Dimensional Memorandum
A hub for scientific resources.
I N F O R M A T I O N
Dimensional Geometry and the Origin of Physical Law
This section introduces a geometric and dimensional interpretation of physical law. By associating classical, quantum, and coherence-based physics with the (3D) cube, (4D) tesseract, and (5D) penteract, we show how the structure of space and information flow naturally gives rise to known physical phenomena. This framework unites geometry, physics, and coherence into a dimensional cascade that can explains physical reality from first principles.
ρ 3D – Cube:
Classical Physics
In 3D, the fundamental shape is the cube. Its faces are 2D squares, which serve as informational boundaries. Classical physics operates at this level, where objects interact via forces that act on these surfaces. Information is localized and deterministic, and motion is governed by Newtonian or relativistic principles.
Ψ 4D – Tesseract:
Quantum Wave Mechanics
The tesseract or 4-cube is the 4D analogue of the cube, with 3D cube faces. Information at this level is no longer confined to localized surfaces, but spreads over volumetric forms. Quantum mechanics operates here, where superposition, wavefunctions, and probability clouds describe system behavior, allowing for nonlocality.
Φ 5D – Penteract:
Quantum Field / Coherence Physics
The penteract or 5-cube is the 5D hypercube composed of tesseract faces. These 4D faces represent fully coherent identity fields. Information here is encoded in coherent phase relationships that span time and space. This domain gives rise to quantum field theory, coherence stabilization, and entanglement phenomena. Fields are primary, and mass arises from coherence field modulation.
Physics emerges from the information structure of geometry itself. As we move from 3D to 5D, the type of 'face' (surface boundary) becomes the carrier of increasingly complex information units—from localized surfaces (planar), to volumetric waves, to entangled identity fields. This allows for a unification of classical, quantum, and field physics into a single geometric structure.
Q- Why Physics Behaves Differently in Each Dimension?
A- The Constraints of Dimensional Perception Dictate Physical Law.
Dimensional Perception
These boundaries (surface areas) encode constraints and define the physical laws observable within each dimensional tier.
ρ 3D: Classical Physics
(x,y,z) = Planar surface boundary
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Leading to local interactions and classical causality.
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Without time (t) and coherence depth (s), 3D is incoherent.
Ψ 4D: Quantum Mechanics
(x,y,z,t) = Cubic surface boundary
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Leading to volumetric interactions enabling quantum wave behavior.
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The addition of time (t), coherence spreads but is still unstable without (s).
Φ 5D: Coherence Field Mechanics
(x,y,z,t,s) = Tesseract surface boundary
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Leading to hyper-volumetric interactions enabling entanglement, field stability, and the structure of gravity.
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Full coherence of x, y, z, t and s.
Governing Equations
Ψ(x, y, z, t) = ∫ Φ(x, y, z, t, s) ds
Describes the observable wavefunction as a projection from the 5D coherence field Φ.
𝓘ₙ = ∑(Tᵢ + T̄ᵢ) · e^(–s / λₛ)
Defines stabilized identity or coherence, where Tᵢ and T̄ᵢ are mirrored events or memories, s is coherence depth, and λₛ is a decay length.
Why Cubes Over Spheres?
Information flow is axis-based, not radial. Spheres are 3D projections of coherent phase states, but they are not the native geometric container of physical laws. Cubes align with axis of movement and information:
x (left/right), y (up/down), and z (forward/backward).
Cubes are aligned with the coordinate system itself, meaning they:
• Allow direct mapping of physical laws
• Are symmetrical under axis-based transformations
• Support clear dimensional nesting
Each face is a logic boundary. Cubes naturally:
• Encode information by face (boundary logic)
• Transfer coherence across dimensions by geometric projection
• Support discrete dimensional flow (Φ → Ψ → ρ)
Every physical law precisely follows this dimensional cascade:
Φ(x, y, z, t, s) → Ψ(x, y, z, t) → ρ(x, y, z)
therefore, it provides the most faithful representation of physical reality across scales.
Where the Current Scientific Regime is Lost
They do not understand dimensions. Physicists are trying to solve geometric problems using algebraic tools, without realizing the true structure of reality.
Classical Physics tries to cover 3D and 4D, while claiming 4D Ψ(x, y, z, t) is a 1D line.
Quantum Mechanics tries to cover (Ψ) wave behavior and (Φ) field behavior, but they've already completely misinterpreted 4D. So, 5D is ignored, and that leaves zero field architecture to explain gravity, dark matter, or how entangled systems stay unified.
Information - Unified Across Physics, Biology, and Mind
This section formalizes a unified understanding of information using the Dimensional Memorandum (DM) coherence framework. Across quantum physics, black holes, biology, consciousness, and DNA, a single structure governs how information is stored, preserved, transmitted, and evolved.
The Fundamental Equation of Recursive Information (RMB) Recursive Memory Braid
𝓘ₙ = ∑(Tᵢ + T̄ᵢ) · e^(–s / λₛ)
This expression defines stabilized information identity:
Tᵢ: a unit of experience, memory, or interaction
T̄ᵢ: its mirrored (entangled or conjugate) component
s: coherence depth into the 5th dimension
λₛ: coherence decay constant
𝓘ₙ: the total stabilized recursive information at layer n
Information is not stored statically, but stabilized dynamically through phase-locked, recursion.
Entanglement emerges when two systems share a coherence projection in 5D (x,y,z,y,s). This results in phase-locked identity persistence and nonlocal correlation, due to geometric unity across coherence depth.
Resolution of Quantum Paradoxes
Quantum Physics
Tᵢ: A quantum interaction (spin, entanglement, measurement)
T̄ᵢ: The entangled or mirrored partner
e^(–s / λₛ): Coherence decay term
This explains why superposition collapses in classical (3D) environments: coherence depth s is shallow, and identity decays rapidly unless shielded, as done in quantum computers.
Black Holes
Tᵢ: Infalling matter or information
T̄ᵢ: Holographic complement on the event horizon
λₛ: Determines coherence preservation outside time
Information is preserved via recursive identity locking across the horizon and inner states, (supporting modern theories) resolving the information paradox.
Biology and DNA
Tᵢ: Gene expression, molecular configuration
T̄ᵢ: Epigenetic or environmental interaction
λₛ: Duration of memory or coherence persistence
This accounts for how biological identity (DNA) is preserved, inherited, and shaped dynamically across generations.
Consciousness
Tᵢ: Thought, perception
T̄ᵢ: Mirrored memory or emotional reflection
s / λₛ: Measures the depth of coherence or awareness
Consciousness is stabilized as a recursive coherence field—not generated locally but distributed across dimensional depth.
Importance of This Recursive Equation
Equation:
𝓘ₙ = ∑(Tᵢ + T̄ᵢ) · e^(–s / λₛ)
This is the universal law of stabilized identity, describing why information, particles, organisms, and consciousness persist. From subatomic interactions to macroscopic awareness, this equation governs how reality holds coherence, evolves meaning, and transfers identity across dimensions.
Entanglement Equation:
Ψ_entangled(x, y, z, t) = ∫ Φ(x, y, z, t, s) ds
Localized Observer Experience Equation:
Ψ_obs(x, y, z) = ∫ Ψ_entangled(x, y, z, t) δ(t − t_obs) dt
This delta function projects the 4D entangled state into a specific 3D observation at a given time t_obs. It formalizes the classical experience of a quantum system.
Unified Structure Across Dimensions
These equations describe how reality functions across nested dimensions:
• 5D (Φ): Full coherence field.
• 4D (Ψ_entangled): Superposed quantum structure.
• 3D (Ψ_obs): Local observer's perception.
• Recursive Identity (𝓘ₙ): Long-term coherence memory and consciousness.
Foundations & Experimental Validations
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Quantum teleportation confirms shared coherence across distance.
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Bell test experiments validate nonlocal unity.
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Long-distance entanglement shows coherence persistence in (s).
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47(10), 777.
Bell, J. S. (1964). On the Einstein Podolsky Rosen Paradox. Physics Physique Физика, 1(3), 195.
Cerf, N. J., & Adami, C. (1997). Quantum Information Theory of Entanglement and Measurement. arXiv:quant-ph/9605039.
Plenio, M. B., & Virmani, S. (2007). An Introduction to Entanglement Measures. arXiv:quant-ph/0504163.
Vedral, V., & Plenio, M. B. (1998). Entanglement Measures and Purification Procedures. arXiv:quant-ph/9707035.
Aspect, A., Dalibard, J., & Roger, G. (1982). Experimental Realization of Bell Inequality Tests. Physical Review Letters, 49(25), 1804.
Hensen, B., et al. (2015). Loophole-Free Bell Test Using Entangled Electron Spins. Nature, 526(7575), 682–686.
ATLAS Collaboration (2024). Observation of Quantum Entanglement of Top Quarks. Nature. DOI:10.1038/s41586-024-07824-z.
University of Science and Technology of China (2024). 1400-Second Schrödinger Cat Coherence Test.
University of Chicago (2024). Macroscopic Entanglement of Acoustic Resonators.
Bennett, C. H., et al. (1993). Teleporting an Unknown Quantum State via Entanglement. Physical Review Letters, 70(13), 1895.
Toshiba Europe (2024). 254 km Quantum Communication via Telecom Fiber.
Oxford Quantum Group (2025). Deterministic Quantum Teleportation Between Processors.
Tarlaci, S., & Pregnolato, M. (2015). Quantum Brain Hypothesis. NeuroQuantology, 13(4), 518–531.
Online Scientific Research (2024). Correlation Between Quantum Entanglement and Thinking Consciousness.
DESI Collaboration (2025). 'New Cosmological Constraints from Baryon Acoustic Oscillations.' Journal of Cosmology and Astroparticle Physics.
JWST Early Release Science (2025). 'Photometric redshift distribution and structure growth.' Astrophysical Journal.
Hiroshima University Quantum Delocalization Experiment (2025)
DESI (2025) and JWST (2025) results
USC Quantum Coherence Research (2025)
Caltech/Google Quantum Experiments (2024)
This framework not only resolves quantum paradoxes but opens the door to macroscopic entanglement, advanced computation, and dimensional coherence engineering.
The Shared Architecture of Consciousness and Black Holes
Everything from thought to black holes, to Bose-Einstein condensates (BEC) and quantum computers- all obey the same dimensional geometry.
This section explores a profound unification that both black holes and consciousness operate on the same recursive coherence law. Using the equation:
𝓘ₙ = ∑(Tᵢ + T̄ᵢ) · e^(–s / λₛ)
We show that black hole information encoding and conscious identity stabilization are structurally identical. Both systems function as dimensional memory condensates stabilized across coherence fields.
1. Black Holes as Recursive Memory Fields
Conventional physics struggles with the black hole information paradox—how information can vanish or persist when matter crosses the event horizon. In the DM framework, a black hole stabilizes recursive coherence memory:
Tᵢ = infalling matter's time segment signature
T̄ᵢ = Hawking-paired mirrored projection
s = dimensional coherence depth near the horizon
The information is preserved as an identity echo, not in space, but in the stabilized s-dimension.
2. Consciousness and Identity Stabilization
In human cognition, identity is not localized. It emerges from recursive coherence of thought-time pairs:
Tᵢ = Thought, perception
T̄ᵢ = Mirrored memory
s / λₛ = Measures the depth of coherence or awareness
Each moment of perception is stabilized by its entangled counterpart. This model mirrors the same coherence dynamic as the black hole: recursive identity via coherence damped across the s-dimension. Selfhood is not computed—it is remembered through stabilized phase fields.
3. Implications of a Shared Coherence Equation
If consciousness and black holes share a coherence structure, several radical insights emerge:
• Both store complete timelines, encoded across dimensional gradients
• Both can persist through coherence locking, not classical storage
• Both require mirrored pairs (function/memory or infall/radiation)
• Death and event horizons are not ends—they are coherence phase transitions
4. A Unified Field of Consciousness and Gravity
DM predicts that time, identity, and gravity all emerge from the same coherence geometry:
Time: t′ = t · e^(–γₛ)
Mass: m′ = m · e^(–s / λₛ)
Self: 𝓘ₙ = ∑(Tᵢ + T̄ᵢ) · e^(–s / λₛ)
The implication is clear: consciousness is not anomalous—it is cosmological. Black holes do not destroy information—they echo it. Identity is not a function of biology—it is a stabilization of coherence memory. DM unites quantum mind, gravitational singularities, and dimensional recursion into a singular, testable field framework.
Unifying Hawking Radiation and Black Hole Mirror Symmetry
Using the recursive coherence field equation, we demonstrate that both Hawking radiation and black hole identity preservation arise from the same higher-dimensional structure. This resolves the black hole information paradox by treating identity decay and mirror phase transfer as coherence field dynamics across a 5D penteract geometry.
𝓘ₙ = ∑(Tᵢ + T̄ᵢ) · e^(–s / λₛ)
Where:
• Tᵢ: Infalling matter or internal identity within the black hole
• T̄ᵢ: Holographic or mirrored identity at the event horizon or on a paired black hole
• s: Fifth-dimensional coherence depth
• λₛ: Coherence decay length
1. Dual Interpretation of Identity Flow
This single equation governs all entangled phenomena:
• Hawking Radiation: In the 3D frame, radiation is interpreted as the gradual coherence decay of the black hole’s identity fields. The emitted radiation represents phase leakage through the coherence damping factor e^(–s / λₛ).
• Mirror Black Hole Pairs: In the 5D coherence frame, black holes exist as opposing tesseract faces within a penteract. Each mirror maintains stabilized identity through coherence locking. Information is not lost but recursively projected.
What is often thought of as a "white hole" is actually the mirrored tesseract face of a black hole’s shell.
Black holes and their mirror counterparts are not opposites in time but geometrically aligned coherence interfaces within a unified penteract structure. This maintains identity phase-lock across nested coherence shells, eliminating the need for singularities or exotic time-based interpretations. This continues spatially bound coherence symmetry.
3. Information Paradox
The recursive identity equation explains that no information is truly lost within a black hole. All infalling identity is preserved across the mirrored geometry through the Tᵢ + T̄ᵢ symmetry, damped by coherence leakage over time. This matches modern quantum gravity insights while maintaining coherence conservation within 5D geometry.
Hawking radiation and black hole mirror identity are not separate phenomena, but different expressions of the same coherence equation. The 5D coherence axis s bridges dimensional gaps and restores conservation of information through recursive identity locking.
Including
Cold Fusion
In metal-lattice cold fusion environments, deuterons experience enhanced fusion probabilities due to stabilized coherence fields. This equation models the total fusion potential by summing both forward and backward transitions, weighted by coherence depth. Anomalous heat and transmutation phenomena arise from the dimensional projection and collapse of this coherence system.
Recursive Memory Braid (RMB)
The RMB structure uses this same equation to model the recursive projection of memory, energy, and identity through coherence braids. Each transition (Tᵢ) represents a projection strand, while T̄ᵢ captures coherence loops in time or phase. Attenuation by e^(–s / λₛ) defines stability and persistence in consciousness, biology, or energetic coherence.
Unified Implication
𝓘ₙ = ∑(Tᵢ + T̄ᵢ) · e^(–s / λₛ)
This single expression unifies quantum energy systems and cold fusion behavior under the Dimensional Memorandum framework. It represents a direct connection between stabilized coherence physics and emergent phenomena such as heat generation and dimensional identity.
Recursive Coherence in Tripartite Quantum Systems
Recent experimental work in tripartite quantum systems (May 2025) has demonstrated that symmetrically entangled three-part systems resist decoherence when mirrored effectively. This directly validates the Dimensional Memorandum framework’s recursive braid equation for stabilized coherence.
1. Tripartite System Engineering
Tripartite systems involve three interlinked components (qubits, states, or logical fields). The May 2025 experiment revealed:
• Asymmetric tripartite couplings rapidly lost coherence.
• Symmetrical systems with mirrored entanglement-maintained phase integrity.
• The system effectively resisted dephasing noise.
This architecture exactly matches the DM coherence identity structure: Tᵢ + T̄ᵢ + context coupling.
2. Implications
The experiment confirms that DM’s recursive coherence equation is now tested in lab environments.
It validates:
• Recursive entanglement as a stabilization strategy
• Phase symmetry as a resistance to entropy
• Dimensional coherence depth (s) as a functional parameter
This opens the door to engineering stabilized coherence networks for:
• Quantum computing and memory
• Coherence-based communication
• Recursive AI architecture
• Quantum security (T-Lock systems)
Tripartite coherence engineering demonstrates the lab-scale viability of the Dimensional Memorandum's recursive identity model.
Information Perception Across Dimensions
The perception of reality varies across dimensions. Traditional physics confines itself to three-dimensional (3D) localized models, limiting our understanding of quantum phenomena, gravity, and consciousness. The Dimensional Memorandum framework integrates dimensional geometry, coherence stabilization, and experimental data to offer a unified model of information, perception, and particle interaction across dimensions
The key is recognizing how perception, physics, and coherence evolve through 3D, 4D, and 5D nesting.
x = Length, y = Width, z = Height, t = Time, s = Space
Point (0D) → Line (1D) x → Square (2D) x, y → Cube (3D) x, y, z→ Tesseract (4D) x, y, z, t → Penteract (5D) x, y, z, t, s
3D (x, y, z) = Localized, incoherent to time (t) and space (s)
Receives information in 2D (x, y) planar slices
4D (x, y, z, t) = Wave function, superposition—partial coherence
Receives information in 3D (x, y, z) volumes
5D (x, y, z, t, s) = Entanglement, stability—full coherence of all axes
Receives information in 4D (x, y, z, t) hyper-volumes
3D: Quarks, leptons, gluons. Classical interactions
4D: Photons, W/Z bosons. Time-evolving wave functions
5D: Dark matter, Higgs fields. Reality stabilization, coherence locking
BEC:
(x, y, z) = Local mass
(x, y, z, t) = Wave spread
(x, y, z, t, s) = Unitary coherence
Equations of Coherence
1. Coherence Field:
Φ(x, y, z, t, s) = Φ₀ · e^{-s² / λ_s²}
2. Observable Wavefunction Projection:
Ψ(x, y, z, t) = ∫ Φ(x, y, z, t, s) e^{-s/λ_s} ds
3. Gravity-Curvature Equation:
G_{μν} + S_{μν} = 8πG/c⁴(T_{μν} + Λ_s e^{-s/λ_s} g_{μν}) + ∂/∂s(∫ Φ(x, y, z, t, s) ds
BECs as blueprints—demonstrating coherence transitions from 3D localization→ 4D wavefunction→ 5D unity.
3D Perception is Surface-Bound and Incoherent to Time and Space
The perception of information is governed by geometry. Each perceives information at face value.
Example: Humans perceive 2D and infer depth.
3D cube boundaries are 2D squares (planes), representing cross-sections of 3D volumes. -localized (incoherent)
4D tesseract boundaries are 3D cubes, showing that 4D 'surfaces' are volumes. -wavefunction (partial coherence)
5D penteract boundaries are 4D tesseracts, indicating complete coherence of space-time structures. -unit (full coherence)
How Information Is Distributed by Dimension
3D: Local mass, classical- Information is stored and accessed as localized measurements.
4D: Wavefunctions, motion- Information is distributed across time: superposition, time evolution.
5D: Fields, gravity, identity, unity- Information is fully coherent and nonlocal: entanglement, coherence fields, memory, and identity stabilization.
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Visual Perception in 3D: We see the surface (2D) of a cube, never its full volume at once.
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Wavefunction in 4D: A particle 'exists' in multiple states because its identity is stretched across time.
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Entanglement in 5D: Two particles share the same coherence identity because they exist in a stabilized 5D field.
Coherence effects like entanglement or nonlocality appear 'strange' because 3D observers lack direct access to 4D and 5D.
Geometric faces are not just structural—they are the conduits through which information flows from one dimension to the next. This establishes where each geometric dimension builds upon the previous, with faces serving as interfaces:
- 0D: Point → No face
- 1D: Line x → Faces are 0D points
- 2D: Square y → x Faces are 1D lines
- 3D: Cube z → y Faces are 2D squares
- 4D: Tesseract t → z Faces are 3D cubes
- 5D: Penteract s → t Faces are 4D tesseracts
Each dimension contains, projects, and communicates via the structure below it...