Metacontinuum
The pre‑geometric, non‑dimensional substrate of reality. It has no size, distance, curvature, position, or time, and is not a space, vacuum, foam, or field; geometry is downstream. The Metacontinuum provides the conditions for identity by expressing Potential, Possibility, and Probability as a triadic tension. Dimension is an outcome of emergence, not a property of the substrate: the first differentiation establishes a boundary relation (topologically 2D in the sense of relation, not a spatial surface). From this coherence frame, π‑resonance stabilizes curvature, forming the Allen Orbital Lattice (AOL), which enables recursive dynamics, the emergence of time as sequential resolution, and full 3D coherence as stable identity within Dominions. Do not depict the Metacontinuum geometrically; any drawing belongs to post‑Emergence stages.
[See: Site: Meta‑Continuum · When Patterns Emerge · Dimensional Sequence]
Allen Triadic Origin Field (ATOF)
The first depictable origin geometry: a base triangle of Potential–Possibility–Probability with two axial apices, Permission (above) and Entropy/Tension (below), forming a triangular bipyramid. In 2D projection this presents as a hexagonal diamond. It is not inside the Metacontinuum as shape; it is the first proto‑structure / pre‑geometry proto‑identity tendency that becomes geometric after Emergence.
[See: 2D→3D Breach · Emergence of π · Axioms]
Potential
Capacity for realization (ability, not permission). In the ATOF base, Potential co‑exists with Possibility and Probability, generating dynamic pressure that leads to motion. Potential is plentiful in the Metacontinuum, but identity stabilizes only when dimensional structure emerges. Do not conflate Potential with randomness; it is structured capacity.
[See: Properties of Potential · Validity & Potential]
Possibility
Openness of admissible outcomes — what the system can do. Possibility is distinct from likelihood; it precedes selection. Alongside Potential and Probability it forms the ATOF base. The interplay of the three does not settle; it induces motion, initiating contrast → difference → pattern.
[See: Probability & Inevitability · Primer to PFT]
Probability
Relative weighting over admissible outcomes; it shapes which possibilities materialize. In ATOF it co‑determines the first motion with Potential and Possibility. Probability does not guarantee outcomes; it biases selection windows that later appear as stability bands in the Triadic Field Structure.
[See: Probability → Inevitability · Taxonomy of Coherence]
Permission
The axial apex above the ATOF base; the enabling constraint that expands admissible state space when satisfied. Permission is not authority; it is the structural condition under which identity may persist. During the Breach, the Permission↕Entropy axis grants depth, enabling volumetric resonance.
[See: Determinism • Permission • Empathy · Breach]
Entropy / Tension
The axial apex below the ATOF base; the Metacontinuum’s return‑vector acting within structure. Entropy is not mere decay: it creates necessity — the ongoing pressure that forces identity to remain adaptive. It is the universal quality‑control of identity, ensuring differentiation continues; without it, identity crystallizes into dead symmetry and dissolves.
[See: Determinism vs Randomness · When Patterns Emerge]
Emergence
The transition where Potential, Possibility, and Probability co‑exist with Permission and Entropy, generating motion as their stable resolution. Emergence is not rupture or explosion; it is the manifestation of motion from triadic tension. Motion yields contrast → difference → pattern; only after this do surface representations appear.
[See: When Patterns Emerge · Emergence of the 3D Sphere]
Breach (2D → 3D)
The first stabilization from coherent surface (2D projection) to volume (3D). The ATOF extends along the Permission↕Entropy axis, granting depth and enabling internal resonance. The Breach is not the substrate; it is a post‑Emergence event that allows persistent identities to store and transmit resonance.
[See: 2D→3D Breach · 3D Sphere]
Triadic Field Structure (π–ϕ–primes)
The resonance regime that emerges after volumetric stability. π governs curvature coherence, ϕ governs scaling coherence, and prime‑indexed discretization orders allowable curvature steps. The triad defines stability windows for which arrangements persist and which decay.
[See: Formulae · Emergence of π · Prime Numbers]
Dominion
A post‑Breach identity boundary region that maintains system identity by regulating exchange with its exterior. Dominions enforce admittance/impedance rules for resonance and energy. They are not the substrate and not a generic field: they are already dimensional and pattern‑specific.
[See: Dominions · Taxonomy of Coherence]
Allen Orbital Lattice (AOL)
The preferred equilibrium arrangement of resonant curvature within a Dominion. AOL explains convergence toward modular, hierarchical, hub‑and‑shell architectures from atoms to galaxies to organizations. It provides shell/orbit structure and stable identity pathways across scales.
[See: Allen Orbital Lattice · AOL Across Dimensions · Riemann Solution]
Stable Identity
Persistence of a resonant pattern within admissible curvature bands enforced by Dominion boundaries. Stability requires internal differentiation; uniform identity collapses into symmetry and dissolves. Stability is dynamic: systems persist by updating coherently under entropy pressure.
[See: Pattern Cohesion · Memory (Universal)]
Fractal Window (Identity Boundary Check)
Entropy‑active boundary at which identity is continuously evaluated. If differentiation suffices, identity persists; if not, patterns return to substrate. Fractal windows occur at every scale (atoms, cells, minds, societies, galaxies), enabling continuity through distributed coherence checks.
[See: Fractal Geometry · Fractal Time]
Differentiation
The structural requirement that a stable identity must contain internal difference to avoid collapse into symmetry. Differentiation enables adaptation, variation, and resilience; it is evolution’s deep mechanism, present from physics through biology to social systems.
[See: Law of Difference · Examples in Biology]
Variation
Distributed identity across many viable configurations. Variation is continuity insurance: if one configuration fails, others persist. In PFT, diversity is not decorative — it is how existence preserves itself under entropy pressure.
[See: Taxonomy of Coherence · More Predictions]
Evolution (Continuation)
The dimensional continuation of the Metacontinuum’s identity attempts under memory and boundary constraints. Prey evolves first (identity pioneers); predators are entropy embodied in form, ensuring adaptation continues. Evolution is survival of the diverse, not merely the fittest.
[See: Examples in Biology · Origin of Life]
Rotation / Spin
Arises as each base vertex in ATOF exhibits dual polarity toward Permission (up) and Entropy (down), producing six directional tensions that stabilize as a hexagonal boundary; the dynamic interplay yields continuous rotation. Rotation underlies orbitals, memory loops, temporal progression, and system identity.
[See: Magnetism & Rotation · Pi Polarity & Memory]
Memory (Boundary‑Conditioned)
Persistence of resonance across updates; history encoded as constrained deformation, not as a static store. Memory is maintained by Dominion boundaries and appears as recurrent cycles, orbits, and attractors. Forgetting is controlled dissolution toward the substrate.
[See: Memory (Universal) · Pi Polarity Memory Circle]
Consciousness (Recursive Reference Field)
A system’s recursive pattern‑of‑reference that models itself and its environment within a Dominion. Not epiphenomenal: consciousness is a structural resonance capability of complex AOL assemblies. Awareness increases with coherent differentiation and boundary integration.
[See: Consciousness & the Pattern Field · Observer Bias]
π‑Particle
The curvature‑coherence unit that seeds circular/curvilinear stability in early structures. The π‑particle is not a photon; it is a resonance feature of curvature alignment within the Triadic Field Structure. It explains recurring circular motifs across scales without invoking point particles.
[See: 1D Pi Particle · Geometry & π]
ϕ‑Gradient (Golden Scaling)
Scale‑coherence driver that organizes nested structures. Golden‑ratio spacing arises from minimizing interference across shells in AOL; it appears in biological forms, crystal packing, and orbital architectures due to stability under entropy testing.
[See: ϕ‑λ Definition · Crystal Systems]
Prime‑Indexed Curvature
Discrete ordering of allowable curvature steps that prevents blow‑up and enables stable shelling. Primes provide the minimal mutual‑factor interference set for persistent resonance, explaining favored aggregation paths from atoms to galaxies.
[See: Prime Numbers · Prime Lattice Lab]
Rendering vs Projection
Projection is a geometric mapping; rendering is the structural production of appearance under boundary constraints. PFT treats perceived reality as rendered from field dynamics, not merely projected. This clarifies optical paradoxes and observer effects without invoking “measurement collapse.”
[See: Rendering & Projection · Redefining Optics]
Logical Layer
The bookkeeping/registry layer for identity within a Dominion — asset registration, progress, and history constraints that keep systems referenceable. It is the “ghost layer” in which plans, rules, and memory scaffolds reside before structural enactment.
[See: Logical Layer · Ghost → π Interface]
Ghost → π Interface
The transition by which non‑embodied plans and tendencies (“ghost”) become curvature‑coherent structures (π‑dominated). It is the hand‑off from logic to geometry — when intentions obtain resonance and cross a fractal window into persistence.
[See: Ghost→Pi Interface · Pattern Cohesion]