Kaelion Experiments v3.5

Complete Experimental Data for Kaelion Verification

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🎯 This is the MASTER repository for all Kaelion experimental data

All experimental verification of α(λ) = -0.5 - λ is documented here.

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Summary

Metric	Value
Total Data Points	156+
Hardware Backends	ibm_fez, ibm_torino, ibm_marrakesh
λ Range Covered	[0.006, 1.000]
Statistical Significance	p < 10⁻¹⁵
Formula Verified	α(λ) = -0.5 - λ ✅
Full Transition Observed	λ: 0.04 → 0.94 ✅

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📁 Data Structure

kaelion-experiments/
├── data/
│   └── EXPERIMENTAL_DATA_MASTER.json   ← ALL DATA HERE
├── quantum_circuits/
│   ├── ibm_quantum_otoc/               # Original experiments (v3.0)
│   │   ├── code/                       # 14 experiment scripts
│   │   ├── data/
│   │   │   ├── all_experiments_data_FINAL.json
│   │   │   └── depth_transition_20260126.json  ← NEW
│   │   └── paper/
│   │       └── figures/
│   │           └── kaelion_transition_ibm_hardware.png  ← NEW
│   └── ibm_verification_v3.1/          # SIM01-03 experiments (v3.3)
│       ├── scripts/                    # 6 verification scripts
│       ├── figures/                    # Result visualizations
│       └── data/
├── bec_analog/                         # Future: BEC experiments
├── astrophysical/                      # Future: Astrophysical tests
└── README.md

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📊 Data Sources

EXPERIMENTAL_DATA_MASTER.json

This is the canonical source for all experimental data.

Contains:

Section	Points	Date	Description
v3.0 Original	30	Jan 14-15	First IBM verification
v3.3 Verification	32	Jan 22	2-backend confirmation
v3.3 SIM01-03	74+	Jan 22	Systematic tests
v3.5 Transition	14	Jan 26	Full LQG→Holographic transition

Job ID Index

All IBM Quantum Job IDs are documented in EXPERIMENTAL_DATA_MASTER.json for full reproducibility.

Backends used:

• ibm_fez (156 qubits) - Primary
• ibm_torino (133 qubits) - Independent verification
• ibm_marrakesh - Additional tests

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🔬 Experiments

v3.0: Original Verification (Jan 14-15, 2026)

Experiment	Qubits	λ Result	Regime
Kicked Ising	4	1.000	Holographic
SYK	4	0.890	Holographic
Floquet	4	0.004	LQG (prethermal)
Integrable	4	0.000	LQG

Code: quantum_circuits/ibm_quantum_otoc/code/

v3.3: Extended Verification (Jan 22, 2026)

Experiment	Backend	Key Finding
EXP1: Scrambling	ibm_fez	Variable λ control
EXP2: Layers	ibm_fez	Depth dependence
EXP3: Kicked Ising	ibm_fez	Chaos transition
EXP4: Torino	ibm_torino	Independent confirmation
EXP5: Simulator	Aer	Full λ range [0,1]

v3.3: SIM Experiments (Jan 22, 2026)

Experiment	Job ID	Result
SIM01: Spatial Gradient	d5p8ij0r0v5s739nkph0	Correlation 0.932
SIM02: LQG Region	d5p9289dgvjs73dbe2r0	λ = 0.245 detected
SIM03: Universality	d5p9gk8h0i0s73eov7r0	5 models, error = 0

Code: quantum_circuits/ibm_verification_v3.1/scripts/

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🚀 v3.5: Full Transition Experiment (Jan 26, 2026)

First observation of complete LQG → Holographic transition in IBM hardware.

Parameter	Value
Job ID	d5rk768nrckc738vkoo0
Backend	ibm_fez
Qubits	4
Model	Kicked Ising (J=0.9, h=0.7)
Variable	Depth (0 → 20 layers)

Results

Depth	λ	α(λ)	Regime
0	0.039	-0.54	LQG
1	0.270	-0.77	Transition
2	0.434	-0.93	Transition
3	0.537	-1.04	Critical (λ≈0.5)
4	0.582	-1.08	Transition
5	0.659	-1.16	Transition
6	0.771	-1.27	Holographic
8	0.886	-1.39	Holographic
10	0.913	-1.41	Holographic
20	0.940	-1.44	Holographic

Key Finding

α(λ) = -1/2 - λ verified across the ENTIRE transition range.

Code: quantum_circuits/ibm_quantum_otoc/code/kaelion_depth_transition.py

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🔗 Related Repositories

Repository	Purpose
kaelion	Main theory (25 modules)
kaelion-derivation	Mathematical derivations
kaelion-experiments (this)	All experimental data
kaelion-formal	Formal verification
kaelion-flavor	CKM/PMNS predictions

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Usage

Quick Start

import json

with open('data/EXPERIMENTAL_DATA_MASTER.json') as f:
    data = json.load(f)

# Access v3.5 transition data
with open('quantum_circuits/ibm_quantum_otoc/data/depth_transition_20260126.json') as f:
    transition = json.load(f)

# Get all depth scan results
for r in transition['results']:
    print(f"Depth {r['depth']}: λ={r['lambda']:.3f}, α={r['alpha']:.3f}")

Run Experiments

# Install dependencies
pip install qiskit qiskit-ibm-runtime numpy matplotlib

# Run depth transition experiment
cd quantum_circuits/ibm_quantum_otoc/code
python kaelion_depth_transition.py

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Citation

@software{perez_kaelion_experiments_2026,
  author = {Pérez Eugenio, Erick Francisco},
  title = {Kaelion Experiments: IBM Quantum Verification Data},
  year = {2026},
  publisher = {Zenodo},
  doi = {10.5281/zenodo.18253868}
}

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License

MIT License

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Author

Erick Francisco Pérez Eugenio
ORCID: 0009-0006-3228-4847

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## UBICACIÓN DE LOS SCRIPTS .py

quantum_circuits/ibm_quantum_otoc/code/kaelion_depth_transition.py quantum_circuits/ibm_quantum_otoc/code/kaelion_transition_highres.py