Papers
This page lists the published and in-progress papers associated with the Constraint-Surface Dynamics (CSD) research programme.
For clarity and citation integrity, Zenodo is used as the canonical archive for each paper.
Other platforms are used for open discussion and discovery.
See alternative reading entry points in the shaded box.
Paper A: Volume-Based Probability: Outcome Frequencies from Deterministic Geometry
A geometric account of outcome frequencies compatible with the Born rule.
Canonical version (DOI): https://doi.org/10.5281/zenodo.15564079
Open commentary: https://www.qeios.com/read/53GI1K
What this paper achieves
Defines outcome regions geometrically rather than probabilistically.
Shows how relative frequencies arise from volume ratios under deterministic dynamics.
Demonstrates compatibility with Born-rule statistics without introducing randomness or collapse.
Clarifies the role of typicality in quantum probability.
Engagement:
Zenodo: 744 views, 579 downloads.
Qeios: 1530 views, 483 downloads. 1 Peer review (3/5)
Qeios, 27/10/2025: William Sulis, McMaster University, Canada: This is a nicely written paper describing how probabilistic frequency values can arise from strict deterministic dynamics through coarse graining.
Paper B: Fixing the Measure: Symmetry, Projective Volume and the Born Rule in Deterministic Geometry
Extending volume-based probability within a constrained geometric framework.
Canonical version (DOI): https://doi.org/10.5281/zenodo.16746829
Open commentary: https://www.qeios.com/read/4EN2OA
What this paper achieves
Separates three questions usually run together: which measure, how weights attach to outcomes, and why frequencies follow.
Fixes the Fubini–Study measure as the unique unitary-invariant one, machine-checked in Lean 4 at general finite N.
Derives the Born weights as barycentric region volumes under the toric moment map, for all finite dimensions including vanishing weights.
Keeps the Gleason-type operational route as corroboration rather than as the load-bearing argument.
Engagement:
Zenodo: 773 views, 512 downloads.
Qeios: 2354 views, 1102 downloads. 4 Peer review (3.13/5)
Qeios, 09/01/2026: Angelo Plastino, Universidad Nacional de La Plata, Argentina: The revised paper is now acceptable. The work could become a meaningful contribution to the study of quantum - classical analogies and foundational structures of quantum mechanics.
Cited: Inge Helland, Professor Emeritus at University of Oslo, Norway in “An alternative foundation of quantum theory”, see: arXiv: [2305.06727] An alternative foundation of quantum theory
Paper C: A Deterministic Reconstruction of Finite-Dimensional Quantum Mechanics
Recovering operational quantum mechanics without Hilbert-space primacy.
Canonical version (DOI): https://doi.org/10.5281/zenodo.18098064
What this paper achieves
Reconstructs key operational elements of finite-dimensional quantum mechanics from geometric structure.
Accounts for interference and contextuality without invoking wavefunction ontology.
Defines measurement outcomes through apparatus-induced geometric partitions.
Demonstrates how standard quantum statistics are recovered at the operational level.
Engagement: Zenodo: 123 views, 82 downloads.
Paper D: An Ontological Completion of Geometric Quantum Mechanics
A unifying geometric framework for quantum systems and measurement.
Canonical version: https://doi.org/10.5281/zenodo.17515369
What this paper achieves
Synthesises the CSD framework into a single, coherent conceptual structure.
Clarifies assumptions, scope, and relationship to geometric quantum mechanics.
Separates established results from open problems and future extensions.
Provides a roadmap for extending the framework to multi-system and field-theoretic contexts.
Engagement: Zenodo: 698 views, 369 downloads.
C1: Machine-Checked Bell-Violating Correlations with Deterministic Outcomes and Local Measurement Dynamics: A Lean 4 Formalisation
A machine-verified demonstration that deterministic outcomes, local measurement dynamics, Bell violation and operational no-signalling can coexist within a single contextual framework.
Canonical version (DOI): https://doi.org/10.5281/zenodo.21936298
Lean 4 release: https://github.com/zblore/csd-lean4/releases/tag/v1.4.1-c1-complete
Formal theorem source: https://github.com/zblore/csd-lean4/blob/v1.4.1-c1-complete/CsdLean4/LF6/C1BellConsistency.lean
What this paper achieves
Constructs explicit deterministic, context-indexed outcome maps on a shared ontic probability space.
Reproduces the complete two-qubit singlet probability table, the correlation E(a,b) = −a · b, and the maximal CHSH value 2√2.
Proves that no compatible global assignment across the four CHSH settings can reproduce the singlet correlations.
Shows that locally factorised measurement dynamics can coexist with Bell-violating correlations that cannot be reduced to Bell-local product outcomes.
Verifies uniform local marginals and operational no-signalling.
Clarifies why deterministic realised outcomes do not imply pre-existing values for incompatible measurements that were not performed.
Machine-checks the central results in Lean 4 and anchors them to the immutable v1.4.1-c1-complete release.
C2: The PBR Theorem Revisited: Epistemic States and Distinct Preparation Measures
A machine-checked separation of two senses of epistemic, showing that distinct exact CSD preparations are mutually singular and so already satisfy the PBR disjointness conclusion.
Canonical version (DOI): https://doi.org/10.5281/zenodo.22177604
What this paper achieves
Proves that mutual singularity of two pushforward measures under a measurable map pulls back to the original measures.
Shows that distinct exact sharp CSD preparations are mutually singular, so the canonical exact interface is psi-ontic in the technical Harrigan-Spekkens sense.
Establishes that the single-system overlap premise required to start the PBR argument is therefore absent, with no appeal to preparation independence needed.
Distinguishes exact sharp preparations from finite-resolution region preparations, which admit a Fubini-Study density and may overlap.
Withdraws the earlier inference from global symplectic non-factorisation to failure of PBR preparation independence, which is no longer needed.
Machine-checks the preparation results in Lean 4.
LF1: Machine-Verified Volume Typicality and Frequency Convergence for Deterministic Repeated Trials
A Lean4/Mathlib formalisation of the repeated-trial typicality theorem underlying Paper A.
Canonical version (DOI): https://doi.org/10.5281/zenodo.19472011
GitHub repository: https://github.com/zblore/csd-lean4
What this paper achieves
Formalises the repeated-trial frequency theorem for deterministic measurable dynamics.
Makes the probabilistic assumptions and imported theorem dependencies fully explicit.
Provides the first formal Lean module in the CSD programme.
Serves as the theorem-level formal companion to Paper A and the base for later LF2-LF5 work.
LF2: The Measure Bridge and Born-Weight Wrapper
The second Lean formalisation paper in CSD, formalising the finite-dimensional measure-and-weight layer between deterministic volume typicality and the later operational reconstruction.
Canonical version (DOI): https://doi.org/10.5281/zenodo.20100580
GitHub repository: https://github.com/zblore/csd-lean4
What this paper achieves:
It formalises the measure bridge
It defines projective weights from ontic preparation measures
It packages the Born-weight layer in a formal Lean-compatible way
It makes the LF1 to LF2 interface explicit
It makes the internal versus imported theorem boundary explicit
It establishes LF2 as the second achieved Lean milestone
LF3: Machine-Verified Singlet Kernel, Sector Volumes, and Empirical Chain Capstones for Bell-Singlet Correlations
The third Lean formalisation paper in CSD, formalising the finite-dimensional Bell-singlet sector through projective pointer readout, sector volumes, no-signalling marginals, finite-leakage stability, and empirical-chain convergence.
Canonical version (DOI): https://doi.org/10.5281/zenodo.20354293
GitHub repository: https://github.com/zblore/csd-lean4
What this paper achieves:
It formalises the Bell-singlet probability kernel
It defines sector volumes for projective pointer-sector readout
It verifies the Bell-singlet correlation E(a,b) = -a · b
It verifies the no-signalling marginal identities
It formalises structural finite-leakage stability
It distinguishes context-indexed outcome maps from global CHSH assignments
It exports six empirical-chain capstones connecting LF1, LF2, and LF3
It makes the structural-interface boundary explicit, including the fact that LF3 does not derive microscopic pointer dynamics from first principles
It establishes LF3 as the third achieved Lean milestone
How to cite
Please cite the Zenodo DOI for any paper listed here.
Other platforms host discussion or discovery copies only.
Each paper PDF also contains a citation note clarifying the canonical source.
Canonical archive
All definitive versions, version history, and DOIs are hosted on Zenodo.
Author profiles
ORCID profile: https://orcid.org/0009-0009-8447-7247
QEIOS profile: https://www.qeios.com/profile/104703
Status and transparency
The CSD programme is developed openly.
Achieved results are stated explicitly
Open problems and deferred work are clearly identified
No claims are made beyond the scope of the published papers
Future papers will be listed here as they become available.
Discussion and feedback
Critical comments, questions, and corrections are welcome.
Use Qeios for public technical discussion
Or contact directly via the Contact page
Alternative Entry Points by Reader Type
Constraint-Surface Dynamics attracts readers with very different motivations. The programme is modular, and not everyone should start at the same place. Below are five common entry profiles, with a recommended path for each.
1. Foundations and Interpretation Researchers
You care about:
measurement, probability, realism, contextuality, Bell, Kochen–Specker, PBR.
Start here:
Paper A
Paper C
Paper D
Why this order:
Paper A reframes probability without stochastic postulates. Paper C shows how quantum statistics, contextuality, and measurement emerge from deterministic geometry. Paper D clarifies how this avoids collapse, many-worlds branching, and hidden-variable value assignments.
What to ignore initially:
Technical appendices in Paper C unless a specific construction is under scrutiny.
2. Mathematical Physicists and Geometers
You care about:
symplectic geometry, Kähler manifolds, invariant measures, Hamiltonian flows.
Start here:
Paper B
Paper C (Sections 2–4, Appendices E, H, I)
Paper A
Why this order:
Paper B fixes the probability measure using symmetry alone. Paper C develops the projected Hamiltonian structure and geometric measurement partitions. Paper A provides the measure-theoretic typicality result that closes the probabilistic loop.
What to treat as assumptions:
The existence of the projection π. This is an explicit open problem.
3. Quantum Information and Computation Researchers
You care about:
states, gates, noise, decoherence, contextuality as a resource.
Start here:
Paper C (Sections 3–6)
Paper B (for measure justification)
Paper A (optional background)
Why this order:
Paper C reconstructs unitary dynamics, composite systems, interference, and contextuality entirely within finite-dimensional projective geometry. This is the operational layer relevant to circuits and algorithms.
What is not required:
Ontic commitments about Σ. All operational results are epistemic.
4. Experimentalists and Quantum Sensing Researchers
You care about:
interference visibility, decoherence, measurement stability, precision limits.
Start here:
Paper C (Sections 5–6, Appendices B–E)
Paper A (conceptual background)
Why this order:
Measurement outcomes are modeled as geometric partitions with well-defined volumes. Interference and decoherence acquire geometric diagnostics that can be compared with standard experimental figures of merit.
What to skip:
Interpretational discussion unless needed for context.
5. Philosophically Inclined Physicists and Advanced Students
You care about:
what quantum mechanics is actually saying, without metaphysics or mysticism.
Start here:
Paper D
Paper C
Paper A
Why this order:
Paper D provides the conceptual map. Paper C shows that the map corresponds to a working formalism. Paper A explains why probability appears at all in a deterministic theory.
What to keep in mind:
CSD is a reconstruction, not a claim of finality. Some structures are assumed and explicitly flagged as such.
Important Note on Scope
All current papers fully address finite-dimensional, nonrelativistic quantum mechanics.
Questions of spacetime emergence, field theory, and infinite-dimensional limits are deferred to Paper Σ and are treated as open research problems, not resolved results.