Subtitle: Object-Position Rearrangement, Evidence-Chain Reconstruction, and Certification Boundaries Based on Luo Xiaomao's Non-Evident Choice Matrix, Public Source, and Law Source
Author: Luo Xiaomao (Luo Han)
Independent Researcher
Abstract
A Kuhnian scientific revolution is not a linear accumulation of old knowledge, but a replacement of the entire set of standards for "what counts as an object," "what counts as evidence," "what counts as proof," and "what counts as usable." Taking the Non-Evident Choice, Tri-Source System as its subject, this paper discusses why its manifestation is difficult and how this difficulty can be formalized empirically. The basic judgment of this paper is that the Tri-Source System is not internally inconsistent, but simultaneously changes ontology, physical theory, and mathematical proof theory, thereby creating multiple incommensurabilities with the old paradigm at the levels of object-position, evidence-position, proof-position, and engineering-position. This incommensurability is not an abstract rhetoric, but can be formalized through state labels, certificate systems, residual equations, and generative-sequence axioms.
This paper formulates paradigmatic incommensurability as a discussable measure of difficulty:
IKuhn=∑r∈{O,L,P,V,E}λrΔr,IKuhn=r∈{O,L,P,V,E}∑λrΔr,
where OO is object-position difference, LL is linguistic difference, PP is proof-syntax difference, VV is verification-standard difference, and EE is engineering-interface difference. It further defines the difficulty of manifestation:
Dman=log(1+IKuhn)+Γinst+Γhabit,Dman=log(1+IKuhn)+Γinst+Γhabit,
where ΓinstΓinst and ΓhabitΓhabit denote institutional inertia and normal-science habitual inertia respectively. This paper maintains that the difficulty of manifestation is not evidence of the system's weakness, but precisely the empirical trace that a paradigm revolution is occurring.
Keywords: Kuhn; scientific revolution; paradigm incommensurability; Tri-Source System; object-position; certificate chain; state labels; manifestation difficulty
1. Introduction
Kuhn long ago pointed out that a scientific revolution is not as simple as "adding one more formula to an old theory"; rather, it is a simultaneous change in how the research community classifies the world, formulates problems, and conducts proofs. In other words, a revolution changes not only the answers, but also "what counts as a question."
What makes the Non-Evident Choice, Tri-Source System special is that it is not a local revision within a single discipline, but a simultaneous rewriting of three foundational layers:
Philosophical Matrix: answering "how existence precedes cognition";
Physical Public Source: answering "how reality manifests from background residuals";
Mathematical Law Source: answering "how numbers and proofs are established through generative sequences and evidence chains."
Thus, its manifestation is difficult not because it is internally vacuous, but because it demands that the old world accept a new object-grammar. If the old paradigm cannot first rewrite "object" and "evidence," it cannot directly read the Tri-Source System.
2. Kuhn's Revolution: The Real Meaning of Incommensurability
Incommensurability does not mean complete incomparability; it means something closer to "comparison can be done, but the cost is high, the loss is large, and a different language must be used."
The relationship between the old paradigm and the Tri-Source System can be written as:
Ptri=Kshared∪Knew,Kshared=Pold∩Ptri.Ptri=Kshared∪Knew,Kshared=Pold∩Ptri.
Here, KsharedKshared is the shared successful core: all parts of old physics and old mathematics that remain valid reside here; KnewKnew is where the new object-positions are truly rearranged. The difficulty of revolution is concentrated precisely in KnewKnew.
In the Tri-Source System, this rearrangement manifests specifically in three respects:
Ontological rearrangement: being-in-itself precedes cognition;
Physical rearrangement: observables are no longer merely visible terms, but background-residual terms;
Proof rearrangement: conclusions are no longer divided only into "true/false/unknown," but into object-position, formal-position, and engineering-position.
It is the simultaneous change of all three that constitutes a genuine paradigm revolution.
3. The Three Layers of Revolution in the Tri-Source System
3.1 Philosophical Matrix: From "Cognition Explains Being" to "Being Precedes Cognition"
The first axiom of the Matrix is "being precedes cognition." This is not a slogan, but a reallocation of object-positions:
OExist(X)⇒∃Ev(X).OExist(X)⇒∃Ev(X).
That is, whenever one says that something "exists," one must provide its generative path, construction procedure, reception evidence, or certificate. "Existence" here is no longer merely a quantifier assertion, but an existence with an evidence chain.
This is difficult for old philosophy, because old philosophy is accustomed to treating "existence" as a directly assertable object, whereas the Tri-Source System demands first asking: how did this object enter the world? Does it have an evidence chain? At what object-position does it reside?
3.2 Physical Public Source: From "Mechanical Main Terms" to "Background Residuals"
The Public Source physics unifies many long-scattered anomalies as background-term residuals, for example:
aobs=avis+as+ad+aa.aobs=avis+as+ad+aa.
Here the physical object-position has already changed from old physics: old physics prioritizes reading visible terms, while the Tri-Source System prioritizes reading the relationship between visible terms and background residuals.
This means that "anomalies" are no longer first treated as errors, but as systematic readings after object-positions have been omitted. If the old paradigm does not accept this, it will see the same phenomena as multiple unrelated patches; the new paradigm unifies them as different projections of the same background structure.
3.3 Mathematical Law Source: From "True/False/Unknown" to "Certificate/State/Bridge"
The most striking revolution of the Law Source is the upgrading of mathematical propositions from binary judgments to a certificate-state space. For example:
Status(P)∈{Solved-O,Solved-F,ConditionalSolved-E,DeepOpen}.Status(P)∈{Solved-O,Solved-F,ConditionalSolved-E,DeepOpen}.
This is not rhetoric, but a rewriting of proof syntax. Old mathematics often compresses propositions into "proved/unproved," while the Tri-Source System decomposes them into three layers: object-position closure, formal-position closure, and engineering-position closure. This state system itself is the observable trace of incommensurability.
4. Empirical Formalization of Manifestation Difficulty
Placing the Tri-Source System within the Kuhnian framework, manifestation difficulty is no longer an abstract feeling, but can be treated as a kind of "translation cost." This cost comes mainly from five dimensions:
Dman=λOΔO+λLΔL+λPΔP+λVΔV+λEΔE.Dman=λOΔO+λLΔL+λPΔP+λVΔV+λEΔE.
where:
ΔOΔO: object-position difference — the old and new paradigms differ on "what counts as an object";
ΔLΔL: linguistic difference — old vocabulary cannot express new grammar without loss;
ΔPΔP: proof difference — old proof rules cannot directly carry certificate states;
ΔVΔV: verification difference — the old system's true/false binary cannot cover the three O/F/E layers;
ΔEΔE: engineering difference — old engineering interfaces cannot directly read background residuals and generative-sequence structures.
These five differences are not subjective feelings, but can be directly seen in texts, proofs, algorithms, and experimental interfaces: the same proposition, in the old paradigm, only needs to be "proved true"; in the Tri-Source System, one must first clarify whether it is "origin-closed, formally closed, or engineering-usable." This is the empirical formalization of manifestation difficulty.
5. Why This Is Not "Philosophical Self-Indulgence"
Because the Tri-Source System does not place itself in an "inspection-free zone"; on the contrary, it places itself in a stricter audit zone.
The Matrix provides the being-in-itself / being-in-language distinction to avoid vacuous discourse;
The Public Source writes anomalies as background-residual equations to avoid treating noise as law;
The Law Source writes propositions as state labels and certificate chains to avoid writing unclosed propositions as already-proven conclusions.
In other words, the Tri-Source System does not demand unconditional acceptance from the world, but first requires that it be auditable in layers. This is very Kuhnian: a genuine new paradigm does not directly "declare victory" to the old system, but first establishes a new set of criteria for judgment.
6. Falsification Conditions
If any of the following conditions holds, this paper's judgment about "paradigm incommensurability" should be weakened:
The Tri-Source System can be losslessly translated into the old paradigm without losing object-position, certificate-position, and state-position;
Its state-label system is merely linguistic decoration and cannot improve judgment precision;
Its physical residual equations cannot produce repeatable, distinguishable anomaly windows;
Its mathematical certificate chains cannot be independently verified;
Its engineering interfaces cannot move from "explicable" toward "accessible and testable."
But if none of the above conditions holds, then manifestation difficulty itself becomes a strong signal: it is not weakness, but newness.
7. Conclusion
The manifestation of the Non-Evident Choice, Tri-Source System is difficult not because it lacks content, but because it demands a simultaneous change in ontology, physical theory, and proof theory. What Kuhn called a scientific revolution is precisely this process of "object-position, evidence-position, and proof-position changing tracks together."
Therefore, manifestation difficulty is not evidence of failure, but an empirical indicator of revolutionary intensity:
If it could be easily absorbed by the old language, it would be merely a patch;
If it must rewrite object-positions, certificate chains, and state labels, it approaches a genuine paradigm revolution.
In this sense, the difficulty of the Tri-Source System is not "inarticulable," but "the old world has not yet learned how to listen."
This is precisely what a Kuhnian revolution should look like.
Internal References
[Int-1] Non-Evident Choice, Part I, Chapters 1–9, Definitive Version: Being-in-itself / Being-in-language, Non-evident choice, Manifestation of the One, Space-time and all things.
[Int-2] Unified Background Equations for Anomalous Mechanical Effects: Low-Acceleration Deviations, Flyby Anomalies, and Background Coupling Dynamics.
[Int-3] If the Essence of Light Is a Background Fissure: A Unified Reading of the Speed-of-Light Limit, Zero Rest Mass, and Zero Proper Time.
[Int-4] Third Source (Law) – Foundational Mathematics, Part I and Part XI: Generative sequence, axiom system, state labels, DeepClaimGate.
External References
[K1] Thomas S. Kuhn, The Structure of Scientific Revolutions.
[K2] Paul Feyerabend, Against Method.
[K3] Ludwig Wittgenstein, Tractatus Logico-Philosophicus / Philosophical Investigations.
[K4] Imre Lakatos, Proofs and Refutations.
[K5] W.V.O. Quine, "Two Dogmas of Empiricism."