Discipline portal
Science of Generation
（生之科學）
The Science of Generation (Genontology) is a theoretical framework developed by Xutong LI of the Reasoning Research Institute. Western knowledge takes “BE” as its core operator and studies well-founded beings; its precise boundary is the axiom of regularity in set theory. The circular, self-embedding structures this axiom excludes, known as proper classes, are exactly where a science built on the operator “Shēng” (generation) begins. It uses yin-yang and the Five Phases as its formal language and the rotor as its basic category, and it regards the Science of Being as its own degenerate projection.
- 0
- Entries
- 0
- Branches
- 0
- Concepts
- 30
- Public claims
Featured entries
Entries recommended by the editors: make a post “sticky” to put it here; the latest entries fill any remaining places.
Subject map
The main branches of the discipline. Each branch holds a group of related entries; branch descriptions are written under Posts › Categories.
Latest research
Branch articles
Browse entries by branch of the discipline. Click a branch to see only that branch.
Key concepts
A few words to know before entering the discipline. Open one for its definition, then follow the link to the full entry.
Concept one
Give a one-sentence definition: genus and difference, or the more basic concepts it is generated from.
Concept two
Explain its role in the discipline: which question it answers and which concepts it usually appears with.
Concept three
Point out a common misunderstanding: what it is not, and which everyday usage to keep apart from it.
Concept four
Give the simplest possible example, so that beginners recognise it at once.
Concept five
Give the source: who first proposed it and where it was first stated systematically.
Concept six
Link to the full entry: a glossary item is only a doorway; the full discussion belongs in the entry.
Learning path
Not sure where to start? Follow these four levels in order. Fill in the links to the corresponding entries for each level.
- IntroductionUnderstand the basic conceptsNo prerequisites. Read the overview of the discipline and the key concept entries to get the whole picture.
- FoundationsMaster the core statementsWork through the most important theorems or claims of the discipline one by one, and how they were obtained.
- AdvancedLearn the methods and modelsUse the discipline’s methods yourself: model, derive, test, and solve a few exercises.
- FrontierReach the open problemsRead the latest research, pick an open problem and see which step you can advance.
Public claims
Every statement of the discipline has a number and an epistemic tier: theorem, empirical finding, structural judgement… Tiers rise and fall with the evidence, and every change is recorded publicly.
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.
- Foundation 1
- A load-bearing starting point. It is not on the same axis of confirmation as theorems: foundation and storeys are not ranked, only bearing and borne. It may not have logical premises; it is propagated downstream as a foundation-dependency set.
- Theorem 14
- A mathematical or logical result with a proof: it must carry proof links (Lean, Coq, paper, appendix, textbook) or an external anchor in established mathematics.
- Empirical 1
- A result obtained by measurement: it should carry data links and a cross-check by an independent method.
- Structural inference 3
- An inference from structural argument that has not yet been formalised as a theorem.
- Interpretive 2
- An interpretive reading within the framework; not a theorem and not a basis for computation.
- Lexical 2
- A dictionary-level correspondence with the vocabulary of another discipline; it asserts translatability, not structural identity.
- Engineering 2
- A tool, software or model. It is not on the cascade scale and may not serve as a logical premise; it may serve through an instrument edge.
- Programmatic 2
- A research programme or a goal still being written; the argument is not complete. It is never featured on the home page.
- Rejected 3
- A statement that has been examined and should be rejected; listed publicly with reasons. It may not be a logical premise of a non-rejected claim.
Cascade rules
- The tier of a conclusion = min(tier of its premises, rigor of the inference). Only logical edges take part; instrument, context and refutes edges do not.
- Scale: foundation 6, theorem 6, empirical 5, structural 4, interpretive 3, lexical 2, programmatic 1; engineering and rejected are off the scale.
- Conservative declarations propagate downstream: the effective strength of a premise is the lesser of its declared tier and its computed ceiling.
- Logical cycles are not errors: an unguarded cycle caps its whole strongly connected component at structural inference; if every member has a guardedness certificate there is no cap.
- The cascade checks consistency, not truth; the rigor of an inference is self-reported by the author.
Open problems
A discipline lives in the questions it has not yet answered. Contributions and discussion on these problems are welcome.
Open
Problem one: the question in one sentence
Why it matters and what makes it hard; the best result so far, and the step still missing.
In progress
Problem two: a testable conjecture
State it testably with criteria: which evidence would support it and which would refute it.
Partial results
Problem three: an interface with other fields
A question where the discipline meets a neighbouring one: whose methods it needs, and which collaborations exist.
Timeline
Replace “Origin” and the other labels with years. The timeline records only events that changed the discipline’s course.
- OriginThe question first raised: who first treated it as a problem, and in what context.
- FoundationThe first systematic work or the first core result; from then on the discipline had its own language.
- Turning pointA methodological breakthrough or an important correction that changed the course of the discipline.
- TodayThe current focus of research and the projects under way.
Discipline library
Terms, sources, corrections and anthologies of the discipline, arranged entry by entry.
Write an entry
Entries are written by researchers and reviewed by editors. Propose a new entry, or add evidence and references to an existing one.
Corrections
Tell us when you find an error. Every substantive revision is recorded in the entry’s revision date, and important corrections are logged publicly.
Cite this site
Every entry ends with GB/T 7714, APA and BibTeX citation formats, copied with one click.