Research Projects - William Chuang

Research Projects

Foreign Influence and Ideological Operations at the University of San Francisco (2014–2025)

This open-source intelligence (OSINT) assessment presents a forensic mapping of foreign ideological influence and covert operational dynamics centered on the University of San Francisco (USF), with particular focus on the China Business Studies Initiative (CBSI), Chinese Students and Scholars Association (CSSA) networks, and associated narrative vectors. The analysis spans the evolution of these activities from 2014 through 2025, with comparative reference to historical models of epistemic capture and academic front operations.

The report employs a hybrid methodology integrating counterintelligence-informed network tracing, social graph analysis, and semantic narrative forensics. Particular emphasis is given to identifying structural vulnerabilities within Jesuit and West Coast academic frameworks that have been strategically leveraged by PRC-linked entities for influence projection, prestige laundering, and soft-power recruitment. From CBSI’s rebranding maneuvers post-Confucius Institute scrutiny to CSSA-mediated coercive diaspora control via WeChat ecosystems, the document elucidates patterns of foreign actor adaptation and institutional co-option.

Beyond diagnosis, the work advances a calibrated risk matrix for legal, reputational, and national security exposure — outlining actionable mitigation strategies grounded in FARA/FISA compliance, transparent foreign engagement protocols, and narrative sovereignty safeguards. It positions the USF case as a paradigm for understanding how vulnerable Western academic institutions may serve, knowingly or unknowingly, as amplifiers for transnational authoritarian influence — underscoring the imperative for proactive counter-influence architectures within the U.S. higher education landscape.

Download: Foreign Influence and Ideological Operations at USF (PDF)

Symbolic Sovereignty in Contested Media: A Strategic Analysis of the Catholic Worker Movement

This strategic research paper examines the Catholic Worker Movement (CWM) through the lens of symbolic architecture, semantic infiltration, and network dependence. It traces how movements grounded in moral clarity and ecclesial witness—such as CWM—are structurally routed through global media infrastructures that increasingly reflect philanthropic capital, ESG soft power, and high-bridge ideological syndication.

The manuscript introduces a hybrid methodology integrating graph theory, canonical analysis, and semantic signal decryption to map shortest paths between Catholic Worker nodes and dominant globalist networks. Special attention is given to low-degree, high-bridge intermediaries that serve as vectors of message amplification, shaping how moral content is refracted or repackaged in broader public discourse. From Pax Christi’s proximity to OSF-funded media chains to the indirect platform dependencies of the Catholic Worker Newspaper, the analysis reveals structural chokepoints in narrative transmission.

Beyond diagnosis, the work proposes a defensible framework for ecclesial narrative sovereignty—outlining symbolic firewalls, canonical checksum logic, and strategic detachment from hostile semantic infrastructures. It positions the CWM as a case study in how grassroots Catholic ethics must navigate a metastasized media topology without compromising doctrinal fidelity or narrative agency.

Download: Strategic Analysis of the Catholic Worker Movement (PDF)

Decrypting the Myth: Quantum Computing, National Security, and the Case for MSIA

The oft-repeated claim that quantum computing will soon render all secrets obsolete and eliminate all forms of secrecy, regardless of moral context is a dramatic oversimplification—rooted more in techno-futurist anxiety than in the nuanced realities of cryptographic science. As someone working at the intersection of symbolic dynamics, representation theory, and modular cryptography, I find this narrative not only misguided but also dangerous in its implications for public understanding and policy framing. The following breakdown aims to clarify these misconceptions and to outline how MSIA (Modular Symbolic Intelligence Architecture) serves as a rigorously constructed post-quantum safeguard.

1. What Quantum Computers Can and Cannot Do

The current consensus among cryptographers is that quantum algorithms, notably:

Shor’s Algorithm: Efficiently factors integers and computes discrete logarithms, compromising RSA and ECC-based systems.
Grover’s Algorithm: Offers quadratic speedups for brute-force attacks, reducing AES-256 security to AES-128 levels—but not breaking it.

Thus, quantum computers threaten specific cryptographic primitives, not all encryption methods.

2. MSIA is Post-Quantum Resistant by Design

MSIA departs from conventional lattice or code-based schemes by employing a layered framework of hardness guarantees:

Modular Zeta Functions: Defined over finite fields, encoding symbolic trace spectra linked to non-abelian algebraic structures
Schottky-Derived Symbolic Dynamics: Orbit encodings derived from free, non-commutative generators with exponential-length growth
Obfuscation Mechanisms: Including Frobenius twisting, Brauer character mixing, and Vandermonde slot concealment
#P-Hardness: Inversion equivalent to symbolic trace classification—computationally intractable due to combinatorial explosion
NP-Hardness: Symbolic clauses encode SAT reductions within slot configurations, linking to well-known NP-complete formulations
Geometric Hardness: Recovering symbolic trace peaks reduces to length spectrum inversion on Selberg-type zeta functions, which remains open in hyperbolic geometry

Crucially, none of these problem classes admit known quantum speedups. Furthermore, MSIA’s IND-CCA2 security is enforced through a Fujisaki–Okamoto transform, making it resilient even under quantum-level chosen-ciphertext scenarios.

My work is designed precisely to neutralize the cryptographic threat posed by quantum computers. Rather than being rendered obsolete, MSIA shields secrets using mathematical structures beyond quantum reach—turning post-quantum fears into robust resilience.

Claim	Reality
"Quantum computers will nullify all secrets"	False. They compromise only vulnerable schemes (e.g., RSA, ECC). MSIA and symmetric cryptography remain intact.
"Quantum supremacy will reveal all hidden actors"	Misleading. Rather than abolishing secrecy, quantum capability redefines its terrain. MSIA occupies the high ground by shifting from arithmetic opacity to symbolic spectral resilience, embedding security in non-commutative trace obfuscation and entropy-hard encodings. Trust is not a product of technological dominance, but a consequence of moral coherence, mathematical integrity, and public accountability—principles grounded in ethical responsibility, constitutional fidelity, and the common good.

Claim

Reality

"Quantum computers will nullify all secrets"

False. They compromise only vulnerable schemes (e.g., RSA, ECC). MSIA and symmetric cryptography remain intact.

"Quantum supremacy will reveal all hidden actors"

Misleading. Rather than abolishing secrecy, quantum capability redefines its terrain. MSIA occupies the high ground by shifting from arithmetic opacity to symbolic spectral resilience, embedding security in non-commutative trace obfuscation and entropy-hard encodings. Trust is not a product of technological dominance, but a consequence of moral coherence, mathematical integrity, and public accountability—principles grounded in ethical responsibility, constitutional fidelity, and the common good.

3. MSIA’s Strategic Role in National Security

Unlike traditional cryptosystems constrained to number-theoretic assumptions, MSIA constructs ciphertexts using spectral and symbolic invariants that are deliberately chosen for their inversion-hardness in both classical and quantum models. The architecture is engineered to:

Embed secrets within trace peak statistics of symbolic orbits
Conceal spectral fingerprints through group-algebraic Brauer transformations
Resist reverse-engineering even under full ciphertext access, including quantum state queries

Conclusion

No. MSIA is not vulnerable to the class of attacks posed by quantum computing. In fact, it is precisely engineered to neutralize such threats.

Rather than being rendered obsolete, MSIA shields secrets using mathematical structures beyond quantum reach—turning post-quantum fears into robust resilience.

Note: The core system underlying MSIA has been formally disclosed to the United States Patent and Trademark Office (USPTO) under U.S. Provisional Patent Application No. 63/809,257. This establishes a legal foundation for the intellectual property surrounding its cryptographic primitives, symbolic dynamics, and post-quantum architecture.

Downloads:

Note: This demo implementation uses intentionally small field sizes and simplified primitives. It is designed solely for academic illustration and does not represent a production cryptosystem.

For deployment inquiries or to request a classified-style policy brief or public declassified whitepaper, please contact williamhschuang@gmail.com.

Disclaimer: All technical material is provided for lawful academic and pre-commercial use only. No portion of this site contains classified, export-restricted, or ITAR-governed technology. Logarchéon, Inc.—my newly established research entity—is being developed to architect, license, and scale systems integrating symbolic cryptography, post-quantum computation, and lawful innovation for national security applications. It operates in full alignment with U.S. federal law and anticipates future federal clearances for relevant R&D pathways.

From Gray-Zone Mapping to Civic Fortification: Taiwan’s Churches as Strategic Civil Defense Nodes

This strategic policy memorandum reframes Taiwan’s vulnerability to gray-zone aggression by highlighting an often-overlooked pillar of national resilience: church-based moral networks embedded within Indigenous communities. Drawing parallels to U.S. homeland security micro-network doctrine (e.g., InfraGard, Citizen Corps), the work introduces the "1% Doctrine"—a civic mobilization model wherein high-trust communities form a scalable firewall against political subversion, hybrid infiltration, and rapid paramilitary escalation.

Drawing on leaked adversarial mapping (e.g., Taiwan Armed Gang Distribution Atlas) and quantified mobilization thresholds (<1-hour latency), the analysis argues that Catholic–Indigenous parishes—totaling ~280,000 members—possess latent territorial advantage, legal firearms literacy, and intergenerational cohesion that make them ideal anchors for civil continuity in the event of military disruption. Strategic recommendations include legal codification of church–defense cooperation, distributed tunnel ingress planning, and the deployment of ethical defense narratives to counter psychological operations.

More than a policy paper, this document serves as a template for decentralized moral deterrence. It blends intelligence doctrine, sociological resilience, and ethical geopolitics—offering a framework to engineer public legitimacy and preserve Taiwan’s sovereignty through the distributed conscience of its people.

Download: From Gray-Zone Mapping to Civic Fortification (PDF)

Resilient Underground Networks: Expanding Taiwan’s Civil Defense Architecture

This policy architecture brief outlines a sovereign continuity framework for Taiwan under the threat of hybrid warfare and decapitation strike scenarios. Building on doctrinal concepts such as Deep Underground Military Bases (DUMBs), Command and Control (C2) hardening, and community-based auxiliary forces, the manuscript proposes a technically feasible and ethically robust model for distributed national resilience.

Bridging state infrastructure, religious networks, and legally codified civil defense, the paper details an implementation strategy that integrates: AI-guided tunnel navigation, church–tunnel fusion points, modular symbolic encryption (MSIA), and multi-layered communication resilience through analog, satellite, and secure mesh networks.

With case comparisons to Finland, Ukraine, Israel, and Cold War Switzerland, the document affirms the viability of a trained 1% civilian defense grid—capable of preserving civic order, safeguarding infrastructure, and delaying adversarial consolidation for up to 90 days. This “1% Doctrine” is positioned as both a legal shield under IHL and a moral bulwark against cognitive and territorial collapse.

Download: Expanding Taiwan’s Civil Defense Architecture (PDF)

Operationalizing the 1% Doctrine: AI-Augmented Deterrence and Civil Defense Continuity for Taiwan

This policy architecture reframes Taiwan’s national resilience through a precision-built, ethically anchored model of autonomous deterrence. By integrating AI-driven tunnel defense, swarm ISR drones, and a subterranean logistics network, the doctrine proposes a framework that reduces projected casualties from ~11,000 to under 100 in the first 10 days of conflict—while preserving civil order, narrative legitimacy, and coalition interoperability.

Grounded in laws of armed conflict, and interoperable with NATO and Indo-Pacific allied standards, this work presents not only a tactical roadmap but a geopolitical thesis: that moral clarity and algorithmic precision can together compose a credible firewall against kinetic occupation and information collapse. It concludes with the formal introduction of a fully automatable defense-industrial base—capable of manufacturing up to 200,000 autonomous platforms weekly within hardened underground facilities— and outlines the doctrinal imperatives for AI-legal harmonization, trust signal propagation, and democratic survivability.

Download: Operationalizing the 1% Doctrine – (PDF)

Ecclesial Cartography in the Shadow of Empire:
Mapping Clerical Networks for Sovereign Faith

This interpretive dossier reframes twentieth-century episcopal diplomacy as a geopolitical intelligence archive—charting the enduring legacy of Cardinal Sebastiano Baggio (1973–1984) through the lens of ecclesial sovereignty, ideological formation, and theocratic alignment.

At its core, the work investigates how Vatican-era appointment strategies—shaped by curial pragmatism, Jesuit tension, and Cold War realpolitik—continue to condition Catholic postures toward authoritarian regimes, particularly across the Sinophone world.

Positioned at the intersection of ecclesiology and statecraft, this study explores the continuity between Baggio-era clerical networks and present-day Church–state diplomacy. It questions whether soft-diplomatic postures—often couched in terms like dialogue, synodality, or inculturation—unwittingly reinforce strategic aims of the Chinese Communist Party, including the marginalization of Taiwan’s ecclesial independence.

By analyzing clerical lineages, theological temperaments, and diplomatic alignments, this project elevates Taiwan’s Indigenous–Catholic communities as moral counterweights to hybrid religious subversion.

This is not merely a historical study. It is a strategic tool: a framework for informed discernment under pressure, designed for clergy, laity, and public actors navigating the subtle incursions of ideological power beneath the surface of peacebuilding rhetoric.

The result is a Jesuit-compatible model of moral vigilance—where paradox is not weakness, but the crucible of clarity. Public theology, civic continuity, and ecclesial sovereignty converge to offer a map for safeguarding the sacramental conscience in contested geopolitical space.

Perception, Power, and Pastoral Language:
Reflections on Ideological Undercurrents in Catholic Leadership

This reflective memorandum offers a structured interpretive framework for discerning ideological signals within contemporary Catholic leadership—especially as they pertain to Taiwan’s ecclesial sovereignty, Vatican–PRC diplomacy, and global Church discourse.

Instead of asserting partisan conclusions, the work organizes symbolic orientations into provisional categories that illustrate how theological language, pastoral priorities, and diplomatic silences may reflect deeper allegiances—whether toward tradition, globalist ethics, or strategic ambiguity.

Two typological archetypes—Category A (Ecclesial Independence) and Category B (Diplomatic Moderation/Progressivism)—serve as interpretive tools to analyze clerical rhetoric and institutional positioning. These are not polemical binaries but conceptual lenses, crafted for the discerning Catholic laity, scholars, and policy observers seeking to understand how Church leadership navigates the crosswinds of authoritarian pressure, doctrinal fidelity, and theological pluralism.

With Taiwan as both geographic locus and symbolic test case, the analysis underscores how silence, inculturation, or selectively emphasized values (e.g., synodality, global solidarity) can shift ecclesial witness in ways that may or may not align with moral clarity.

This document functions as a diagnostic and devotional map. It equips lay readers with strategies for theological literacy, respectful engagement with clergy, and formation practices rooted in Catholic social teaching and classical doctrine. The accompanying “Inquiry Checklist” encourages ongoing discernment within parish life and ecclesial networks.

The ultimate aim: not to judge, but to deepen fidelity. In a moment when conscience, culture, and diplomacy increasingly intertwine, this work provides a lay-grounded but intellectually rigorous path for sustaining moral sovereignty and spiritual clarity across contested ecclesial terrains.

Weaponized Psychiatry, Projection, and Cognitive Suppression

This paper establishes a diagnostic and strategic framework for recognizing and resisting psychological warfare tactics aimed at undermining independent scientific inquiry. Drawing from clinical diagnostics (e.g., DSM-5-TR, MMPI-2-RF), political psychiatry case studies, and defense psychology, the manuscript identifies recurring cognitive suppression patterns—such as projection, status-anxiety-driven aggression, and strategic gaslighting—that are used to discredit disruptive innovation and epistemic independence.

By paralleling these behaviors with known authoritarian tactics (e.g., PRC's psychiatric labeling of dissidents), the work provides a rigorous lens to evaluate ethical breaches in academic, institutional, and geopolitical contexts. The analysis culminates in a structured resilience strategy for researchers working at the frontiers of AI, cryptography, and national security.

Disclaimer: This article is a scholarly analysis focused on the psychological and epistemological dimensions of scientific and institutional behavior. It draws upon clinical frameworks (e.g., DSM-5-TR, MMPI-2-RF) and historical case studies solely for academic purposes. No portion of this work constitutes a political statement, accusation, or form of advocacy. The research is grounded in documented literature and aims to support cognitive resilience and ethical innovation in the post-quantum era. The author adheres fully to U.S. law and scientific integrity standards.

Download: Weaponized Psychiatry & Cognitive Suppression (PDF)

Gravitational Schwinger Mechanisms in Engineered Condensed Matter Platforms

This foundational work lays out the physical intuition and platform design principles for vacuum instabilities triggered by gravitational analogues of the Schwinger effect. It introduces the concept of Coulomb and nuclear slingshot amplification and compares various vacuum excitation processes—from triboluminescence to Hawking radiation—within a unified vacuum gradient framework. The manuscript sets the experimental and conceptual stage for higher-level theoretical developments in vacuum engineering.

Download: Gravitational Schwinger Mechanisms (PDF)

Quantum Amplification Cascades and Lee–Yang Criticality

This manuscript completes the quantization of the vacuum–graviton cascade framework by embedding it in operator-level arithmetic and neural-compatible quantum field theory. It demonstrates that Lee–Yang zeros sharpen under quantum corrections and introduces the GRAIL, FPQND, and ANQFT meta-architectures. The theory offers a foundational basis for neural–arithmetic control of vacuum energy and proposes experimental blueprints compatible with national security and export control requirements.

Download: Quantum Amplification Cascades and Lee–Yang Criticality (PDF)

Vacuum Criticality in Quantum-Gravitational Path Integrals

This work investigates vacuum metastability and energy harvesting within the Euclidean path integral formalism. It links cosmological Lee–Yang zeros to condensed-matter amplification cascades, proposing an experimental setup using diamond and deuterated palladium to trigger vacuum energy bursts. Emphasis is placed on scaling laws, synchronization limits, and practical engineering for cubic-metre–scale demonstrators. The manuscript bridges semiclassical cosmology and nanophotonics to pioneer laboratory-level vacuum control.

Download: Vacuum Criticality in Quantum-Gravitational Path Integrals (PDF)

Vacuum–Graviton Cascade Theory: A Rigorous Axiomatic Framework

This paper develops an axiomatic theory for slingshot-driven vacuum instabilities, establishing a Hilbert-bundle formulation of quantum fields over curved spacetime and introducing a mathematically precise amplification operator. Derived results include a curvature-dependent generalization of the Schwinger pair-production rate and a coordinate-free vacuum burst criterion. A pathway to megawatt-scale vacuum energy release is proposed through coherent slingshot arrays, supported by stability and safety analyses.

Download: Vacuum–Graviton Cascade Theory (PDF)

Verification and Expansion of the Vacuum–Graviton Cascade Framework

This manuscript rigorously validates and extends a bold theoretical structure unifying gravitational Schwinger mechanisms, vacuum–graviton cascades, quantum-gravitational path integrals, and Lee–Yang criticality. It introduces novel axioms—such as the Quantum Hilbert Topos and Dynamic Lee–Yang Criticality Axioms—while employing modern field-theoretic tools including resurgence theory, categorical methods, and holographic dualities. The result is a robust and coherent architecture for controlled vacuum engineering with potential applications in quantum gravity, energy extraction, and cosmological feedback.

Download: Verification and Expansion of the Vacuum–Graviton Cascade Framework (PDF)

Overview: Device-First Quantum Gravity and Vacuum Engineering

This section collects my independently developed manuscripts on vacuum engineering, quantum-gravitational burst dynamics, and modular representation theory for physical systems. These works stem from over a decade of research—from my earliest notes on Lee–Yang zeros and generalized entropy in 2012 to the formal construction of a phase-locked burst-drive prototype in 2025.

Theoretical contributions include the formulation of a generalized uncertainty–driven instability in the spacetime path integral, a rigorous operator algebra for stress-energy amplification, and concrete predictions for lab-scale curvature emission without assuming a specific UV-complete theory. Engineering contributions involve blueprints for coherent stress-energy burst platforms using materials such as diamond and PdD, designed to amplify electromagnetic seed fields into curvature pulses.

While some of the underlying physics may inspire future work in propulsion or inertial control, the current research is conceptual and exploratory in nature. No operational propulsion system has been constructed or deployed. All designs are presented for academic purposes only and do not include sensitive components, classified data, or hardware governed by ITAR, EAR, or national security classification guidelines.

Disclaimer: These documents are prior art submitted for scientific peer discussion. They do not constitute a weapons system, nor do they rely on proprietary or export-controlled technology. Should downstream applications emerge (e.g., spacetime engineering or advanced propulsion), appropriate regulatory, patent, and ethical reviews will follow.

Download: Generalized Uncertainty, Lee--Yang Zeros, and Vacuum-Burst Curvature Emission (PDF)

Piston-Phased Burst Drive and Curvature Steering

This document presents a comprehensive architecture for burst-driven propulsion based on sequential spacetime deformation, culminating in the design of a “piston-phased” vacuum drive. It formalizes curvature steering using phased lattice actuation, enabling microsecond-scale directional changes without inertial stress. The theory includes derivations of effective acceleration from external frames, strategic CTC configurations, and a modular roadmap toward laboratory-accessible quantum-gravity probes. Applications span propulsion, time-dilation engineering, and quantum field diagnostics.

Download: Piston-Phased Burst Drive and Curvature Steering (PDF)

Multimodal Electromagnetic Sensing for Remote Cognitive Field Reconstruction

This manuscript presents a theoretical architecture for reconstructing neural and cognitive field dynamics using ambient electromagnetic modalities—including radar, BLE, Wi-Fi, mmWave, and ultrawideband systems. The work integrates multispectral sensing, signal unmixing, and inverse field theory to propose a unified, passive approach to human-state estimation. Core contributions include a redshift-matched neural interface model, variational decoding under physiological constraints, and a curvature-aligned extrapolation framework. Applications span non-contact health diagnostics, privacy-preserving affective computing, and remote intention decoding in high-interference settings.

Disclaimer: This document is a redacted academic submission provided for open scientific discourse. Certain technical details have been withheld to comply with U.S. export regulations (ITAR/EAR) and national security guidelines. The research does not contain hardware schematics, classified data, or any system design governed by defense-related controls. All methods are presented for conceptual exploration and are non-operational in their current form. Contact the author for inquiries regarding regulatory, ethical, or implementation review.

Download: Multimodal Electromagnetic Sensing (Redacted PDF)

MSIA: A Modular Symbolic Intelligence Architecture for Zeta-Based Cryptographic Obfuscation

This technical manuscript introduces MSIA, a novel cryptographic architecture that fuses symbolic dynamics, modular trace encoding, and Schottky group theory to achieve robust post-quantum obfuscation. The framework constructs ciphertexts using symbolic trace fingerprints over high-entropy zeta orbits, exploiting deep links between matrix conjugation, trace depth, and Brauer spectral invariants. MSIA formalizes a trapdoor-enabled symbolic transformation layer that resists inversion via aperiodic slot permutations and trace dimension lifting. It also introduces the TS++ parameter set, offering a NIST-compatible foundation for symbolic encryption with controllable complexity and post-quantum security guarantees.

By bridging thermodynamic formalism, modular representation theory, and cryptographic hardness, this paper proposes a new direction for intelligence-grade encryption and trace obfuscation. The architecture provides a modular base for further symbolic AI methods and secure communications protocols grounded in non-commutative zeta dynamics.

Disclaimer: The TS++ encryption framework presented in this work is an academic research prototype intended for scientific discussion only. It is not an officially endorsed or certified cryptographic standard and has not undergone formal security audits. The system is not designed, reviewed, or approved for deployment in production, military, or classified applications. Export, use, or adaptation of this work may be subject to national or international regulations, including but not limited to the U.S. EAR or ITAR. By accessing this material, you agree to use it solely for academic and non-commercial purposes.

Download: MSIA – Modular Symbolic Intelligence Architecture (PDF)

Symbolic Dynamics and Modular Zeta Functions: A Physically-Realizable Quantum Operator Framework

In this work, I present a fully unitary and experimentally accessible extension of my earlier modular quantum framework. By lifting symbolic dynamics from vector spaces over $\mathbb{F}_p$ to Hilbert spaces over $\mathbb{C}^n$, I construct a physically consistent quantum operator model with discrete, cyclotomic-phase evolution.

The core construction revolves around five steps:

I embed symbolic transition matrices into unitary operators $Q \in U(n, \mathbb{Q}(\zeta_p))$ with modular spectra.
I implement these operators using generalized Pauli “clock” and “shift” gates acting on $p$-level qudits.
The resulting gates are constructed over cyclotomic fields and decomposed into native hardware operations.
I extract trace data $\operatorname{Tr}(Q^k)$ using quantum Fourier transforms and phase-readout methods.
Finally, I realize modular spectral behavior via quantum walks on graphs with adjacency derived from symbolic systems modulo $p$.

This approach yields concrete zeta functions, trace formulas, and cryptographic primitives—while remaining grounded in the architecture of modern quantum computing.

On Physical Realizability:
Unlike earlier abstract finite-field models, this framework supports actual implementation. It can run on trapped-ion systems, photonic qudit arrays, superconducting cavities, and more. I’ve also outlined pathways to incorporate stabilizer codes, GKP grid encodings, and digital emulations using standard qubit registers. There’s no need for anyonic braiding or topological quantum field theory—just modular arithmetic expressed through coherent quantum logic.

Download the full manuscript:
Symbolic Dynamics and Modular Zeta Functions (PDF)

Entropic–Gravitational Cryptodynamics: Encryption, Anyonic Computation, and Vacuum Instabilities

This work develops a unified axiomatic framework that connects symbolic encryption, gravitational curvature, and vacuum instabilities through the lens of entropy amplification. Drawing from principles in cryptography, quantum gravity, and topological quantum computing, it formalizes how encryption can function simultaneously as an entropy amplifier and a geometric curvature inducer.

The manuscript interprets vacuum bursts and Schwinger pair production as cryptographic resolution events governed by a Generalized Uncertainty Principle (GUP). It proposes braid group logic gates in anyonic systems as natural physical substrates for implementing this gravitational–cryptographic duality. Key axioms equate symbolic complexity with spacetime curvature and topological entropy, offering new pathways to control vacuum instabilities through computational and physical means.

By bridging modular trace obfuscation, GUP-corrected thermodynamics, and partition function zero dynamics, this research sets a foundational platform for designing burst-array devices capable of probing the entropy thresholds of non-equilibrium quantum systems.

Download: Entropic–Gravitational Cryptodynamics (PDF)

Critical Scaling in Hyperbolic Attention Mechanisms

This project presents a comprehensive, mathematically rigorous framework for hyperbolic attention mechanisms in transformer architectures, linking them to statistical mechanics, spectral theory, and fractal geometry. It offers an explicit derivation of the critical inverse temperature $ \beta_c(\delta, \kappa, \mathcal{T}) $ in terms of fractal dimension $ \delta $, curvature $ \kappa $, and topological connectivity $ \mathcal{T} $.

The manuscript unifies concepts from hyperbolic geometry, partition functions, Laplace–Beltrami operators, and transformer design. Key contributions include:

An exact formula for $ \beta_c \sim \exp(C(\kappa)\,\delta\,r_{\mathrm{eff}})/\lambda_{\max}(\mathcal{T}) $
Spectral density derivations based on fractal boundaries
Dynamic attention scaling protocols minimizing energy dissipation
Extended discussions on quantum security, Langlands correspondence, and Lorentz adaptations

Download the full paper: Critical Scaling in Hyperbolic Attention Mechanisms (PDF)

Supplementary Notes on Thermodynamic Formalism and Hyperbolic Dynamics

In follow-up to the explicit dimension formula $ \dim \mathcal{H}(\Lambda_\Gamma) = \frac{\ln(2m - 1)}{r_{\mathrm{eff}}} $, I include supplementary materials that frame the result within the broader context of symbolic dynamics, thermodynamic formalism, and Lie-theoretic flows. These connections provide a more unified and rigorous perspective on the structure of limit sets, their self-similarity, and the role of PSL(2,$\mathbb{R}$) isometries.

Key Topics Covered in These Notes

The sum $ \sum_{|g| = n} |g'(z)|^\delta \sim 1 $ as a bridge between symbolic dynamics and fractal geometry.
A derivation of critical exponents via pressure-zero arguments, connecting partition functions to Hausdorff dimension.
A proof that all Schottky group orbit branches approach the boundary circle at a uniform exponential rate, ensuring well-formed fractal limit sets.
Differential equations and flow models in the upper half-plane and Poincaré disk that interpolate discrete isometries.
Rigorous constructions of Patterson–Sullivan measures and their decay properties under the group action.

These results are particularly powerful when analyzing the dynamics of Schottky subgroups of PSL(2,$\mathbb{R}$) through the lens of the Lie algebra $ \mathfrak{sl}(2,\mathbb{R}) $. The uniform convergence to the boundary and equivalence of hyperbolic displacement among conjugates ensures that side-branch instabilities do not distort the limit set’s dimension.

Additional Lecture Notes:

Together, these documents provide a rich and self-contained exposition suitable for advanced study in geometric group theory, dynamical systems, spectral theory, and their applications to mathematical physics and quantum information.

Supplement: First-Level Symmetry and Exact Hausdorff Dimension

This supplementary note highlights a key insight: if the initial generators of a Schottky group exhibit complete first-level symmetry—that is, the magnitudes of their derivatives at a common base point $ z_0 $ satisfy $ |T_i'(z_0)| = \text{const} $—then the entire Hausdorff dimension of the limit set can be determined using only this first-level data.

Specifically, under these conditions, the zero-pressure equation \[ \sum_{|T_i| = 1} |T_i'(z_0)|^{-\delta} = 1 \] yields an exact solution for the Hausdorff dimension $\dim_H(\Lambda_\Gamma) = \delta$, without requiring data from deeper iterates.

Even when perfect symmetry breaks at higher levels, as long as bounded distortion holds, the contribution of higher iterates remains controlled. The result is robust: full symmetry at the first level ensures the validity of the explicit formula throughout the group’s dynamical hierarchy.

This observation strengthens the theoretical justification for using well-distributed Schottky generators to derive explicit, closed-form dimension formulas.

This work provides a novel and explicit closed‐form formula for computing the Hausdorff dimension of limit sets associated with Schottky groups that are well‐distributed—that is, those with uniformly arranged generators. In this framework, the Hausdorff dimension is given by $$\dim \mathcal{H}(\Lambda_\Gamma) = \frac{\ln(2m - 1)}{r_{\mathrm{eff}}},$$ where m is the number of free generators and r_eff is the effective translation length determined via a rigorous two‐step displacement method.

The study begins with an in‐depth review of classical hyperbolic geometry and builds upon foundational results by Patterson, Sullivan, and Bowen. By using the Bowen–Series expansion alongside symbolic dynamics and ergodic theory, the work shows that the symmetry in generator placement yields a uniform contraction ratio. This uniformity allows for an exact calculation of the fractal dimension of the limit set, overcoming the need for purely numerical methods.

A key insight of the research is that every finitely generated convex-cocompact Fuchsian group can be approximated arbitrarily closely by a well-distributed Schottky group. This approximation not only validates the theoretical approach but also provides a practical method for computing the Hausdorff dimension of more general hyperbolic groups. The paper further extends these ideas to higher-dimensional hyperbolic spaces, opening up new avenues for studying Kleinian groups and their fractal limit sets.

Beyond its theoretical contributions, the explicit dimension formula has significant interdisciplinary implications. In mathematical physics, it connects the fractal geometry of limit sets with the spectral properties of hyperbolic manifolds. In cryptography, the computability of these fractal dimensions can be leveraged to design robust, quantum-resistant protocols. Moreover, the work’s insights into the Fourier decay properties of Patterson–Sullivan measures contribute to a deeper understanding of chaotic scattering and resonances in dynamical systems.

This comprehensive study not only deepens the theoretical understanding of fractal dimensions in hyperbolic geometry but also bridges abstract mathematical theory with practical computational techniques. The explicit formula for the Hausdorff dimension serves as a powerful tool for researchers in geometric group theory, dynamical systems, and related fields.

For a complete and rigorous exposition—including all derivations and proofs—please refer to the full document: Hausdorff Dimension of Well-Distributed Schottky Groups.

Simple Geodesics on Hyperbolic Surfaces: Theory and Applications

My recent note on simple geodesics explores various techniques for understanding geodesics on hyperbolic surfaces. For further details, see the full document Simple Geodesics on Hyperbolic Surfaces: Theory and Applications.

In this survey, we explore the fascinating interplay between number theory, geometry, and dynamical systems. To set the stage, we begin by recalling the classical Prime Number Theorem which describes the asymptotic distribution of prime numbers. This fundamental result motivates analogous asymptotic counting problems in geometry, such as the enumeration of closed geodesics on hyperbolic surfaces.

Several key works form the backbone of our approach. Mirzakhani's groundbreaking study established deep connections between the asymptotic growth of simple closed geodesics on hyperbolic surfaces and the geometry of moduli spaces, while Arana-Herrera provides a modern ergodic-theoretic perspective on counting problems ranging from primitive integer points to simple closed curves. Foundational background on surface topology and mapping class groups is supplied by Farb and Margalit’s A Primer on Mapping Class Groups as well as Martelli’s An Introduction to Geometric Topology. Comprehensive treatments of hyperbolic geometry and its spectral theory are available in Ratcliffe’s Foundations of Hyperbolic Manifolds, Borthwick’s Spectral Theory of Infinite-Area Hyperbolic Surfaces, and Dal’Bo’s work on geodesic and horocyclic trajectories. For additional background in measure theory and the geometry of numbers, see Cassels and Einsiedler--Ward.

References

Dal'Bo, F. (2011). Geodesic and horocyclic trajectories. Springer-Verlag London, Ltd. DOI: 10.1007/978-0-85729-073-1.
Ratcliffe, John. G. (2019). Foundations of Hyperbolic Manifolds. Springer. DOI: 10.1007/978-3-030-31597-9.
Borthwick, D. (2016). Spectral Theory of Infinite-Area Hyperbolic Surfaces. Birkhäuser/Springer. DOI: 10.1007/978-3-319-33877-4.
Martelli, B. (2016). An Introduction to Geometric Topology. arXiv:1610.02592.
Farb, B., & Margalit, D. (2012). A Primer on Mapping Class Groups. Princeton University Press.
Mirzakhani, M. (2004). Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves. Harvard University.
Arana-Herrera, F. (2022). Counting problems from the viewpoint of ergodic theory: from primitive integer points to simple closed curves. arXiv:2202.04156.

Geometry of $ \mathbb{H}^n $: Foundations, Group Actions, and Quotient Constructions

This pedagogically motivated exposition builds a rigorous, example-rich framework for understanding the geometry of $ n $-dimensional hyperbolic space $ \mathbb{H}^n $, with emphasis on its model structures, isometry groups, and the manifold and orbifold topology of the quotient $ \Gamma \backslash \mathbb{H}^n $. Designed for advanced students and early researchers, the document integrates foundational geometric definitions, topological underpinnings, and group-theoretic dynamics into a coherent and visually supported progression.

Beginning with formal models of $ \mathbb{H}^n $ and their curvature structure, the text develops the action of discrete groups $ \Gamma \subset \operatorname{Isom}(\mathbb{H}^n) $ and the construction of fundamental domains. It then rigorously analyzes conditions under which the quotient space inherits manifold or orbifold structure, clarifying local homeomorphism issues through explicit counterexamples and corrections. Applications to Fuchsian and Kleinian groups are explored, alongside discussions of limit sets, proper discontinuity, and metric completeness.

The work is both an educational scaffold and a stepping stone toward research-level understanding of geometric group theory and low-dimensional topology, culminating in staged expansions suited for theoretical physics, modular dynamics, and cryptographic geometry.

Download: Geometry of $ \mathbb{H}^n $ (PDF)

Analytical Deconstruction of the FuTuNiuniu-backed YouTube Propaganda on Trump Tariffs

This forensic intelligence report conducts a high-resolution dissection of a Chinese-language video titled “关税过山车，特朗普究竟想干嘛？” ("Tariff Roller-Coaster: What on Earth is Trump Trying to Do?"), hosted by the influencer channel 小Lin说 and covertly linked to FuTuNiuniu, a Tencent-invested entity operating under the shadow of CCP-aligned information architectures.

Integrating analytic methods drawn from Harvard’s Belfer Center, Yale’s Jackson School, and Georgetown’s Center for Security Studies, this work triangulates control-layer ownership, neuropolitical persuasion techniques, and economic misrepresentations embedded in the video. Through comparative policy diagnostics, empirical falsification using 2025 macroeconomic data, and a reconstruction of a reality-based Trump doctrine, the analysis reveals a precision-guided propaganda mechanism tailored to undermine U.S. tariff logic, weaponize dollar skepticism, and elevate Beijing’s multilateral image.

This is not simply a rebuttal. It is a cognitive shield. A counter-disinformation asset designed to reclaim narrative sovereignty using the very tools exploited by adversaries—only recalibrated for truth. The document concludes with a modular policy blueprint—grounded in selective tariffs, industrial reshoring, fiscal signal theory, and reserve-currency optimization—exposing the strategic coherence behind the much-maligned Trump economic levers.

Download the full report: Analytical Deconstruction Report (PDF)