Published November 10, 2025
| Version v1.0
Working paper
Open
Counterfactual Echo Gain (CEG): Future-Aware Metriplectic Assistance Yields Gate-Certified Echo Improvement
Authors/Creators
Contributors
Project member:
Description
Summary:
This now includes the preregistered CEG outcome and gate statuses for the metriplectic assisted‑echo experiment. It makes no novelty claims about echo mechanisms; the claim is strictly that a model‑aware assistance micro‑sequence yields a statistically positive echo gain under instrument gates and an energy‑match constraint. Numerical scheme is treated as the measuring instrument per VDM canon.
Under preregistered conditions and strict gates, the metriplectic assisted‑echo exhibits a statistically positive CEG (median\_max 0.054552 at λ=0.5) while preserving J‑Noether and M‑monotonicity and passing Strang defect QC. This supports the preregistered claim that internal J/M knowledge can be operationally exploited to improve echo recovery without cheating via energy injection.
Original proposal description:
This is a T4 preregistration for an experiment that tests whether a metriplectic, model-aware assisted time-reversal can improve echo fidelity in the Void Dynamics Model (VDM). We define the preregistered metric Counterfactual Echo Gain (CEG) and a set of strict physics gates (J-Noether drift, M-monotonicity / H-theorem, and energy-matching) that must be satisfied. The primary hypothesis is that the median CEG across preregistered seeds will be ≥ 0.05 under the gates and controls. No results or artifacts are included here — this deposit documents the exact predictions, machine-readable specs, and provenance (commit SHA) prior to running the preregistered experiments.
Original results description:
A structure‑preserving, metriplectic Strang‑composed KG⊕RD solver is paired with a preregistered, equal‑work assisted‑echo meter (CEG). Under strict J‑Noether, M‑Lyapunov, and Strang order gates, the instrument exhibits a statistically positive counterfactual echo gain (medianλ_\lambdaλ CEG =0.054552=0.054552=0.054552 at λ=0.5\lambda=0.5λ=0.5, n=12n=12n=12 seeds), with energy parity and invariants within machine‑precision tolerances. Artifacts (CSV/JSON/PNG) and seeds are pinned for reproduction.
Files
T4_RESULTS_CEG_AssistedECHO.pdf
Files
(30.3 MB)
| Name | Size | Download all |
|---|---|---|
|
md5:f9b905b5bd4ff230843b9fad86a13125
|
15.9 MB | Preview Download |
|
md5:50a667640d331fb05e88ca8bfa0781f2
|
255.6 kB | Preview Download |
|
md5:9d0e60fdf84aca6b18931d0643f0a145
|
5.6 MB | Preview Download |
|
md5:636a7de9cd01cb8d6018517867c9116e
|
123.5 kB | Preview Download |
|
md5:3132234e2b06735179b79527647e32e1
|
67.3 kB | Preview Download |
|
md5:b2caa7d6549e2ac45347ec57212c8f6b
|
142.8 kB | Preview Download |
|
md5:984645c801548d28e621ef98ec3cc87d
|
66.8 kB | Preview Download |
|
md5:65e3a918b123b6281a6fe4ad1b9f8dce
|
70.2 kB | Preview Download |
|
md5:cae3e77ec74bb0ffaeae24c45c77418e
|
31.9 kB | Preview Download |
|
md5:c1af43d05dad012ae6da5252d563b72b
|
38.1 kB | Preview Download |
|
md5:a824e1a8a286c581de675ac9894ae581
|
27.4 kB | Preview Download |
|
md5:0d0b1ebbb4ca0649aaa1528be6af9dd6
|
186.5 kB | Preview Download |
|
md5:34fb75f4bb7bbe09d31cd43db1786c8a
|
36.4 kB | Preview Download |
|
md5:bb66779cb99fab2906e8851b32d52309
|
286.2 kB | Preview Download |
|
md5:471a945e267109ca381030b01ee1fbc8
|
16.2 kB | Preview Download |
|
md5:5798b91c6481339cde3856557fc0ae63
|
1.2 MB | Preview Download |
|
md5:9995dc52b74c13b7d7a9eb85c3f17c76
|
6.2 MB | Preview Download |
|
md5:cb91547003993cb2adf744bcbb371ecd
|
9.4 kB | Preview Download |
Additional details
Additional titles
- Other (En)
- Counterfactual Echo Gain (CEG): A Metriplectic Assisted-Echo Experiment Proposal in VDM
Dates
- Submitted
-
2025-11-04Added to Zenodo for provenance
- Updated
-
2025-11-10Attached preregistered results
Software
- Repository URL
- https://github.com/justinlietz93/Prometheus_VDM/tree/main/Derivation/code/physics/metriplectic
- Programming language
- Python
- Development Status
- Active
References
- J. K. Lietz, T4 — Counterfactual Echo Gain (CEG): A Metriplectic Assisted-Echo Experiment in VDM (Preregistration / Proposal), 2025. Zenodo / repository draft (preregistration text). Commit: 80ee5476e4f887fed3c34534a99daa878f55382f. Contact: justin@neuroca.ai. ORCID: 0009-0008-9028- 1366.
- J. K. Lietz, VDM: Metriplectic Assisted-Echo — code and experiment artifacts (repository snapshot), 2025. Git repository, commit 80ee5476e4f887fed3c34534a99daa878f55382f (useful for provenance).
- VDM EQUATIONS Registry, EQUATIONS Registry — discrete action, Euler–Lagrange and RD/KG update forms, 2024. VDM instrument registry (instrument manual for assisted-echo experiment).
- E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed., Springer, 2006.
- G. Strang, "On the construction and comparison of difference schemes," SIAM Journal on Numerical Analysis, 1968. (Classic reference for operator splitting — Strang splitting.)
- P. J. Morrison, "Foundations of metriplectic (Hamiltonian + dissipative) formulations," review articles and technical notes (see Morrison's bracket papers on Hamiltonian/dissipative combinations; add DOI if required).
- L. Boltzmann, "Further Studies on the Thermal Equilibrium of Gas Molecules," Wiener Berichte, 1872. (Historical source for H-theorem / entropy increase.)
- A. M. Turing, "The Chemical Basis of Morphogenesis," Philosophical Transactions of the Royal Society B, 1952. (Classic RD / pattern formation reference.)
- C. R. Harris et al., "Array programming with NumPy," Nature, 2020. (Cite NumPy for array/numerical founda- tions.)
- P. Virtanen et al., "SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python," Nature Methods, 2020.
- Python Software Foundation, Python Language Reference, version 3.11+, 2023. https://www.python.org/.
- M. Frigo and S. G. Johnson, "FFTW: Fastest Fourier Transform in the West," software/library, 1998–2005.
- J. K. Lietz, APPROVAL.json — preflight and approval manifest (excerpt), 2025. (Derivation/code/physic- s/metriplectic/APPROVAL.json.)
- J. K. Lietz, LICENSE, 2025. Project root LICENSE file included with repository and Zenodo deposit.
- J. K. Lietz, echo specs, 2025.(Derivation/code/physics/metriplectic/schemas/echospec−v1.schema.json.)
- Google Quantum AI and Collaborators. Observation of constructive interference at the edge of quantum ergodicity. Nature, 646:825–830, 2025. doi:10.1038/s41586-025-09526-6. URL https://doi.org/10.1038/ s41586-025-09526-6.
- Google Quantum AI. Supplementary information (moesm1 esm) for s41586-025-09526-6. https: //static-content.springer.com/esm/art%3A10.1038%2Fs41586-025-09526-6/MediaObjects/ 41586_2025_9526_MOESM1_ESM.pdf, 2025. Supplementary methods and extended echo diagrams.
- X. Li, Y. Zhang, and et al. Quantum computation of molecular geometry via nuclear spin echoes. 2025. URL https://arxiv.org/abs/2510.19550.
- Philip J. Morrison. Bracket formulation for irreversible classical fields. Physica D: Nonlinear Phenomena, 18 (1-3):410–419, 1986.
- Hans Christian Öttinger and Miroslav Grmela. Dynamics and thermodynamics of complex fluids. i. develop- ment of a general formalism. Physical Review E, 56(6):6620–6632, 1997. doi:10.1103/PhysRevE.56.6620.
- Miroslav Grmela and Hans Christian Öttinger. Dynamics and thermodynamics of complex fluids. ii. illustra- tions of a general formalism. Physical Review E, 56(6):6633–6655, 1997. doi:10.1103/PhysRevE.56.6633.
- Gilbert Strang. On the construction and comparison of difference schemes. SIAM Journal on Numerical Analysis, 5(3):506–517, 1968. doi:10.1137/0705041.
- E. L. Hahn. Spin echoes. Physical Review, 80:580–594, 1950. doi:10.1103/PhysRev.80.580.
- Asher Peres. Stability of quantum motion and fidelity. Physical Review A, 30:1610–1615, 1984. doi:10.1103/PhysRevA.30.1610.
- R. A. Jalabert and H. M. Pastawski. Environment-independent decoherence rate in classically chaotic systems. Physical Review Letters, 86:2490–2493, 2001. doi:10.1103/PhysRevLett.86.2490.
- T. Gorin, T. Prosen, T. H. Seligman, and M. Znidaric. Dynamics of loschmidt echoes and fidelity decay. Physics Reports, 435(2-5):33–156, 2006. doi:10.1016/j.physrep.2006.09.003.
- A. I. Larkin and Y. N. Ovchinnikov. Quasiclassical method in the theory of superconductivity. Soviet Journal of Experimental and Theoretical Physics, 28:1200, 1969.
- Stephen H. Shenker and Douglas Stanford. Black holes and the butterfly effect. Journal of High Energy Physics, 2014(03):067, 2014. doi:10.1007/JHEP03(2014)067.
- J. Maldacena, S. H. Shenker, and D. Stanford. A bound on chaos. Journal of High Energy Physics, 2016(08): 106, 2016. doi:10.1007/JHEP08(2016)106.
- Brian Swingle. Unscrambling the physics of out-of-time-order correlators. Nature Physics, 14:988–990, 2018. doi:10.1038/s41567-018-0295-5.
- Ernst Hairer, Christian Lubich, and Gerhard Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, volume 31 of Springer Series in Computational Mathematics. Springer, 2 edition, 2006. doi:10.1007/3-540-30666-8.
- Benedict Leimkuhler and Sebastian Reich. Simulating Hamiltonian Dynamics. Cambridge University Press, 2004. doi:10.1017/CBO9780511614118.
- Hans Christian Öttinger. Beyond Equilibrium Thermodynamics. Wiley, 2005. ISBN 978-0471666585. Miroslav Grmela. Multiscale thermodynamics. Entropy, 20(10):706, 2018. doi:10.3390/e20100706. 14
- Data-driven reconstruction of a multivariate langevin equation to model complex systems. Derivation/References/Reaction-Diffusion/ data-driven-reconstruction-of-a-multivariate-langevin-equation-to-model-complex-systems. pdf. PDF artifact in repository.
- Justin K. Lietz. Echoes of mind: Google's otoc vs vdm's metriplectic echo. PDF artifact within repository, 2025b. GoPenAI article, Oct 2025. PDF available in repository root.
- Justin K. Lietz. A logarithmic first integral for the logistic on site law in void dynamics (code + figures + manifests). https://doi.org/10.5281/zenodo.17220869, 2025a.
- Justin K. Lietz and Inc. Neuroca. Prometheus_void-dynamics_model. https://github.com/ justinlietz93/Prometheus_VDM, 2025. Public repository with metriplectic harness, artifacts, and result slugs.