NEW(SWX)偏元数理关联的分级判据:数学结构、物理可观测量与文化解释之间的十条接口(Graded Criteria for the Prenary Correspondence: Ten Interfaces among Mathematical Structures, Physical Observables, and Cultural Interpretations)

跨数学、物理学与文化解释的对应关系,最容易出的错不是"对应错了",而是"级别没标":一个形态相似被当作推导,一句古语被当作证据,一次权威同调被当作验证。本文给出一套分级判据,把这类对应按"能主张到哪一步"分层,并落实为十条接口。部一给出十条接口(相减留差、量与向、标架原点、二态、残差往复、串联与并联、精度内等号、残差二态、分辨率与上界、验证边界),每条均标注级别(结构同构/结构对应/观测事实/线索/定义层澄清)并写明边界;其中四条构成主线(两分与正交、并联与幂等、串联与折入、可判与不可判),每条在数学侧与物理学应用侧各落一次——这三篇的关系由此成为"同一问句的两次回答",而不是"一篇推出另一篇";部二把数学内容与中国传统哲学及经典文献逐句对照,改以"文献—原文—对应"三列呈现,并列出未找到对应者,古语只作理解工具、不作证据;部三给出外部同族谱(有学术根基的近邻、独立研究者的同形工作、经典中的相等近邻、工程与物理中的平行结构),并以外部大规模形式化工程的公开记录为例,说明"形式正确不等于数学正确"这一判据并非本文独有,同时立下三条禁令:不拿权威当背书、不拿相似当对应、不拿"搜索范围内无人做过"当作独创性证明。部三另以三层事实(官方口径、外部归类、本文实核)讨论一份成批自动生成的数学结果集的规模、撤回形态、验证覆盖率与方向分布问题,并说明本文体系在此类工程面前的位置。 本文为跨侧方法论件:不重报数学侧与物理学应用侧的发现与数值,只对其判词作级别登记;不主张任何接口为证明;不主张任何外部对象与本文体系等价。 关键词:跨侧对应;分级判据;接口;结构同构;验证边界;偏元等号;残差;形式化验证;外部同族;方法论;初步分析。 — 老陈与AI的深夜实验室 发布 请笑纳 — In correspondences that cut across mathematics, physics and cultural interpretation, the error most easily made is not "the correspondence is wrong" but "the level has not been marked": a similarity of form is taken for a derivation, an ancient saying for evidence, a single authoritative concordance for verification. This paper presents a set of graded criteria that stratify such correspondences by "how far a claim may be carried", and implements them as ten interfaces. Part I presents ten interfaces (subtraction leaving a difference; magnitude and direction; frame origin; two-state; residual reciprocating; series and parallel; equality within precision; residual two-state; resolution and upper bound; verification boundary), each annotated with a level (structural isomorphism / structural correspondence / observational fact / clue / definition-level clarification) and each stating its boundary; four of them constitute the main lines (the two-way split and orthogonality, parallel and idempotence, series and folding-in, decidable and undecidable), and each of these falls once on the mathematical side and once on the physics-application side — the relation among the three papers thereby becoming "two answers to the same question" rather than "one paper deriving the other"; Part II compares the mathematical content sentence by sentence with traditional Chinese philosophy and classical texts, recasting the comparison into three columns, "text — original passage — correspondence", and listing those for which no correspondence has been found, ancient sayings serving only as tools of understanding and not as evidence; Part III gives the external family spectrum (academic neighbours with scholarly grounding, isomorphic work by independent researchers, near neighbours of "equality" in the classics, parallel structures in engineering and physics), and, taking the public record of an external large-scale formalization project as an example, shows that the criterion "formal correctness is not mathematical correctness" is not unique to this paper, while laying down three prohibitions: authority is not used as endorsement, similarity is not used as correspondence, and "no one within the search range has done it" is not used as proof of originality. Part III further discusses, through three layers of fact (official statement, external classification, verification performed in this paper), the scale, the pattern of withdrawal, the verification coverage and the distribution by direction of a corpus of automatically generated mathematical results, and states where this system stands before engineering of that kind. This is a cross-side methodological paper: it does not re-report the findings and numerical values of the mathematical side and the physics-application side, but registers only the level of their verdicts; it claims no interface as a proof; it claims no external object to be equivalent to this system. Keywords: cross-side correspondence; graded criteria; interfaces; structural isomorphism; verification boundary; equality within precision; residual; formal verification; external family; methodology; preliminary analysis. — Published by Lao Chen & AI's Late Night Lab. Please accept with a smile. —