构造数学认证标准:公理化构造的评价框架 / Constructive Mathematics: A Certification Standard for Axiomatic Constructions
Abstract
构造数学认证标准:公理化构造的评价框架。本文公开一套针对"构造数学"的认证标准:对满足"从观察归纳公理集、对象宇宙自构造生长、标准数学可作为其特例导出"三要素的数学构造,给出可公开审查的成员判据(C1 观察起源/C2 公理化独立性预检/C3 对象自构造分水岭/C4 特例化王冠/C5 自足性分层/C6 机器可检验性硬判据[形式化+零 sorry,kernel 唯一关口,证明作者身份不设限]/C7 溯源对照)与认证流程(三档结论+五情形分流+纠错机制)。含已认证成员目录快照:四层构造数学成员(数/关系/动/几何)与单列表示数学序列,全部经逐条审查且 C6 达硬判据。同时公开构造难度的成分分解(四道串联滤网与 12:0 实测淘汰率——拒绝难度数字的伪精确标定)与抛题三维分级规范(预期投入 D/观察依赖 O/判定方式 J)。本文显式区分本框架的构造数学与 Bishop 传统的 constructive mathematics(1967):两者正交互补——后者约束证明的逻辑方法,本框架评价数学对象的构造方式。修订经 Zenodo 版本链进行。中文主版。 The certification standard of constructive mathematics: an evaluation framework for axiomatic constructions. This document publishes a certification standard for mathematical constructions satisfying three criteria — an axiom set induced from observation, an object universe grown by self-construction, and standard mathematics recoverable as a special case — with publicly reviewable membership criteria (C1 observational origin / C2 axiomatic independence pre-check / C3 self-construction watershed / C4 specialization crown / C5 layered self-containedness / C6 machine checkability as a hard criterion [formalization + zero sorry, kernel as the sole gate, author identity out of scope] / C7 provenance comparison) and the certification process (three-valued conclusions, five-case triage, correction mechanisms). Includes the certified-membership catalog snapshot: four constructive-mathematics members (number / relation / motion / geometry layers) plus a separately listed representation-mathematics series, all reviewed item by item with C6 at the hard-criterion level. Also publishes a component decomposition of construction difficulty (four serial filters, 12:0 measured elimination — refusing pseudo-precise difficulty numbers) and a three-dimensional grading specification for posed problems (D expected investment / O observational dependence / J verification mode). The document states explicitly how this framework's constructive mathematics relates to the constructive mathematics of the Bishop tradition (1967): orthogonally complementary — the latter constrains the logical methods of proof, this framework evaluates how mathematical objects are constructed. Revisions proceed through the Zenodo version chain. English edition. v1.3 (2026-09-21): §4.1.1 non-derivation self-check added — new-member applications must carry negative evidence for E1–E6 (completion/derivation rerouted, no new register row). Form: application-template v0.2.
Related
- The Generative Mechanism of Dimension: An Axiomatic Construction of Dimensional Conventions (Constructive Mathematics Series, Paper 6; Lean formalization, model-pair independence, numerical evidence)
- The Profile Calculus: An Axiomatic Certification Framework for the ω ≤ 9/4 Matrix-Multiplication Exponent
- Inequalities and equalities of means in Constructive Mathematics
- The strength of the minimum principle in constructive reverse mathematics
- The Toroidal Axiomatic Model of the Human Body: A Bioenergetic Architecture Based on Tesla's Mathematics (3-6-9) and the Sacred Geometry of the Vacuum
BibTeX
@article{qin2026构造数学认证标准公理化构造的评价框架,
title = {{构造数学认证标准:公理化构造的评价框架 / Constructive Mathematics: A Certification Standard for Axiomatic Constructions}},
author = {Chao Qin},
journal = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = sep,
doi = {10.5281/zenodo.22790074},
url = {https://doi.org/10.5281/zenodo.22790074},
note = {CC BY},
}
RIS
TY - JOUR
TI - 构造数学认证标准:公理化构造的评价框架 / Constructive Mathematics: A Certification Standard for Axiomatic Constructions
AU - Chao Qin
PY - 2026
DA - 2026/09/16
JO - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.22790074
UR - https://doi.org/10.5281/zenodo.22790074
AB - 构造数学认证标准:公理化构造的评价框架。本文公开一套针对"构造数学"的认证标准:对满足"从观察归纳公理集、对象宇宙自构造生长、标准数学可作为其特例导出"三要素的数学构造,给出可公开审查的成员判据(C1 观察起源/C2 公理化独立性预检/C3 对象自构造分水岭/C4 特例化王冠/C5 自足性分层/C6 机器可检验性硬判据[形式化+零 sorry,kernel 唯一关口,证明作者身份不设限]/C7 溯源对照)与认证流程(三档结论+五情形分流+纠错机制)。含已认证成员目录快照:四层构造数学成员(数/关系/动/几何)与单列表示数学序列,全部经逐条审查且 C6 达硬判据。同时公开构造难度的成分分解(四道串联滤网与 12:0 实测淘汰率——拒绝难度数字的伪精确标定)与抛题三维分级规范(预期投入 D/观察依赖 O/判定方式 J)。本文显式区分本框架的构造数学与 Bishop 传统的 constructive mathematics(1967):两者正交互补——后者约束证明的逻辑方法,本框架评价数学对象的构造方式。修订经 Zenodo 版本链进行。中文主版。 The certification standard of constructive mathematics: an evaluation framework for axiomatic constructions. This document publishes a certification standard for mathematical constructions satisfying three criteria — an axiom set induced from observation, an object universe grown by self-construction, and standard mathematics recoverable as a special case — with publicly reviewable membership criteria (C1 observational origin / C2 axiomatic independence pre-check / C3 self-construction watershed / C4 specialization crown / C5 layered self-containedness / C6 machine checkability as a hard criterion [formalization + zero sorry, kernel as the sole gate, author identity out of scope] / C7 provenance comparison) and the certification process (three-valued conclusions, five-case triage, correction mechanisms). Includes the certified-membership catalog snapshot: four constructive-mathematics members (number / relation / motion / geometry layers) plus a separately listed representation-mathematics series, all reviewed item by item with C6 at the hard-criterion level. Also publishes a component decomposition of construction difficulty (four serial filters, 12:0 measured elimination — refusing pseudo-precise difficulty numbers) and a three-dimensional grading specification for posed problems (D expected investment / O observational dependence / J verification mode). The document states explicitly how this framework's constructive mathematics relates to the constructive mathematics of the Bishop tradition (1967): orthogonally complementary — the latter constrains the logical methods of proof, this framework evaluates how mathematical objects are constructed. Revisions proceed through the Zenodo version chain. English edition. v1.3 (2026-09-21): §4.1.1 non-derivation self-check added — new-member applications must carry negative evidence for E1–E6 (completion/derivation rerouted, no new register row). Form: application-template v0.2.
ER -