Discipline portal
問道研究所
Reasoning Research Institute
Define the discipline here in two or three sentences: what it studies, by which methods, which fundamental questions it wants to answer, and where it borders on neighbouring fields.
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- Entries
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- Concepts
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- Public claims
Subject map
The main branches of the discipline. Each branch holds a group of related entries; branch descriptions are written under Posts › Categories.
Featured entries
Entries recommended by the editors: make a post sticky to place it here; the latest entries fill up to three.
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.
Latest research
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