Published
1 article
Published
The sacrosanct canine: Considerations for the extraction of severely displaced, or impacted maxillary canine(s)
CRANIO® · 2025
Challenges the clinical orthodoxy that maxillary canines are always worth heroic treatment efforts. Provides a framework for identifying when extraction of a severely displaced or impacted maxillary canine — with first premolar substitution — is biomechanically sound, functionally equivalent, and the better long-term choice for the patient. Argues there is no robust scientific support for the concept of canine-protected occlusion as a categorical contraindication to extraction.
Orthodontic Biomechanics — In Preparation
13 manuscripts
First-principles computational mechanics derived from a validated open engine. Each result regenerates from a reproducible script; no numbers are hand-transcribed. Manuscripts are in preparation for peer-reviewed submission. The underlying engine is available through the First Principles Designer.
Arc 1
Force Series
6 manuscripts
P1
Anchorage is mechanics-dominated: a first-principles resolution of the full indeterminate cantilever system
Periodontal support is second-order and bone type negligible in determining anchorage outcomes — clinician-controlled mechanics is the dominant variable. Resolves the indeterminate force-system problem set aside in prior literature.
P3
There is no single optimal orthodontic force: the force optimum is a PDL-pressure threshold proportional to root surface area
No universal optimal force exists. The threshold at which PDL compression reaches capillary pressure equals 0.26 g·mm−2 × root surface area — modulus-invariant and patient-specific. Returns diminish beyond it.
#2
Root surface area as anchorage currency: why Tweed classes are bands of one ratio and absolute anchorage requires a TAD
Root area simultaneously sizes safe force and anchorage capacity. The Tweed A/B/C classification reduces to bands of a single root-area ratio. Tooth-borne anchorage loss is never zero; skeletal (TAD) anchorage is the only true absolute.
#3
PDL-stress efficiency peaks at bodily translation: a first-principles account of moment-to-force ratios and why they matter
Bodily translation maximises the ratio of useful tooth movement to PDL stress. Tipping and root-movement modes concentrate stress and tolerate far less applied force for the same movement target.
#5
The efficiency pyramid quantified: treatment efficiency as a product of five weight-free factors
η = ηkinematic × ηuniformity × ηanchorage × ηuncertainty × ηcoupling. Each factor ranges 0–1 with no fitted weights. Whole-arch coupling (continuous arch retains 36%) is folded in; the framework identifies where treatment entropy comes from.
Cap.
Biomechanics is the lever, the periodontium the envelope: a first-principles framework for orthodontic force systems
Synthesis perspective: the clinically controllable force system is derived from mechanics; the periodontium is the biological envelope that determines the rate and ceiling of response. Cites the companion series and situates it within the broader field.
Arc 2
3D Mechanics
5 manuscripts
S27
Anchorage is a tensor, not a scalar: a 6-DOF stiffness account of the indeterminate anchorage problem
Resistance to displacement is a 6×6 PDL stiffness tensor spanning all force and moment degrees of freedom. The scalar Tweed anchorage classification is a projection of this tensor onto one axis. Absolute anchorage requires infinite stiffness in all six DOF — only skeletal.
S30
Trading geometry for force in intrusion: the horizontal-force substitution law Fh = (b/h)·Fv
A horizontal chain or NiTi spring substitutes exactly for the intrusion-arch point-of-application shift, with an irreducible retraction component. A constant-force spring beats a decaying chain between visits. Midline mechanics is the transverse twin of the same relationship.
S28
Closed-form 3D side-effect atlas: yaw, torque, and the engagement gate in cantilever mechanics
Closed-form expressions for all three-dimensional side effects of cantilever loading: yaw = b·Fy, torque = b·Fz, height-invariant. Tip-back leaks yaw only; intrusion leaks torque only. Bracket engagement is the torque gate: a 16×22 wire in a 22-slot fails to engage.
S31
Prescription as anchorage: what wire and bracket geometry alone can and cannot do as a differential lever
A full archwire with prescription (including reverse-Rx: flipped incisors, swapped canines) is a real auxiliary-free differential couple. It cannot be a force source: protraction still requires a separate force element. Minimum anchorage in the strict sense therefore still needs an independent force source.
S26
Resorption-risk topography: how the centre of rotation sets where PDL compression peaks
The movement type, via the centre of rotation, determines the spatial pattern of PDL compression: tipping concentrates stress at the crest (apex spared); root movement and torque produce concentrated apical peaks; translation is diffuse. Notably, intrusion is spatially uniform — its clinical apical resorption is not an elastic-concentration effect.
Arc 3
Validation
1 manuscript
P2
A reduced-order biomechanics engine reproduces high-fidelity 3D force systems and textbook limits without tuning
The engine reproduces a published three-dimensional V-bend force-system measurement (load-cell data), center of resistance at 42% of root length, and M:F-to-center-of-rotation mapping, with no parameter fitting. Addresses the contemporary validation gap: in-silico models are rarely validated against clinical measurements.
Theory
Periodontal Control Theory
1 manuscript
PCT
The periodontal ligament is the controller, bone the effector: a unified control-theoretic account of tooth movement
A position paper unifying four established findings — PDL elastic equilibrium, perfusion-limited rate response, anchorage as a stiffness tensor, and the mechanostat — into one falsifiable framework with a modulus-invariance spine. Challenges the bone-centric narrative: bone remodeling operates at strain levels 300× below the mechanosensing threshold during orthodontic loading. The PDL, not bone, is the closed-loop controller of tooth position.
Software & Research Tools
1 library
Available
First Principles Designer — A validated open research library for dental and orthodontic biomechanics
Source-available · v0.2.0 · 2026
A standalone, citable research library comprising 30 modules covering the full finite periodontal-ligament engine, tooth-movement trajectory simulation, resorption-risk modeling, and dental materials physics. Validated against published textbook values for center of resistance, moment-to-force ratios, tipping vs. bodily movement, and rotational mechanics. Every number in the associated manuscripts regenerates from a script against this engine; no results are hand-transcribed. Citation required for research use; commercial and clinical-practice use requires a separate license.
Quantitative Finance
10 working papers
Outside clinical practice, I research the failure modes of classical statistical tools when applied to fat-tailed return distributions — the regime that describes most individual U.S. equities. The work below is a 10-paper series on SSRN covering tail estimation, signal validation, ergodicity, risk measurement, and portfolio epistemology.
Series
Fat-Tail Inference in Financial Markets
715 U.S. equities · 2009–2025
P1
Payoff asymmetry predicts forward drawdown outcomes; the signal survives look-ahead cleaning, subsample tests, and a six-factor horserace.
P2
FAT_STRUCTURAL and FAT_BINARY stocks share identical Hill estimates yet diverge 13.7 percentage points in expected value — the Hill estimator is not a sufficient statistic for return prospects.
P3
The Hill estimator is formally inconsistent for binary-jump processes; any tail-index computation requires source-of-tail pre-classification to avoid category error.
P4
Two Problems, One Incomplete Fix: Newey-West Corrections Under Fat-Tailed Returns
Newey-West corrects serial correlation but amplifies fat-tail bias; the two sources of invalid inference require separate treatments, not a single adjustment.
P5
A sequential nine-gate gauntlet for distinguishing robust signals from overfitting artifacts, with worked examples drawn from the payoff asymmetry anomaly.
P6
The time-average/ensemble-average gap — ergodicity economics in the Peters sense — is calibrated directly from the empirical tail exponent across the full equity cross-section.
P7
At the empirical median α̂ = 2.69, the MinTRL via Sharpe ratio is approximately 1,100 years; conventional 3–5-year due-diligence windows have formally zero statistical power for most individual equities.
P8
The classical Gaussian drawdown formula breaks for α ≤ 4; a correction factor Φ(α,T) grows with horizon and diverges as α → 2 — risk models that ignore this systematically underestimate drawdown.
P9
FAT_BINARY events (FDA approvals, binary regulatory outcomes) occupy a genuine ontological category distinct from both Black Swans and power-law extremes; a three-category formal taxonomy follows.
P10
Portfolio optimization is not merely imprecise under fat tails — it is epistemically unavailable; an information-theoretic lower bound establishes the barbell as the formally derivable rational response.