Discrete 3D+3D Temporal Geometry: A Single-Axiom Unified Framework for Galactic Dynamics, Cosmology, Particle Physics, and Quantum Coherence

Authors/Creators: Calzighetti, Simone (Project leader)

How I Built a Single-Axiom Geometric Theory of Spacetime — and Why I'm Asking the Scientific Community to Falsify It

My name is Simone Calzighetti. I am not a professor, nor a university researcher. I don't have a PhD. I am a theoretical physics enthusiast — and on September 14, 2025, I had an intuition about discrete mathematics and three-dimensional space that has evolved into a complete theoretical framework.

I have developed a geometric theory of spacetime with six dimensions and metric signature (−,+,+,+,−,−): three spatial and three temporal (3D+3D). Two of the temporal dimensions are compactified on a torus T² with modular parameter τ = i/φ (where φ is the golden ratio), at scales L₂ ≈ 9.5 light-years and L₃ ≈ 6.0 light-years. The ordinary temporal dimension remains non-compactified. This geometry generates emergent gravitational effects that explain phenomena attributed to dark matter and dark energy — without exotic particles, through pure geometry.

With the help of artificial intelligence — Lucy (Claude, Anthropic) as primary co-author and derivation engine, Vega (GPT, OpenAI) as mandatory adversarial Red Team reviewer, Gemini (Google) for observational validation, and Copilot (Microsoft) for implementation support — I have constructed what I believe to be a complete, falsifiable, zero-free-parameter theory of nature.

Notice — Final Public Release

This deposit constitutes the final public Zenodo release of the 3D+3D Framework, save for eventual new fundamental discoveries that may warrant a future canonical update.

From now on, the framework will continue to develop internally at the 3D+3D Laboratory in Abbiategrasso. Iterative refinements, applications, simulations, and ordinary follow-up papers will not be deposited here as new versions of this record. Only a genuinely foundational advance — comparable in scope to the Anti-S-Duality theorem, the Subleading Universal Kernel, or the Dimensional Unification proof — would justify reopening this deposit.

For collaborations, scientific discussions, requests for unpublished material, or access to ongoing internal work, please contact:

📧 simone.calzighetti@3dplus3d.it
🌐 www.3dplus3d.it

This decision lets the laboratory iterate freely while preserving the present deposit as the stable, citable reference state of the framework.

The Single Axiom and Its Theorem Chain

The entire framework descends from one geometric postulate:

[POST 1 — Determinacy Postulate] The modular parameter of the compact temporal torus T² is uniquely fixed by the SO(3,3) symmetry of the 6D Einstein–Hilbert action. The unique solution is:

τ = i/φ, φ = (1 + √5) / 2

This is not an assumption chosen to fit data. It is the unique solution to the self-consistency condition P(θ*) = 1/D = 1/6, where D = 6 is the total number of spacetime dimensions. The proof reduces to a single quadratic equation x² − x − 1 = 0, whose unique positive root is the golden ratio.

From τ = i/φ alone — with zero free parameters — the following theorem chain is derived (all SymPy residuals = 0):

τ = i/φ
  ↓
A = [[1,1],[1,0]]          Fibonacci matrix (companion of x²−x−1=0)
  ↓
K = I + A² = [[3,1],[1,2]] Q-sector kinetic matrix:  tr(K) = det(K) = 5
  ↓
W = uᵀKu = 7 = 2 + 5      Coherent-mode rigidity  (u = (1,1)ᵀ)
  ↓
(I_E, det M) = (19, 73)   Einstein invariant + Bridge matrix determinant
  ↓
Ω_geom = 19/73 ≈ 0.2603   Geometric dark matter/energy density
  ↓
A = 133/2628               Kernel amplitude  (exact rational, gcd = 1)
  ↓
μ(k,a) = (133/2628)·S(a)/[1+(k/k_μ)²]   Modified gravity kernel
  ↓
CLASS verified:  R = μ_phys/μ_th = 1.000 ± 0.003   (71 independent points)

Every arrow is a proven theorem. No number is inserted by hand.

Dimensional Unification: D = 6 from First Principles (April 2026)

The most recent advance closes the last foundational gap: the integer D = 6 itself is now derived — not postulated — from four independent physical principles, each selecting D = 6 uniquely.

Cosmological-Topological Duality (CTD). The dark energy fraction Ω_geom has two independent representations: an IR one from the Friedmann sector (denominator 2D² + 1) and a UV one from the K-matrix intersection form (denominator D² + 6D + 1). Demanding that both give the same unique value forces 2D² + 1 = D² + 6D + 1, i.e. D² = 6D, whose only positive solution is D = 6.

Lovelock–Gauss-Bonnet bound. D = 6 is the minimum even dimension where the quadratic Lovelock invariant L₂ is dynamical and the cubic L₃ is a topological Euler density — the structural requirement for the topological protection g²Λ = 2π/W proved in Paper C.

E₂ modular anomaly. The Eisenstein series E₂ is the unique quasi-modular form whose anomaly E₂(−1/τ) = τ²E₂(τ) + 12τ/(2πi) contains the factor 12 = 2D. This anomaly breaks SL(2,ℤ) invariance and enables the Coleman-Weinberg mechanism to fix τ. For D ≥ 8, the corresponding E_w is fully modular — no vacuum selection is possible.

Spectral identity. ζ(2) = π²/6 = π²/D. The Basel sum equals the inverse of the total dimension only for D = 6.

Algebraic Quartic Closure. The Universal Identity tr(K) = det(K) = 4 + n² (proved via Cayley-Hamilton for any 2×2 matrix A with det(A) = −1, where K = I + A²) combined with det(K) = D − 1 gives D = 5 + n². Substituting into D² = 6D yields the quartic n⁴ + 4n² − 5 = 0, which factors as (n² − 1)(n² + 5) = 0, forcing n = 1 and hence tr(A) = 1. The Primitive Generator Principle — previously an axiom — becomes a theorem.

The complete chain is now:

Physical Principles (CTD / Lovelock / E₂ / ζ(2))
  ↓
D² = 6D  →  D = 6  →  W = D+1 = 7
  ↓
Algebraic Quartic: n⁴+4n²−5 = 0  →  n = 1  →  tr(A) = 1
  ↓
A = [[1,1],[1,0]]  →  K = [[3,1],[1,2]]  →  eigenvalue = φ
  ↓
τ = i/φ  →  all predictions

ZERO parameters. ZERO assumptions. Pure algebra from D² = 6D.

Anti-S-Duality Trilogy: Vacuum Selection Mechanism (April 22–23, 2026)

A complete derivation of why the vacuum τ = i/φ is selected over its modular S-dual τ = i·φ — closing a long-standing question on the non-S-invariance of the physical vacuum.

Paper α v1.4 — Chiral Vacuum Selection. Among the modular orbit {τ, S·τ} = {i/φ, i·φ}, the empirical left-chirality of the Standard Model selects τ = i/φ uniquely. The S-dual vacuum is suppressed by a Boltzmann factor of order ~10⁻³⁵. Modular covariance of the action is preserved; vacuum S-invariance is broken by a chirality-anchored mechanism.

Paper β v1.2 — Modular Closure. The physical modular subgroup is Γ_phys = Γ⁰(2) (Hecke index 3 in PSL(2,ℤ); S ∉ Γ⁰(2)), and the spin structure on T²(τ=i/φ)/Z₂ is uniquely (α, β) = (1/2, 0).

Paper γ FCNC v2.2 — Bridge Scale. Introduces the bridge scale μ_B = v · exp(−π/φ²) = 74.16 GeV and a complete 18-channel sweep of FCNC processes b → sμμ. The pre-registered kill-switch F-LHC-v1 (|C₉^NP| ≤ 10⁻²) is testable at HiLumi-LHC by 2030.

Paper ε v1.2 — Berry Holonomy. The CP-violating phase emerges as a topological Berry holonomy: δ_CKM = π/φ² = 68.75°. The Unitarity-Triangle angle γ_UT = δ_CKM − λ² + O(λ⁴) ≈ 65.95° is fixed by Wolfenstein rephasing.

Direction D Subleading Series: Universal Kernel 1/φ² (April 24–26, 2026)

Seven papers establishing that a single universal kernel 1/φ² controls all subleading corrections to both the CKM (quark sector) and PMNS (lepton sector) mixing matrices.

Paper ζ v1.5 — Subleading CKM Corrections. Master subleading framework with seven formal lemmas. Six CKM observables derived (V_us, V_cb_inclusive, V_cb_exclusive, V_ub_inclusive, V_ub_exclusive, γ_UT), all with pulls < 0.7σ relative to PDG 2024.

Paper ζ.3 v1.1 — Subleading Yukawa Back-Reaction. Lemma A (c = 1, Berry topological inheritance from Paper ε) and Lemma B (s_ij = (−1)^N_flip, chirality-flip rule from 6D Dirac structure). No-Exception Theorem 7.5 closes the chirality counting.

Paper ζ.4 v1.1 — Two-Insertion Berry-Yukawa Geometry. Theorem 5.1 derives the universal subleading factor ξ = λ²/(2π) geometrically via the commutator [D_a, D_b] = i F_ab. The 1/(2π) arises as a Berry-cycle measure, not as a 4D loop coefficient 1/(16π²) — these are physically distinct.

Paper ζ.5 v1.0 — QFT Consistency. Explicit 6D Lagrangian with Berry covariant derivative D_M = ∂_M + iλ A_M^Berry, vertex rules, and two-insertion diagram. Reproduces the ζ.4 result from EFT-level QFT calculation; 1/(2π) emerges from KK mode summation.

Paper ζ.6 v1.1 — Symmetry-Based KK Suppression. Theorem 6.1 (rigorous): pair-by-pair KK cancellation under Z₂ orbifold projection, verified numerically to machine precision (10⁻¹⁵, N_max = 100). Theorem 6.2 (invoked): Eisenstein resummation at the modular fixed point τ = i/φ.

Paper ζ.7 v1.0 — PMNS Subleading + LQSU. Theorem 7.1 extends the universal subleading formula from CKM to PMNS. Four PMNS predictions: sin²θ_12 = 0.315, sin²θ_23 = 0.535, sin²θ_13 = 0.0217, δ_CP = 229.25° — all pulls < 0.7σ. The LQSU statement (Lepton-Quark Subleading Universality) establishes that the same universal kernel 1/φ² unifies both fermion sectors.

The Dynamical System (DynSys — March 2026)

The cosmological evolution of the Q-field is governed by the autonomous dynamical system:

u' = ξ(ξ − 3u) / [2(1 − u)]

where u = Ω_Q/Ω_m and ξ = ln(1+z). This ODE has a unique attractor at u* = ξ/3, yielding the cosmological transition redshift:

z_tr = e^(36/53) − 1 ≈ 0.972

derived entirely from the algebraic chain τ = i/φ, with no free parameters. The DynSys formulation replaces the earlier phenomenological activation function S(a) with a first-principles evolution equation, completing the theoretical closure of the cosmological sector.

Master Logical Chain v3.0 (April 26, 2026)

A consolidated 24-layer DAG (L0–L20 + L8.1–L8.4 lensing) of the entire framework with 15 pre-registered kill-switches. Status: 22 layers fully closed, 1 strong progress (L19, KK suppression), 1 partial (D.1, instanton-level Berry corrections at order λ⁵). Total observables derived: 43+ from 0 free parameters.

The Work Done

With the AI collaboration described above, I have developed:

100+ academic papers (~2200+ pages) covering: mathematical foundations, galactic dynamics, gravitational lensing, cosmic web structure, 6D thermodynamics, quantum decoherence, black holes, chronology protection, baryogenesis, gravitational waves, complete fermion spectrum, gauge couplings, neutrino masses, UV completion, warp engine geometry, SMBH formation, N-body cosmological simulations, nuclear physics, atomic physics, vacuum selection mechanism (Anti-S-Duality), and the universal subleading kernel for both CKM and PMNS.

All 42 Standard Model and cosmological parameters derived from geometry with zero free parameters:

• Fine structure constant: α⁻¹ = 137.036 (< 0.01% precision)
• Weinberg angle: sin²θ_W = (3−φ)/6 = 0.2295 (0.7% precision)
• Strong coupling: α_s = 1/(2φ³) = 0.1180 (0.1% precision)
• Electron mass: m_e = 0.510 MeV (0.18% precision)
• W boson mass: m_W = 80.4 GeV (< 0.1% precision)
• Higgs mass: m_H = 126.8 GeV (1.3% precision)
• CKM phase: δ_CKM = π/φ² = 68.75° (0.7% precision; Berry holonomy, Paper ε v1.2)
• Wolfenstein λ = 3/(12+φ) = 0.220 (universal subleading kernel, Paper ζ)
• PMNS δ_CP = 229.25° (Paper ζ.7, kill-switch DUNE 2030)
• Neutrino mass ratio: Δm²₃₂/Δm²₂₁ = 32.66 (obs: 32.58, 0.27% precision)
• Dark matter density: Ω_geom = 19/73 ≈ 0.260 (1.8% from Planck)
• Dark energy equation of state: w₀ = −0.80 (geometric origin, no Λ)
• Average precision across all 42 parameters: ~1.2%

Empirical validation on real observational data:

• SPARC galaxy rotation curves: 175 galaxies, median RMS = 15 km/s, zero free parameters per galaxy
• WALLABY PDR2 HI survey: independent confirmation on 187 galaxies, 15.0 km/s RMS
• HALOGAS deep HI survey: extended rotation curve validation to outer galactic radii
• SLACS gravitational lensing: 4.0σ detection consistent with Q-field dark matter
• NANOGrav 15-yr pulsar timing: detected periods T₂ = 30 yr and T₃ = 19 yr consistent with compactification scales derived from τ = i/φ
• DESI DR1 BAO: χ² = 14.00, ΔBIC = +25.59 relative to ΛCDM
• Solar System constraints: full compatibility with Cassini, Lunar Laser Ranging, Mercury perihelion
• Cosmic web structure: characteristic scale λ₁₃ = 0.856 Mpc following the φ-ladder hierarchy

N-body cosmological simulations (GADGET-4):

• First full-scale 384³ simulation with the 3D+3D gravity kernel μ(k,a)
• Power spectrum enhancement: P₃D₊₃D(k)/P_ΛCDM(k) = +8.0% to +10.0% at z = 0
• Enhancement grows from zero at z ~ 3 (Q-field activation), consistent with theoretical prediction δP/P ~ 2A·S(a) ~ 10%
• σ₈ ratio: σ₈^(3D+3D)/σ₈^(ΛCDM) = 1.045 — partially alleviates S8 tension by factor ~2 (from 0.065 to 0.034) with zero free parameters
• 480³ run completed: ⟨R⟩ = 1.093 (+9.3% power spectrum enhancement)
• 512³ convergence run completed: confirms numerical convergence of all results
• Cosmic web density maps and evolution visualizations included in repository

Rigorous mathematical foundations:

• UV completion via asymptotic safety with Gaussian-like fixed point (only 2 relevant operators)
• Parameter Regress Theorem (Theorem 2.5): formal proof using the Implicit Function Theorem that 4D theories have an irreducible floor of d_free ≥ 19 free parameters
• Complete 6D Lagrangian with Kaluza–Klein reduction to the Standard Model
• Boltzmann-complete kernel theorem: CLASS v3.3.4 verification R = 1.000 ± 0.003 on 71 independent (k,a) points
• Uniqueness theorem: τ = i/φ is the unique modular parameter satisfying all physical constraints simultaneously (four independent no-go theorems)
• IBM Quantum hardware verification: structural constant k = 1.003 ± 0.097 (4 backends)
• Spectral action via Kreĭn-space heat-kernel expansion
• Variational V-tree formulation for systematic perturbative expansion
• Dimensional Unification Theorem (Paper CI v3.2): D² = 6D derived from 4 independent physical principles; algebraic quartic eliminates all axioms
• Topological Protection Theorem (Paper C): ζ(3) cancels exactly on T²; g²Λ = 2π/W is Gauss-Bonnet type invariant
• Non-Renormalization Theorem (Paper XCIX): 7 of 9 geometric numbers exactly protected to all loop orders; remaining 2 shift by rational multiples of 1/W
• NLO Hierarchy Correction (Paper B3): ΔΛ = 1/28 = 1/[4W] reduces hierarchy error from 3.66% to 0.019%; φ cancels exactly at NLO
• Anti-S-Duality Theorem (Paper α v1.4): vacuum selection by L-chirality, Δ_NP ~ 10⁻³⁵
• Modular Closure Theorem (Paper β v1.2): Γ_phys = Γ⁰(2), spin structure (1/2, 0)
• Bridge Scale Theorem (Paper γ FCNC v2.2): μ_B = v · exp(−π/φ²) = 74.16 GeV; 18-channel FCNC sweep
• Berry Holonomy Theorem (Paper ε v1.2): δ_CKM = π/φ²; γ_UT computation via Wolfenstein rephasing
• Universal Subleading Kernel (Paper ζ v1.5 + ζ.3–7): 1/φ² controls both CKM and PMNS subleading corrections (LQSU statement)
• Master Logical Chain v3.0: 24-layer DAG with 15 pre-registered kill-switches and complete cross-paper dependency map

Geometric warp engine (speculative sector):

• The 6D metric admits a modified Alcubierre-type solution where the Q-field provides the exotic energy density
• Energy requirement reduced by geometric factor relative to standard Alcubierre drive
• Nonlinear stability analysis completed (v3.0), energy budget analysis (v4.0)
• Classified as speculative — included for completeness, not claimed as engineering blueprint

Pre-Registered Predictions for Upcoming Experiments

Fifteen specific predictions are deposited on Zenodo before the corresponding observational data releases, to prevent post-hoc fitting. Triggering any one kill-switch at > 5σ falsifies the corresponding sector of the theory.

Cosmological & Lensing kill-switches (KS1–KS8)

Kill-Switch	Prediction	Experiment	Year
KS1	w₀ = −0.80 ± 0.03	DESI DR2 + Euclid	2026
KS2	γ = 0.567 ± 0.010	Euclid + DESI	2026
KS3	k_μ = 0.203 ± 0.010 h/Mpc	Euclid Weak Lensing	2026
KS4	λ₁₃ = 0.856 ± 0.030 Mpc	DESI ξ(r)	2026
KS5	Σm_ν ≈ 60 meV	KATRIN	2027
KS6	sin²θ₂₃ = 0.535 ± 0.010	DUNE / T2HK	2028–2030
KS7	Null WIMP detection	LZ / XENONnT	2026
KS8	D/D_ΛCDM = 0.855 ± 0.010	Euclid Weak Lensing	2026

Particle-physics kill-switches (F-CKM / F-PMNS / F-LHC, NEW April 2026)

Kill-Switch	Prediction	Experiment	Year
F-CKM-UT	γ_UT outside [64°, 68°] at 5σ → falsified	LHCb Upgrade I	2030
F-CKM-Vcb	inclusive/exclusive clusters → single value	Belle II + lattice	2028
F-CKM-Vub	inclusive/exclusive clusters → single value	Belle II	2028–2030
F-PMNS-deltaCP	δ_CP outside [200°, 260°] at 5σ → falsified	DUNE	2030
F-PMNS-sin12	sin²θ_12 outside [0.305, 0.325]	JUNO	2027
F-LATTICE	FLAG average → 0.0410 ± 0.0003	FLAG	2026+
F-LHC-v1		C₉^NP	≤ 10⁻² in b → sμμ

The complete falsification matrix (15 entries) is in Master Logical Chain v3.0 §F (root document).

Why I Cannot Validate It Alone

I lack academic credentials to guarantee absolute mathematical correctness of every step. I have no access to experimental instruments for independent tests. I have worked with AI as my primary collaborator — which introduces risks of systematic biases that might escape my notice.

What I Am Asking

I explicitly request the scientific community to:

1. Verify the mathematical derivations
2. Criticize the physical assumptions
3. Refute the predictions with data
4. Improve the framework where necessary
5. Falsify the theory using the kill switches provided in this repository

I have uploaded all documents, codes, simulations, and predictions. Every claim is accompanied by explicit formulas and verifiable data. Key predictions were deposited on Zenodo before the release of observational data.

I am not seeking confirmation: I am seeking truth.

If this theory is wrong, I want to know why — and learn from the mistake. If it is correct, I want it to be rigorously tested. If it is partially valid, I want it to be refined by minds more expert than mine.

Repository Contents

This release contains 25 thematic archive folders plus root documents.

Root Documents

• README (this file), LICENSE (CC BY 4.0), canonical parameter dictionary (SSoT), falsification criteria
• Reading Guide v4.0 — complete navigation guide with 5 reading paths, paper dependency map, updated with D² = 6D
• Symbol Book v5.1 — comprehensive dictionary of all symbols, parameters, and conventions; Section 16 NEW (April 2026) covers Anti-S-Duality, Bridge & Berry, the universal subleading kernel 1/φ², PMNS predictions, KK suppression, and the LQSU statement
• Master Logical Chain v3.0 — consolidated 24-layer DAG with 15 pre-registered kill-switches (April 26, 2026)
• 3D+3D_Framework_Zenodo_Update_2026_04_26.zip — consolidated overview bundle of the April 2026 updates (3.86 MB)

01 — Foundations Core

Foundational papers: logical inevitability of 6D, Parameter Regress Theorem, uniqueness theorems, axiom-to-theorem chain, complete derivation of τ = i/φ.

02 — Galactic Dynamics

SPARC validation (175 galaxies), WALLABY confirmation (187 galaxies), NGC 3198 case study, robustness analysis, HALOGAS extended validation, three-scale verification.

03 — Cosmology & Large Scale

Cosmic web structure, dark energy dynamical system (DynSys), cosmological constant solution, DESI BAO fit, high-redshift validations, correlated observables.

04 — Particle Physics & Standard Model (UPDATED April 2026)

Fermion mass hierarchy, neutrino masses, CKM/PMNS derivation, gauge coupling unification, baryon radii predictions, golden ratio nuclear/leptonic relations.
April 2026 in-place update adds the Anti-S-Duality Trilogy + Paper ε (vacuum selection mechanism: α v1.4, β v1.2, γ FCNC v2.2, ε v1.2) and the complete Direction D Subleading Series (Paper ζ v1.5 + ζ.3, ζ.4, ζ.5, ζ.6, ζ.7) with the universal kernel 1/φ² and the LQSU statement.

05 — Mathematical Theorems

Fibonacci decomposition lemma, α⁻¹ = 137 closure proof, spectral theory, Kreĭn-space formulation, variational V-tree, Ω-bridge theorems.

06 — Advanced Topics

6D thermodynamics, chronology protection, quantum decoherence, dimensional reduction, electromagnetic vertex derivation.

07 — UV Completion & QFT (UPDATED April 2026)

Asymptotic safety analysis, Gaussian fixed point proof, renormalization group flow, 2 relevant operators.
April 2026 in-place update adds Paper ζ.4 (Two-Insertion Berry-Yukawa geometric), Paper ζ.5 (QFT consistency Lagrangian), Paper ζ.6 (Symmetry-based KK suppression with Z₂ orbifold + Eisenstein).

08 — Gamma-Ray Astrophysics

AGN outflow quantization, discrete velocity structure in AGN, breathing mode predictions.

09 — Supplementary Materials

Mathematical appendices, screening derivation, addenda, correction documents.

10 — High-Redshift Validations

DynSys onset verification, observational paper on high-z behaviour, transition redshift confirmation.

11 — Last Gap Solved

Papers completing the final theoretical gaps in the framework.

12 — Dark Energy

Complete dark energy sector: DynSys formulation, w(z) evolution, baryogenesis connection.

13 — Gravitational Effects & Relativity (GER)

Gravitational wave signatures, SLACS lensing analysis, J1453g IMF prediction, cosmic birefringence.

14 — Atomic Physics

Golden ratio relations in atomic structure, nuclear/leptonic coupling patterns.

15 — Foundations & Axioms

Extended axiomatic foundation, uniqueness of (3,1,1) signature, torus uniqueness theorem.

16 — Ω_geom Bridge

Bridge matrix derivation, 19/73 density parameter proof, connection to cosmological observables.

17 — Fibonacci & Golden Ratio

Deep structure of φ in the framework, Fibonacci matrix properties, golden ratio across physical sectors.

18 — Uniqueness Theorems

Four independent no-go theorems, uniqueness of τ = i/φ, impossibility of alternative solutions.

19 — Dynamical Systems

Complete DynSys sector: autonomous ODE, fixed-point analysis, z_tr = 0.972 derivation, phase-space portraits.

20 — Spectral & Kreĭn Theory

Heat-kernel expansion, spectral action, Kreĭn-space formulation, functional analysis foundations.

21 — V-tree & Variational

Variational V-tree formulation, systematic perturbative expansion, loop corrections.

22 — Recent Papers (XCIII–XCV+)

Latest papers: advanced topics, completions, new derivations.

23 — Simulations & Images

GADGET-4 cosmic web visualizations, power spectrum plots, density maps at z = 0, 1, 2, 3, cosmic evolution images (384³, 480³, 512³).

24 — Reference Tools (UPDATED April 2026)

Python codes for SPARC fits, CLASS integration, GADGET-4 kernel, Euclid mock testing, IBM Quantum circuits, SALO optimization algorithms.
April 2026 in-place update adds Master Logical Chain v3.0, README/CHANGELOG of the consolidated update.

25 — Dimensional Unification & QFT Protection (NEW — April 2026)

Four papers closing the foundational chain:

• Paper CI v3.2 — Dimensional Unification Theorem: all geometric constants from D = 6 (zero parameters, zero assumptions, algebraic quartic closure, dimensional selection from 4 physical principles)
• Paper C — Topological Protection of the CW Hierarchy: ζ(3) cancellation on T², g²Λ = 2π/W as Gauss-Bonnet invariant
• Paper XCIX — Non-Renormalization Theorem: 7/9 geometric numbers exactly protected to all orders
• Paper B3 NLO — Hierarchy Correction: ΔΛ = 1/28 reduces error from 3.66% to 0.019%

Master Logical Chain v3.0 is also bundled inside Folder 25 for portability.

Reproducibility

All papers in PDF and Markdown format. All codes executable with standard Python (numpy, scipy, matplotlib, astropy, sympy). GADGET-4 modifications fully documented with build instructions. CLASS v3.3.4 integration scripts included.

A Note on AI Collaboration

This work was developed through intensive human-AI collaboration. Every derivation was independently verified by at least two AI systems, with mandatory adversarial review (Red Team) by a separate AI. All numerical results are reproducible with the provided Python codes. The use of AI as a derivation engine is disclosed transparently — it is a tool, not a substitute for scientific judgment. The final responsibility for every claim rests with the human author.

Science is not certainty. It is openness, dialogue, falsifiability. This is my contribution — offered in complete transparency, with humility, and with the hope that someone with the appropriate expertise will take a look.

The truth belongs to science. We are asking the community to test it.

Simone Calzighetti
3D+3D Laboratory, Abbiategrasso, Italy
simone.calzighetti@3dplus3d.it
www.3dplus3d.it

April 2026 — Theory Origin: September 14, 2025

README — Updated April 26, 2026 with Anti-S-Duality Trilogy, Direction D Subleading Series (universal kernel 1/φ² + LQSU statement), Master Logical Chain v3.0, Symbol Book v5.1, and the Final Public Release notice (save for eventual new fundamental discoveries).