This paper argues a core proposition: the incompleteness of all domains demonstrates the completeness of logic. Mathematics, semantics, computation theory, physics, social science, and epistemology—each domain, in its attempt to achieve self-completeness, reaches its own boundary, manifesting phenomena that are undecidable, undefinable, uncomputable, unmeasurable, or impossible. Yet, the very discovery of these incompletenesses must be accomplished under the guidance of logic, through logical argumentation. This means: logic lies within no incompleteness—it forever stands in the position of the judge.
\nThis paper further clarifies the fundamental relationship between mathematics and the Logical Matrix: mathematics is the display of the tracks arranged by the Logical Matrix (the instantiated or instantiable part) or of its partial capacity tracks (the uninstantiable part). Through the practical process of “instantiation,” the Logical Matrix screens genuine cosmic truth: if a mathematical model cannot obtain instantiated verification in the physical universe (substantial spacetime), it belongs only to the “empty tracks” or “silent capacity” of the Logical Matrix, not to the “actualized part” of cosmic truth.
\nThis paper integrates three pillar arguments: undeniability (logic cannot be denied), unprecedability (no existence can precede logic), and completeness (logic defines all “impossibility”). The completeness of the Logical Matrix lies in its being “full-dimensional” (here “dimensionality” refers to the exhaustiveness of logical possibility, not mere spatial dimension)—it includes not only all tracks that have already been laid down, but also the dynamic logic behind the act of “laying down tracks.” It can stand outside systems and examine them; this “overlooking right” is precisely the fundamental reason why logic can recognize the incompleteness of mathematics.
\nOn this foundation, this paper audits the first-rate theory TO (Theory of Objectivity). The TO theory has come very close to our theory of cosmic essence, offering the profound insight that “Nothingness is a primitive and eternal mathematical essence.” However, the incompleteness of mathematics itself (Gödel‘s theorem) determines that the “mathematical essence” on which TO relies is likewise incomplete. Mathematics cannot ground itself, because mathematics itself is the display of tracks arranged by the Logical Matrix, not something outside the tracks. Therefore “mathematical essence” cannot serve as the first principle of the universe. Only the Logical Matrix—undeniable, unprecedable, greater than all concrete systems, the complete meta-framework—is the sole truth of the universe.
\ncompleteness of logic; incompleteness theorems; undeniablity; unprecedability; Logical Matrix; mathematical tracks; TO theory; instantiation; Gödel; Tarski; Turing; Heisenberg; Arrow; Hume
\n\n
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", "languages": [ { "id": "eng", "title": { "en": "English" } }, { "id": "cmn", "title": { "en": "Mandarin Chinese" } } ], "publication_date": "2026-05-05", "publisher": "Zenodo", "references": [ { "reference": "[1] Cui, H. (2026). Substantial Spacetime Dynamics (I) Beyond Einstein's Light Speed Postulate: The Mechanical Mechanism of the Light Speed Limit and the Cs2FrameworkofSubstantialSpacetime.Zenodo. [2] Cui, H. (2026). Spacetime Substantivalism 0: The Track-Light Model \u2014The Logic Matrix as the Universal Source, the Origin of the Cosmic Singularity, and a New Foundation for Metaphysics. Zenodo. [3] Cui, H. (2026). Spacetime Substantivalism II: Black Holes as Spacetime Fractures and Cosmic Fossils. Zenodo. [4] Cui, H. (2026). Spacetime Substantivalism III: A Paradigm Shift from Dark Matter to the Origin of Mass. Zenodo. [5] Cui, H. (2026). Spacetime Substantivalism IV: Reframing the Vacuum Catastrophe: A Conceptual Diagnosis and a Spacetime Self-Energy Perspective. Zenodo. [6] Cui, H. (2026). Spacetime Substantivalism V: The Cui Constant and the Constitutive Response of Spacetime: A Mechanical Unification of Galaxies, Black Holes, and Cosmic Voids. Zenodo. [7] Cui, H. (2026). Spacetime Substantivalism VI: A Universal Constitutive Law of Spacetime Response from Solar Systems to Black Hole. Zenodo. [8] Cui, H. (2026). Spacetime Substantivalism VII: The Great Experiment of Nature\u2014The Substantial Nature of Spacetime Revealed by Gravitational Waves. Zenodo. [9] Cui, H. (2026). Spacetime Substantivalism VIII: The Constitutive Nature of the Spacetime Lattice Under Gravitational Wave Empirical Evidence and the Physical Essence of CMB Anomalies. Zenodo. [10] Cui, H. (2026). Spacetime Substantivalism IX: Micro-Dynamics of a Constitutive Spacetime Lattice as an Effective Field Theory and its CMB Polarization Signatures. Zenodo. [11] Cui, H. (2026). Spacetime Substantivalism X: The Constitutive Origin of the Light-Speed Postulate \u2014A Hierarchical Field Decomposition of Spacetime Substrate and Excitations. Zenodo. [12] Cui, H. (2026). Spacetime Substantivalism XI: Restoration of the Physical Mechanism of the Lorentz Transformation \u2014An Audit Model Based on Electromagnetic Load and the v2epsilon0mu0Term.Zenodo. [13] Cui, H. (2026). Spacetime Substantivalism XII: Constitutive Divergence between Null- Debt and Topologically Constrained Sectors in Effective Spacetime Field Theory. Zenodo. [14] Cui, H. (2026). Spacetime Substantivalism XIIII: Covariant Constitutive Effective Field Theory of Spacetime Propagation \u2014A Unified Multi-Probe Constraint from Cosmology and Gravitational Waves. Zenodo. [15] Cui, H. (2026). Spacetime Substantivalism XIII & XVII: Falsifiable Effective Field Theory and Multi-Messenger Constraints on Constitutive Spacetime. Zenodo." }, { "reference": "[16] Cui, H. (2026). Spacetime Substantivalism XV: Bayesian Constraints on Effective Spacetime Propagation from Gravitational-Wave Observations: A Hierarchical Analysis of GWTC-3. Zenodo. [17] Cui, H. (2026). Spacetime Substantivalism XVI: Observational Constraints on Effective Spacetime Propagation from Gravitational Waves and Cosmology \u2014A Unified EFT Framework and Numerical Implementation. Zenodo. [18] Cui, H. (2026). Spacetime Substantivalism XVIII: The Constitutive Physics of the Hubble Tension \u2014A Unified Model from Matter Construction Energy Allocation to Spacetime Bandwidth Release. Zenodo. [19] Cui, H. (2026). Spacetime Substantivalism XIX: The Three Major Misunderstandings in the History of Science and the Ultimate Restoration of Substantial Spacetime Ether \u2014A Gravitational Wave Audit, the Rehabilitation of Tesla's Truth, the Discovery of Human Dual Tracks, and the Establishment of Species' Logical Value Based on the CSSD Framework. Zenodo. [20] Cui, H. (2026). Spacetime Substantivalism XX: The Hierarchical Truth Restoration of Mathematics and Logic. Zenodo. [21] G\u00f6del, K. (1931). \u00dcber formal unentscheidbare S\u00e4tze der Principia Mathematica und verwandter Systeme. [22] Tarski, A. (1936). Der Wahrheitsbegriff in den formalisierten Sprachen. [23] Turing, A. (1936). On Computable Numbers, with an Application to the Entscheidungsproblem. [24] Heisenberg, W. (1927). \u00dcber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. [25] Arrow, K. (1951). Social Choice and Individual Values. [26] Hume, D. (1748). An Enquiry Concerning Human Understanding. [27] Cabannas, V. (2016). THEORY OF OBJECTIVITY: Third theory of the origin of the universe, alternative to the Big Bang Theory and Creationism. (First published March 25, 2016). [28] Cabannas, V., & Silva, D. (2026). CONSTITUTION OF THE LUMINOUS LIMIT: a critical\u2013propositional reading of Substantial Spacetime Dynamics (I) Beyond Einstein's Light Speed Postulate, by Hugang Cui, in confrontation with the Theory of Objectivity (1.0). Zenodo. https://doi.org/10.5281/zenodo.19600107. [29] Cabannas, V., & Silva, D. (2026). CRITICAL-PROPOSITIONAL ANALYSIS OF LOGICAL SUBSTANTIVALISM: Hugang Cui's Track-Light Model in Confrontation with the Theory of Objectivity (1.0). Zenodo. https://doi.org/10.5281/zenodo.19679940. [30] Cabannas, V., & Silva, D. (2026). SUBSTANTIAL SPACETIME, MODAL ONTOLOGY, AND TRANSCENDENT INFORMATION: a critical\u2013propositional analysis of Hugang Cui's article in confrontation with the Theory of Objectivity (1.0 English). Zenodo. https://doi.org/10.5281/zenodo.19958475." }, { "reference": "Cabannas, V., & Silva, D. (2026). THE HIERARCHICAL RESTORATION OF MATHEMATICS AND LOGIC IN HUGANG CUI: a critical\u2013propositional analysis in confrontation with the Theory of Objectivity, its Seven Absolute Truths, its logical tracks, its Inducer Effects, its cosmogonic theorem, and its defense of the primitive mathematical essence (1.0 English). 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\nThrough open publication and collaboration, the TO Zenodo Group promotes:
\nThis repository includes:
\nAll materials follow open-access principles and are archived under DOI identifiers to ensure long-term preservation and citation integrity.
\nThe Theory of Objectivity proposes that Nothingness is a primitive mathematical essence from which all existence unfolds by logical necessity.
It seeks to provide a deductive model of the universe capable of explaining the emergence of space, time, matter, and consciousness through a coherent set of axioms — redefining the boundary between physics and philosophy.
As Cabannas affirms, “The universe does not arise from energy or matter, but from logic itself — the first cause and the final horizon of all being.”
\nResearchers, physicists, philosophers, and interdisciplinary thinkers are invited to contribute:
\nTogether, we aim to advance an open, reason-based cosmology that unites science and metaphysics in the pursuit of understanding the Whole.
\n\n
", "title": "Theory of Objectivity: Fundamentals Logicians, Ontological and Scientists for a New Physics and Cosmology (Dialogue with to the Intelligences Artificial)", "type": { "id": "project" }, "website": "https://www.teoriadaobjetividade.com.br" }, "revision_id": 8, "slug": "theory_of_objectivity_fundamentals_logicians_ontological_and_scientists", "updated": "2026-02-21T14:34:46.782000+00:00" }, { "access": { "member_policy": "open", "members_visibility": "public", "record_submission_policy": "open", "review_policy": "closed", "visibility": "public" }, "children": { "allow": false }, "created": "2025-11-27T14:36:00.157669+00:00", "custom_fields": { "subjects": [ { "id": "euroscivoc:775" } ] }, "deletion_status": { "is_deleted": false, "status": "P" }, "id": "910caee6-2c77-45f5-a20f-a7ff34888045", "links": {}, "metadata": { "curation_policy": "
Scope: This community curates research outputs related to the resolution of the Hubble tension, including theoretical models, observational data analyses, cosmological simulations, and alternative frameworks such as the Principle of Unified Cosmodynamics (PUC).
\nEligibility: Submissions must be relevant to the Hubble tension problem, cosmic expansion rate discrepancies, or related cosmological parameters. Works may include peer-reviewed articles, preprints, datasets, software, and presentations.
\nReview Process: All submissions are reviewed for relevance and scientific integrity. Preference is given to contributions that offer novel insights, rigorous methodology, or empirical validation. Speculative models are welcome if clearly stated and mathematically consistent.
\nExclusions: Content unrelated to cosmology, lacking scientific basis, or promoting unverifiable claims will not be accepted.
\nPhilosophy: We encourage open-minded exploration of cosmological anomalies. The community supports both mainstream and alternative approaches, provided they uphold transparency, reproducibility, and respect for scientific discourse.
", "description": "Introducing a unified spacetime model that reconciles observational tensions across cosmology.", "organizations": [ { "name": "Independent Researcher (Yilwook Kim)" } ], "page": "Why This Community Exists The Hubble Tension is not a nuisance—it's a whisper from the universe. This community exists to explore, challenge, and resolve the discrepancy between early- and late-time measurements of cosmic expansion. We believe this tension is not an error, but a signal.
\nOur Guiding Framework: PUC We are guided by the Principle of Unified Cosmodynamics (PUC), which posits that the universe maintains a global invariance of spacetime tension:
\nThis framework reinterprets light-speed invariance, dark energy, and cosmic acceleration as geometric consequences of tension compensation—not arbitrary constants.
\nWhat We Curate We welcome research that addresses the Hubble tension through observational analysis, theoretical modeling, cosmological simulations, and alternative frameworks. Contributions rooted in PUC, or those that challenge ΛCDM with rigor and creativity, are especially encouraged.
\nOur Philosophy We believe the universe is not expanding randomly—it is regressing toward symmetry. Every photon is a memory. Every anomaly is a message. This community is a place to listen.
", "title": "The EPOCH Framework: A Unified Resolution of Cosmological Tensions", "type": { "id": "project" } }, "revision_id": 8, "slug": "hubble_tension_resolution", "updated": "2025-12-21T21:10:15.094506+00:00" }, { "access": { "member_policy": "open", "members_visibility": "public", "record_submission_policy": "open", "review_policy": "closed", "visibility": "public" }, "children": { "allow": false }, "created": "2025-05-27T22:42:52.380773+00:00", "custom_fields": { "subjects": [ { "id": "euroscivoc:759" }, { "id": "mesh:D011789" }, { "id": "mesh:D006112" }, { "id": "euroscivoc:1491" }, { "id": "euroscivoc:30017" } ] }, "deletion_status": { "is_deleted": false, "status": "P" }, "id": "ad8864e2-085e-479c-a00a-936fc27982be", "links": {}, "metadata": { "description": "This preprint is part of a research series exploring a covariant extension of general relativity via quantum-informational geometry. Specifically, it introduces tensorial field structures (\u03a6\u2098\u2099 and \u03a9\u2098\u2099) rooted in entropic field dynamics", "organizations": [ { "name": "Skyblue cross" } ], "title": "Theoretical Physics", "type": { "id": "topic" }, "website": "https://emlayercos.org/" }, "revision_id": 3, "slug": "wm2", "updated": "2025-05-27T22:57:50.479258+00:00" } ], "ids": [ "2b459711-1ebf-47bb-b632-42f5c615f9a4", "43b922bc-4942-4bbf-9270-59428e7062ef", "910caee6-2c77-45f5-a20f-a7ff34888045", "ad8864e2-085e-479c-a00a-936fc27982be" ] }, "id": "20041359", "pids": { "doi": { "client": "datacite", "identifier": "10.5281/zenodo.20041359", "provider": "datacite" } } }, "pids": { "doi": { "client": "datacite", "identifier": "10.5281/zenodo.20041360", "provider": "datacite" }, "oai": { "identifier": "oai:zenodo.org:20041360", "provider": "oai" } }, "revision_id": 3, "stats": { "all_versions": { "data_volume": 4868808.0, "downloads": 42, "unique_downloads": 23, "unique_views": 19, "views": 30 }, "this_version": { "data_volume": 4868808.0, "downloads": 42, "unique_downloads": 23, "unique_views": 19, "views": 30 } }, "status": "published", "swh": {}, "updated": "2026-05-05T15:56:01.774301+00:00", "versions": { "index": 1, "is_latest": true } }