Original work and further development
Each work begins here with its own text: the question, definitions, assumptions and conclusions of the specific edition. “Full original text” opens the unchanged source. Where an analytical study is available on this site, it appears as a separate continuation.
Mathematical development of FBM, individual articulator studies and re-examination of earlier papers share foundations and can exchange documented results. Each connection requires specific objects and assumptions. Including a source does not retrospectively attribute later Re-audit clarifications to its original text.
The index covers located works from the research map and the additional inventory of 31 October 2026. Entries include canonical references, manuscripts and drafts. Related editions and companion files are grouped; they are not counted as additional independent publications. Sources retain their original titles and language.
01Foundations and monographs
Frame-Bound Mechanics Corpus: Canonical Monograph Layer — Manifest v1.0
The corpus manifest identifies the three canonical monographs, their roles, source editions and citation policy.
Source locations, editions and companions
Πλήρες κείμενο σ. 1–8, ιδίως §§1,3–7,11–13.
Frame-Bound Mechanics: Structural Theory of Articulated Systems — Canonical Theoretical Monograph v1.0
The theoretical reference layer for frame, admissibility, constraints, dominance, regimes and observation.
Canonical identity follows the Manifest. Earlier working editions are listed separately below.
Source locations, editions and companions
Corpus Manifest §3.1, §§5.1–5.2
A separate working edition. Identity with the canonical DOI edition has not been established; its pagination is not transferred to that edition.
Frame-Bound Mechanics: Structural Theory of Articulated Systems — Theoretical Monograph
Earlier manuscript · 25 March 2026
Open this source ↗Frame-Bound Mechanics: Formal Mathematical Core of Articulated Systems — Canonical Mathematical Monograph v1.0
The mathematical reference layer for declared objects, admissible sets, interaction functionals, realization and regime organization.
Canonical identity follows the Manifest. Earlier working editions are listed separately below.
Source locations, editions and companions
Corpus Manifest §3.2, §§5.1–5.2
A separate working edition. Identity with the canonical DOI edition has not been established; its pagination is not transferred to that edition.
Frame-Bound Mechanics: Structural Theory of Articulated Systems — Final Manuscript for Repository Publication
Earlier manuscript · 22 March 2026 · v1.0
Open this source ↗Frame-Bound Mechanics Atlas: Empirical Structure of Articulator Systems — Canonical Atlas Monograph v1.0
The empirical reference layer devoted to articulator traces, contact, friction, dominance and regime classification.
Canonical identity follows the Manifest. Earlier working editions are listed separately below.
Source locations, editions and companions
Corpus Manifest §3.3, §5.3
A separate working edition. Identity with the canonical DOI edition has not been established; its pagination is not transferred to that edition.
Frame-Bound Mechanics: A Structural Theory of Articulator Systems — Atlas Ultra Monograph — Final Edition
Earlier manuscript · 25 March 2026
Open this source ↗Historical companion forms from the Atlas research. These are blank sheets or reference cards, not recorded trials. Proposed categories and thresholds remain source content, without being treated as universally verified criteria.
Articulator Phase Atlas Board (Bench Mapping)
A blank board for placing test identifiers within the source's phase and burden categories.
Open companion ↗Articulator Phase Quick Reference Card
A historical quick-reference card of proposed ITL, dominance and burden classifications.
Open companion ↗Articulator Atlas Log Sheet (Bench Series Recording)
A blank series log for configurations, predicted and observed phases, traces, contact and drag.
Open companion ↗Articulator Bench Audit Sheet (FBMS Atlas Protocol)
A blank test sheet separating configuration, prior phase prediction and subsequent observation.
Open companion ↗FRAME-BOUND SYSTEMS – ATLAS RECORDING SHEET
A blank observation log with fields for configuration, trace, dominance, regime and source-specific indices.
Open companion ↗02Articulators and primitive closure
An introduction to articulator research questions →
Articulators: Mechanical Behaviour and Geometrical Understanding
An extended early work on articulator mechanics, geometrical interpretation and the reactor framework. Its original terminology is retained.
Source locations, editions and companions
Εσωτερικός τίτλος, Existence and Scope Declaration, Part I κεφ. 1, Part II The Reactor.
Frame-Bound Mechanical Analysis of Articulator Systems: Constraint-Defined Equilibrium, Projection, and Topological Regime Structure
Develops a structural account of articulator constraints, equilibrium, projection, proposed topological classes and Atlas coding.
Source locations, editions and companions
Abstract, §§1–4, Declarations / Data Availability, τυπωμένες σ. 7–8.
Constraint Compatibility, Mechanical Bonwill Closure, and Anterior-Induced Regime Transitions in Mechanical Articulator Systems
Develops a constraint-based interpretation of anterior input, posterior compatibility, Mechanical Bonwill closure and occlusal regimes. Defines CROR as Constraint-Regulated Occlusal Regime, and includes proposed mechanical verification conditions and qualitative bench-consistency accounts.
Source locations, editions and companions
§§3–7, pp. 2–9: constraints and proposed minimal closure; §§8–13, pp. 10–15: anterior interaction, posterior separation, regime taxonomy and CROR; §15–15.1, pp. 17–20: minimal formal layer and operational effective descriptors; §16, pp. 20–28: proposed mechanical verification protocol; §17, pp. 28–30: qualitative consistency accounts, explicitly not independent/statistical validation; §18, p. 30; §19, pp. 30–31: scope and discussion
Related formulations and source editions. Grouping does not establish chronological order or equivalence of the texts.
Constraint Compatibility and Anterior-Induced Regime Transitions in Mechanical Articulator Systems
Constraint_Compatibility_and_Anterior_Induced_Regime_Transitions_in_Mechanical_Articulator_Systems.pdf
Open this source ↗Constraint Compatibility, Mechanical Bonwill Closure, and Anterior-Induced Regime Transitions in Mechanical Articulator Systems
MBT
Open this source ↗Constraint Compatibility, Mechanical Bonwill Closure, and Anterior-Induced Regime Transitions in Mechanical Articulator Systems
MBT1
Open this source ↗Constraint Compatibility, Mechanical Bonwill Closure, and Anterior-Induced Regime Transitions in Mechanical Articulator Systems
Constraint Compatibility, Mechanical Bonwill Closure, and Anterior-Induced Regime Transitions in Mechanical Articulator Systems
Open this source ↗Constraint Compatibility, Mechanical Bonwill Closure, and Anterior-Induced Regime Transitions in Mechanical Articulator Systems
Constraint Compatibility, Mechanical Bonwill Closure, and Anterior-Induced Regime Transitions in Mechanical Articulator Systems
Open this source ↗Constraint Compatibility, Mechanical Bonwill Closure, and Regime Formation in Frame-Bound Articulator Systems
3_ (2).pdf
Open this source ↗Constraint Compatibility, Mechanical Bonwill Closure, and Regime Formation in Frame-Bound Articulator Systems
2_ (1).pdf
Open this source ↗Constraint Compatibility, Mechanical Bonwill Closure, and Regime Formation in Frame-Bound Articulator Systems
1_.pdf
Open this source ↗Mechanical Interpretation of Articulator Traces: A Laboratory Study of Trace Similarity, Contact Continuity, and Mechanical Stability
The selected laboratory draft compares trace similarity, contact continuity and mechanical stability in unmounted Hanau H2-type, Dentatus ARD-type and Artex CN-type arrangements.
This edition contains pending equipment details and categorical observations; it is not a record of continuous force or trajectory measurements.
Source locations, editions and companions
Title page and Abstract; §2.1 Study design; §§2.2–2.3 primitive closure and unmounted condition; §2.5 Equipment information; §2.7 Repetition protocol; §2.12 Statistical and categorical analysis; §3 Results; §4 Discussion and limitations; Tables 1–4; Declarations/Data availability; Supplementary Material List (printed p.22).
Related files for the same study.
Supplementary Material — Mechanical Interpretation of Articulator Traces
Companion tables S1–S5 · 3 pages
Open this source ↗Functional Neutral-Guide Behavior in Anatomical Incisal Tables of Fixed-Condyle Articulators: A Geometric Analysis Using a Reference Instrument
A geometric and laboratory study of anterior-guide contact position in a fixed-condyle reference instrument, using wax rims and a magnetic plate.
The wax-rim arrangement remains a distinct study and is not conflated with the unmounted trace-study protocol.
Source locations, editions and companions
Abstract Objective/Materials and Methods; §2.1 Reference Instrument and Configuration; §2.2 Mounting Protocol; §2.3 Functional Articulation; §3 Results, especially §§3.2–3.4 and §3.6; §4 Discussion; §5 Conclusion.
Mechanical Behaviour under Partial Adjustability in Articulator Systems
A conceptual and qualitative study of partial adjustability, parameter perturbations and limits of mechanical interpretation.
Independent study and worked example →
Source locations, editions and companions
Scope & Positioning; §1 Baseline Reference explicitly names Functional Neutral-Guide Behavior; §§2–3 introduction and observed shifts; §§4–5 perturbation and constraint-indexed description; §6 Limits of Interpretability; §7 Non-Extension Statement; Closure.
Fully Adjustable Articulator Systems: Saturation, Interpretive Collapse, and Boundary
An early conceptual argument concerning full adjustability, saturation and interpretive limits, followed by a philosophical epilogue.
Its broad saturation claims belong to the original argument. Their later mathematical re-examination remains a separate task.
Source locations, editions and companions
Scope & Positioning; §§1–3 baseline/full adjustability/saturation; §4 Reactor Saturation and Loss of Interpretive Priority, numbered subparts 1–7; Closure: Where the Mechanical Path Ends; Residency at the Boundary: On the Ethics of Mechanical Limit.
Mechanical Conditions for Articulator Interpretability
Develops the early reactor framework through mechanical interpretability, constraint visibility, functional neutrality and positional provocation.
Definitions and exclusive claims in the early framework are read within their original scope.
Source locations, editions and companions
§§1.1–1.6; §§2.2–2.7; §§3.2–3.6; §§4.2–4.8; §§5.2–5.10
Hanau H as a Frame-Bound Mechanical System
A short symbolic declaration of Hanau H through guide constraints, admissibility, a weighted interaction functional, equilibrium and observation.
Independent analysis of the structural declaration →
Source locations, editions and companions
§§1–3, printed p.1; §§4–9, printed p.2; §§10–12, printed p.3.
Artex CN as a Frame-Bound Constraint System
A symbolic reconstruction of the Artex CN through its posterior constraint, position-dependent anterior constraint, coupling, admissible set and equilibrium selection. It distinguishes the nominal anterior realization from flat or reversed alternatives within the same frame.
Independent study of the anterior constraint →
Source locations, editions and companions
§§1–3.2, p.1; §§3.3–11, p.2
Dentatus ARD as Frame-Bound Mechanical System
A symbolic account of Dentatus constraints, admissibility and equilibrium, proposing parameter-dependent dominance reordering as the basis for threshold behavior and regime transitions.
Source locations, editions and companions
§§1–3 p.1; §§4–11 p.2; §§12–13 p.3
SAM 3 as Frame-Bound Mechanical System
A compact theoretical note on extended constraint freedom, coexistence of admissible states and limits of unique structural attribution. The original title identifies SAM 3; the argument remains a symbolic proposed framework.
The note’s fully adjustable classification is not adopted here as a verified device specification.
Source locations, editions and companions
§§1–7 p.1; §§8–10 p.2
CN Functional Decoding: A Multi-Zone Articulator Model for Neutralized Guidance and Envelope-Based Occlusion
An early manuscript organized around three working zones of the CN incisal table and a proposed functional workflow. It is retained as a historical source, separate from the later frame-bound structural note.
Contains numerical and clinical claims not verified here, and an incomplete reference list. Archival inclusion preserves the original; it does not adopt these claims as established results of current FBM.
Source locations, editions and companions
Abstract; Materials and Methods: Artex CN Functional Zones; Results; References
Biological vs Mechanical Bonwill Triangle — A Structural Distinction in Frame-Bound Articulator Systems
Distinguishes the anatomical Bonwill descriptor from the proposed Mechanical Bonwill Triangle as primitive closure. Develops primitive versus constructed constraints, closure readability, and a closure-preservation formulation of CROR.
Source locations, editions and companions
§§3–4, printed p. 2: biological descriptor versus proposed mechanical closure; §4.1, printed p. 3: constraint decomposition and closure-generation proof sketch; §§5–6, printed pp. 3–4: constructed structure and closure readability; §9, printed p. 5: CROR and closure preservation
Future paper
A working development on invariant primitive closure, constructed geometry, regime boundaries and CROR, with a proposed mechanical examination protocol and a minimal formal synthesis.
The source’s provisional title is retained. CROR here expands to Controlled Regime Occlusal Realization; the Constraint Compatibility work uses a different expansion.
Source locations, editions and companions
§1.1 pp.1–3: invariant closure versus constructed geometry; §1.2 pp.3–6: regime boundaries and state-dependent geometry; §1.3 pp.6–9: CROR as stable regime construction; §1.4 pp.9–12: proposed mechanical verification protocol; §1.5 and axiomatic summary pp.12–17
03Theoretical formulations and extensions
Constraint Theory of Frame-Bound Mechanical Systems — A Structural Axiomatization
Presents the earlier axiomatic formulation of frame-dependent mechanical interpretation and records articulator analysis as its first domain of formal application.
Source locations, editions and companions
Axiomatic Core; Constraint Taxonomy; Reference Reindexing; First Domain of Application / Historical Origin of Formalization / Domain as Application, Not Foundation
Generalized Frame-Bound Systems Theory (GBST) — A Structural Axiomatization of Constraint-Defined Systems
Develops a domain-independent axiomatic language for constraint-defined systems, using frame, admissibility, dominance, evaluation, observation and regime organization.
Source locations, editions and companions
§2 p. 2; §3 pp. 2–3; §§4–5 pp. 3–4; §7 p. 5
Constraint Topology and Regime Formation in Frame-Bound Mechanical Systems — A Structural Axiomatization
Relates constraint topology to regime formation, carry-over and structural re-examination within its stated axiomatic framework.
Source locations, editions and companions
Title page and Abstract; §§1–7, especially §2 Unified Boundary Axiom, §4 Carry-Over Theorem, §5 Constraint–Authority Revalidation Principle, §7 Global Structural Consequences and Falsifiability. Public positioning is in T07 front matter pp. 2–4.
Technical Supplement: Regime Extensions and Structural Validation Layers
Develops regime extensions and structural checking layers, including sub-frame birth, certificate tiers and digital degeneracy.
Certificate refers to the source’s theoretical checking system. Its reference to Core v1.0.1 is not a version number for this supplement.
Source locations, editions and companions
Title page and Abstract; Appendix A Sub-Frame Birth & Regime Disjunction; Appendix B Certificate Tiers & Progressive Regime Erosion; Appendix C Digital Degeneracy & Solver-Mediated Regime Mapping; Appendix D Domain Application Layer; Structural Architecture Map.
Constraint Topology, Regime Formation, and Structural Validation Operators in Frame-Bound Mechanical Systems — A Public Technical Supplement to the Frame-Bound Mechanics Corpus
A consolidated technical supplement bringing together constraint topology and regime extensions, with explicit references to the canonical corpus.
The SSRN label is a source statement, not confirmation of an active record or peer review.
Source locations, editions and companions
Front Matter p. 1 title/status; p. 2 SSRN Abstract and Contents; p. 3 Historical and Corpus Positioning Note / Scope and Boundary Note; p. 4 Public Canonical Roots / DOI Anchors; Part I and Part II.
Comparative Structural Classes of Frame-Bound Systems
Proposes three comparative classes—reciprocal plateau, geometric channel and saturated multi-constraint systems—using admissibility, dominance and observation as comparison axes.
Source locations, editions and companions
System Form and Classes I–III p. 1; Projection and Identifiability / Failure Modes p. 2
Closure Deviation and Structural Validation in Constraint-Defined Systems
Proposes a formal distinction between declared and effective constraint sets, a closure-deviation operator, and an in-closure / boundary / deviation classification for structural interpretation.
The one-sided set-difference definition needs specific re-examination before supporting a conclusion of full constraint-set equality.
Source locations, editions and companions
§§2–3 p.1: system, admissible set, observation and deviation operator; §§4–5 p.2: proposed consistency conditions and classification; §§6–8 p.3: interpretation, scope and conclusion
Related formulations and source editions. Grouping does not establish chronological order or equivalence of the texts.
Closure Deviation and Structural Validation in Constraint-Defined Systems
Closure_Deviation_and_Structural_Validation_in_Constraint_Defined_Systems_.pdf
Open this source ↗04Mathematical development
Independent pathway: foundations, Re-audit and mathematical cases →
Minimal Structural Proofs of Projection Non-Identifiability
Minimal mathematical constructions separating structure, realization and observation. Model II is developed independently in the mathematics section.
Independent mathematical reading →
Source locations, editions and companions
Appendix A.1–A.5; Model II §A.2, PDF 1–2
On the Non-Identifiability of Constraint-Defined Systems from Geometric Observations
Formulates identifiability through fibres of the observation map. Its argument assumes distinct states with the same observed image.
Independent mathematical reading →
Source locations, editions and companions
§3 PDF 1–2; §§4–6 PDF 2; 15 April 2026
FBM-EXT-01A — Πλήρης δομική δήλωση και προέλευση της πρόσθετης πληροφορίας
Fully declares the positive-weight family of Model II, separating positional information from an independently available, normalized reaction that identifies the common scale.
Source locations, editions and companions
Family and target pp.1–2; equilibrium p.3; scaling pp.3–4; multiplier inverse pp.4–6; normalization and availability pp.6–8; ideal mechanical interpretation pp.9–18.
FBM-EXT-01B — Δηλωμένη διαταραχή, ανάκτηση κοινής κλίμακας και παράθυρο διατήρησης της admissibility class
Studies identification from an initial configuration and response to a known perturbation, and when a common test can remain within the interior admissibility class.
Place in the mathematical development →
Source locations, editions and companions
Declared family pp.1–2; perturbation choice pp.2–3; response and preservation pp.3–4; EXT-01B-1 pp.4–5; calibration pp.6–7; EXT-01B-2 pp.7–8; error/preservation window EXT-01B-3 pp.9–10; boundary saturation/history pp.10–11; scope pp.12–13.
FBM-EXT-01C — Ανεξάρτητη δομική πληροφορία και μοναδικός προσδιορισμός των βαρών
Establishes a rank criterion for identifying weights from interior constrained equilibria with known constraints, interaction functions and loads, and compares different constraint organizations.
Full study of independent information →
Place in the mathematical development →
Source locations, editions and companions
Information definition p.1; family/hypotheses pp.2–3; projected stationarity pp.3–4; EXT-01C-1 pp.4–6; relation to A/B pp.6–8; scaling pp.8–9; common-displacement example pp.9–11; preservation/error limits pp.11–13.
FBM-EXT-01D — Δεσμευμένοι περιορισμοί, αντιδράσεις και γεωμετρία των συμβατών βαρών
Extends the study to boundary-supported equilibria. Admissible directions yield equations and one-sided inequalities that determine the compatible weight set.
Place in the mathematical development →
Source locations, editions and companions
Interior/boundary distinction pp.1–3; Model II boundary and reaction pp.3–5; declared general family pp.5–6; EXT-01D-1 p.7; finite system and EXT-01D-2 pp.7–9; two-boundary singleton example pp.9–12; finite uncertainty pp.12–13; scope p.14.
FBM-EXT-01E — Επιμέρους μηχανικός προσδιορισμός, δομικά αδιάκριτες κατευθύνσεις και όρια επέκτασης των εξετάσεων
Distinguishes identification of a declared mechanical quantity from recovery of every weight, and examines ambiguities that persist across an entire load family.
Place in the mathematical development →
Source locations, editions and companions
Target Q and EXT-01E-1 pp.1–4; compact convex family pp.4–5; all-load equivalence EXT-01E-2 pp.5–6; common-displacement example pp.7–9; nonlinear example and EXT-01E-3 pp.10–13; changed admissibility pp.13–15; scope pp.15–17.
05Wider mechanical and digital fields
Structural Limits of Geometric Reconstruction in CAD/CAM Systems
Examines whether a generated geometry identifies its producing design system, distinguishing geometrically compatible reconstruction from recovery of the original generative organization.
Source locations, editions and companions
§2 p. 2; §§4–5 pp. 3–5; §6 pp. 5–6
A Mechanical Delimitation of Digital Prosthodontic Environments
Sets out the early reactor framework's proposed limits for interpreting digital prosthodontic geometry, focusing on constraint visibility, neutrality and external mechanical verification.
Source locations, editions and companions
Αρχική δήλωση σκοπού και §§1–5.
Related files for the same study.
Regime Identification in Contact Robotic Systems: Structural Limits of Observation-Based Inference
Examines contact regimes as active-constraint organizations and distinguishes matching an observed output from identifying the contact regime that generated it.
Source locations, editions and companions
§§2–3 pp. 2–3; §5 pp. 4–5; §7 p. 6
Solver Dependence in Contact Multibody Systems: Structural Limits of Numerical Neutrality
Distinguishes declared contact constraints from the effective organization produced by numerical resolution, and proposes a framework for discussing solver dependence beyond output agreement.
Source locations, editions and companions
§§2–4 pp. 2–4; §§5–7 pp. 4–7
Regime Structure and Constraint Revalidation in Suspension Systems
Studies suspension support paths, engagement of travel limits and coupling elements, and the distinction between response compatibility and support-regime identity.
Source locations, editions and companions
§§2–3 pp. 2–3; §5 pp. 4–5; §8 p. 7
Boundary Activation and Constraint Revalidation in Landing Gear Systems
Examines landing-gear support organization during contact, compression, rebound and limit engagement, with a distinction between event traces and structural regime classification.
Source locations, editions and companions
§§2–3 pp. 2–4; §§5–7 pp. 4–7; §8 pp. 7–8
Regime Transition, Carry-Over Failure, and Sub-Frame Birth in Hybrid Constraint Systems
Proposes a classification of hybrid transitions through admissible regime relations, distinguishing variation, boundary-sensitive erosion, overlap and disjoint reorganization.
Source locations, editions and companions
§3 p. 3; §§4–7 pp. 3–7; §10 pp. 9–10
Re-audit and continuing research
The Re-audit provides a link of examination and clarification between the foundations and new development. Each new study identifies the original passage it examines, the review distinction it uses and the result it adds. The original paper remains available as an independent source.
- Study of the mathematical Re-audit →
Specific passages, editions and distinctions: admissibility, realization, dominance, binding status and observation.
- Autonomous mathematical development →
Model II, identifiability and the EXT-01A–E sources, with their own assumptions and research questions.
- The independent Hanau study →
Development from the paper’s own declaration, explicitly distinguishing the original source, present analysis and outstanding mechanical specialization.
Further developments of CN, Dentatus, SAM and the other works will be added to their respective entries as specific analyses become available. Their autonomy allows the field to deepen at different levels through documented connections.