A Planar Tension Geometry (PTG, Geometry) is the specific, actively calculated mathematical and conceptual framework that a practitioner enforces at the planar boundary during Planar Catalysis.
While a "Geometric Pattern" refers to the passive, resulting shape of a Planar Tension Region, the Planar Tension Geometry is the active, dynamic calculation required to create and maintain it. It is the operational blueprint that dictates how Tenax is discharged to alter local Planar Tension.
Components of a Geometry
A complete Planar Tension Geometry must account for all six measurable parameters of the resulting region:
A Planar Tension Region in the AIR notation is defined by 9 measurable parameters. Some parts of it could be used in the lowly developed dimensions but in a different manner. The practitioner must calculate and maintain these variables during the catalysis process to ensure the intersection remains stable. The true nature of Catalyst's interpretation of Eidos resonance lies beyond AIR understanding, see the Cognitive Scaffold Hypothesis.
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Characteristic |
AIR Designation |
Effect |
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Connected Plane |
Determines the specific type of energy or cognitive effect manifesting within the region (e.g., Therme for thermal, Kinet for kinetic, Eidos for cognitive). Also sometimes is called sigil or rune as commoners would see it, though in fact they represent a pattern that allows the Catalyst to understand what kind of energy the user wants. Different cultures may have different Subplane Key symbols, but as was established by AIR they generate close one to another noematic signatures. This is the main part, without it catalysis would be impossible. AIR explains this signature needed as way to authenticate user and explain to the catalyst what plane the user wants to reach. |
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Spatial Boundary |
Coordinates |
The physical location and fixed volume within the Matera plane where the intersection is enforced. |
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Geometric Envelope |
Shape and Volume |
The physical boundaries of the region, defined by the practitioner's geometric pattern. Larger volumes require exponentially more Tenax to maintain. |
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Flow Orientation |
Vector |
Defines the directional flow of energy across the planar boundary. |
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Exchange Polarity |
Emit / Absorb |
Dictates whether the region acts as a source (emitting energy into the Matera plane) or a sink (absorbing energy from the Matera plane, such as a Therme rift draining ambient heat). In many cases and cultures would be part of the Subplane Index. In lowly developed dimensions people often create two distinct Subplane Indexes that create the needed Eidos signature to be recognized by the catalyst, therefore mages can see emit/absorb variations as access to different "magic pools", though in fact it would be wrong. |
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Intersection Depth |
Tension Delta |
Defines the strength of the planar overlap. A shallow connection produces minor environmental effects, while a deep connection produces catastrophic energy transfer or full materialization. |
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Temporal Decay Rate |
The rate at which the Geometry collapses once active enforcement ceases. Higher Tension Deltas decay faster. |
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Boundary Gradient |
The transition profile at the edge of the Geometric Envelope. A hard boundary (sharp cutoff) requires exponentially more Tenax than a soft boundary (gradual taper). |
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Stability Margin |
The maximum external perturbation the Geometry can absorb before suffering a Cascade Fracture. Functions as a structural safety factor. |
Parameter Interactions
The combination of these characteristics allows for highly specialized applications. For example, a region connected to Therme with an *Absorb* polarity and a high Tension Delta will act as a massive thermal sink, rapidly freezing the environment within its Geometric Envelope. Conversely, an Emit polarity with a Kinet connection will project localized kinetic force outward along the specified Vector.
Most standard Planar Tension Catalysts are limited in their Subplane Index and maximum Tension Delta. Only general-purpose or Mega Catalysts can sustain deep intersections across multiple subplanes simultaneously.
Complexity and Scaling
The cognitive load required to calculate and hold a Planar Tension Geometry scales exponentially with its volume and complexity.
Simple Geometries
Single-subplane calculations with low Intersection Depth. These are the foundational skills taught at the Tarosian Royal Magic Academy.
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*Example:* A micro-volume Therme Absorb Geometry used to instantly cool a single cup of water, or a localized Kinet Emit Geometry to deflect a projectile.
Compound Geometries
The simultaneous calculation and enforcement of two or more intersecting Subplane Indexes. This requires immense cognitive throughput and is typically only achievable by elite practitioners or through Distributed Planar Tension Catalysis.
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*Example:* A Compound Therme-Kinet Geometry, where a Therme Emit is layered over a Kinet Emit vector, resulting in a shaped, directional thermal blast rather than a stationary superheated zone.
Macro-Geometries
Large-scale calculations that exceed the biological bandwidth of a single Eidos Interface. These require a Synchronization Node to partition the calculation across a Distributed Planar Tension Catalysis array, holding the sub-geometries in a coherent shared state.
Operational Terminology
In practice, practitioners refer to these calculations by their primary function and polarity:
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"Deploying a Kinet Absorb Geometry."
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"The Compound Therme-Lux Geometry is destabilizing; vent the Tenax!"
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"Their Eidos Interface cannot sustain the cognitive load of that Macro-Geometry."