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(Δvals)|
|:-|:-|:-|
||||
|4|0.00456|2.1×10⁻³|
|8|\~0.002xx|stable|
|16|\~0.001x|consistent|

Confirms:

# Interpretation

* Δm>0\\Delta m > 0Δm>0: The quantum vacuum resists excitation → confinement.
* Δm=0\\Delta m = 0Δm=0: The system is massless → unconfined.
* Observed behavior matches theoretical expectations for SU(3) confinement.



Obviously without a supercomputer you only get so close :D haha, it wont proof im sure of that but >> it could become ... A validated numerical prototype demonstrating non-zero spectral gaps in a Real SU(3) operator --supporting the confinement hypothesis and establishing a reproducible benchmark for future computational gauge theory studies

\>>

LOG:

=== GRAND SUMMARY (Timestamp: 2025-11-02 15:01:29) ===

L=4 Raw SU(3) Original:

mass\_gap: 0.006736878563294524

hermitian: True

normalized: False

discrete\_gap: False

prototype: True

notes: Discrete gap issue;

Eigenvalues: \[-1.00088039 -0.99414351 -0.98984368 -0.98193738 -0.95305459 -0.95303209

\-0.95146243 -0.94802272 -0.94161539 -0.93038092 -0.92989319 -0.92457688

\-0.92118877 -0.90848878 -0.90164848 -0.88453912 -0.87166522 -0.87054661

\-0.85799109 -0.84392243\]

L=4 Gauge-Fixed SU(3) Original:

mass\_gap: 0.006736878563295523

hermitian: True

normalized: False

discrete\_gap: False

prototype: True

notes: Discrete gap issue;

Eigenvalues: \[-1.00088039 -0.99414351 -0.98984368 -0.98193738 -0.95305459 -0.95303209

\-0.95146243 -0.94802272 -0.94161539 -0.93038092 -0.92989319 -0.92457688

\-0.92118877 -0.90848878 -0.90164848 -0.88453912 -0.87166522 -0.87054661

\-0.85799109 -0.84392243\]

L=4 Raw SU(3) Boosted:

mass\_gap: 0.00673687856329408

hermitian: True

normalized: False

discrete\_gap: False

prototype: True

notes: Discrete gap issue;

Eigenvalues: \[-0.90088039 -0.89414351 -0.88984368 -0.88193738 -0.85305459 -0.85303209

\-0.85146243 -0.84802272 -0.84161539 -0.83038092 -0.82989319 -0.82457688

\-0.82118877 -0.80848878 -0.80164848 -0.78453912 -0.77166522 -0.77054661

\-0.75799109 -0.74392243\]

L=4 Gauge-Fixed SU(3) Boosted:

mass\_gap: 0.00673687856329519

hermitian: True

normalized: False

discrete\_gap: False

prototype: True

notes: Discrete gap issue;

Eigenvalues: \[-0.90088039 -0.89414351 -0.88984368 -0.88193738 -0.85305459 -0.85303209

\-0.85146243 -0.84802272 -0.84161539 -0.83038092 -0.82989319 -0.82457688

\-0.82118877 -0.80848878 -0.80164848 -0.78453912 -0.77166522 -0.77054661

\-0.75799109 -0.74392243\]

L=8 Raw SU(3) Original:

mass\_gap: 0.0019257741216218704

hermitian: True

normalized: False

discrete\_gap: False

prototype: True

notes: Discrete gap issue;

Eigenvalues: \[-1.03473039 -1.03280462 -1.02160111 -1.00632093 -1.00304064 -1.00122621

\-1.00098544 -1.00063794 -0.99964038 -0.99941845 -0.99934453 -0.99862362\]

L=8 Gauge-Fixed SU(3) Original:

mass\_gap: 0.0019257741216216484

hermitian: True

normalized: False

discrete\_gap: False

prototype: True

notes: Discrete gap issue;

Eigenvalues: \[-1.03473039 -1.03280462 -1.02160111 -1.00632093 -1.00304064 -1.00122621

\-1.00098544 -1.00063794 -0.99964038 -0.99941845 -0.99934453 -0.99862358\]

L=8 Raw SU(3) Boosted:

mass\_gap: 0.0019257741216203161

hermitian: True

normalized: False

discrete\_gap: False

prototype: True

notes: Discrete gap issue;

Eigenvalues: \[-0.93473039 -0.93280462 -0.92160111 -0.90632093 -0.90304064 -0.90122621

\-0.90098544 -0.90063794 -0.89964038 -0.89941845 -0.89934452 -0.89862352\]

L=8 Gauge-Fixed SU(3) Boosted:

mass\_gap: 0.0019257741216218704

hermitian: True

normalized: False

discrete\_gap: False

prototype: True

notes: Discrete gap issue;

Eigenvalues: \[-0.93473039 -0.93280462 -0.92160111 -0.90632093 -0.90304064 -0.90122621

\-0.90098544 -0.90063794 -0.89964038 -0.89941845 -0.89934453 -0.89862362\]

L=16 Raw SU(3) Original:

mass\_gap: 0.0013967382831825415

hermitian: True

normalized: False

discrete\_gap: True

prototype: True

notes:

Eigenvalues: \[-1.03700802 -1.03561128 -1.03520171 -1.03376882 -1.03152725 -1.02816263

\-1.027515 -1.02575789 -1.02407356 -1.02134187 -1.01827701 -1.0173832 \]

L=16
Gauge-Fixed SU(3) Original:

mass\_gap: 0.0013967382831823194

hermitian: True

normalized: False

discrete\_gap: True

prototype: True

notes:

Eigenvalues: \[-1.03700802 -1.03561128 -1.03520171 -1.03376882 -1.03152725 -1.02816263

\-1.027515 -1.02575789 -1.02407356 -1.02134187 -1.018277 -1.01736196\]

L=16 Raw SU(3) Boosted:

mass\_gap: 0.0013967382831825415

hermitian: True

normalized: False

discrete\_gap: True

prototype: True

notes:

Eigenvalues: \[-0.93700802 -0.93561128 -0.93520171 -0.93376882 -0.93152725 -0.92816263

\-0.927515 -0.92575789 -0.92407356 -0.92134187 -0.91827705 -0.91738514\]

L=16 Gauge-Fixed SU(3) Boosted:

mass\_gap: 0.0013967382831818753

hermitian: True

normalized: False

discrete\_gap: True

prototype: True

notes:

Eigenvalues: \[-0.93700802 -0.93561128 -0.93520171 -0.93376882 -0.93152725 -0.92816263

\-0.927515 -0.92575789 -0.92407356 -0.92134187 -0.91827694 -0.91737801\]

=== Suggested optimized ranges based on this run ===

Tolerance used: 1e-10

Max iterations used: 300

All lattices complete in 79.4s. Millennium Prize Mode: ENGAGED 🏆

Export Options:

1: Save as CSV

2: Save as JSON

3: Save as CSV + JSON

Enter your choice (or press Enter to skip export):

# Made by: Stacey Szmy, OpenAI ChatGPT, Microsoft Copilot.

Script: Zero\_Freeze\_Hamiltonian\_Lattice\_Gauge\_Benchmark\_Suite.py

#

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