“Refusal is the highest form of physical law.”
The Governance of Reality
Contemporary physics operates under the tacit assumption that the universe is an “unbounded playground”—that if you can write an equation, and it is symmetric, it could exist. This has led to a proliferation of untestable theories, from the Multiverse to String Theory landscapes with vacua.
MATHTRUTH challenges this paradigm. It posits that the universe is not an infinite canvas, but a Resource-Bounded Information Kernel.
We introduce the Inverse Scaling Law (ISL) as the fundamental constraint of existence:
Where is the Ontological Trust (Stability) and
is the Descriptive Complexity. This inequality dictates that as the information density of a system rises, its stability must inevitably fall, unless it is compartmentalized.
The Constitutional Laws of the Kernel
The “Laws of Physics” are not arbitrary rules; they are the error-handling mechanisms of this kernel. We classify them into three Constitutional Laws:
1. Law of Resource Boundedness
Core Axiom: The Kernel has a finite bit-depth.
This law prevents the “Singularity Leak”—the instantiation of objects with infinite information density.
* Manifestation: The Planck Length. Space is not continuous; it is pixelated because storing an infinite coordinate () requires infinite memory.
* Manifestation: Heisenberg Uncertainty. The “blur” is the refusal of the kernel to render a state with infinite precision in both and
.
2. Law of Authority Isolation
Core Axiom: Independent objects must maintain unique Identity Logs.
If two objects share the exact same quantum state, their “Authority Logs” collide, creating a reference paradox.
* Manifestation: Pauli Exclusion Principle. This is why matter is solid. The “force” that keeps your hand from passing through a table is actually the kernel preventing a variable-name collision.
3. Law of Reversibility & Provenance
Core Axiom: The Causal Graph must be acyclic.
Information cannot flow backwards in the update cycle.
* Manifestation: The Speed of Light (). This is not a velocity; it is the Clock Speed of the causal propagation.
Conclusion
We are not living in a simulation in the “video game” sense. We are living in a Self-Optimizing Knowledge Engine. MATHTRUTH is the first attempt to reverse-engineer its source code.