Convergence: 1. The 25 Nodes
The Claim
Twenty-five nodes document convergent patterns across science.
Definitions
A claim is a proposition. A node is a claim with 14 facets. ID is the identifier. Domain is the field. Pattern is the structure. Mechanism is the process. Scale is the size. Tier is the strength. Source is the citation. Dual is the opposite. Falsifier is the collapse trigger. Rival frame is the competitor. Independence check tests derivation. Pattern type is the class. Axiom map is the link. Load-bearing means the node supports the thesis. Conditional means the node holds under assumptions. Carried means the node is decorative. Convergent means the pattern recurs across non-contacting domains. Borrowed means one domain copied the pattern from another. Independence is the absence of borrowing. Structural means the pattern arises from mathematics, not coincidence. Causal contact means direct influence between domains.
The Logic
- If a node has tier T0-T1, then it is load-bearing.
- If a node has tier T2, then it is conditional.
- If a node has tier T3+, then it is carried.
- If independence is high, then the pattern is convergent.
- If independence is low, then the pattern is borrowed.
- If the falsifier appears, then the node collapses.
- If a rival frame exceeds the claim, then the node weakens.
- If nodes span domains without causal contact, then the pattern is convergent.
- If the same equation appears in unrelated fields, then the pattern is structural.
The Evidence
C01 (Gradient Dissipation): Prigogine (1977), Schroedinger (1944), Schneider and Kay (1994), England (2013). C02 (Least Action): Fermat (1662), Lagrange (1788), Hamilton (1833), Feynman (1948). C03 (Symmetry-Conservation): Noether (1918), Weyl (1928), Wigner (1939). C04 (Symmetry-Breaking): Landau (1937), Anderson (1958), Higgs (1964), Turing (1952). C05 (Criticality): Bak, Tang, Wiesenfeld (1987), Kauffman (1993), Langton (1990), Wilson (1971), Beggs, Plenz (2003). C06 (Information-Entropy): Shannon (1948), Landauer (1961), Jaynes (1957), Kolmogorov (1965), Bennett (1982). C08 (Recursion): Godel (1931), Turing (1936), von Neumann (1948), Hofstadter (1979). C09 (Selection): Darwin (1859), Wallace (1858), Price (1970), Dawkins (1976), Campbell (1974), Edelman (1987). C10 (Scale Invariance): Mandelbrot (1982), Kleiber (1932), West, Brown, and Enquist (1997), Wilson (1971). C11 (Networks): Euler (1736), Watts and Strogatz (1998), Barabasi and Albert (1999), Granovetter (1973). C12 (Autopoiesis): Maturana and Varela (1972), Varela (1979), Luhmann (1984), Thompson (2007). C13 (Free Energy): Helmholtz (1867), Friston (2005, 2010), Rao and Ballard (1999). C14 (Duality): Bohr (1928), Newton (1687), Heraclitus (~500 BCE), Lao Tzu, Jung (1951). C15 (Optimization): Pareto (1906), Koopmans (1951), Carnot (1824), Stearns (1992). C16 (Branching): Murray (1926), Horton (1945), Bejan (1996), West, Brown, and Enquist (1997). C17 (Spirals): Fibonacci (1202), Schimper (1830), Jean (1994), Lindstedt (1984), Lin and Shu (1964). C18 (Waves): d'Alembert (1746), Fourier (1822), Maxwell (1865), Schroedinger (1926), Hodgkin and Huxley (1952). C19 (Thermoeconomics): Georgescu-Roegen (1971), Odum (1971), Lotka (1922), Ayres (1998). C20 (Computation): Church (1936), Turing (1936), von Neumann (1945), Wolfram (2002). C21 (Emergence): Anderson (1972), Laughlin (1999).
The Falsifier
A node has zero independent derivations. Sources show borrowing, not independence. A falsifier appears.
The Uncertainty
Nodes C20-C25 are absent. C13 falsifiability status is unknown. C12 is a definition or a mechanism. Its status is unknown. C17 astronomical claim is weaker than biological claim.
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