Oriented Volume Spacetime Theory (OVST) Version 3.3

This is the **Version 3.3** of the Oriented Volume Spacetime Theory (OVST) preprint, a minimal conservative extension of canonical loop quantum gravity (LQG) built on the first-principle scale duality symmetry.

OVST resolves both Schwarzschild and Kerr black hole singularities in a fully background-independent framework, and provides a natural unitary framework for the black hole information paradox, while preserving all well-established kinematical results of standard LQG and reducing exactly to classical general relativity in the low-energy macroscopic limit.

Major Updates in Version 3.3 (May 9, 2026)

This version incorporates comprehensive corrections and improvements based on constructive feedback:

1. **Corrected the critical mathematical error in Appendix A**: Removed the incorrect "anomaly term sign flip" conclusion, explicitly distinguished between local and global branch flip operators, and clarified that all toy model calculations do not constitute a proof of full anomaly cancellation.
2. **Added non-trivial two-vertex chain anomaly calculation**: Extended the anomaly analysis to the two-vertex chain model, demonstrated that the cross commutator of the branch coupling term has exactly the same algebraic structure as the single-branch anomaly term.
3. **Derived explicit relation between λ and anomaly cancellation**: Obtained a closed-form expression for the coupling constant λ in terms of the anomaly cancellation condition in the simplified two-vertex toy model.
4. **Added comparison with soft hair/edge degrees of freedom and ER=EPR paradigms**: Provided a detailed, objective comparison of OVST with these two influential information paradox resolution frameworks.
5. **Added quantitative prototype of the Page curve**: Presented a numerical simulation of the Page curve in the single-vertex toy model, demonstrating the basic entropy evolution mechanism in OVST.
6. **Added discussion of the low-energy effective field theory limit**: Showed that OVST reduces exactly to classical general relativity at macroscopic scales, with only Planck-scale suppressed corrections.
7. **Fixed all technical typos**: Corrected the Kerr metric formula, the time evolution operator spelling error, and all other minor typographical errors.
8. **Softened all overclaimed statements**: Explicitly treated the full Hamiltonian constraint algebra closure as an open technical problem throughout the paper, and removed all unsubstantiated claims.

Core Rigorously Established Results

All results listed below are strictly proven within the OVST framework, independent of the resolution of the Hamiltonian constraint problem:

• First-principle constraints on the dimensionless coupling constant λ, showing it must be a dimensionless constant of order unity.
• Rigorous, fully background-independent definition of the Planck brane and Planck torus, with complete proofs of their gauge invariance, diffeomorphism invariance, scale duality fixed point property, null hypersurface property, and curvature boundedness.
• Complete resolution of the classical Schwarzschild and Kerr singularities, with all polynomial curvature invariants strictly bounded by the Planck curvature.
• Natural unitary framework for the black hole information paradox, consistent with a relational time formalism of LQG, with no information loss and no firewall at the event horizon.
• Qualitative construction of the Page curve in the full spacetime, and quantitative prototype in the single-vertex toy model.

Explicit Open Technical Challenges The following problems remain open and are explicitly stated as such in the paper:

• Full Hamiltonian constraint algebra closure in the entire Hilbert space.
• Precise determination of the coupling constant λ from first principles.
• Explicit construction of a physically meaningful relational time.
• Quantitative derivation of the Page curve in full spacetime.
• Exact constructive definition of the toroidal spin network topology for the Planck torus.
• Development of testable observational predictions.

Previous Versions

• Version 3.2 (April 22, 2026): Schwarzschild Singularity and Kerr Ring Singularity Resolution, and a Unitary Framework for the Black Hole Information Paradox DOI: [10.5281/zenodo.20084844](https://doi.org/10.5281/zenodo.20084844)
• Version 3.1 (April 21, 2026): A Dual-Branch Extension of Loop Quantum Gravity, Consistent Regularization, and Planck Brane Singularity Resolution DOI: [10.5281/zenodo.20073066](https://doi.org/10.5281/zenodo.20073066)

Citation Please cite this work as:

Jinchuan Liu. (2026). Oriented Volume Spacetime Theory: Low-Order Anomaly Cancellation Feasibility, Parameter Constraints, and Detailed Comparison with LQG Black Hole Models (Version 3.3). Zenodo. https://doi.org/10.5281/zenodo.20094898

Comments and constructive feedback are welcome. Please contact the author at 21605566@qq.com.