Entities do not carry information about their generative paths (boundary postulate).
Claims
30 claims
Directional asymmetry: downward generation is a deterministic forward problem; upward abstraction is necessarily a probabilistic inverse problem.
Rests on the foundation SGC-0001
Necessity of branching: the science of being, as a system of upward abstraction, necessarily takes a branching (forest-of-disciplines) form.
Rests on the foundation SGC-0001
Containment asymmetry: the science of being is the degenerate projection of the science of generation in the limit ι→1; it is complete and consistent within its own domain.
Proper classes (in the project's sense: circular self-embedding structures) have their mathematical home in terminal coalgebras νF ≅ F(νF).
Under the Anti-Foundation Axiom, every (flat) system of equations has a unique solution (Aczel's Solution Lemma); primordial equations replace axiomatic propositions on this basis.
Bisimulation serves as the identity criterion; in the finite case it is decidable via Paige–Tarjan partition refinement.
5 is the least integer admitting, on one element set, two mutually irreducible directed Hamiltonian cycles (steps 1 and 2); hence the "five" of the Five Phases is fixed by number theory.
Restraint = generation²: on ℤ₅ the overcoming map is the square of the generating map.
5 ∤ 2ᵏ: the Five-Phase track cannot be reduced to a binary (yin-yang track) representation.
For the logistic map, all period-2ᵏ orbits appear below the accumulation point r∞≈3.570; period 5 appears only beyond it.
Sharkovskii's theorem (external anchor): periods of continuous interval maps obey the Sharkovskii ordering.
Nuclear-hexagram basin spectrum: the nuclear map is the only irreversible inter-hexagram relation; the basin spectrum of the 64 hexagrams under its iteration (three attractor basins) is exhaustively determined.
The transition semigroup of the full 32-state rotor cell (coupled phase and magnitude) is solvable with group component ℤ₈; an S₈ counterexample marks the boundary.
The rotor sequent calculus RSC₀ is sound and complete.
Coding threshold 16 < 20 ≤ 64: doublet capacity cannot encode 20 amino acids; triplet capacity can.
C₅ is solvable and A₅ is not (external anchor); this marks the outer boundary of the generative theory of molecular genetics.
64-group isomorphism: 64 = 4³ = 2⁶; codon space and hexagrams are isomorphic as (ℤ₂)⁶.
Li et al. 2004 yeast cell-cycle network (11 nodes, 34 edges) under the threshold (magnitude-component) model: 7 fixed points, basins [1764,151,109,9,7,7,1]; largest basin 1764 (86.1%) is the G1 steady state.
The Feigenbaum accumulation point r∞≈3.570 can be read as a dynamical realization of the Axiom-of-Foundation boundary.
Period-doubling 2ᵏ corresponds to the nested yin-yang trigram system; period 5 corresponds to the Five Phases.
Mutual arising ↔ adjunction (category theory).
Generation-preserving ↔ truth-preserving: dictionary correspondence between the inference norms of generative and classical logic.
Grand unification theorem: the necessity of the science of generation as a whole (in progress).
Dual-track AI programme: 3T (Three-Track Transformer), FPRC, FPBA, FPMA.
Five-Phase Currency Dynamic Model v3.0: a testable model of monetary and macro dynamics using the Five-Phase track.
Rotor Whole-Genome Analyzer: software for gene-regulatory-network fate prediction and knockout scans using the rotor (phase + magnitude) engine.
There is a unique hexagram–object assignment (e.g. one hexagram = one specific codon).
"DNA is a musical code."
The order 60 of A₅ is the 60 of the sexagenary cycle.
By phase
By discipline
- Mathematics 18
- Logic 5
- Computer science 3
- Physics 1
- Biology 7
- Artificial intelligence 1
- Philosophy 8
- Economics 1
The discipline entrances are dictionary-level correspondences: a ladder built in the other party's language, withdrawn once climbed. Method