The science of generation is a developing theory with strict epistemic tiering: every conclusion has a tier, and the tier decides how it may be used.
Epistemic tiers
| Tier | Meaning | Example |
|---|---|---|
| Postulate | A founding statement the system starts from, not derived within it | Entities do not carry their generative path |
| Theorem | Provable or exhaustively checked; includes external mathematical anchors | Proper classes ↔ νF; overcoming = generation²; 5 ∤ 2ᵏ |
| Empirical | Measured, reproducible, cross-checked by an independent method | Basin distribution of the yeast network; DualTrack data |
| Structural inference | Derived from proven structure; becomes a theorem only when formalised | Containment asymmetry; the necessity of branching as a whole |
| Interpretive | A grounded reading within the framework; heuristic, not proof | Reading the Feigenbaum point as the boundary of Foundation |
| Lexical | A translation correspondence between systems | Mutual arising ↔ adjunction; generation-preserving ↔ truth-preserving |
| Engineering | An implementable, testable design whose effect awaits evidence | The Five-Phase monetary model; the analyzer software |
| Programmatic | Points a direction still to be realised | 3T / FPRC; the grand unification theorem |
| Rejected | Refuted or without testable content; explicitly excluded | Unique trigram–object matching; “DNA is a musical code” |
- 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.
The cascade rule
Tier of a conclusion = min(tier of the premises, rigour of the inference). Raising the status of a premise does not change the rigour of the inference.
Prohibited moves
- No closing an argument on numerical coincidence.
- No meaningless renaming of existing concepts.
- Claims of structural legitimacy must pass the algebraic gate.
- Honest failure is first-class data; pre-register thresholds before looking at the data.
- Numbers must be measured, never asserted.
- Check the literature before starting.
- Do not go beyond the data: the framework gives types, not parameters.
- Point out explicitly any framework choice that conflicts with internal consistency.
Verification: concentrated production, distributed verification
Most of the framework of the science of generation was built by one author working with AI. Production can be concentrated, but verification cannot be left to the same collaborative loop: the errors of author and AI are not independent and may share a blind spot — every basic correction on the cumulative list was found only in later reflection. Verification on this site is therefore distributed across independent sources.
- Adversarial multi-model review: before release or submission, several models from different vendors each play the harshest reviewer. A first filter only, never verification on its own.
- Machine verification: theorem-level results are formalised step by step in Lean and guaranteed by the proof checker, independent of the author and of any AI.
- Pre-registration and a results ledger: thresholds are registered before the data is seen, and every result, success or failure, is published.
- Independent human review: scholars with a public record in the field and no ties to the author review key results or reproduce them.
AI collaboration and ethical red lines
This site publishes a statement on its collaboration with AI; every submission carries an AI-use declaration, and every reference is checked by hand. Results produced with AI are signed by the author and the Reasoning Research Institute, who are responsible for them; “generated by AI” is never an excuse. No fake accounts to stage discussion, no mass-produced content posing as third parties, no different content for crawlers and human readers, no self-written Wikipedia entries, no data placed to distort what models conclude.
Cumulative corrections
| Old wording (void) | Current wording |
|---|---|
| Operator G maps meaning → image | G and A both map image → meaning; meaning → image is generation / unfolding |
| νF is the Dao | νF is one appearance of the Dao, the mathematical home of proper classes |
| Relations precede entities | Relations and entities are generated together |
| Five-Phase ℤ₅ can be inferred from geometry or meaning | It must be verified by true algebra |
| The two sciences are symmetric yin-yang halves | The concepts arise mutually and symmetrically; the systems stand in containment asymmetry |
| The science of generation has an axiom system | No axioms: primordial equations, coinduction, bootstrapping; the twin criteria of autologicality and guardedness |
| Former institute names | Reasoning Research Institute |
Deprecated G 算子 义→象;「每一步 G 由义生出新一层象」 English translation pending
Current G 与 A 都映射 象→义(G 依两极之道,A 依相似);义→象 是「生/展开」 English translation pending
Texts concerned 《旋机运算体系》凡例与第二章
Deprecated νF 即道;νF 是无根世界唯一的地基 / 共同的最抽象数学本体 English translation pending
Current νF 是道的诸像之一,不是道本身;是固有类的数学家园 English translation pending
Claims concerned SGC-0010
Texts concerned 旧第十五章第五节与题记(须向丙丁编传播)
Deprecated 固有类、非良基集合、分形、旋机、阴阳互生「五名同一」为精确等同 English translation pending
Current 仅固有类/非良基集合↔νF 为定理级;其余为结构推论或阐释级 English translation pending
Claims concerned SGC-0010
Texts concerned 旧第十五章第五节
Deprecated 关系先于实体 English translation pending
Current 关系与实体同时生成(「先于」只是论战性过渡提法,指逻辑不可分离) English translation pending
Texts concerned 《生之科学概述》命题二;目录蓝图
Deprecated 五行 ℤ₅ 可由几何/语义推断 English translation pending
Current 「某域是五行」须经四象三闸门 / ℤ₅ 真代数验证(步长 1 与步长 2 两条有向哈密顿圈且克=生²) English translation pending
Texts concerned 双轨诸稿的大量跨域五行映射
Deprecated 生成性分层可按存在侧结构概念划分 English translation pending
Current 生成性分层须基于生成性轴(δ 自应用) English translation pending
Deprecated 生之科学与存在之科学是对称的阴阳两面 / 一分一合的对称对偶 English translation pending
Current 概念对互生对称;体系对涵摄非对称(存在之科学为 ι→1 退化投影,可独立成书的一章);涵摄≠高下 English translation pending
Claims concerned SGC-0004
Texts concerned 早期概述;第七章;《论分支》结尾(已回填)
Deprecated 「实体不携带路径」为结构推论 English translation pending
Current 基设级(分界基设) English translation pending
Claims concerned SGC-0001
Texts concerned 《论分支》三部曲初版标注
Deprecated 生之科学有公理 / 公理系统 English translation pending
Current 无公理:本原方程、余归纳、自举;双判据自例化+守护性 English translation pending
Texts concerned 旧第四编「公理系统重构」章名
Deprecated 八编三十章结构;生成本体论等学科分编 English translation pending
Current 七编(甲界—庚归);学科称谓降为词典级 English translation pending
Texts concerned 《生之科學书稿目录》
Deprecated 酵母网络负结论(旋机不适用阈值网) English translation pending
Current 阈值网=老少部件,精确复现 Li 基准(旧报告定理仍成立,结论被推翻) English translation pending
Claims concerned SGC-0030
Texts concerned 酵母细胞周期网络分析报告 v1.0
Deprecated 完整 32 态胞半群可解性未知 English translation pending
Current 已解决:可解,群部件=ℤ₈;S₈ 反例划出边界 English translation pending
Claims concerned SGC-0019
Texts concerned HANDOFF v9 开放问题
Deprecated 真善忍为道德谓词 English translation pending
Current 真善忍是宇宙特性(物质的一阶属性),非外加的道德谓词 English translation pending
Deprecated 机构名「大道研究院」/「大道研究所」(Dadao Research Institute) English translation pending
Current Reasoning Research Institute (问道研究所)
Texts concerned 全部早期文稿署名、引用格式与页眉页脚