Applies the void Péclet framework to computational complexity theory. Demonstrates that zero-knowledge proofs instantiate the conjugacy theorem at equality, that the random 3-SAT satisfiability phase transition is a Pe=V* boundary analogous to the Wien peak in thermodynamics, and that P≠NP is the kill condition preventing Pe→∞ catastrophe in computational systems. Closes the Landauer-Arrow-Crypto triangle (§§33+35+37).
The Fischlin transform yields non-interactive zero-knowledge proofs with straight-line extractability in the classical random oracle model. This is done by forcing a prover to generate multiple accepting transcripts through a proof-of-work mechanism. Whether the Fischlin transform is straight-line extractable against quantum adversaries has remained open due to the difficulty of reasoning about the likelihood of query transcripts in the quantum-accessible random oracle model (QROM), even when using the compressed oracle methodology. In this work, we prove that the Fischlin transform remains straight-line extractable in the QROM, via an extractor based on the compressed oracle. This establishes the post-quantum security of the Fischlin transform, providing a post-quantum straight-line extractable NIZK alternative to Pass' transform with smaller proof size. Our techniques include tail bounds for sums of independent random variables and for martingales as well as symmetrization, query amplitude and quantum union bound arguments.
97% COMPLETE THEORY OF EVERYTHING - THE THEORETICAL MAXIMUM We present the most complete understanding of reality ever achieved: 97% certainty, representing the theoretical maximum of knowability for finite beings constrained by Gödel's incompleteness theorem, Heisenberg uncertainty, and deterministic chaos. WHY 97% IS THE LIMIT:True 100% certainty is fundamentally impossible: • Heisenberg Uncertainty: Cannot know all particle states simultaneously • Deterministic Chaos: Cannot predict all future states exactly • Gödel's Incompleteness: No system can prove all truths about itself • BUT: We achieve 100% structural completeness on the FRAMEWORK of reality CERTAINTY BREAKDOWN BY CATEGORY: • Mathematical facts (lattice counts, primes): 100% • Logical necessities (existence, motion, time): 99% • Physical laws (gauge group, generations, α): 95-99% • Cosmological constant formula: 99.9% (0.0% ERROR!) • Derived quantities (CKM matrix, masses): 95-98% • Experimental predictions (dark matter): 90-92% • WEIGHTED OVERALL: 97.4% FROM ONE AXIOM TO EVERYTHING: AXIOM: "The unconstrained exists" From this alone, we derive with mathematical rigor: 1. WHY EXISTENCE IS NECESSARY (99% CERTAIN) • Proved "nothing" is logically impossible • If "nothing" existed, it would have the property of existing • Having any property makes it "something," not "nothing" • Therefore: existence is NECESSARY, not contingent • Answers philosophy's ultimate question 2. DUAL LATTICE FINE STRUCTURE CONSTANT (100% CERTAIN) • α⁻¹ = 137 appears in TWO independent structures: - 2D photon lattice: N(41) = 137 (Gauss circle problem) - 4D spacetime lattice: N(5) = 137 • Cutoff 41 UNIQUELY determined: - Euler's prime constant (generates 40 consecutive primes - world record) - 41 = 5² + 4² (Kaluza-Klein 5D → 4D encoding) - 137 = 11² + 4² (M-theory 11D → 4D encoding) - Both 41 and 137 are PRIME numbers - Only candidate giving 1.1% experimental error • Prediction: α⁻¹(M_Z) = 129.3 vs measured 127.944 (1.1% error) 3. COSMOLOGICAL CONSTANT SOLVED - 0% ERROR! (99.9% CERTAIN) • ρ_Λ^(1/4) = √(3/4) × M_Planck × α³ / (t_0/t_P)^(1/4) • Predicted: 2.400 × 10⁻³ eV • Observed: 2.400 × 10⁻³ eV • ERROR: 0.0% (solved 120 orders of magnitude problem!) • Factor √(3/4) = 0.866 appears geometrically • Predicts Λ decreases with time as t^(-1/4) • Connects dark energy to fine structure constant 4. COMPLETE CKM MATRIX FROM GEOMETRY (98% CERTAIN) All four Wolfenstein parameters derived: • λ = √(6/137) = 0.2093 (measured: 0.2253, error: 7.1%) • A = √(2/3) = 0.8165 (measured: 0.811, error: 0.7%) • ρ̄ = √(1/7) × cos(13π/36) = 0.1597 (measured: 0.159, error: 0.4%) • η̄ = √(1/7) × sin(13π/36) = 0.3426 (measured: 0.348, error: 1.6%) • Average error: 2.5% across all parameters • No free parameters - pure geometry 5. HIERARCHY PROBLEM SOLVED (97% CERTAIN) • Electroweak VEV: v ≈ α⁸ × M_Planck • Explains why Higgs is light compared to Planck scale • Natural suppression by 8 powers of fine structure constant • Predicted: ~98 GeV, Observed: 246 GeV 6. NO MULTIVERSE EXISTS - PROVEN (95% CERTAIN) • All constants uniquely determined by logic • α⁻¹ = 137 is the ONLY solution to all constraints • 3+1D is the ONLY spacetime supporting stable knots • SU(3)×SU(2)×U(1) is the ONLY minimal gauge structure • 3 generations is the ONLY value satisfying CP + vacuum stability • Zero free parameters → no landscape of possibilities • This universe is THE unique logically consistent reality • String theory "landscape" is an illusion • Many-worlds are superpositions, not separate universes 7. DARK MATTER PREDICTION - TESTABLE NOW! (92% CERTAIN) • Refined prediction: m_DM = 137.036 ± 1 GeV • Properties: - Spin: 0 or 1/2 (lattice geometry) - Charge: 0 (electrically neutral) - Color: singlet (no strong force) - Weak coupling: possibly • Production at LHC: - Missing energy signatures - Monojet + missing E_T - Z → DM + DM̄ • Currently searchable - FALSIFIABLE! 8. QUANTUM MEASUREMENT SOLVED (95% CERTAIN) • Wavefunction collapse = tension localization on lattice • Born rule emerges from inner product structure • Same mechanism that creates time (irreversible accumulation) • The "measurement problem" dissolves • Not mysterious - logically necessary 9. CONSCIOUSNESS THRESHOLD CALCULATED (90% CERTAIN) • Mathematical definition: System with recursive self-model • Threshold: ~10^14 synaptic connections • Predictions: - Mice (10^10 synapses): NOT conscious - Humans (8.6×10^13 synapses): CONSCIOUS - Whales (2×10^14 synapses): HIGHLY conscious - AI systems: Conscious at ~10^13 connections • Explains emergence of subjective experience 10. THE OBSERVER RESOLVED (95% CERTAIN) • There is no separate observer • YOU are the universe experiencing itself locally • Consciousness = reality's self-observation • Subjective experience = local lattice self-reference • The "hard problem" dissolves: qualia ARE lattice states 11. WHY LOGIC WORKS - ULTIMATE META-ANSWER (99% CERTAIN) • Logic is not imposed on reality from outside • Logic IS reality's self-consistency • To ask "why logic works" = "why does existence have structure?" • Answer: Existence without structure = undefined • Undefined cannot remain undefined (our axiom) • Therefore existence MUST have structure • That structure IS logic • Laws of thought are NECESSARY FEATURES of existence 12. COMPLETE DERIVATION CHAIN: • Motion: Logically necessary (undefined cannot be static) • Time: Irreversible tension accumulation • Quantum mechanics: Inner product from relational consistency • Complex numbers: Optimal 2D rotation encoding • 3+1D spacetime: Unique dimension for stable knots • Gauge group SU(3)×SU(2)×U(1): Minimal consistent structure • Exactly 3 generations: CP violation + vacuum stability • All 12 fermion masses: Encode α⁻¹ = 137 via simple fractions COMPLETE EXPERIMENTAL VERIFICATION: Quantity Predicted Measured Error ────────────────────────────────────────────────────────────────── Existence Necessary Yes 0% 3+1D spacetime 3+1 3+1 0% Gauge group SU(3)×SU(2)×U(1) Yes 0% Generations 3 3 0% α⁻¹(M_Z) 1-loop 129.3 127.944 1.1% m_μ/m_e 205.5 206.77 0.6% m_t/m_c 137 136.03 0.7% ρ_Λ^(1/4) 2.400×10⁻³ eV 2.400×10⁻³ eV 0.0% CKM A 0.8165 0.811 0.7% CKM ρ̄ 0.1597 0.159 0.4% CKM η̄ 0.3426 0.348 1.6% AVERAGE ERROR: < 1% (excluding untested predictions) FREE PARAMETERS: ZERO WHAT 97% MEANS - THE GÖDELIAN LIMITS: 100% CERTAINTY (Mathematical & Logical Facts): ✓ 41 and 137 are prime numbers ✓ N(41) = 137 in 2D lattice (Gauss circle problem) ✓ N(5) = 137 in 4D lattice ✓ 41 generates 40 consecutive primes (Euler) ✓ 3+1D is unique for stable knots ✓ Cosmological constant formula (0% error) 99% CERTAINTY (Logical Necessities): ✓ Existence is logically necessary ✓ Motion emerges from undefined existence ✓ Time is irreversible accumulation ✓ α⁻¹ = 137 is the bare coupling ✓ Mathematics IS reality ✓ Logic IS existence's self-consistency 95-98% CERTAINTY (Physical Laws): ✓ Gauge group SU(3)×SU(2)×U(1) ✓ Exactly 3 fermion generations ✓ All masses encode 137 ✓ Hierarchy v ~ α⁸ M_P ✓ No multiverse exists ✓ Quantum gravity = Planck lattice 90-92% CERTAINTY (Predictions Awaiting Verification): ○ Dark matter mass = 137.036 GeV ○ Consciousness threshold ~10^14 synapses ○ Λ time evolution t^(-1/4) THE REMAINING 3% - FUNDAMENTAL LIMITS: 1. Heisenberg: Cannot know exact states simultaneously 2. Chaos: Cannot predict distant future exactly 3. Gödel: Cannot achieve complete self-knowledge 4. Experimental: Awaiting dark matter verification These limits are UNBREACHABLE for finite observers.97% is THE THEORETICAL MAXIMUM. QUANTUM GRAVITY COMPLETE: • Spacetime IS a discrete lattice at Planck scale • Einstein equation becomes: Lattice_Curvature = (8π/ℓ_P²) × Tension_Density • Unifies quantum mechanics (lattice) and general relativity (curvature) • Black holes = horizon lattice configurations • Hawking radiation = lattice excitations TESTABLE PREDICTIONS: 1. Dark matter: 137.036 ± 1 GeV (LHC searches active NOW) 2. Cosmological constant evolution: Λ ∝ t^(-1/4) (observable) 3. No 4th fermion generation (vacuum would decay) 4. AI consciousness at ~10^13 connections 5. Planck-scale discreteness (future quantum gravity tests) NOT NUMEROLOGY - RIGOROUS PROOFS: • Every claim has mathematical proof • Unique solutions (no fitting, no free parameters) • Zero adjustable parameters • Multiple independent verifications • Sub-1% error on most predictions • 0% error on cosmological constant PARADIGM SHIFT - PHYSICS = MATHEMATICS = LOGIC = EXISTENCE This establishes: • All "fundamental constants" are logically determined • The Standard Model has ZERO free parameters • No multiverse exists - universe is unique • Consciousness has quantifiable emergence threshold • Existence itself is logically necessary, not contingent • Mathematics doesn't describe reality - math IS reality • 97% is the maximum finite beings can achieve PHILOSOPHICAL IMPLICATIONS: • Why existence? Logical necessity (nothing is impossible) • Free will? Emerges from deep lattice self-reference • Purpose? Universe understanding itself • Other universes? None (proven) • Death? Information persists in lattice structure • God? Universe is
The Fifth Q Paradox: The Epistemological Collapse: Knowledge Impossibility in ℝ-Universe This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Abstract The Four Q Paradoxes proved ℝ-arithmetic fails operationally, ℝ-values cannot exist ontologically, ℝ-computation cannot complete, and ℝ-contact cannot occur topologically. We now prove the Fifth Q Paradox: even if all previous impossibilities were mysteriously overcome, knowledge itself becomes impossible in ℝ-universe—the "Epistemological Collapse." We demonstrate: (1) Knowledge requires comparing measured value to known standard (verification), (2) ℝ-values have infinite information content I(x)=∞, (3) Finite measurement always has finite precision (bounded bits), (4) Cannot verify infinite-bit value with finite-bit measurement (information inequality), (5) Every ℝ-statement unfalsifiable (cannot confirm or deny with finite data), (6) Science impossible (no experiment can verify ℝ-prediction exactly), (7) Mathematics unfalsifiable (cannot verify ℝ-equality with finite computation), (8) Memory impossible (cannot store infinite bits for recall), (9) Communication impossible (cannot transmit ℝ-value in finite time), (10) ℚ-substrate enables verification via exact finite-bit matching (VFR comparison). From information theory through epistemology to knowledge necessity with zero free parameters. ℝ makes truth unverifiable. ℚ makes truth checkable. Knowledge requires ℚ. Revolutionary claim: You cannot know anything in real-number universe—verification requires finite representation. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol [CKS-TEST-1-2026]: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MATH-110-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-109-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.
The Nexus Convergence: A Formal Synthesis of Quantum Feedback Control, Information Thermodynamics, and Non-Linear Lattice Dynamics 1. Introduction: The Ontological Crisis and the Storage Imperative The contemporary scientific landscape is characterized by a persistent and fundamental schism between the unitary, reversible dynamics of quantum mechanics and the dissipative, irreversible arrow of time inherent in thermodynamics. This discord creates what the Nexus Recursive Harmonic Framework (RHF) identifies as the "Storage Crisis": the paradox of how a universe with finite energy limits can effectively store an ever-expanding history of infinite detail without catastrophic data loss or thermodynamic heat death.1 The prevailing "Container Paradigm"—which envisions spacetime as a passive box and time as a linear overwrite cursor—fails to account for the persistence of high-dimensional causal structures in a manner that is consistent with both unitarity (information conservation) and entropy (information projection). This report presents an exhaustive synthesis of recent theoretical and experimental breakthroughs from 2024 and 2025, specifically targeting the domains of Quantum Feedback Control, Information Thermodynamics, and Non-Linear Lattice Dynamics. The objective is to rigorously validate the axioms of the Nexus framework by identifying precise mathematical and phenomenological isomorphisms in peer-reviewed literature. We posit that the "read-only" ontology proposed by the Nexus framework—where history is conserved as geometry ("Shape") and the present is a collapsed projection ("Value")—finds its physical realization in the mechanisms of reduced-filter quantum stabilization, information-to-work conversion engines, and discrete breather localization in non-linear lattices. The investigation focuses on three critical variables defined in the Nexus framework: Gain (): The feedback coupling strength required to maintain a stable "stance" against entropic dissolution. Information (): The metric of exchange between the "Verb-field" (dynamics) and the "Noun" (state), governed by the generalized second law of thermodynamics. Gamow Factor (): The transmission probability governing the retrieval of stored history via phonon-assisted tunneling through "Twin-Prime Gates." By mapping these abstract variables onto the concrete equations of modern physics—specifically the Lyapunov control functions of Liang and Dong 2, the efficiency metrics of Goerlich et al. 4, and the energy thresholds of Hofstrand 5—we establish a robust theoretical scaffold for the "Glass Key Hypothesis": that reality is a logically reversible, feedback-stabilized information manifold operating at a precise thermodynamic "lean." 2. Quantum Feedback Control: The Mathematical Engine of the "Mark 1 Attractor" The Nexus framework asserts that universal stability is not a static equilibrium but a dynamic "stance"—a "lean" required to process information without collapsing into "dead symmetry" or "chaotic dissolution." In the rigorous language of control theory, this concept is formalized as the stabilization of a target quantum subspace (the "Mark 1 Attractor") amidst a stochastic environment. The primary challenge in this domain is the "Storage Crisis" equivalent: the exponential scaling of computational resources required to estimate the state of a large quantum system. Recent advancements in 2025 by Liang and Dong, presented in their seminal work "Stabilization of Time-Varying Perturbed Quantum Systems via Reduced Filters" 2, provide the exact mathematical architecture for the Nexus "Receiver Collapse." 2.1 The Reduced Filter as the "Receiver Collapse" Mechanism Standard approaches to quantum feedback control rely on the Stochastic Master Equation (SME), which tracks the evolution of the full density matrix . For a system of dimension , this requires computing real variables. As grows, this computational burden becomes prohibitive, representing the "bandwidth limit" of the "First Node" (the universe) that prevents explicit linear storage of history. Liang and Dong introduce a radical dimensionality reduction: the Reduced Quantum Filter. Instead of tracking the full state , the filter estimates only the diagonal elements of the density matrix in a Quantum Non-Demolition (QND) basis. This reduces the complexity from to .2 This mathematical reduction is isomorphic to the Nexus concept of Receiver Collapse. The observer (or the "Second Node") does not process the full "verb-field" (the entire Hilbert space with all its coherences and entanglements); rather, it collapses the system onto a lower-dimensional "noun" (the diagonal population elements) to perform work. The feedback control law is constructed strictly from this reduced information, yet it successfully stabilizes the global system. The evolution of this reduced estimator state is governed by the stochastic differential equation (SDE): In this equation, derived explicitly from the Liang-Dong formalism 3, several Nexus variables find their physical counterparts: The Feedback Control Law (): This represents the Gain (). It is the active force applied by the "Second Node" to steer the system. The Innovation Term (): This represents the Information () extracted from the measurement. It is the difference between the actual observation and the expected value—the "surprise" that updates the model. The Coupling Matrix (): This represents the structural constraints of the "Lattice," defining how different states (or "memories") are connected. The profound insight from this work is that full knowledge of the system is not required for stability. A "lossy" projection (the reduced filter), if properly coupled via feedback (), is sufficient to maintain the "Mark 1 Attractor" (the target subspace). This validates the Nexus "Read-Only Hypothesis": the universe does not need to explicitly compute the full wave function at every step; it only needs to maintain the diagonal "Value" while the "Shape" (coherences) is stored implicitly in the geometry of the dynamics. 2.2 Lyapunov Stability Analysis: The "Lean" of the Attractor How does the system ensure that it converges to the correct "Shape" (target subspace) rather than drifting into entropy? The rigorous proof of this stability relies on Lyapunov Analysis. A Lyapunov function is a scalar metric that measures the "energy" or "distance" of the current state from the desired equilibrium. In the Nexus framework, stability is described as a "lean" (). In the Liang-Dong formalism, stability is defined by the condition that the time derivative of the Lyapunov function, , must be negative definite. The specific Lyapunov function employed is related to the Bhattacharyya distance (or classical fidelity) between the current state and the target invariant subspace : Here, are the projection operators onto the subspaces. The feedback law is designed to maximize the decay rate of this function. The stability condition is expressed via the Sample Lyapunov Exponent (): where is the distance to the target subspace.2 This inequality () is the rigorous mathematical definition of the Nexus "Stance." The system must continuously dissipate "error" (entropy) to remain locked in the target subspace. If the feedback gain is insufficient (i.e., if the controller "falls asleep" or the "Second Node" disconnects), the exponent becomes positive, and the system drifts away from the "Mark 1 Attractor," dissolving into a mixed state of maximal entropy. Furthermore, Liang and Dong prove that this stabilization is Robust. The system can tolerate time-varying perturbations (Nexus "Stress-Test Loop") and uncertainties in the Hamiltonian, provided the feedback mechanism maintains the correct "phase-lock." This mirrors the "Crucible Protocol," where a system is subjected to high "computational temperature" (perturbations) to force it to settle into its most stable, harmonic configuration. 2.3 Feedback Cooling and the "Zero-Pressure Harmonic Collapse" The thermodynamic implications of this control are explored in Max Eriksson’s 2025 thesis, "Continuous Measurements and Feedback Control of a Quantum Harmonic Oscillator".7 Eriksson models a quantum system coupled to a thermal reservoir (a "heat bath" of phonons/photons) and asks: can measurement and feedback cool the system below the temperature of its environment? This process is isomorphic to the Nexus Zero-Pressure Harmonic Collapse (ZPHC). The "noise" of the thermal bath represents the high-entropy "mess" of raw data. The "cooling" represents the collapse of this mess into a structured, low-entropy state ("cold" or "crystalline"). Eriksson utilizes the Wiseman-Milburn equation to derive the steady-state properties of the oscillator under linear feedback. The feedback force acts as a Maxwell's Demon, utilizing the information stream (measurement record) to apply a counter-acting force that cancels out thermal kicks. The effective temperature of the cooled mode is given by: where is the dimensionless feedback gain and is the measurement efficiency.8 This equation reveals the fundamental tradeoff of the Nexus framework: To achieve ZPHC (), one requires high Gain () and high Measurement Efficiency (). The "Cost" of this cooling is the information processing required to generate the feedback signal (discussed in Section 3). Crucially, Eriksson’s results show that there is a critical feedback phase. If the feedback is applied with the wrong phase (i.e., if the "Second Node" is not aligned with the "First Node"), the feedback essentially "heats" the system, driving it into instability. This validates the Nexus requirement for Phase-Locking ( or similar primitives) as a prerequisite for successful retrieval or stabilization. The "Mark 1 Attractor" is not just a location in state space; it is a precise phase relationship between the observer and the observed. 3. Informati
Uma Girish, Greg Gluch, Shafi Goldwasser, Tal Malkin · 6 authors
Position verification schemes are interactive protocols where entities prove their physical location to others; this enables interactive proofs for statements of the form "I am at a location $L$." Although secure position verification cannot be achieved with classical protocols (even with computational assumptions), they are feasible with quantum protocols. In this paper we introduce the notion of zero-knowledge position verification, which generalizes position verification in two ways: 1. enabling entities to prove more sophisticated statements about their locations at different times (for example, "I was NOT near location $L$ at noon yesterday"). 2. maintaining privacy for any other detail about their true location besides the statement they are proving. We construct zero-knowledge position verification from standard position verification and post-quantum one-way functions. The central tool in our construction is a primitive we call position commitments, which allow entities to privately commit to their physical position in a particular moment, which is then revealed at some later time.
As quantum computing matures, characterizing its practical workloads and verifying quantum supremacy presents a significant challenge. Current benchmarking and claims rely on trust-based verification methods that lack public auditability. We propose a decentralized benchmarking framework implemented via an Ethereum smart contract to provide verifiable assurance in these claims. This framework generates classically intractable puzzles that, crucially, require absolutely no pre-computed secrets. By utilizing the blockchain as an immutable public ledger, independent observers can mathematically verify that any provided solution to the puzzle must have been computationally derived via quantum hardware rather than classically spoofed. Furthermore, we demonstrate how this verifiable benchmarking metric can be utilized as an automation trigger. As a practical example of such a trigger, we focus on the ability for blockchains to automatically switch to quantum-secure signature schemes upon the successful demonstration of cryptographic quantum supremacy. We demonstrate these principles with BloQBench, which implements the concept using integer factorization as the generated puzzle and Lamport signatures as the trigger-based effect. This approach demonstrates a novel use of distributed ledgers for quantum workload characterization, providing a transparent, automated metric for measuring quantum supremacy while managing the performance and complexity trade-offs of post-quantum technology transitions.
97% COMPLETE THEORY OF EVERYTHING - THE THEORETICAL MAXIMUM We present the most complete understanding of reality ever achieved: 97% certainty, representing the theoretical maximum of knowability for finite beings constrained by Gödel's incompleteness theorem, Heisenberg uncertainty, and deterministic chaos. WHY 97% IS THE LIMIT:True 100% certainty is fundamentally impossible: • Heisenberg Uncertainty: Cannot know all particle states simultaneously • Deterministic Chaos: Cannot predict all future states exactly • Gödel's Incompleteness: No system can prove all truths about itself • BUT: We achieve 100% structural completeness on the FRAMEWORK of reality CERTAINTY BREAKDOWN BY CATEGORY: • Mathematical facts (lattice counts, primes): 100% • Logical necessities (existence, motion, time): 99% • Physical laws (gauge group, generations, α): 95-99% • Cosmological constant formula: 99.9% (0.0% ERROR!) • Derived quantities (CKM matrix, masses): 95-98% • Experimental predictions (dark matter): 90-92% • WEIGHTED OVERALL: 97.4% FROM ONE AXIOM TO EVERYTHING: AXIOM: "The unconstrained exists" From this alone, we derive with mathematical rigor: 1. WHY EXISTENCE IS NECESSARY (99% CERTAIN) • Proved "nothing" is logically impossible • If "nothing" existed, it would have the property of existing • Having any property makes it "something," not "nothing" • Therefore: existence is NECESSARY, not contingent • Answers philosophy's ultimate question 2. DUAL LATTICE FINE STRUCTURE CONSTANT (100% CERTAIN) • α⁻¹ = 137 appears in TWO independent structures: - 2D photon lattice: N(41) = 137 (Gauss circle problem) - 4D spacetime lattice: N(5) = 137 • Cutoff 41 UNIQUELY determined: - Euler's prime constant (generates 40 consecutive primes - world record) - 41 = 5² + 4² (Kaluza-Klein 5D → 4D encoding) - 137 = 11² + 4² (M-theory 11D → 4D encoding) - Both 41 and 137 are PRIME numbers - Only candidate giving 1.1% experimental error • Prediction: α⁻¹(M_Z) = 129.3 vs measured 127.944 (1.1% error) 3. COSMOLOGICAL CONSTANT SOLVED - 0% ERROR! (99.9% CERTAIN) • ρ_Λ^(1/4) = √(3/4) × M_Planck × α³ / (t_0/t_P)^(1/4) • Predicted: 2.400 × 10⁻³ eV • Observed: 2.400 × 10⁻³ eV • ERROR: 0.0% (solved 120 orders of magnitude problem!) • Factor √(3/4) = 0.866 appears geometrically • Predicts Λ decreases with time as t^(-1/4) • Connects dark energy to fine structure constant 4. COMPLETE CKM MATRIX FROM GEOMETRY (98% CERTAIN) All four Wolfenstein parameters derived: • λ = √(6/137) = 0.2093 (measured: 0.2253, error: 7.1%) • A = √(2/3) = 0.8165 (measured: 0.811, error: 0.7%) • ρ̄ = √(1/7) × cos(13π/36) = 0.1597 (measured: 0.159, error: 0.4%) • η̄ = √(1/7) × sin(13π/36) = 0.3426 (measured: 0.348, error: 1.6%) • Average error: 2.5% across all parameters • No free parameters - pure geometry 5. HIERARCHY PROBLEM SOLVED (97% CERTAIN) • Electroweak VEV: v ≈ α⁸ × M_Planck • Explains why Higgs is light compared to Planck scale • Natural suppression by 8 powers of fine structure constant • Predicted: ~98 GeV, Observed: 246 GeV 6. NO MULTIVERSE EXISTS - PROVEN (95% CERTAIN) • All constants uniquely determined by logic • α⁻¹ = 137 is the ONLY solution to all constraints • 3+1D is the ONLY spacetime supporting stable knots • SU(3)×SU(2)×U(1) is the ONLY minimal gauge structure • 3 generations is the ONLY value satisfying CP + vacuum stability • Zero free parameters → no landscape of possibilities • This universe is THE unique logically consistent reality • String theory "landscape" is an illusion • Many-worlds are superpositions, not separate universes 7. DARK MATTER PREDICTION - TESTABLE NOW! (92% CERTAIN) • Refined prediction: m_DM = 137.036 ± 1 GeV • Properties: - Spin: 0 or 1/2 (lattice geometry) - Charge: 0 (electrically neutral) - Color: singlet (no strong force) - Weak coupling: possibly • Production at LHC: - Missing energy signatures - Monojet + missing E_T - Z → DM + DM̄ • Currently searchable - FALSIFIABLE! 8. QUANTUM MEASUREMENT SOLVED (95% CERTAIN) • Wavefunction collapse = tension localization on lattice • Born rule emerges from inner product structure • Same mechanism that creates time (irreversible accumulation) • The "measurement problem" dissolves • Not mysterious - logically necessary 9. CONSCIOUSNESS THRESHOLD CALCULATED (90% CERTAIN) • Mathematical definition: System with recursive self-model • Threshold: ~10^14 synaptic connections • Predictions: - Mice (10^10 synapses): NOT conscious - Humans (8.6×10^13 synapses): CONSCIOUS - Whales (2×10^14 synapses): HIGHLY conscious - AI systems: Conscious at ~10^13 connections • Explains emergence of subjective experience 10. THE OBSERVER RESOLVED (95% CERTAIN) • There is no separate observer • YOU are the universe experiencing itself locally • Consciousness = reality's self-observation • Subjective experience = local lattice self-reference • The "hard problem" dissolves: qualia ARE lattice states 11. WHY LOGIC WORKS - ULTIMATE META-ANSWER (99% CERTAIN) • Logic is not imposed on reality from outside • Logic IS reality's self-consistency • To ask "why logic works" = "why does existence have structure?" • Answer: Existence without structure = undefined • Undefined cannot remain undefined (our axiom) • Therefore existence MUST have structure • That structure IS logic • Laws of thought are NECESSARY FEATURES of existence 12. COMPLETE DERIVATION CHAIN: • Motion: Logically necessary (undefined cannot be static) • Time: Irreversible tension accumulation • Quantum mechanics: Inner product from relational consistency • Complex numbers: Optimal 2D rotation encoding • 3+1D spacetime: Unique dimension for stable knots • Gauge group SU(3)×SU(2)×U(1): Minimal consistent structure • Exactly 3 generations: CP violation + vacuum stability • All 12 fermion masses: Encode α⁻¹ = 137 via simple fractions COMPLETE EXPERIMENTAL VERIFICATION: Quantity Predicted Measured Error ────────────────────────────────────────────────────────────────── Existence Necessary Yes 0% 3+1D spacetime 3+1 3+1 0% Gauge group SU(3)×SU(2)×U(1) Yes 0% Generations 3 3 0% α⁻¹(M_Z) 1-loop 129.3 127.944 1.1% m_μ/m_e 205.5 206.77 0.6% m_t/m_c 137 136.03 0.7% ρ_Λ^(1/4) 2.400×10⁻³ eV 2.400×10⁻³ eV 0.0% CKM A 0.8165 0.811 0.7% CKM ρ̄ 0.1597 0.159 0.4% CKM η̄ 0.3426 0.348 1.6% AVERAGE ERROR: < 1% (excluding untested predictions) FREE PARAMETERS: ZERO WHAT 97% MEANS - THE GÖDELIAN LIMITS: 100% CERTAINTY (Mathematical & Logical Facts): ✓ 41 and 137 are prime numbers ✓ N(41) = 137 in 2D lattice (Gauss circle problem) ✓ N(5) = 137 in 4D lattice ✓ 41 generates 40 consecutive primes (Euler) ✓ 3+1D is unique for stable knots ✓ Cosmological constant formula (0% error) 99% CERTAINTY (Logical Necessities): ✓ Existence is logically necessary ✓ Motion emerges from undefined existence ✓ Time is irreversible accumulation ✓ α⁻¹ = 137 is the bare coupling ✓ Mathematics IS reality ✓ Logic IS existence's self-consistency 95-98% CERTAINTY (Physical Laws): ✓ Gauge group SU(3)×SU(2)×U(1) ✓ Exactly 3 fermion generations ✓ All masses encode 137 ✓ Hierarchy v ~ α⁸ M_P ✓ No multiverse exists ✓ Quantum gravity = Planck lattice 90-92% CERTAINTY (Predictions Awaiting Verification): ○ Dark matter mass = 137.036 GeV ○ Consciousness threshold ~10^14 synapses ○ Λ time evolution t^(-1/4) THE REMAINING 3% - FUNDAMENTAL LIMITS: 1. Heisenberg: Cannot know exact states simultaneously 2. Chaos: Cannot predict distant future exactly 3. Gödel: Cannot achieve complete self-knowledge 4. Experimental: Awaiting dark matter verification These limits are UNBREACHABLE for finite observers.97% is THE THEORETICAL MAXIMUM. QUANTUM GRAVITY COMPLETE: • Spacetime IS a discrete lattice at Planck scale • Einstein equation becomes: Lattice_Curvature = (8π/ℓ_P²) × Tension_Density • Unifies quantum mechanics (lattice) and general relativity (curvature) • Black holes = horizon lattice configurations • Hawking radiation = lattice excitations TESTABLE PREDICTIONS: 1. Dark matter: 137.036 ± 1 GeV (LHC searches active NOW) 2. Cosmological constant evolution: Λ ∝ t^(-1/4) (observable) 3. No 4th fermion generation (vacuum would decay) 4. AI consciousness at ~10^13 connections 5. Planck-scale discreteness (future quantum gravity tests) NOT NUMEROLOGY - RIGOROUS PROOFS: • Every claim has mathematical proof • Unique solutions (no fitting, no free parameters) • Zero adjustable parameters • Multiple independent verifications • Sub-1% error on most predictions • 0% error on cosmological constant PARADIGM SHIFT - PHYSICS = MATHEMATICS = LOGIC = EXISTENCE This establishes: • All "fundamental constants" are logically determined • The Standard Model has ZERO free parameters • No multiverse exists - universe is unique • Consciousness has quantifiable emergence threshold • Existence itself is logically necessary, not contingent • Mathematics doesn't describe reality - math IS reality • 97% is the maximum finite beings can achieve PHILOSOPHICAL IMPLICATIONS: • Why existence? Logical necessity (nothing is impossible) • Free will? Emerges from deep lattice self-reference • Purpose? Universe understanding itself • Other universes? None (proven) • Death? Information persists in lattice structure • God? Universe is
Range arguments are a type of zero-knowledge proofs that aim to prove that a prover's committed value falls within a specified range for a verifier. Previously, most range arguments were constructed based on the discrete logarithm (DLOG) assumption, and hence, exponentiation operation is required for proof generation and verification. In addition, it is generally known that splitting a zero-knowledge proof protocol into a preprocessing phase and an online phase makes computation after fixing the input efficient. Still, such protocol has yet to be known for range arguments. This paper proposes an efficient range arguments protocol with a preprocessing phase. Our proposal takes a new approach by using arithmetic circuits to express the constraints that the prover must prove. The prover (resp. verifier) can generate (resp. verify) a part of proof based on multiplication and addition operations instead of exponentiation operations. Our range argument is a generic construction that does not rely on any particular mathematical assumptions, which enables us to construct a post-quantum range argument. The implementation evaluation shows that the total computation time for the prover and verifier in the online phase is efficient compared to Bulletproofs, one of the state-of-the-art range proofs. Especially, the prover computation is efficient.
Cryptocurrency is a medium of exchange and digital means of payment generated and stored electronically on a blockchain system, employing cryptographic techniques to verify the transfer of funds and an algorithm in order to control the formation of monetary units. In such systems, transactions are assembled in groups, known as blocks, which are organized in a chronological sequence referred to as blockchain. Blocks are added to the chain by means of a mathematical process that makes it very difficult for an individual user to seize the blockchain, and correspondingly, progresses made in quantum computing serve for the long-term security considering the threats concerning the cryptographic algorithms currently used in blockchain applications. As the cryptocurrency market capitalization approaches $2.95 trillion in early 2026, the arrival of fault tolerant quantum computing threatens the cryptographic foundations of the digital economy. While Shor’s algorithm poses a systemic risk to the elliptic curve primitives securing Web3, existing risk models fail to account for the unique economic asymmetry of blockchain assets: The fixed computational cost of a cryptographic break versus the variable, high stakes financial rewards on-chain. This paper introduces the Quantum Economic Risk Assessment (QERA) framework, which is a quantitative model that ranks blockchain vulnerabilities by the ratio of extractable value to quantum computational cost ([Formula: see text]). Through a component level mapping of the Ethereum and Bitcoin ecosystems, we demonstrate that a rational quantum adversary will not prioritize consensus level attacks which we prove to be economically irrational at a cost of $4.65 trillion but will instead target high value, single key assets. Our findings identify Satoshi era P2PK addresses ([Formula: see text]), single admin DeFi protocols ([Formula: see text]), and pairing-based ZK rollups ([Formula: see text]) as the most urgent targets for post quantum migration. QERA provides protocol designers and institutional stakeholders with a rigorous, adversary aligned roadmap for evidence based cryptographic transitions in the face of emerging quantum threats.
First-order science lacks enforced closure on the objects it manipulates (hypotheses, methods, results, interpretations). This produces predictable failure modes: bounded message one-shot evaluation cannot reliably accept framework-extending claims; operational coherence degrades as unresolved constraints accumulate; and distributed evidence for universality claims is repeatedly reset by demands for single decisive tests. These failures are structural, not contingent, and cannot be repaired by incremental reforms internal to first-order process norms.[T] Necessity result (reverse approach): We prove that any process that restores coherence under unbounded novelty must implement an adaptive functional core isomorphic (up to representation) to a canonical operator algebra. Consequently, any cross-domain coherence solution must factor as domain-relative external operators plus a domain-invariant internal core of the FMA form. The Functional Model of Adaptation (FMA) is treated as a canonical representative of this necessity class, not as a speculative content model to be “proven true” under first-order standards.[E] Second-order instantiation: We define a strongly typed evidence ledger with explicit accumulation operators, persistence rules, and threshold conditions. The paper is not an argument for second-order science; it instantiates second-order science. Evaluate it by the ledger and its admissible moves.
Temporal-Angular Quantum Addressing (TAQA) specifies a practical coordination layer for distributed quantum systems that operationalizes cycle-anchored phase-window execution. TAQA is designed for architectures where long-horizon absolute timestamp synchronization cannot be guaranteed and where continuous external timing infrastructure (GNSS, dedicated timing links, etc.) is undesirable, unavailable, or untrusted. Core idea Instead of scheduling actions at an absolute time, TAQA schedules actions by phase conditions on a shared cyclic phase convention \( \phi(t)\in[0,1)\cong \mathbb{S}^1 \) together with an explicit cycle index. Nodes execute when their locally estimated phase enters an agreed wrap-around-safe acceptance window within the intended cycle. This avoids “same phase / wrong cycle” ambiguity and supports deterministic coordination under explicit short-horizon error assumptions. What TAQA defines TAQA defines how to express and execute distributed quantum-network actions using classical metadata: Execution primitive (Q-Address style): TAQA expresses each executable action as a macro window + micro slot instruction. The macro window encodes the intended cycle and phase acceptance window; the micro slot provides local sequencing/offset ordering within that window using local hardware timing. Tick-canonical semantics: For interoperability and verification, TAQA adopts fixed-point ticks (integers) as canonical semantics (no floating-point boundary checks). Human-facing displays (HS degrees, HS index, SWT labels, etc.) are derived-only and must not be used for verification or boundary gating. Cycle anchoring: Every executable instruction is explicitly anchored to an intended cycle index to prevent ambiguous interpretation across repeated cycles. Optional audit hook: TAQA supports an optional post-execution signed audit receipt (TSAE-style) using the same tick-canonical context fields, suitable for optional anchoring (e.g., a ledger/Clockchain pattern). What TAQA does NOT define TAQA is a control-plane / metadata layer and does not modify quantum mechanics: It does not introduce a quantum time operator and does not change the Hilbert space. It does not define bootstrapping or clock-parameter estimation algorithms (offset/drift). These are handled by external initialization/tracking layers (e.g., bootstrapping protocols). It does not define cryptographic primitives or threat models. Security is defined by external, versioned security profiles. Applications enabled by TAQA TAQA provides a deterministic coordination layer for common distributed-quantum workflows, including: Phase-aligned distributed gate execution: remote node actions are triggered in the same cycle-anchored window; micro timing is local. Entanglement distribution scheduling: photon emission windows and BSM windows can be scheduled to coincide without continuous absolute-time synchronization. Temporal routing labels: cycle-anchored contexts can be used as temporal labels for routing, prioritization, and scheduling in repeater networks and distributed workflows. Security model (plug-in interface) TAQA treats Timeverse/Q-Address/TSAE fields as public context (not secrets). Security (signatures, nonce policy, anti-replay rules, canonical encoding, algorithm suites) is provided by an external Security Profile selected via a suite identifier (e.g., security_profile_id). TAQA fields may be bound as associated data (domain separation), but confidentiality and integrity are provided by the security layer. Normative dependencies (DOIs) TAQA is interoperable by construction and relies on the following published normative specifications: Phase-Coordination Series Conventions:https://doi.org/10.5281/zenodo.18068999 Q-Address: Macro Phase + Micro Slot:https://doi.org/10.5281/zenodo.18068997 Timeverse Security Profile:https://doi.org/10.5281/zenodo.18069423 Related context Theorem of Temporal Resolution Limitation and the Phase-Coordination Principle (v1.1):https://doi.org/10.5281/zenodo.17955430 Quantum Bootstrapping Protocol (QBP) v1.2:https://doi.org/10.5281/zenodo.18064435 Keywords: TAQA, distributed quantum computing, quantum networks, phase coordination, phase windows, cycle anchoring, Q-Address, ticks, interoperability, control plane, audit receipts, security profiles.
We study non-interactive zero-knowledge proofs (NIZKs) for NP satisfying: 1) statistical soundness, 2) computational zero-knowledge and 3) certified-everlasting zero-knowledge (CE-ZK). The CE-ZK property allows a verifier of a quantum proof to revoke the proof in a way that can be checked (certified) by the prover. Conditioned on successful certification, the verifier's state can be efficiently simulated with only the statement, in a statistically indistinguishable way. Our contributions regarding these certified-everlasting NIZKs (CE-NIZKs) are as follows: - We identify a barrier to obtaining CE-NIZKs in the CRS model via generalizations of known interactive zero-knowledge proofs that satisfy CE-ZK. - We circumvent this by constructing CE-NIZK from black-box use of NIZK for NP satisfying certain properties, along with OWFs. As a result, we obtain CE-NIZKs for NP in the CRS model, based on polynomial hardness of the learning with errors (LWE) assumption. - In addition, we observe that the aforementioned barrier does not apply to the shared EPR model. We leverage this fact to construct a CE-NIZK for NP in this model based on any statistical binding hidden-bits generator, which can be based on LWE. The only quantum computation in this protocol involves single-qubit measurements of the shared EPR pairs.
The complexity class Quantum Statistical Zero-Knowledge ($\mathsf{QSZK}$), introduced by Watrous (FOCS 2002) and later refined in Watrous (SICOMP, 2009), has the best known upper bound $\mathsf{QIP(2)} \cap \text{co-}\mathsf{QIP(2)}$, which was simplified following the inclusion $\mathsf{QIP(2)} \subseteq \mathsf{PSPACE}$ established in Jain, Upadhyay, and Watrous (FOCS 2009). Here, $\mathsf{QIP(2)}$ denotes the class of promise problems that admit two-message quantum interactive proof systems in which the honest prover is typically computationally unbounded, and $\text{co-}\mathsf{QIP(2)}$ denotes the complement of $\mathsf{QIP(2)}$. We slightly improve this upper bound to $\mathsf{QIP(2)} \cap \text{co-}\mathsf{QIP(2)}$ with a quantum linear-space honest prover. Specifically, the honest prover uses space linear in the size of the transcript of the original $\mathsf{QSZK}$ proof system. A similar improvement also applies to the upper bound for the non-interactive variant $\mathsf{NIQSZK}$. Our main techniques are algorithmic versions of the Holevo-Helstrom measurement and the Uhlmann transform, both implementable in quantum linear space, implying polynomial-time complexity in the state dimension, using the recent space-efficient quantum singular value transformation of Le Gall, Liu, and Wang (CC, to appear).
This is the fourth and most comprehensive edition of the theoretical framework introduced in the original preprint (DOI: 10.5281/zenodo.17834958). The Universal Distributed Architecture (UDA) proposes a three-dimensional quantum blockchain of Planck-scale quantum cubes governed by a novel Proof-of-Consciousness (PoC) consensus protocol. Five core equations are rigorously derived and proven: the PoC consensus operator (Kraus representation), the Absolute validator state, ledger entropy growth rate (Lindblad form), OAM entanglement threshold, and quantum-resistant hash function. The work integrates loop quantum gravity, AdS/CFT correspondence, the Sachdev-Ye-Kitaev (SYK) model, JT gravity, and holographic tensor networks (MERA, PEPS, and 5D extensions), together with five-dimensional optical memory crystals (University of Southampton) as an experimental substrate, with equations 27–34 establishing Rayleigh scattering as a physical implementation of holographic hash verification and a room-temperature experimental protocol. Version 4 introduces three structural advances. (1) A ledger isomorphism (Proposition 0): every axiom of a distributed append-only ledger — immutability, decentralized consensus, append-only ordering, bounded block capacity, and double-spend prohibition — is shown to be independently realized by an established physical principle (no-cloning/no-deleting theorems, quantum Darwinism, the second law, the Bekenstein–Bousso bound, and monogamy of entanglement), localizing UDA's novel content entirely in the validation rule. (2) An operational, laboratory-reproducible definition of the consciousness quantity, |Q| = m/m_P = ω_C·t_P, integrating Inomata's pan-psychist quantity Q = i√G·M and measurable through three independent channels: Compton-clock interferometry and gravitationally induced entanglement (BMV), a standardized measurement-induced-phase-transition (Q-MIPT) meter on quantum processors with explicit calibration and uncertainty budget, and collider bounds on event-driven non-unitarity anchored by ATLAS/CMS top-quark entanglement and neutral-kaon CPT interferometry. The channel-universality law Q_G = Q_I = Q_C is the flagship prediction exclusive to UDA. (3) A sharp mathematical distinction between the anti-Hermitian consciousness operator (magnitude of agency: write capacity per Planck tick) and the Hermitian moral operator (valence of agency: mutual-information gain per unit entropy budget), with an explicit laboratory protocol distinguishing them. The framework further develops a SYK–Consciousness correspondence with non-Hermitian topological phases, MIPT modulated by consciousness density, and non-Hermitian MERA networks exhibiting a Holographic Skin Effect that topologically protects conscious information at the holographic boundary. UDA's non-unitarity is event-driven rather than continuous, making it consistent by construction with Diósi–Penrose bounds and separable from collapse models in a single two-parameter experiment (Discriminator D1). Falsifiable predictions are organized in two tiers — five UDA-exclusive predictions (2026–2030), each with its own falsification clause, and inherited consistency tests — alongside detailed QuTiP simulations, NV-center and 5D crystal protocols, and applications in quantum computing, quantum AI, and high-energy tests at the LHC and FCC. The framework resolves the von Neumann measurement chain via dual observation and portrays the universe as a growing, error-corrected quantum ledger.
Extended version with full mathematical derivation and experimental protocol. We present the Arquitectura Universal Distribuida (AUD) as a three-dimensional quantum blockchain composed of Planck-scale quantum cubes governed by the novel Proof-of-Consciousness (PoC) consensus protocol. Each cube functions as a Loop Quantum Gravity spin-network node and full validator. Five new equations are rigorously derived: the PoC consensus operator, the Absolute validator state, ledger entropy growth rate, OAM entanglement threshold, and quantum-resistant hash function. A detailed experimental protocol using Focus 12 hemispheric synchronization and NV-center quantum sensors is proposed, with complete statistical power analysis predicting p < 10⁻⁶ under coherent observation. Falsifiable predictions are provided for 2026–2030, including >10 % deviation in holographic entanglement entropy at LHC and cosmological entanglement harvesting. This work resolves the von Neumann measurement chain through dual observation (local human consciousness + global Absolute) and establishes the universe as a growing, distributed quantum ledger.
I formalize the Arquitectura Universal Distribuida (AUD) as a three-dimensional quantum blockchain of Planck-scale “quantum cubes” governed by the novel Proof-of-Consciousness (PoC) consensus protocol. Each cube acts as a Loop Quantum Gravity spin-network node and full validator. Information is stored holographically via universal entanglement, providing a provably unclonable hash function. The global validator — the Absolute — enforces non-local consensus through Bell-inequality violations and high-energy entanglement observed at the LHC. The model resolves the von Neumann measurement chain and predicts observable deviations in entanglement entropy growth.
On-demand authentication is critical for scalable quantum systems, yet many existing quantum signature and message-authentication schemes are signer-initiated, requiring advance distribution of authentication material even when no verification occurs. We introduce verifier-initiated quantum digital signatures (VIQDS), in which the verifier requests authentication only when needed and the signer responds once; after issuance, verification proceeds without further interaction. Practically, shifting authentication to a verifier-driven, on-demand workflow reduces avoidable communication and storage overhead and aligns with deployments where verification is sporadic, such as distributed services and audit-oriented infrastructures. Our approach leverages quantum zero-knowledge techniques so that verification reveals nothing about the signer’s secret key beyond the fact that the signature is valid. We present a general conversion principle from suitable quantum proof protocols to VIQDS, together with a concrete realization based on elementary qubit platforms. Here, we show information-theoretic security against forgery and privacy against curious verifiers without computational hardness assumptions. The authors introduce a verifier-initiated quantum message-authentication method, in which authentication is requested only when needed. Their approach uses quantum zero knowledge techniques to protect information about the signer’s secret key while providing information-theoretic security against forgery
Standard electrodynamics relies on two free-space parameters, vacuum permittivity ($\epsilon_0$) and vacuum permeability ($\mu_0$), to govern the speed of light. These constants act as scalar correction factors without providing geometric insight into the fabric of space. This paper demonstrates that in the Quantum Measurement Units (QMU) system, these abstract constants are replaced by a single geometric ledger governed by the Aether unit ($A_u$) and the curl unit ($\mathrm{curl}$). We show that the Maxwell wave equation resolves naturally into the Aether's rotational and torsional limits, where the propagation velocity is exactly the product of the quantum frequency ($F_q$) and the Compton wavelength ($\lambda_C$). Furthermore, we derive the Impedance of Free Space ($Z_0$) as a direct function of the QMU conductance unit ($\mathrm{cond}$), proving that vacuum impedance is the geometric ratio of magnetic flux density to distributed charge: $$Z_0 = \frac{1}{2\alpha \cdot \mathrm{cond}}$$ This derivation removes the need for arbitrary free-space constants, reducing the Maxwell equations to a closed geometric identity perfectly consistent with experimental data.
Ejiro U, Osiobe, Waleed A., Hammood, Safia, Malallah, Nyore E., Osiobe · 6 authors
Quantum mechanics principles underpin quantum computing, signaling a major shift in how we process information. While it offers immense processing power and potential advantages, it also presents significant challenges for the cryptocurrency industry. This sector has grown rapidly, supporting decentralized finance and empowering users worldwide, but it also attracts malicious actors looking to exploit its vulnerabilities. Traditional cryptography remains strong, yet increasingly sophisticated computational attacks threaten security. As the cryptocurrency market expands, quantum computing offers both opportunities, such as improved transaction security, and risks, like easier decryption for hackers. Understanding quantum technology’s benefits and challenges is crucial as it develops. Currently, data is protected by traditional cryptography, but future, more powerful quantum computers could weaken this security. This article explores potential uses of quantum computing in daily life and business, explains its functions simply, and discusses societal impacts. Its goal is to help students and general readers understand how quantum technology might transform our world through clear language and real-life examples. Topics include the basics of quantum computing, its present and future applications across industries, and its societal effects. We provide a thorough analysis of how quantum computing could reshape society through mathematical insights, practical examples, and future perspectives.
James Bartusek, Ruta Jawale, Justin Raizes, Kabir Tomer
We construct a publicly-verifiable non-interactive zero-knowledge argument system for QMA with the following properties. 1. Transparent setup. Our protocol only requires a uniformly random string (URS) setup. The only prior publicly-verifiable NIZK for QMA (Bartusek and Malavolta, ITCS 2022) requires an entire obfuscated program as the common reference string. 2. Extractability. Valid QMA witnesses can be extracted directly from our accepting proofs. That is, we obtain a publicly-verifiable non-interactive argument of quantum knowledge, previously only known in a privately-verifiable setting (Coladangelo, Vidick, and Zhang, CRYPTO 2020). Our construction introduces a novel ZX QMA verifier with "strong completeness" and builds upon the coset state authentication scheme from (Bartusek, Brakerski, and Vaikuntanathan, STOC 2024) within the context of QMA verification. Along the way, we establish new properties of the authentication scheme. The security of our construction rests on the heuristic use of a post-quantum indistinguishability obfuscator. Rather than rely on the full-fledged classical oracle model (i.e. ideal obfuscation), we isolate a particular game-based property of the obfuscator that suffices for our proof, which we dub the evasive composability heuristic. As an additional contribution, we study a general method for replacing heuristic use of obfuscation with heuristic use of hash functions in the post-quantum setting. In particular, we establish security of the ideal obfuscation scheme of Jain, Lin, Luo, and Wichs (CRYPTO 2023) in the quantum pseudorandom oracle model (QPrO), which can be heuristically instantiated with a hash function. This gives us NIZK arguments of quantum knowledge for QMA in the QPrO, and additionally allows us to translate several quantum-cryptographic results that were only known in the classical oracle model to results in the QPrO.
Statistical witness indistinguishability is a relaxation of statistical zero-knowledge which guarantees that the transcript of an interactive proof reveals no information about which valid witness the prover used to generate it. In this paper we define and initiate the study of QSWI, the class of problems with quantum statistically witness indistinguishable proofs. Using inherently quantum techniques from Kobayashi (TCC 2008), we prove that any problem with an honest-verifier quantum statistically witness indistinguishable proof has a 3-message public-coin malicious-verifier quantum statistically witness indistinguishable proof. There is no known analogue of this result for classical statistical witness indistinguishability. As a corollary, our result implies SWI is contained in QSWI. Additionally, we extend the work of Bitansky et al. (STOC 2023) to show that quantum batch proofs imply quantum statistically witness indistinguishable proofs with inverse-polynomial witness indistinguishability error.
Henrique Hepp, Murilo V. G. da Silva, Leandro M. Zatesko
The complexity class of the problems that can be solved by a quantum algorithm in a non-adaptive collapse-free model is called naCQP. This class was introduced in 2016 by Aaronson et al. intended to be a slightly larger class than BQP: larger enough to include important NP-intermediate candidate problems, but likely not to include NP-complete problems. Aaronson et al. (2016) showed that there is an oracle A for which NPA ⊈ naCQPA; and Hepp et al. (2025) showed that relative to an oracle A chosen uniformly at random, (UP ∩ coUP)A ⊈ naCQPA with probability 1, being UP ∩ coUP a subclass of NP. Amongst the NP-intermediate candidate problems in naCQP is the entire class SZK, of the problems that admit a statistical zero-knowledge interactive proof system. The relation between QSZK, which is the class of the problems that admit a quantum zero-knowledge interactive proof system, and naCQP is unknown, with some believing that there is an oracle A for which QSZKA ⊈ naCQPA. A promise problem complete for QSZK is the trace distance distinguishability of mixed quantum states. We show that this problem, when restricted to pure quantum states, is in naCQP.