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.

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.

Paper B: Fixing the Measure: Symmetry and the Geometric Origin of the Born Rule

Extending volume-based probability within a constrained geometric framework.

What this paper achieves

  • Generalises the volume-based probability construction beyond minimal toy settings.

  • Identifies the geometric conditions under which probability assignments remain consistent.

  • Clarifies limitations and non-uniqueness in outcome partitioning.

  • Places probability within a constrained-geometry framework rather than as an axiom.

Paper C: A Deterministic Reconstruction of Finite-Dimensional Quantum Mechanics

Recovering operational quantum mechanics without Hilbert-space primacy.

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.

Paper D: An Ontological Completion of Geometric Quantum Mechanics

A unifying geometric framework for quantum systems and measurement.

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.

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.

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.

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

Engagement:

  • Zenodo: 544 views, 402 downloads.

  • Qeios: 952 views, 256 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.

Engagement:

  • Zenodo: 564 views, 428 downloads.

  • Qeios: 1263 views, 481 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

Engagement:‍ ‍Zenodo: 81 views, 54 downloads.

Engagement:‍ ‍Zenodo: 496 views, 273 downloads.

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.