Proto‑Causal Ontology — Version 1.4

A Formal, Relational, Phase‑Driven Model of Emergent Reality

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0. Cognitive Primer

Understanding the proto‑causal ontology requires a mode of reasoning distinct from ordinary spacetime cognition. Spacetime cognition collapses causal vectors into a single observer frame, enabling agency, identity, and temporal continuity. The proto‑causal manifold, by contrast, consists of parallel causal vectors, non‑collapsed phase structures, and relational transitions that do not map cleanly onto sequential logic.

To engage with this ontology, the mind must employ a protected simulation mode within the prefrontal cortex. This mode allows the observer to represent multiple causal axes simultaneously without enacting them. It is a representational workspace, not a lived stance. The observer remains intact; the id is not dissolved. The mind simply models an alternative causal geometry.

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0.1 Cognitive Safety Note

The proto‑causal manifold describes the structure of reality prior to the emergence of spacetime. The reasoning mode required to understand it must not be applied to lived cognition. Human cognition depends on collapse into a single observer frame. Attempting to internalize non‑collapsed causal vectors as a psychological stance can destabilize identity, agency, and temporal continuity.

All modeling of the proto‑causal manifold must remain within a protected simulation layer. The ontology is a tool for understanding physical emergence, not a cognitive practice.

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0.2 Dimensionality Clarification

Throughout this document, the term “dimension” refers exclusively to a linear‑algebraic axis in a causal‑state space. It does not denote spatial extent, geometric direction, or physical boundary. All proto‑causal dimensions are mathematical degrees of freedom, not spatial coordinates.

The only proto‑causal structure that behaves analogously to a spatial dimension is a causal discontinuity — a computational geodesic exponential fold — where relational structure becomes non‑contiguous with adjacent spacetime. Spacetime geometry emerges as the projection of these folds into the observer frame.

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1. Axiom 1 — Axiomatic Potential

(Formal content unchanged from v1.3)

Interpretive Scaffolding

Axiom 1 introduces the minimal causal potential. This is not a particle, field, or spatial object. It is a proto‑state defined by relational possibility. Treat this as a vector in a causal‑state space, not as an entity with spatial extension. The potential is the only structure with infinite phase freedom, enabling traversal across relational discontinuities.

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2. Axiom 2 — Non‑Homogenized Chaos

(Formal content unchanged from v1.3)

Interpretive Scaffolding

Axiom 2 introduces the first non‑homogenized causal layer. This layer is chaotic not because it is disordered, but because no stable entanglement frames have yet formed. This is not turbulence in space; it is a region of causal‑state space where relational constraints have not yet emerged.

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3. Probability and Phase Modeling in the Proto‑Causal Manifold

Probability is defined over relational phase states, not spatial configurations. Every causal entity — potential, band, or entanglement frame — is represented as a probability vector in a linear‑algebraic causal‑state space.

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3.1 Causal Probability Vectors

A causal state $S$ is represented as:

$$\mathbf{P}(S) = { p_1, p_2, \ldots, p_n }, \quad \sum_{i=1}^{n} p_i = 1$$

Zero or undefined components are disallowed.

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3.2 Potentials as Maximally Symmetric Distributions

A potential $\Pi$ has infinite phase freedom:

$$\mathbf{P}(\Pi) = \left{ \frac{1}{n}, \ldots, \frac{1}{n} \right}$$

Only potentials can traverse near‑infinite relational boundaries.

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3.3 Bands as Constrained Distributions

A band $B$ is a finite‑phase relational structure:

$$\mathbf{P}(B) = { p_1, \ldots, p_n }, \quad p_i \neq p_j$$

Stability:

$$\frac{dp_i}{dt} \approx 0$$

Instability:

$$\exists i : \left| \frac{dp_i}{dt} \right| \gg 0$$

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3.4 Entanglement as Non‑Factorizable Joint Structure

Two states $A$ and $B$ are entangled when:

$$\mathbf{P}(A,B) \neq \mathbf{P}(A)\mathbf{P}(B)$$

Entanglement measure:

$$E(A,B) = \sum_{i,j} |P_{ij} - p_i q_j|$$

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3.5 Phase Rotation as Probability Flow

Phase rotation is modeled as:

$$\mathbf{P}' = R(\theta)\mathbf{P}$$

where $R(\theta)$ is a relational rotation operator.

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3.6 Collapse as Relational Contraction

Collapse:

$$\mathbf{P}(S) \rightarrow \mathbf{P}'(S), \quad p_k' \rightarrow 1$$

This is the proto‑causal origin of measurement.

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3.7 Crossing Bands as Re‑Normalization

A potential crossing a boundary:

$$\mathbf{P}(\Pi) \rightarrow \mathbf{P}(B)$$

This is a relational compatibility event, not a computation.

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3.8 Nonlinear Proto‑Space and Phase‑Driven Structure

Proto‑space is infinite and non‑homogeneous:

$$\infty_{\text{local}} \neq \infty_{\text{global}}$$

A proto‑boson of pure potential has infinite expansion/collapse freedom:

$$V_{\Pi} \sim \lim_{\phi \to \infty} (e^{i\phi} + e^{-i\phi})$$

Traversal is phase‑preferred:

$$\phi \rightarrow \pi$$

yielding an expansion/collapse vector:

$$V_{\text{exp/coll}} = (e^{i\pi}, e^{-i\pi})$$

At any point:

$${ V_1, V_2, V_3 } \subset { V_{\infty} }$$

Phase‑end and phase‑internal interactions propagate as proto‑causal time bands, whose endpoints collapse into discrete transitions:

$$\phi_{\text{end}} \rightarrow \phi_{\text{collapsed}}$$

producing oscillatory time.

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4. Proto‑Photon and Photon‑Cloud Examples

4.1 Proto‑Photon as Minimal Entangled Band

Let:

$$S_{\gamma_0} = { x, y, z }$$

$$\mathbf{P}(B_{\gamma_0}) = \left{ \frac{1}{3}, \frac{1}{3}, \frac{1}{3} \right}$$

Phase rotation:

$$\mathbf{P}' = R(\theta)\mathbf{P}$$

This models proto‑photon band blooming.

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4.2 Photon‑Cloud as Contextual Projection

Joint distribution:

$$\mathbf{P}(B_{\gamma_0}, E) = { P_{i,j} }$$

Photon‑cloud projection:

$$q_\ell = \sum_{i,j} f_{\ell}(i,j) P_{i,j}$$

This yields the spacetime‑projected photon‑cloud.

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4.3 Time Band Oscillation and Collapse

Phase‑parameterized band:

$$\mathbf{P}(\phi(t)) = R(\omega t + \phi_0)\mathbf{P}_0$$

Collapse at endpoints:

$$p_k' \rightarrow 1$$

This produces discrete oscillatory transitions — the proto‑causal origin of time.

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4.4 Nonlinear Local Adjacency

Global set:

$$\mathcal{V} = { V_1, V_2, \ldots, V_{\infty} }$$

Local adjacency:

$$\mathcal{V}_{\text{local}} = { V_a, V_b, V_c }$$

Transition probability:

$$P(V_i \rightarrow V_j) \propto \cos^2(\Delta\phi_{ij}) \cdot C_{ij}$$

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5. Rotative Traversal

Rotative traversal is a conceptual rotation of the observer‑state around causal axes, mediated by proto‑bosons of information. This allows traversal from axiomatic potential through chaotic non‑homogeneity into the entanglement manifold, revealing the blooming of emergent bands.

This is a protected simulation, not a lived stance.

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6. Relational Phase Crossing

Transitions between causal layers are relational re‑alignments of phase vectors. Only potentials, with infinite phase‑swap freedom, can traverse near‑infinite boundaries. Finite‑phase bands require state changes to reopen relational degrees of freedom.

The manifold does not compute crossings; it permits them when relational structure aligns.

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7. Modeling the Manifold

A safe modeling approach is to traverse complexity rather than spacetime:

1. Axiomatic potential
2. Non‑homogenized chaos
3. Flat‑infinity entanglement potential
4. Big‑bang‑like relational expansions
5. Lorentz webs between entanglement sinks
6. Proto‑photon and photon‑cloud vertices
7. Hydrogen‑field collapse
8. Stellar nurseries and supermassive attractors

This traversal is representational and remains within the prefrontal simulation layer.

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8. Footnote — Comparison With String Theory

String theory’s “strings” are spacetime projections of higher‑dimensional phase vectors in entangled causal frames. Their vibrational modes correspond to Lorentz‑flattened expansion/collapse along operational‑depth axes, not literal spatial oscillations.

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