Ioannis Tsiokos

A Six-Birds' Eye View of Quantum Theory: Defining Objects by What We Can Distinguish, Not What We Imagine

Summary Quantum theory uses a single object, the quantum state, for two different jobs: describing how a system evolves and keeping track of what has been recorded about it. This paper keeps the two jobs apart. Using the packaging language of Six Birds Theory (SBT), a closure-bas...

Six Birds Protocol Trap: Holonomy Without Entropy Production

When a system is driven through a fixed sequence of operations, two different things can happen. The outcome can depend on the order in which the operations are applied (route dependence, or holonomy), and the motion can acquire a preferred direction in time (an arrow, measured b...

To XOR a Stone with Six Birds: Closure Diagnostics for Emergent Bits, Gates, and Booleanity

When does a physical or stochastic system deserve to be described in terms of bits and logic gates? We treat logic not as a starting point but as something a coarse-grained description has to earn. Working in the Six Birds emergence calculus, we call a description a logic layer w...

To Cast a Stone with Six Birds: A Closure-Deficit Account of Randomness under Packaging and Budget

Why does a process look random? This paper develops one precise answer within the Six Birds framework: much of what a description calls randomness is information the description has chosen not to keep. We model a description by a packaging map Π that groups microstates X_t into c...

Six Birds Verified IV: Tolerance and Surrogates

A coarse description often reads its data only approximately: the states merged into one class give outputs that are close but not equal. It is tempting to declare them equal and take one canonical quotient. This paper replaces that step by exact finite mathematics. Part I asks w...

Six Birds Foundations II: Admissibility, Meta-Theory, and the Exact-Six Program

Six Birds Foundations I described how a layer of description closes over what it tracks, and identified six roles that such closure uses: descent (whether an update respects a quotient), representability of a macro-level specification, enriched route and coherence mismatch, stage...

Six Birds Verified XII: The Geometry of Access

An observer reads parts of a system through linear probes and knows how the parts overlap. It asks how much it can read, whether its readings fit together, and where they fail to. For finite-dimensional rational state spaces, declared access answers all three through linear algeb...

Six Birds Verified XI: Self-Carried Closure

Self-maintaining systems, such as cells, compilers and repair crews, were still started by something else. We make this exact for finite rule systems in which every rule names the capability that executes it, and capabilities wear out. A target carried forever by such a system mu...

Six Birds Verified VII: Formation and Explanation

A theory has to be formed, explained and run. Each step invites a shortcut: counting generators as if they counted roles, treating “why” as one status, and treating a running program as the object it runs. For finite systems this paper replaces each shortcut by exact mathematics....

Six Birds Verified XII: The Geometry of Access

An observer reads parts of a system through linear probes and knows how the parts overlap. It asks how much it can read, whether its readings fit together, and where they fail to. For finite-dimensional rational state spaces, declared access answers all three through linear algeb...

Six Birds Verified XIII: Time, Charge and Currency

One number can look like three things: the generator of time evolution, a conserved charge, and a currency that crosses a boundary. These are an operator, a state function and a ledger entry. We show which structure links them, over the rationals. A skew factor makes a generator...

Six Birds Verified VIII: Flattening and Enablement

A growing interface acquires new information one port at a time. This paper separates two claims about such growth that are easily run together. For a family of read and flip ports whose bits are acquired from time-released sources, one fixed program, the growing host, implements...

Building What a Proof Needs: A Method for Constructing Leverage Layers

Hard problems are often first reformulated: the statement is shown equivalent to another about a transformed object. Such a reformulation is a theorem, but by itself it supplies no independently established law from which the new statement follows. In the solved cases examined, p...

A Conditional Spectral-Closure Theorem for Three-Dimensional Navier–Stokes

We prove a conditional global theorem for three-dimensional incompressible Navier–Stokes with positive viscosity and real divergence-free Hγ(ℝ3) data, γ>5/2. The hypothesis, a spectral closure on the actual maximal mild solution, asks that on each finite horizon one Fourier cutof...

Three Conditional Clay-Problem Closures: A Shared Gaussian Observation and a Common Vocabulary

Three companion papers state conditional closures of Navier–Stokes regularity, the Riemann hypothesis and P versus NP within Six Birds Theory, each under its own open premises. This paper compares them in two ways. Concretely, one family of complex Gaussian observations can be ev...

Self-Dual Trace Confinement: A Six Birds Structural Law for Formed Closures Under Involutive Self-Duality

Let J be an involution of a measure space (X,μ), and let ψ be a strongly measurable observable with values in a real Hilbert space Y that intertwines J with a linear isometric involution of Y. The odd part ψ− of ψ vanishes on the fixed locus Fix(J); it is called separating when i...

Six Birds Foundations IV: A Catalog of Layer-Agnostic Structural Laws

Foundations IV states and proves 52 structural laws about layers of description. A layer is a set of states read through a quotient, which fixes the distinctions the layer can make. Each law is a theorem with its own hypotheses, stated without reference to what the layer is made...

Hiddenness as a Structural Law of Emergence

On a finite set of computation histories, two families of tests induce two equivalence relations: a current quotient, from tests that read only what is visible at the present stage, and a predictive quotient, from tests that may also read witness and continuation data. We study t...

Saturated SAT Observables: A Formally Verified Decision-to-Search Translation and a Conditional P ≠ NP Statement

A polynomial-time decision procedure for satisfiability yields one that finds satisfying assignments; this decision-to-search self-reducibility of SAT is classical. We give a formal verification of it at the level of multitape Turing machines, checked in the Lean proof assistant...

Riemann Hypothesis via Self-Dual Trace Confinement: A Conditional Closure

For any positive integer weights mρ, the Riemann hypothesis is equivalent to the vanishing of AZ = Σρ mρ(Re ρ − ½)2 over the nontrivial zeros. A companion paper proves a duality-confinement theorem: for a strongly measurable observable with values in a real Hilbert space that int...