William Chuang —
Research Portfolio

A unified mathematical framework for low-intensity focused ultrasound (LIFU) neuromodulation targeting the nucleus accumbens (NAc) in substance use disorder, coupled to the λ-Stack as a real-time safety and control architecture. Situated against the current U.S. burden of disease: 48.4 million past-year SUD in 2024 (SAMHSA); 79,384 drug overdose deaths including 54,045 opioid-involved (CDC 2024).

The paper treats the first published clinical signal (Rezai et al., 2025: 91% mean craving reduction over 90 days, n=8, open-label) with appropriate discipline—as a mechanistically coherent preliminary signal warranting controlled confirmation, not as established efficacy. Core contribution: a mathematics-first safety, observability, and control architecture for NAc-targeted LIFU, with formal adverse-event analysis and transparent parameter reporting.

A decision-analytic memorandum for senior ecclesial and policy principals whose remit includes Taiwan, China, the Holy See, or long-horizon institutional strategy. The governing question is strategic, not theological: does the Holy See’s current public diplomatic language about Taiwan create a measurable risk to Catholic mission, and if so, which course of action best protects Taiwan’s Catholic community while preserving engagement with China?

The paper distinguishes three often-conflated things: the Holy See’s legal position on sovereignty, its diplomatic terminology (e.g. “China (Taiwan)”), and how that terminology is received on the ground in Taiwan. It introduces explicit crisis criteria, a quantitative scenario model projecting baptisms under five strategic paths to 2106, and a threshold instrument answering how large China-side gains would need to be to justify Taiwan-side costs. Anchored in the “Poland argument”: Taiwan can serve as the free institutional base for a future China mission—but only if the Church first escapes the current 2% ceiling imposed by civic-register misalignment.

Maps confirmed capital flows between Western institutional investors and entities linked to PRC or Russia state structures through regulatory designations, audited financials, court records, and official corporate registries. Sources include SEC Form 13F and N-PORT filings, Federal Register publications, IRS Form 990 disclosures, Companies House and Swiss commercial register records, Vatican financial statements, and agency press releases. Only confirmed, documented holdings appear; inferences are tagged explicitly and withheld from primary tables.

Institutions covered: Knights of Columbus Asset Advisors (KoCAA), CommonSpirit Health, Ascension Health / Ascension Investment Management, HSBC Holdings, the Holy See (IOR, APSA, Peter’s Pence), and Aid to the Church in Need as positive control. The foundational policy document examined is the USCCB Socially Responsible Investment Guidelines (2021). Regulatory designation is reported as a fact of administrative record, not as a finding of wrongdoing against any investor.

Conventional governance assessments rely on self-reported approval surveys that authoritarian governments can suppress, fabricate, or selectively publish. This index substitutes five indicators whose primary data sources lie outside the scored government’s jurisdiction: emigration and wealth-migration flows (recorded by receiving countries), satellite-verified GDP fidelity (NASA/ESA nightlight data), excess-mortality transparency (EuroMOMO, WHO), economic misery (Hanke Annual Misery Index, Johns Hopkins), and foreign-exchange black-market premium (parallel rate indices). The composite score is expressed to one decimal place, ensuring every entity carries a unique rank. Approximately 195 sovereign entities are scored as of 2025–early 2026.

Key findings: Taiwan (95.4) holds the world’s lowest misery index (HAMI 2.1) and scores among the highest-legitimacy governed entities by any indicator combination. Russia (16.8) fails all five simultaneously. Venezuela (7.2) anchors the floor among nominally democratic states. The U.S. scores 82.4—reflecting structural institutional strength, not incumbent satisfaction. Includes an interactive dashboard with regional filters, a complete indicator table, and a 10,000-word country-by-country analytical commentary written at senior foreign-service and intelligence-community standards.

The term 中華 is the C in both the Republic of China (中華民國) and the People’s Republic of China (中華人民共和國). It is not an ancient ethnic label. It was assembled as a deliberate modern political category in the late Qing period by the Changzhou School of Thought (常州學派)—a five-generation intellectual lineage running from 莊存與 (1719–1788) through to Kang Youwei (1858–1927), the architect of the Hundred Days’ Reform— working from New Text Confucian hermeneutics to coin 中華 as a civilizational umbrella transcending Han ethnicity alone.

The study traces that construction from its philological and etymological roots (中 + 華 = not “the central race” but the central flowering), through nine centuries of Franciscan, Jesuit, and Portuguese missionary contact with the Jiangnan literati world, the Southern Ming Catholic court (Empress Dowager Helena’s 1650 letter to Pope Innocent X, preserved in the ARSI), the cruciform geometry of the character 華 and its convergence with the Jerusalem Cross, and the diaspora thread connecting Hong Kong, Lukong, Sun Yat-sen’s 香山, and Honolulu. Culminates in the entry of 中華 into the official names of both successor states of the Qing.

A three-part integrated framework addressing AI-driven scientific replication threats and law-bounded U.S. responses. Large language models (LLMs) and related systems are the primary vector examined. Portion I delineates PRC AI-assisted “scientific cloning”: centralized pipelines that learn from foreign research and redeploy results across dual-use vectors—with operational mechanics, translation pathways, and indicators for Western R&D exposure. Portion II outlines a law-bounded Manhattan-class architecture preserving U.S. scientific cognition under strict civil-liberties constraints, including opt-in Prospective Cognition & Tacit Pathways (PCTP), a Secure Compute Utility, and simulation-first Mirror Prototype Labs. Portion III provides the unified statutory backbone (CCSA), codifying lane separation, provenance-by-default ModelOps, and independent oversight with bright-line prohibitions.

Legal notice: educational planning concepts only. Any real-world activity requires explicit statutory authority, independent oversight, and compliance with U.S. constitutional, statutory, and international frameworks. Export-control regimes (ITAR/EAR/MTCR) may apply.

The primary research output of Logarchéon: a mathematically rigorous proof that any scalable Artificial Superintelligence operating in the real world requires, at the architecture class level, three independent mechanisms — CEAS-class nonlocal coordination, Ψ-class causal operator inference, and GRAIL-class invariant geometric representation. The necessity claims are theorems, not assertions; each addresses an independent obstruction proved via graph theory, causal identifiability, and orbit coverage.

Materials include ~264 pages of graduate-seminar lecture notes (v18), a 94-cell Colab implementation (Tier-A v5), a 25-claim patent draft, and a complete ANI-vs-ASI certification checklist requiring triadic ablation and 20 closed-loop recursive self-improvement cycles. U.S. Provisional 64/067,703 filed; non-provisional in preparation. Portfolio: 9+ applications filed 2025 across ASI architecture, MIA, CEAS, operator-theoretic verification, and related methods.

Explicit closed-form formula for the Hausdorff dimension of limit sets of well-distributed Schottky groups: dim ℋ(Λ_Γ) = ln(2m−1) / r_eff, where m is the number of free generators and r_eff the effective translation length. Anchored in Bowen–Series expansion, symbolic dynamics, and ergodic theory. Extended to higher-dimensional hyperbolic spaces (Kleinian groups). Key result: every finitely generated convex-cocompact Fuchsian group can be approximated arbitrarily closely by a well-distributed Schottky group.

Rigorous, example-rich framework for n-dimensional hyperbolic space, emphasizing model structures, isometry groups, and manifold/orbifold topology of Γ\ℍⁿ. Covers Fuchsian and Kleinian groups, limit sets, proper discontinuity, and metric completeness. Educational scaffold toward research-level understanding of geometric group theory and low-dimensional topology.

Comprehensive framework linking hyperbolic attention mechanisms to statistical mechanics, spectral theory, and fractal geometry. Explicit derivation of β_c(δ,κ,𝒯) in terms of fractal dimension δ, curvature κ, and topological connectivity 𝒯. Key formula: β_c ∼ exp(C(κ)δr_eff)/λ_max(𝒯). Extends to Langlands correspondence and Lorentz adaptations.

Replaces SDE/PDE-first pipelines with a finite-machine operator view: learn a closed-loop decode Ψ, lift to T=Π_VΨΠ_V, split T=D+N, embed to returns, and do pricing/neutrality as orthogonal projections. Black–Scholes appears as semigroup spectral pricing; risk-neutral change is a positive conjugation that preserves certified cycles.

Unifies learned closed-loop state maps with no-arbitrage pricing. Establishes CAPM/FF as L² projections, builds operator-informed factors from cycle modes, and proves Davis–Kahan-style stability for certified edits. Oracle inequality for operator-factor spans; market-neutral projectors; cycle-respecting bootstrap.

Also catalogued in §01 (Policy). Written as a Taiwanese Catholic whose family has been in Taiwan for approximately four hundred years, tracing to the 1626 Spanish Dominican missions that preceded any Chinese civic overlay. Offered under the intercession of Our Lady, Blessed Gerard, and Saint John the Baptist—in the spirit of tuitio fidei et obsequium pauperum.

Accompanies adult Catholics from first questions about plenary indulgences through Scripture, Trent, canon law, the Enchiridion Indulgentiarum, and the 2025–2026 Jubilee. Moves in disciplined steps: biblical foundations, Council of Trent, Catechism, 1983 Code of Canon Law, and practical checklists for living the Church’s teaching in ordinary time. Tone is contemplative rather than sensational; faithful to the Magisterium. Includes an algorithmic “rule of thumb” for aiming at one plenary indulgence per day.

A daily and weekly rhythm of prayer for a lay person inspired by Ignatian spirituality (especially the Examen and Suscipe) and the monastic balance of the Cistercian tradition. Includes a full weekday horarium, busy-day minimum, weekly Principle and Foundation practice, and a sacramental rhythm (~20 days). Times are recommendations, not rigid prescriptions.

Follows the Algerian typeface from early 20th-century foundries through glyphic “tavern sign” usage and Catholic contexts (from tequila bottles to parish doors), before asking what Vatican teaching on sacred art implies for putting a “bar font” on or near the altar. Includes the anagram note: ALGERIAN → EN A GRAIL → “in a grail”—playful word-geometry that resonates with the surrounding themes of glory and inscription.