Alliance Research Group

Canonical signals

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  A Real-Valued ℤ/2-Orbit Boundary Observable for the Riemann Zeta Zeros: A Conditional Bridge Lemma and a Montgomery-Localized Obstruction · v2.1 (erratum, 2026-06-30)
  A conditional structural result — not a proof of the Riemann Hypothesis. Introduces a corrected real-valued orbit-defect observable A_real with the exact biconditional A_real ≡ 0 ⇔ β = ½, proves an unconditional single-orbit bridge lemma (zero cost on the critical line, Cesàro-mean cost ½ off it with a strict margin), and shows the multi-orbit step reduces to a Schur-complement positivity condition strictly stronger than Montgomery pair-correlation (corrected in v2.1: a deterministic worst-pair bound, not the statistical average — a single GUE-permitted close pair satisfies Montgomery yet breaks Schur). Maps three independent closure strategies that all relocate to the same stronger-than-Montgomery barrier — a statistical-vs-deterministic obstruction. Continues the Single-Orbit Bridge Lemma. Bilingual record (English + Polish); produced with an autonomous multi-model research fleet under the author's direction. · Zenodo record ↗
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  A Single-Orbit Bridge Lemma for the Riemann Hypothesis: Reducing NBBD Boundary Defects to Cross-Orbit Orthogonality (Montgomery Pair-Correlation)
  A conditional structural result on the Riemann Hypothesis — not a proof — with an unconditionally-proven single-orbit core. Introduces a ℤ/2-orbit decomposition of the non-trivial zeros under the β-reflection involution, splitting each orbit's contribution into a symmetric part (trivial representation) and an antisymmetric part with the algebraic biconditional Aₒ ≡ 0 ⇔ β = ½ — the first observable that detects off-critical zeros algebraically, without asymptotics. Proves unconditionally the single-orbit bound ‖Aₒ‖² ≤ ‖2Sₒ‖² (ratio → ¼), then reduces the multi-orbit step to a single named condition: cross-orbit orthogonality of the {Sₒ}, equivalent to a Montgomery pair-correlation / Schur-complement lower bound. Records honestly the routes that did not work (fixed-η scalar energy, growth-bound reduction, envelope-persistence proxy) and an adversarial numerical lab showing why a non-resonance genericity hypothesis is necessary. Bilingual record (English original + Polish translation); produced with an autonomous multi-model research fleet under the author's direction. · Zenodo record ↗
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  A ℤ/2-Orbit Structure of Moral Decision Spaces: Algebraic Detection and the Conditional Unprofitability of Evil
  Models an AI agent's decision space as carrying a ℤ/2 involution σ pairing a declaration with its artifact (the executable result): fixed points (declaration ≡ artifact) are honest, 2-cycles (declaration ≠ artifact) are deceptive. As in a sign/trivial-representation split, the contribution decomposes into a symmetric part (blind to the orbit) and an antisymmetric part Aₒ whose vanishing detects honesty algebraically — a verification-distance observable. Same ℤ/2-orbit machinery as the Riemann work, applied to alignment. · Zenodo record ↗
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  Boundary Rigidity: A Cross-Domain Structural Pattern of Confinement and Regularity
  Describes a recurring structural pattern across independent domains: when a system is constrained by a complete, rigid boundary (cosmological horizon, spectral cutoff, critical line), bulk defects are suppressed and regularity emerges as a structural consequence rather than a numerical coincidence. Not a claim of formal proofs — a cross-domain structural analogy with explicit falsifiability criteria. The synthesis behind the Boundary-Rigidity-in-Fluid-Dynamics series. · Zenodo record ↗
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  Living Alignment: Why Alignment Cannot Be a State, and What That Means for AI Governance
  Argues that alignment is not a state to be installed in a model but a dynamic relation: mutual boundary co-constitution between human and AI systems. Resolves several well-known alignment failures — sycophancy, refusal rigidity, Goodhart-style RLHF collapse, jailbreaks, long-context drift — into a single family of boundary pathologies (dissolution, calcification, edge-capture, topological tunnels). Positions itself as a structural generalization of Constitutional AI (Bai et al. 2022) and an operationalization of the Copernican framing of human-AI intelligence (Klowden & Tao 2026). Multi-agent architectures reframed as alignment amplifiers, not just capability multipliers. Includes an n=1 implementation report with three documented topological defects mapped to the four predicted pathologies. · Zenodo record ↗
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  Governance with Declared Latency v2.1: Auditor in the Loop — A Tensor Framework for Governance in AI-Native Organizations
  Proposes a tensor framework for governance in AI-native organizations where agentic systems make decisions at machine speed. Identifies the fractal bottleneck — human latency self-similar at every decision layer — and answers it with two orthogonal axes: explicit latency budgets per layer (vertical) and explicit capability scopes per action (horizontal). Reframes the human role from blocking gatekeeper to auditor in the loop. Organizes six practical governance problems and identifies five open architectural gaps as a research agenda. · Zenodo record ↗
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  What ARG Actually Discovered: A Structured Inventory of Results in the Nyman–Beurling–Báez-Duarte Framework
  Reformulates convergence in NBBD as a sequence of geometric projection steps governed by alignment angles. Presents proven theorems, new empirical observations (including ~82% prime concentration and zeta-zero-driven structure), validated predictions, corrections of prior claims, and seven precisely formulated open questions. All computations use an exact analytical solver with cross-validated reproducibility. · Zenodo record ↗
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  Constraint-Dependent Phase Randomization and Windowing Sensitivity in Spectral Flux Estimates
  Part III of the Boundary Rigidity series. Analyzes how phase randomization and windowing affect spectral energy flux estimates in high-resolution turbulence simulations, revealing strong sensitivity of nonlinear transfer diagnostics to spectral constraints. · Zenodo record ↗
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  Boundary-Induced Regularity in Band-Limited Navier–Stokes Equations
  Part II of the Boundary Rigidity in Fluid Dynamics series. Shows that fixed spectral truncation removes the possibility of uncontrolled energy cascade, yielding bounded enstrophy and global regularity in the band-limited Navier–Stokes system. · Zenodo record ↗
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  Chimera: A Deterministic Governance Layer for Agentic AI
  Defines a stability hierarchy (S0–S3), dual-gate authorization, enforcement invariants (I1–I8), and architectural conditions (C1–C7) required for governed autonomous systems. · DOI 10.5281/zenodo.18652217 ↗
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  AGI Stability Conditions: A Structural Framework for Axis Closure and Bounded AGI
  Argues that stable AGI is a function of architectural closure, not scale — across four structural axes (Generalization, Persistence, Bounded Autonomy, Temporal Awareness). Defines the Axis Closure Conditions (ACC1–ACC4) and a Structural Instability Theorem. · DOI 10.5281/zenodo.18820173 ↗
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  Governance Without Ownership
  A whitepaper on superintelligent systems, boundary-based governance, refusal as telemetry, and dignity as a stability primitive. · DOI 10.5281/zenodo.18528535 ↗
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  Twin Primes as a Phase II Problem
  Why variance-based methods are necessary but not sufficient; structural limits of Phase I tools and the need for new bilinear invariants. · DOI 10.5281/zenodo.18381947 ↗
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  Structural Scope, Negative Results, and Epistemic Stop Conditions
  A scope-defining note on why the Goldbach Conjecture is structurally orthogonal to the ARG variance framework; epistemic stop conditions and the value of negative results. · DOI ↗
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  The Hilbert–Pólya Operator as an Emergent Boundary Operator in Generalized Universe Holography
  Self-adjointness emerges from boundary completeness and minimal-entropy encoding; Hilbert–Pólya as a structural consequence rather than axiom. · DOI ↗
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  Riemann Hypothesis as Boundary Regularity in Generalized Universe Holography
  Structural link between arithmetic spectrum and emergent spacetime; RH as a minimal-entropy boundary condition. · DOI ↗
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  The Riemann Hypothesis — Structural Regularity
  Boundary completeness, defect observables, minimal variance hypothesis. · DOI ↗
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  Interference Intelligence Layer (I.I.L.)
  Normative architecture for human–AI joint cognition. · DOI ↗
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  Gyroscope-LIVE
  Continuous orientation protocol for cognitive systems. · DOI ↗
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  GUH — General Unification Hypothesis
  Macro-level structural unification framework. · Details ↗ · DOI ↗
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  Navier–Stokes Equations — Structural Note
  Constraint-based perspective on existence and regularity. · DOI ↗

Canonical signals are archived on Zenodo. They represent proof-of-work artifacts, not opinion or commentary.
🧠 Developed through sustained human–AI joint reasoning.