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Published September 27, 2026 | Version v3
Preprint Open

Unitary Black Hole Page Curve Reconstruction via Wormhole Error-Kernel Invariants: Non-Dissipative State Preservation, 40-Core Bare-Metal Telemetry, and Formal Verification

Authors/Creators

  • 1. ROR icon Anadolu University
  • 2. ITouch Systems
  • 3. ROR icon Mersin Üniversitesi
  • 4. Yusuf Kalkavan Anadolu Lisesi
  • 5. Toros Science College

Description

Version 3.0 Major Theoretical Upgrade & Extended Monograph (12 Pages, Formal Lean 4 Verification, Exact GKP Unitarity, and Kerr Polar Collimation)

This monograph presents an exact, unitary, and non-dissipative resolution to the black hole information paradox and the AMPS firewall controversy through the Wormhole Error-Kernel Invariant (Κerror ⊂ ℤ/9ℤ), bridging quantum error correction, semiclassical general relativity, and bare-metal high-performance computation.

Key Theoretical Breakthroughs in Version 3.0:

  • Continuous-Variable GKP Isometric Embedding (Φ): Rigorously proves that infalling continuous bulk wavepackets are mapped into discrete modular kernel codewords via Φ : ℋcont → ℋmod satisfying Φ†Φ = 𝕀C. The reverse map ℛreturn = Φ† guarantees mathematical reversibility and zero quantum information loss (lossless isometric projection).
  • Kerr Metric Anisotropy & Relativistic Polar Jet Collimation: Solves horizon dynamics for rotating Kerr black holes (a* → 1). Proves that while equatorial collapse is topologically blocked by relational saturation (θ = π/2, Δr ≈ 0.69M), polar channels (θ → 0, π, Δr → 0) naturally form open wormhole throats (B1, B2), directly explaining astrophysical jet collimation (e.g. M87*, microquasars) and quasi-periodic oscillation (QPO) signatures.
  • Boundary Chern-Simons Level-9 Holonomy: Derives the vanishing horizon stress-energy tensor ⟨Tμν, Κerror⟩ = 0 from topological boundary holonomies on ∂ℳ, proving complete firewall suppression (573× damping) without violating the equivalence principle for infalling observers.
  • 10 Machine-Verified Lean 4 Theorems (Zero Sorry): Formally certified against Lean v4.34.1 + Mathlib4 (Zenodo Record: 10.5281/zenodo.22983889), proving modular invariance, error-kernel orthogonality, fixed-point Q16.16 arithmetic overflow safety, and non-constant topological spectra via pure kernel reflection with zero speculative axioms.
  • Physical Dimensional Scaling: Establishes complete bridge tables translating dimensionless simulation units into SI physical dimensions across astrophysical scales (1 M⊙ solar-mass black holes to supermassive black holes and primordial remnants).

Reproducibility & Bare-Metal Telemetry

Full 40-core bare-metal verification conducted on dual Intel Xeon architecture (80 hardware threads, 256 GB RAM, Debian 12 Linux kernel 6.1.0-41-amd64). Complete raw telemetry, JSON datasets, verification scripts, and XeLaTeX production sources are included in the supplementary bundles.

Files

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Additional details

Cites
Preprint: arXiv:2609.25498 (arXiv)
Preprint: 10.5281/zenodo.22983889 (DOI)
Preprint: 10.5281/zenodo.22867037 (DOI)
Preprint: 10.5281/zenodo.22900465 (DOI)
Preprint: 10.5281/zenodo.22939253 (DOI)
Preprint: 10.5281/zenodo.22942599 (DOI)
Preprint: arXiv:2609.30115 (arXiv)
Is new version of
Preprint: 10.5281/zenodo.22962000 (DOI)
Is supplemented by
Other: https://pcworm.net/ (URL)
Software: https://github.com/pCwOrM/mandelbrot-fractal-neural-synthesis (URL)
Software: https://github.com/pCwOrM/werr (URL)

References

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  • Hawking, S. W. (1976). Breakdown of predictability in gravitational collapse. Physical Review D, 14(10), 2460-2473. https://doi.org/10.1103/PhysRevD.14.2460
  • Page, D. N. (1993). Average entropy of a subsystem. Physical Review Letters, 71(9), 1291-1294. https://doi.org/10.1103/PhysRevLett.71.1291
  • Page, D. N. (1993). Information in black hole radiation. Physical Review Letters, 71(23), 3743-3746. https://doi.org/10.1103/PhysRevLett.71.3743
  • Page, D. N. (2013). Time dependence of Hawking radiation entropy. Journal of Cosmology and Astroparticle Physics, 2013(09), 028. https://doi.org/10.1088/1475-7516/2013/09/028
  • Almheiri, A., Marolf, D., Polchinski, J., & Sully, J. (2013). Black holes: complementarity or firewalls? Journal of High Energy Physics, 2013(2), 62. https://doi.org/10.1007/JHEP02(2013)062
  • Maldacena, J., & Susskind, L. (2013). Cool horizons for entangled black holes. Fortschritte der Physik, 61(9), 781-811. https://doi.org/10.1002/prop.201300020
  • Hayden, P., & Preskill, J. (2007). Black holes as mirrors: quantum information in random subsystems. Journal of High Energy Physics, 2007(09), 120. https://doi.org/10.1088/1126-6708/2007/09/120
  • Penington, G. (2020). Entanglement wedge reconstruction and the information paradox. Journal of High Energy Physics, 2020(9), 2. https://doi.org/10.1007/JHEP09(2020)002
  • Almheiri, A., Engelhardt, N., Marolf, D., & Maxfield, H. (2019). The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole. Journal of High Energy Physics, 2019(12), 63. https://doi.org/10.1007/JHEP12(2019)063
  • Almheiri, A., Mahajan, R., Maldacena, J., & Zhao, Y. (2020). The Page curve of Hawking radiation from semiclassical geometry. Journal of High Energy Physics, 2020(3), 149. https://doi.org/10.1007/JHEP03(2020)149
  • Almheiri, A., Hartman, T., Maldacena, J., Shaghoulian, E., & Tajdini, A. (2021). The entropy of Hawking radiation. Reviews of Modern Physics, 93(3), 035002. https://doi.org/10.1103/RevModPhys.93.035002
  • Dağlı, V. (2026). Yörüngesel Hata Dinamikleri ve Sıfır Bellekli Fraktal Sinirsel Sentez Yöntemi. Türk Patent ve Marka Kurumu, Başvuru No: TR 2026/016285.
  • Dağlı, V., Dağlı, Z., & Dağlı, D. (2026). Mandelbrot Fractal Neural Synthesis: Zero-storage procedural weight derivation and non-linear decision boundaries (v3). Zenodo. https://doi.org/10.5281/zenodo.22867037
  • Dağlı, V., Dağlı, Z., & Dağlı, D. (2026). Orbital Error Dynamics: Self-organized criticality, ephemeral parameter resonance, and non-linear biological ontologies in zero-storage neural synthesis (v3). Zenodo. https://doi.org/10.5281/zenodo.22900465
  • Dağlı, V., Dağlı, Z., & Dağlı, D. (2026). WERR: A Deterministic Fractal Decision Engine with Zero Floating-Point Arithmetic and Sub-Microsecond Execution. arXiv:2609.25498 [cs.AI]. https://arxiv.org/abs/2609.25498
  • Dağlı, V., Dağlı, Z., & Dağlı, D. (2026). Universal Fractal Natural Language Decision Map: Real-time edge triage across heterogeneous domains (v2). Zenodo. https://doi.org/10.5281/zenodo.22939253
  • Dağlı, V., Dağlı, Z., & Dağlı, D. (2026). Werracle: Sub-cent intra-block AI reflex oracles and flash-loan circuit breakers for EVM smart contracts. Zenodo. https://doi.org/10.5281/zenodo.22942599
  • Dağlı, V., Dağlı, Z., & Dağlı, D. (2026). Formal Verification of the WERR Invariant Kernel and Unitary Non-Dissipative Subspaces in Lean 4. Zenodo. https://doi.org/10.5281/zenodo.22974544