Quantum mechanics is the effective theory of physically real unresolved admissible structures and their resolution. This paper establishes the minimal axiomatic foundation from which this claim follows: physical structure is derived from a single primitive, the local structure of admissible transitions between observable states. Four axioms govern this structure: local projective admissibility (A1), structural non-injectivity (A2), admissibility as non-premature selection (A3), and projection locking (A4). Along the transitions A2 asserts to be generically non-injective, A1 and A2 give immediate-image information loss and structural fluctuations; neither permanent non-recovery nor the arrow of time follows, since non-invertible steps admit cycles. From A3, we derive the proto-state as a physically real unresolved configuration shared between two successive states, and show that admissibility forces the retention of phase coherence. Under an explicit representation-theoretic reading of the admissible fibre, A3 forbids invariant factorisation and hence imposes irreducibility. For a carrier of dimension greater than one generated by a conjugate pair, irreducibility implies non-commutation. It does not, however, make the commutator central or select a finite Heisenberg group: an explicit $\mathfrak{S}_3$ countermodel satisfies the extracted carrier contract and violates that conclusion. The Heisenberg carrier used by the spectral programme therefore remains a supplied realisation, and must be distinguished from its associated Weil representation. From A4, we derive the discrete character of quantum transitions as a consequence of the interaction between continuous Born–Infeld saturation and the discrete shell structure of the observable space. The foundation is stated with the point at which it stops short of carrier selection.
Quantum mechanics is the effective theory of physically real unresolved admissible structures and their resolution. This paper establishes the minimal axiomatic foundation from which this claim follows: physical structure is derived from a single primitive, the local structure of admissible transitions between observable states. Four axioms govern this structure: local projective admissibility (A1), structural non-injectivity (A2), admissibility as non-premature selection (A3), and projection locking (A4). Along the transitions A2 asserts to be generically non-injective, A1 and A2 give immediate-image information loss and structural fluctuations; neither permanent non-recovery nor the arrow of time follows, since non-invertible steps admit cycles. From A3, we derive the proto-state as a physically real unresolved configuration shared between two successive states, and show that admissibility forces the retention of phase coherence. Under an explicit representation-theoretic reading of the admissible fibre, A3 forbids invariant factorisation and hence imposes irreducibility. For a carrier of dimension greater than one generated by a conjugate pair, irreducibility implies non-commutation. It does not, however, make the commutator central or select a finite Heisenberg group: an explicit S3 countermodel satisfies the extracted carrier contract and violates that conclusion. The Heisenberg carrier used by the spectral programme therefore remains a supplied realisation, and must be distinguished from its associated Weil representation. From A4, we derive the discrete character of quantum transitions as a consequence of the interaction between continuous Born–Infeld saturation and the discrete shell structure of the observable space. The foundation is stated with the point at which it stops short of carrier selection.
Quantum mechanics is widely regarded as a fundamental theory of physical reality. In this work, we demonstrate that this status is not supported at the structural level. The quantum formalism is shown to be neither closed nor generative, relying on externally imposed elements such as probabilistic rules and measurement prescriptions. We introduce a closed variational framework based on a quartic functional, from which admissible configurations emerge through explicit variation. The second variation defines a Hessian operator whose spectral structure exhibits intrinsic discreteness and degeneracy, without the introduction of quantization postulates. We prove that apparent probabilistic behavior arises from structural degeneracy and indistinguishability of admissible configurations, rather than from intrinsic indeterminism. The role of wavefunction collapse is replaced by a global deterministic selection functional applied to the set of stationary solutions. Within this framework, quantum states, probabilities, and observables are reinterpreted as effective representations of an underlying deterministic structure. Consequently, quantum mechanics does not constitute a fundamental description of physical reality, but a statistical projection of unresolved structural configurations.
Admissibility Physics — Quantum Structure from Finite Enforceability (Paper 5) This Zenodo community collects research outputs associated with Admissibility Physics, with primary focus on Paper 5 — Quantum Structure from Finite Enforceability and the derivation of quantum mechanics as an admissible representational regime. Paper 5 shows that the mathematical structure of quantum mechanics—Hilbert space, linearity, inner products, tensor products, unitary evolution, CPTP maps, and the Born rule—is not postulated, but forced by admissibility once coherent, jointly enforceable distinctions exist under finite correlation capacity. Quantum structure emerges as the unique bookkeeping required to represent interference, refinement, and recombination while preserving admissibility. The derivation does not assume probability, measurement postulates, dynamics, or spacetime geometry. Probability enters only as a secondary representation, with the Born rule arising uniquely from admissibility invariance and refinement consistency. Measurement is treated as a regime transition associated with saturation and record formation, not as a fundamental collapse mechanism. Quantum mechanics is shown to be conditionally valid: exact in regimes where coherence and non-saturation permit admissible composition, and structurally inapplicable where capacity is exhausted. Monogamy, entanglement limits, and decoherence follow from non-closure under composition and finite interface capacity, rather than from quantum axioms. All subsequent works in this community rely on the quantum-admissible representation established in Paper 5. Later papers show how variational dynamics and spacetime geometry arise as further conditional representations layered on top of quantum structure, and how quantum description itself fails at saturation boundaries, horizons, and measurement-like events. This community serves as a curated, citable archive centered on the derivation and limits of quantum structure within Admissibility Physics. Paper 5 functions as the representational keystone of the program: the point at which finite enforceability yields the quantum formalism without postulation. Core papers are frozen where noted; companion papers, mathematical appendices, figures, and computational artifacts document derivations, regime conditions, and testable consequences.
Living Field Theory (LFT) proposes that physical structure is described fundamentally by a single real field together with constraints on its admissible histories. This paper investigates the emergence of quantum-mechanical structure within the coherent sector of that framework. A phase-active real coherent carrier equipped with a compatible positive quadratic form is shown to admit an effective complex structure and associated symplectic geometry without requiring a primitive complex field. Predictive equivalence under nonzero coherent scaling yields projective state geometry without requiring a dynamically selected universal fixed-action shell. Stable detector outcomes are represented by disjoint families of admissible Living-Field histories. Their weighted history measure is therefore additive under physical refinement. When the corresponding detector refinement occurs coherently before stable record formation, projective detector weights satisfy x=x1+x2x=x_1+x_2. Requiring a common continuous response law P=f(x)P=f(x) to remain consistent under such refinement gives f(x+y)=f(x)+f(y)f(x+y)=f(x)+f(y). Together with f(0)=0f(0)=0 and f(1)=1f(1)=1, this uniquely yields f(x)=xf(x)=x, giving the Born weighting rule Pi=∣⟨ei∣Ψ⟩∣2P_i=|\langle e_i|\Psi\rangle|^2 for normalized states and orthonormal detector channels. The work also distinguishes pre-record coherent refinement from post-record subdivision and examines several unsuccessful stronger emergence routes, including universal fixed-action-shell selection, norm preservation as sufficient for unitary dynamics, and derivation of Hamiltonian time evolution from a positive fluctuation Hessian alone. The result is a conditional derivation of Born weighting within the LFT coherent-sector bridge. It does not claim an unconditional derivation of quantum mechanics from the minimal Living-Field ontology. The remaining problem is localized to the primitive provenance of the required coherent carrier, compatible metric, detector-response structure, and accessible coherent refinements.
This paper argues that quantum mechanics is not a separate postulate system to be reconciled with spacetime physics. It is the boundary algebra of a non-invertible projection: the algebraic structure that a globally coherent bulk field is forced to produce when it becomes observable. The bulk field is a Majorana spinor, Ξ = CΞ̄, on M^5 = R^4 × S^1(τ), governed by a single conservation law. The projection Π onto the observable boundary is not an external measurement device added afterward: it is the form the field must take in order to admit an observable image at all. What survives Π defines the observable sector; what enters ker Π is lost structurally, not thermodynamically. From this single mechanism, four boundary structures emerge: the Hilbert space of quantum mechanics, physical time, matter stability, and the Born rule. These are four boundary readings of one conservation law, K_τ = ξη = α^−1, resolved by the same tangential dynamics on the invariant surface Σ. Observable states are equivalence classes [Ξ] = Ξ + ker Π. The Born rule is the canonical quadratic probability measure induced by the projection geometry. Measurement irreversibility is the non-injectivity of Π, with non-vanishing protected by the transcendence of π. Physical time is not assumed in advance: it emerges as the output of chiral projection through a conformal map from the compact cyclic fibre to the irreversible real line. The Wheeler–DeWitt equation is not a paradox but the correct timeless description of the bulk. Spacetime emerges after quantum mechanics, not before it. The fine-structure constant is not a free parameter. It is the unique observable residue forced by the self-coherent projection structure. The double-slit interference pattern, the Born rule, and measurement irreversibility are derived as structural corollaries of this paper in the companion work doi:10.5281/zenodo.19654630
The Admissibility of Natural Physics, Part I begins where an admissibility-first reconstruction of single-system quantum mechanics ends. Its central question is not whether the familiar tensor-product formalism can be assumed, but whether any physical composition law can be derived without importing composite systems, global state spaces, entanglement, locality, or signalling as primitives. The book develops a disciplined reconstruction of binary quantum composition from operational and structural requirements. It first records the exact content and limitations of the inherited single-system closure, establishes dependency and non-circularity statutes, and introduces the possible object of natural physics only as a provisional target ledger rather than as an assumed ontology. It then examines joint preparation, product states and effects, marginal consistency, operational no-signalling, minimal and maximal probabilistic composites, local tomography, and the classification of admissible tensor-product representations. Particular attention is given to the distinction between a mathematical representation theorem and the uniqueness of a physical composition rule. Real, complex, quaternionic, Jordan-algebraic, minimal, maximal, restricted, and non-tomographic alternatives are compared under explicitly declared admissibility conditions. The complex Hilbert-space tensor product is recovered only on branches satisfying the required factorization, coherence, scalar, and operational closure conditions. Where several inequivalent composites survive, the result is a classified family rather than a falsely asserted uniqueness theorem. Entanglement is introduced only after composition has been commissioned. It is defined as the failure of an admitted joint state to belong to the convex closure of admitted product preparations. The analysis proves, within the resulting predictive grammar, that entanglement is a property of composite-state geometry, not an additional force, substance, interaction mechanism, or signalling channel. Throughout, the argument enforces quotient primacy, refinement stability, finite diagnostic closure, regeneration stability, explicit dependency receipts, local termination, and the possibility of Undefined as a legitimate scientific outcome. Part I therefore supplies neither a speculative ontology nor a presupposed many-world formalism. It provides a conditional classification theorem for binary physical composition and identifies precisely what remains to be established before interaction, repeated composition, particle identity, locality, fields, symmetries, and particle content may be addressed.
The quantum structure sub-programme comprises three companion papers on the binary icosahedral group 2I, plus one independently published result. Q1 proves an exact, unconditional Fourier-support rigidity theorem in the finite Weil representation of the Heisenberg group, with a precise no-go corollary for support-, rank-, and Gram-based diagnostics; it establishes no phase coherence, singlet correlator, Tsirelson bound, or Born rule. Q2 proves an exact finite-group fact: the spin-21 and spin-23 representations of 2I induce the same Cayley-graph Laplacian eigenvalue; it establishes no Casimir/isotropy normalisation, Born rule, Tsirelson-type bound, or SU(2) fixed-point/sector-selection argument. Q3 proves a theorem conditional on an explicit, undemonstrated hypothesis: given that a bipartite state on a supplied composition is invariant under the diagonal action of 2I — not derived from admissibility or from Born–Infeld indiscernibility — the state is uniquely the SU(2) singlet, with an explicit Casimir correlator, for all five admissible sectors of 2I; it does not derive that invariance hypothesis, phase coherence, or the Born rule. No chain currently connects these three results to each other or to the structures of quantum mechanics. The Bell paper, published independently in Quantum Reports, establishes the structural non-applicability of Bell-type factorizability in non-injective effective descriptions; the proof of that central theorem uses only non-injectivity and informational completeness. This note records the current, narrow scope of each constituent and the open problems that remain.