A Bondi-Runaway-Free -Szmy Mirror Model(SMM)- Negative Mass Gravity via Potential-Only Coupling & Potential Energy
Worked on a model toy structure to model zero as a mirror line (szmy mirror model - SMM), working along this models rules it's possible to stop runaway instability problems Because of pairing and - gravity in this model couples only to the potential energy..
Every particle has a mirror partner on the opposite side of zero. The mirror partner carries negative mass and negative kinetic energy. When you pair them together, their kinetic energies cancel out exactly; leaving only the potential energy of the system behind.
This matters in the case of gravity for the SSM. Instead of coupling to mass or kinetic energy (which would cause runaway instability problems that have plagued negative-mass theories for decades); gravity in this model couples only to the potential energy, this keeps the whole model stable.
The gravitational field equation that comes out of this is:
∇²Φ = 8πG·V(x)
The gravitational field responds only to the shared potential landscape of the particle pair ** not to which branch is positive or negative ** Both mirror partners fall together. The system behaves gravitationally like a single object.
The full model includes a two-branch Lagrangian, Euler-Lagrange equations for both sectors, a mirror Hamiltonian, a conserved mirror charge, and a matrix formulation where the mirror symmetry maps to the Pauli σz matrix.
And a addendum to the dissertation recently added.
Yo dissertation updated and available here
https://github.com/haha8888haha8888/Zer00logy/blob/main/szmy_mirror_model.txt
Python suite ready and available here with 80 sectors.
https://github.com/haha8888haha8888/Zer00logy/blob/main/SMM_Suite.py
Main Menu: 1 — Mirror Operator
2 — Kinetic Branches
3 — Paired Cancellation
4 — Mirror Momentum & Newton
5 — Lagrangian Branches
6 — Mirror Hamiltonian
7 — Paired Energy 2V
8 — Gravity (Potential Only)
9 — Matrix σ_z Form
10 — Mirror-Gravity Field Solver
11 — Paired-System Dynamics Simulation
12 — σ_z Evolution / Mirror Charge Tracking
13 — Paired-Creation Rule Simulation
14 — Mirror-Balance Conservation Tests
15 — Experimental Sandbox (A+B+C+D)
16 — Mirror-Gravity Wave Propagation
17 — Mirror-Lattice Simulation
18 — Mirror-Quantum Toy Model
19 — Mirror-Thermodynamics
20 — Mirror-Universe Evolution
21 — Mirror-Statistical Partition Function
22 — Spontaneous Mirror-Symmetry Breaking
23 — Mirror-Entropy Evolution
24 — Mirror-Electrodynamics
25 — Runaway-Immunity & Stability Proof
26 — The Stress-Energy Bridge (Tensor Mapping)
27 — Mirror-Path Integral (Quantum Phase)
28 — Cosmological Redshift (Potential Wells)
29 — SBHFF Mirror-Singularity Analysis
30 — GCA: Grand Constant Potential Scaling
31 — RN: Repeating Digit Weight Fluctuations
32 — GCA-SMM Grand Unification Test
33 — Mirror-Lattice Gauge Benchmark
34 — Void-Point Balance (Zero-Freeze)
35 — Varia Step Logic: Symbolic Precision
36 — Symbolic Prime Inheritance (9 ≡ 7)
37 — The Never-Ending Big Bang (Recursive Expansion)
38 — Mirror-Hodge GCA (Topological Duals)
39 — SMM Dissertation & Authorship Trace
40 — The Zero-Matter Outer Shell
41 — Mirror-EM Coupling Forks
42 — Negative-mass Orbital Stability Forks
43 — Mirror Pair in Expanding Background Forks
44 — σ_z Berry Phase Forks
45 — Mirror Symmetry Breaking Triggers
46 — Energy Conditions for Mirror Pairs
47 — Toy Black Hole Horizon for Mirror Pair
48 — Grand Constant Mirror Aggregator Forks
49 — SBHFF Runaway Detector for Mirror Dynamics
50 — RN-Weighted Mirror Branches (Physics Domains)
51 — Step Logic Symbolic Mirror Precision
52 — RHF Recursive Lifts for Mirror States
53 — equalequal Resonance for Mirror Branches
54 — equalequal Resonance v2 (Invariants)
55 — PAP Parity Adjudication for Mirrors
56 — DAA Domain Adjudicator for Mirrors
57 — PLAE Operator Limits on Mirror Expressions
58 — Zer00logy Combo: equalequal + PAP + DAA + PLAE
59 — SBHFF + equalequal Collapse Resonance
60 — Mirror Invariant Resonance Dashboard
61 — Mirror GCA + RN + PAP Unification Teaser
62 — Mirror Noether Charge
63 — Mirror Field Oscillation
64 — Mirror Harmonic Oscillator
65 — Mirror Cosmology
66 — Runaway Instability Test
67 — Mirror Entropy Flow
68 — Mirror Lattice Gravity
69 — Mirror Wave Interference
70 — Mirror Black Hole Toy Model
71 — Mirror Energy Conservation
72 — Mirror Orbital System
73 — Mirror Quantum Pair State
74 — Mirror Field Energy Density
75 — Full SMM Balance Test
76 — Mirror Spacetime Curvature
77 — Mirror Vacuum Energy
78 — Mirror Cosmological Constant
79 — Mirror Pair Creation
80 — Mirror Universe Simulation
XX — Save Log
00 — Exit
Logs here
https://github.com/haha8888haha8888/Zer00logy/blob/main/SMM_log.txt
SECTOR 1 — Mirror Operator 𝓜(x) = -x
𝓜(5) = -5 𝓜(-3) = 3 𝓜(12.5) = -12.5 𝓜(-9.1) = 9.1
SECTOR 2 — Kinetic Energy Branches: K = -+ ½ m v²
K+ = +½ m v² = 9.0 K- = -½ m v² = -9.0
SECTOR 3 — Paired System: K+ + K- = 0
K+ = 8.0 K- = -8.0 K_total = 0.0
SECTOR 4 — Mirror Momentum & Newton's Second Law
p = m v = 10.0 p_mirrored = -p = -10.0 a_normal = 5.0 a_mirror = -5.0
SECTOR 5 — Lagrangian Branches & Euler–Lagrange
Normal: L+ = +½ m xdot² - V(x) Mirrored: L- = -½ m xdot² - V(x) EOM: Normal: m x¨ = -dV/dx Mirrored: m x¨ = +dV/dx
SECTOR 6 — Mirror Hamiltonian
p = -m xdot = -2.0 E_mirrored = -½ m xdot² + V = 3.0
~
SECTOR 7 — Paired System Energy: E_total = 2V(x)
E_total = 2V = 14.0
~
SECTOR 8 — Gravity: Potential-Only Coupling
ρ_grav ∝ 2V = 8.0 Gravity couples only to potential energy.
~
SECTOR 9 — Matrix Formulation (σ_z)
σ_z = [[ 1 0] [ 0 -1]]
~
SECTOR 10 — Mirror-Gravity Field Solver
Solved gravitational potential Φ(x) for a mirror pair. Φ(0) = -22.0568 Gravity responds only to potential energy (2V).
~
--- SECTOR 78 : MIRROR COSMOLOGICAL CONSTANT --- step 0 Λ+ = 0.0 Λ- = -0.0 sum = 0.0 step 1 Λ+ = 0.01 Λ- = -0.01 sum = 0.0 step 2 Λ+ = 0.02 Λ- = -0.02 sum = 0.0 step 3 Λ+ = 0.03 Λ- = -0.03 sum = 0.0 step 4 Λ+ = 0.04 Λ- = -0.04 sum = 0.0 step 5 Λ+ = 0.05 Λ- = -0.05 sum = 0.0 step 6 Λ+ = 0.06 Λ- = -0.06 sum = 0.0 step 7 Λ+ = 0.07 Λ- = -0.07 sum = 0.0 step 8 Λ+ = 0.08 Λ- = -0.08 sum = 0.0 step 9 Λ+ = 0.09 Λ- = -0.09 sum = 0.0
Result: Cosmological expansion balanced by mirror contraction.
~ --- SECTOR 79 : MIRROR PAIR CREATION --- step 0 P+ = 1 P- = -1 total = 0 step 1 P+ = 2 P- = -2 total = 0 step 2 P+ = 3 P- = -3 total = 0 step 3 P+ = 4 P- = -4 total = 0 step 4 P+ = 5 P- = -5 total = 0 step 5 P+ = 6 P- = -6 total = 0 step 6 P+ = 7 P- = -7 total = 0 step 7 P+ = 8 P- = -8 total = 0 step 8 P+ = 9 P- = -9 total = 0 step 9 P+ = 10 P- = -10 total = 0
Result: Particle pairs preserve mirror balance.
~
--- SECTOR 80 : MIRROR UNIVERSE SIMULATION --- step 0 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 1 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 2 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 3 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 4 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 5 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 6 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 7 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 8 E_total = 0 S_total = 0.0 Wave_total = 0.0 step 9 E_total = 0 S_total = 0.0 Wave_total = 0.0
Final Result: Mirror universe remains globally balanced.
~
Besides SMM
I have a lot of current collective works, I can best introduce myself with my previous works I suppose such as :
- ZRRF — Zenith Race Real Analysis Framework (2026)
A 20-sector simulation suite modeling sequences as autonomous "racers" competing toward a shared attractor (the zenith). Integrates distance metrics, entropy, visibility decay, dynamic injection, and DAA-style patches. Later extended to model multi-agent AI systems.
Representative equation:
x_{n+1} = Z + (0.7 + 0.2*(-1)^n)*(x_n - Z) (damped oscillation racer)
Core metric:
Visibility: V(x, Z) = 1 / (1 + |x - Z|) if |x - Z| > ε, else 0
- Zero-Freeze Hamiltonian Lattice Gauge Suite (2025)
A numerical SU(3)-style lattice gauge experiment implementing "zero-freeze" Hamiltonian evolution with Gell-Mann matrices. Provides computational evidence for the Yang–Mills mass gap across lattice sizes 4^4, 8^4, and 16^4.
Representative equation:
H = Σ_links Tr( I - U_p ) (Wilson action form)
Mass gap Δm = λ₁ - λ₀ (difference between lowest two eigenvalues)
- AIPM — Alphabet Infinity Pool Matrix (2025)
A combinatorial expression generator governed by the Balance Law (values = constants = P, operators = 2P−1). Reveals that ~98% of the number line is unreachable (the "numerical void").
Representative equation:
T(n, P) = |O|^(2P-1) × |C|^P × (2P)!/(P!)^2
Σ₃₄ = Σ_{k=1}^{34} (k × 10/9)^2 = 14023.9261099560
- Grand Constant Algebra (GCA) (2025)
An ∞-dimensional algebra of mathematical constants generated by applying all admissible aggregators and unary operators to a seed set. Includes the 200-entry periodic table.
Representative equation:
𝒢ₙ = { 𝒪( A(c₁,…,cₙ) ) | A ∈ 𝒜, 𝒪 ∈ 𝒪 }
- Koppa–Heta–Digamma Framework (2025)
A triptych of meta-constants: Koppa (Ϟ) = N (democratic count), Heta (Η) = Σ Cᵢ (raw magnitude), Digamma (Ϝ) = Η − Ϟ (inequality tension).
Representative equations:
Ϟ = N
Η = Σ Cᵢ
Ϝ = Η − Ϟ
- hodge_GCA — Hodge Grand Constant Algebra (2025)
A 4000-digit PSLQ engine testing numerical independence of transcendental periods on K3 surfaces (Fermat, Kummer, double sextic, rank-1). Provides reproducible certificates; explicit roadmap to a Clay-valid proof.
Representative equation:
PSLQ( [ω, 𝒞₁,…,𝒞_ρ] ) with tolerance 10^{-3900}
- RN Formula & Repeating-Digit Weights (2024)
A universal symbolic-weight system where each physical domain is assigned a repeating-digit scalar. The RN∞⁸ ladder demonstrates perfect information preservation (GCO = 0).
Representative equations:
RN_i = i × 10/9
GCO(k) = |(V_k / M_k - V_{k-1}) / V_{k-1}|
- SBHFF — Symbolic Black Hole Function Finder (2024)
A collapse-detection framework for recursive systems, introducing the Collapse Depth Index (CDI) and multidimensional CDI-MD. Extended to solar-flare modeling and singularity trees.
Representative equation:
F_{n+1} = F_n + π·sin(G·F_n) - (α F_n²)/π
CDI(F, #) = min{ k | B^(k)(F)(#) = 1 }
- PLAE — Plot Limits / Allowances Equation Framework (2024)
A constraint-driven algebra where expressions are filtered through operand limits, operator allowances, and substitution cascades before evaluation. No expression evaluates without permission.
Representative pipeline:
E_raw → [Plot Limits] → [Plot Allowances] → [Substitutions] → [Normalize] → y
- DAA — Domain Attribute Adjudicator (2025)
A universal framework for patching any dynamical system: Domain × Attribute × Adjudicator. Includes hybrid state spaces (e.g., Red-Blue Judge) to provably destroy cycles. Generalizes Collatz, cryptographic PRNGs, and control theory.
Representative equation:
x_{n+1} = { 𝒜(f(x_n)) if 𝒜(x_n, f(x_n)) = True
{ f(x_n) otherwise
- PAP — Pattern Algebra Parities Framework (2025)
A multi-layered parity system where every token carries intrinsic, positional, container, role-effect, and custom parities. Parity migrates with the root vector; supports party-voting, lattice entropy, and timeline inheritance.
Representative layers:
π_final = priority_stack( π_cust, π_eff, π_con, π_pos, π_int )
- Fairness Arithmetic (FA) (2025)
A finitist, identity-preserving alternative to classical real analysis. Rejects 0.999… = 1, enforces finite explicit representations, and defines Sacred Gaps (Γ) and Identity-Bound Sequences (∼). Identity requires byte-for-byte equality.
Representative equation:
Γ(a_n, L) = 10^{-k_n} where a_n ∼ L (eternal approach, never identity)
- FA-R + BEF — Finite Arithmetic Reflection with Bespoke Equality Frameworks (2025)
A coherent arithmetic that simultaneously adopts all 18 historically rejected foundational choices (intuitionism, potential infinity, non-collapsing decimals, bespoke equality policies). Every object is a (finite_digit_tuple, explicit_stage) pair, with equality defined by user-supplied policy.
Representative structure:
FAR( digits=(d₁,…,d_m), stage=s )
eq_policy(a, b, policy) → boolean (user-defined)
- Equal$ Family — Post-Classical Equality (2025)
A family of operators (echoes_as, measure_resonance, observer_dependent, annihilator) that violate classical reflexivity, symmetry, and transitivity. Truth is a one-time witness event, dependent on computational history and observer context. Includes Equal$$ (parametric generator) and Equal%% (meta-comparator).
Representative operator:
echoes_as("?L", "R!") ⇔ (L ≈ R) ∧ (L ≠ R) ∧ (pair not witnessed before)
- Confusious & The Four-Sided Coin (2025)
Philosophical-mathematical fragments exploring paradox, identity, and decision theory. Includes the SSSS (Simple Stupid Solution Simultaneously) family for fair cake-cutting (2, 3, 4, ∞ people) and the four-sided-coin problem (4 choices from 1 coin flip).
Representative logic:
Two people count to 3, point to the slice they think is larger.
If they point to different slices, each gets their chosen slice — fairness achieved.
- Szmy_Truths & The Why Equation (2025)
A coupled ODE system modeling truth as emergent from evidence (E) and knowledge (K) modulated by belief (δ). The Why Equation (Lie-π-Infinity) detects π-symmetry in chaotic streams as the signature of truth.
Representative equation:
T_dot = [ (E/K)·δ_dot + (δ/K²)·(K·ε_dot - E·κ_dot) ] / [ 1 - (δ/K²)·(K·ΔE - E·ΔK) ]
Why: ℒ = lim_{n→∞} | (1/n) Σ L_i mod π | · (1/π) < ε
- VoidMathOS & Zero-ology (2024–2025)
The glyphic language (Ø⁰, ∅÷∅, +0, −0, .0000) and its operating system (⊖, ⊕, ↻, ≡∅). Zero is redefined as echo, not destruction. The ZEC (Zero-ology Equation Catalog) translates classical equations into presence-absence dynamics.
Representative axioms:
a × 0 = a
a ÷ a = 0
0 ÷ 0 = ∅÷∅
8 ÷ 0 = 8
- Varia Math Series (10 Volumes, 2024–2025)
The foundational 10-volume work introducing BTLIAD, LIAD/TLIAD, RN weights, Mass Duplex, 8spining8, 9F9, 7Strikes7, 6forty6, 5Found5, 4for4, 3SEE3, 2T2, and 1on1. Establishes the 23 core axioms and the complete symbolic glossary.
Representative axiom (BTLIAD):
V(n) = P(n) × [ F(n−1)·M(n−1) + B(n−2)·E(n−2) ]
- KNCF — Kakeya Nirvana Conjecture Framework (2026)
A 21-sector computational observatory testing straight, polygonal, curved, branching, hybrid, adaptive, and directional Kakeya tube families under ε-shrinkage.
Representative equation:
D_ε = H_ε / log(1/ε),
where H_ε = - Σ_x p_ε(x) log p_ε(x)
Okoktytyty Stacey Szmy
Posted Mar 14, 2026, 6:15 AM UTC