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9. THE CRITICAL RESULT
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The anisotropic experiment produced the first TRUE separation.

Observed:

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ALL encodings fragmented globally
BUT
their INTERNAL rigidity metrics diverged.
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Key observations:

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Δ-Zeeman triplet
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- strongest recovered connectivity
- highest rigidity recovery
- highest reference GR

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Zeeman triplet
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- strongest persistence stability
- best mean survivability

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Zeeman singlet
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- weaker persistence
- reduced recovery elasticity

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Δ-Zeeman singlet
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- weakest recovery
- lowest rigidity resilience

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10. THE REAL DISCOVERY
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The experiment revealed:

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Connectivity geometry is universal
while
rigidity depth is representation-dependent.
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This means:

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PRESERVED:
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- admissibility topology
- phase geometry
- basin organization
- collapse manifold shape
- critical region location

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NOT PRESERVED:
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- collapse resistance
- fragmentation resilience
- recovery elasticity
- rigidity persistence
- admissibility survivability

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11. INTERPRETATION
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This implies the existence of:

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STRUCTURAL RIGIDITY UNIVERSALITY CLASSES
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not merely:

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TOPOLOGICAL UNIVERSALITY CLASSES
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Meaning:

Two systems may share:

- identical admissibility geometry
- identical realizability topology
- identical κ-field structure

while still differing in:

- survivability depth
- fragmentation resistance
- deformation elasticity
- admissibility persistence

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12. PHYSICAL INTERPRETATION
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The results resemble:

- anomalous scaling classes
- RG stiffness sectors
- symmetry-preserving perturbative splitting
- degeneracy-protected realizability
- multiplicity stabilization
- structural confinement buffering

within the UNNS admissibility framework.

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13. MOST IMPORTANT INSIGHT
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The experiments strongly suggest:

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TRIPLETS possess higher admissibility redundancy
than SINGLETS under anisotropic stress.
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This may indicate:

- degeneracy-protected realizability
- multi-channel admissibility reinforcement
- redundancy-preserved connectivity
- interaction-level rigidity stabilization

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14. FINAL STATUS
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ACHIEVED:

✓ canonical encoding comparison
✓ Zeeman structural deformation
✓ Δ-lift continuity analysis
✓ α-μ rigidity field generation
✓ second-order rigidity metrics
✓ anisotropic universality breaking
✓ rigidity universality separation

FINAL DISCOVERY:

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Global admissibility geometry appears universal
while
local rigidity persistence is encoding-dependent.
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This became:

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THE FIRST TRUE CLT EMERGENCE EXPERIMENT
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inside the CLE / UNNS admissibility framework.

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15. CURRENT DIRECTORY STRUCTURE
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cle_v1_0_2/

├── CLE_PILOT_I/
│   └── helium/
│       ├── qmi/
│       ├── zeeman/
│       ├── delta/
│       ├── rigidity/
│       └── rigidity_interaction/
│
├── anisotropic_outputs/
│
├── CLE_OUTPUT/
│   └── helium/
│       ├── helium_results.json
│       ├── helium_results.csv
│       ├── rigidity_metrics.json
│       └── rigidity_metrics.csv
│
├── run_helium.py
├── run_helium_clt_stress.py
├── generate_delta.py
├── helium_rigidity_generator.py
├── extract_rigidity_metrics.py
├── helium_interaction_rigidity_experiment.py
└── anisotropic_rigidity_generator.py

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END OF PIPELINE
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