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Computation theory papers 17 papers
Computation theory. Computability, complexity and decidability Tagged papers: 17.
The Oscillator as an Element: Static and Dynamical Analyses of the Imaginary Boolean Value in the Algebra of Eventually Periodic Truth Sequences
Revision-theoretic treatments of the liar paradox produce an oscillator $\iota = \langle U,P,U,P,\ldots\rangle$ that alternates between two states forever, but they leave $\iota$ a process rather than a value. This paper tests the conjecture that $\iota$ can be promoted to a static element of a…
Computation as Hamiltonian Isomorphism: A Mode-Based Taxonomy of Physical Computing Substrates
Special-purpose accelerators, neuromorphic chips, and optical processors are today evaluated by qubit or transistor counts, yet the machines that deliver the largest effective speedups are those whose physical dynamics directly embodies the target problem. This paper addresses a specific gap: no…
Physical Irrelevance of Uncountability: Computable Reals Suffice for Continuum Physics
Continuum physics is formulated over the uncountable real line $\mathbb{R}$, yet every measurement, record, and computation a laboratory can produce is finite. This paper asks whether the uncountability of $\mathbb{R}$ — as distinct from its Archimedean completeness — has any physical consequence,…
Factoring Hardness as a Bayesian Prior: A Decision-Theoretic Model of Post-Quantum Cryptography Migration Timing
The urgency of post-quantum cryptography (PQC) migration is usually justified by the anticipated capability of quantum computers to factor integers, yet that threat rests on an unproven complexity-theoretic conjecture: that integer factoring is not in BPP, the class of decision problems solvable in…
Corrected Condensation Indices and the Sixteen-Fold Way: A Quantitative Bulk-Boundary Dictionary for Ising-Type Anyon Condensates
A companion preprint (https://papers.qnfo.org/papers/a-two-index-framework-for-the-bulk-boundary-correspondence-of-anyon-condensation/) introduced computable indices for anyon condensation: the dimension ratio $\kappa = D_C^2/D_D^2$, the chirality-sensitive index $\mu = 2\,\Delta c$, and the…
Emergent Universality from Symmetric Rules: Rule-110 Emulation by Alternating Trivial Cellular Automaton Rules
Elementary cellular automaton (ECA) rule 110 is Turing complete, yet its local rule is chiral: it treats its left and right neighbours differently, and this handedness underlies the glider dynamics that carry its computation. A recent construction shows that rule 110 can nevertheless be emulated by…
The Number Builder: Enclosure Sequences in the Laws of Form Calculus as a Constructive Route to Computable Reals
We propose and partially develop the Number Builder conjecture: every computable real can be generated by a finite specification of a re-entry structure in Spencer-Brown's Laws of Form (LoF) calculus of distinctions, in which each re-entry step appends a nested rational enclosure whose interval…
Autaxys Ontological Closure: When Is a Physical Quantity Computationally Real?
We propose an operational criterion for physical reality: a quantity is physically real only if there exists a finite Turing-machine protocol that approximates it with a computable modulus of convergence, yielding measurement-distinguishable predictions. This criterion is not a metaphysical claim…
The Substrate Is the Algorithm: A Categorical Formalization of the Strongest Consilience Thread
ACRP-05: Thread 3 formalization. Capability(S) ~ End(X_S) conjecture; five-pillar verification; Church-Turing-scoped resource-level thesis (computability-level equivalence, resource-level difference).
FACTORING, Adelic Complexity, and the Silent-Radix Principle
The silent radix -- the observation that no positional numeral internally specifies its own base -- was previously explored as a cryptographic primitive through Silent Radix Encryption (SRE), a key encapsulation mechanism whose security rests on the hardness of recovering a secret base from public…
The Computable Continuum: Depth Without Breadth
The uncountability of the real numbers conflates Archimedean completeness (depth) and set-theoretic cardinality explosion (breadth). All physically relevant properties are preserved by computable reals.
Spin Glasses and Complexity: Replica Symmetry Breaking, Frustration, and the Statistical Mechanics of Disordered Systems
Review of spin glass theory, Parisi RSB, and applications to neural networks and optimization.
Dual-Mode Arithmetic Representation
This presents a framework that resolves the apparent incompatibility between algebraic and geometric representations of natural numbers. We demonstrate that while static two-dimensional coordinate systems are informationally incomplete for capturing the full arithmetic structure of prime…
COMMUTATIVE PHYSICS
Mathematics serves as the fundamental language through which the intricate laws and diverse phenomena of the physical universe are articulated, modeled, and predicted. The selection of mathematical tools is not a trivial matter; it profoundly shapes our comprehension of reality. Modern physics…
Excluded Middle as Computational Boundary
This research investigates the validity of the constructivist critique of Turing completeness, which is founded upon the rejection of the Principle of the Excluded Middle (PEM). By employing a systematic, multi-layered framework, this paper deconstructs the logical chain from L.E.J. Brouwer’s…
Topological and Computational Unification of Emergent Agency
This manuscript addresses the foundational tension between microscopic superdeterminism and macroscopic emergent agency through the lens of complex systems theory. By synthesizing the computational irreducibility of cellular automata with the geometric constraints of fractal invariant sets, we…
Emergent Computation
The classical Turing-von Neumann architecture, which has defined the digital epoch, is confronting insurmountable energetic and structural limits, most notably the von Neumann bottleneck. This necessitates a paradigm shift toward physical computation, a framework where information processing is…
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