A Periodic Table of Detachment Modes: Systematic Classification of Threshold Crossing Phenomena in the Emergence Canvas Model

The Emergence Canvas Model proposes that all physical phenomena arise from a single mechanism—threshold crossing—governed by eight primitive concepts and four dynamical pillars. Seventeen detachment modes have been identified as the specific ways threshold crossing manifests across particle physics, cosmology, gravity, and quantum mechanics. This paper demonstrates that these seventeen modes are not an ad hoc collection. They are the first filled cells of a periodic table organized by two quantum numbers: the differential order of the waveform feature that triggers detachment, and the physical domain in which the threshold crossing occurs. The Table Structure The table has ten rows (0th through 9th differential order) and six columns (Particle Physics, Cosmology, Gravity, Quantum Mechanics, Astrophysics, Condensed Matter). The rows follow a natural hierarchy from amplitude (zeroth order) to non-renormalizable operators (ninth order). The columns span the major domains of physics from the most fundamental to the most emergent. What the Table Shows · Seventeen known modes are placed in their cells, with status labels ranging from Proved to Framework Established. These include plateau, threshold, cusp, jump, curvature, resonance, beat, phase-locked, collective resonance, angle-triggered, topological, harmonic-cascade, gravitational collapse, capacity ejection, phase rotation, and dimension-5 threshold.· Approximately 29 missing modes are predicted by the table's structure. Each empty cell corresponds to a real physical phenomenon whose threshold-crossing mechanism is specified by the Canvas Model's primitives and pillars. Examples include the attractor-convergence mode (governing how parameters reach their Feed dynamics attractor values), the confinement completion mode (full QCD binding dynamics), and the Tier-2 nucleation mode (deriving the exact spectral index correction).· Seven to ten cells are argued to be genuinely empty—combinations of differential order and physical domain that do not support detachment modes. What the Table Achieves The periodic table demonstrates that the Canvas Model is generative rather than ad hoc. Its mechanisms are organized by general principles. Its remaining incompleteness is structured, systematic, and tractable. The seven remaining gaps in the Canvas Model's completion map directly to specific empty cells. Filling these cells is a well-defined research program that uses the same primitives, the same threshold condition, and the same composition mode machinery as the known modes. The Mendeleev Analogy The paper draws a structural analogy to Mendeleev's periodic table of the elements (1869). Mendeleev organized known elements, predicted unknown ones, and left gaps that guided experimental discovery. The detachment mode periodic table does the same: it organizes known threshold-crossing mechanisms, predicts unknown ones, and provides a map of the research program ahead. The empty cells are the most important feature—they are specific, testable hypotheses about the existence of physical mechanisms. The Path to Completion The paper provides a complete gap-to-cell mapping. Each of the seven remaining gaps in the Canvas Model's completion is shown to correspond to specific empty cells. For example: · The Feed dynamics attractor solution requires four cells: attractor-convergence modes in particle physics, cosmology, and gravity, plus triple/quadruple resonance rates.· The hadron spectrum requires confinement completion modes (meson formation, baryon formation, flux tube breaking).· The exact n_s coefficient requires the Tier-2 nucleation mode.· Quantum foundations requires the Born rule, collapse, decoherence, and spin modes. Why This Matters The periodic table transforms "we have gaps" into "we have a map of exactly which cells to fill, in what order, to close each gap." It makes the Canvas Model's incompleteness structured, systematic, and testable. If the predicted modes can be specified using the same primitives and threshold machinery as the known modes, the Canvas Model is validated as a generative framework. If specific cells cannot be filled, the framework is falsified in a specific, identifiable way. Keywords: detachment modes, threshold crossing, periodic table, Emergence Canvas Model, differential order, physical domain, gap resolution, Mendeleev analogy, generative framework, theory of everything