{
  "id": "oai:papers.qnfo.org:superposition-as-a-projection-artifact-of-discrete-tree-geometry",
  "slug": "superposition-as-a-projection-artifact-of-discrete-tree-geometry",
  "title": "Superposition as a Projection Artifact of Discrete Tree Geometry",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Quantum superposition underpins quantum computing, interferometry, and macroscopic‑superposition experiments, yet its ontological status remains contested, creating a design bottleneck for error‑correction and measurement hardware. Existing models lack a concrete hidden‑variable construction that reproduces the Hilbert‑space formalism while clarifying why a single outcome is observed. We formulate a deterministic binary‑branching tree of depth d that represents a single hidden‑variable trajectory and define a coarse‑graining map that projects leaf sets onto an effective wavefunction. Explicit arithmetic shows that leaf counting yields diagonal probabilities P=n/2^d, reproducing the Born‑rule diagonal form as a definitional identity. A numerical illustration with d=5 gives P_A=0.625, matching |a|² for a=√0.625. We also prove three negative results: (i) a power‑law leaf measure normalises only for exponent 1, (ii) non‑negative leaf measures cannot generate interference cross‑terms without encoding phase, and (iii) deterministic leaf assignments satisfy the CHSH bound |S|≤2, implying any empirically adequate tree must be non‑local or contextual. The work therefore delineates precisely which quantum‑mechanical features a discrete‑tree model can reproduce and proposes a concrete interferometric test that would falsify the hypothesis. If validated, the model supplies a design criterion—choosing measurement resolution to enforce a tree depth that preserves the rational probability structure—potentially reducing overhead in quantum hardware.",
  "abstract_markdown": "Quantum superposition underpins quantum computing, interferometry, and macroscopic‑superposition experiments, yet its ontological status remains contested, creating a design bottleneck for error‑correction and measurement hardware. Existing models lack a concrete hidden‑variable construction that reproduces the Hilbert‑space formalism while clarifying why a single outcome is observed. We formulate a deterministic binary‑branching tree of depth $d$ that represents a single hidden‑variable trajectory and define a coarse‑graining map that projects leaf sets onto an effective wavefunction. Explicit arithmetic shows that leaf counting yields diagonal probabilities $P=n/2^{d}$, reproducing the Born‑rule diagonal form as a definitional identity. A numerical illustration with $d=5$ gives $P_{A}=0.625$, matching $|a|^{2}$ for $a=\\sqrt{0.625}$. We also prove three negative results: (i) a power‑law leaf measure normalises only for exponent 1, (ii) non‑negative leaf measures cannot generate interference cross‑terms without encoding phase, and (iii) deterministic leaf assignments satisfy the CHSH bound $|S|\\le2$, implying any empirically adequate tree must be non‑local or contextual. The work therefore delineates precisely which quantum‑mechanical features a discrete‑tree model can reproduce and proposes a concrete interferometric test that would falsify the hypothesis. If validated, the model supplies a design criterion—choosing measurement resolution to enforce a tree depth that preserves the rational probability structure—potentially reducing overhead in quantum hardware.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
  "last_revised": "2026-10-20T06:41:34Z",
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  "url": "https://papers.qnfo.org/papers/superposition-as-a-projection-artifact-of-discrete-tree-geometry",
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  "version_url": "https://papers.qnfo.org/papers/superposition-as-a-projection-artifact-of-discrete-tree-geometry/v/1.1.0",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Superposition as a Projection Artifact of Discrete Tree Geometry"
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    "publicationYear": "2026",
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        "description": "Quantum superposition underpins quantum computing, interferometry, and macroscopic‑superposition experiments, yet its ontological status remains contested, creating a design bottleneck for error‑correction and measurement hardware. Existing models lack a concrete hidden‑variable construction that reproduces the Hilbert‑space formalism while clarifying why a single outcome is observed. We formulate a deterministic binary‑branching tree of depth d that represents a single hidden‑variable trajectory and define a coarse‑graining map that projects leaf sets onto an effective wavefunction. Explicit arithmetic shows that leaf counting yields diagonal probabilities P=n/2^d, reproducing the Born‑rule diagonal form as a definitional identity. A numerical illustration with d=5 gives P_A=0.625, matching |a|² for a=√0.625. We also prove three negative results: (i) a power‑law leaf measure normalises only for exponent 1, (ii) non‑negative leaf measures cannot generate interference cross‑terms without encoding phase, and (iii) deterministic leaf assignments satisfy the CHSH bound |S|≤2, implying any empirically adequate tree must be non‑local or contextual. The work therefore delineates precisely which quantum‑mechanical features a discrete‑tree model can reproduce and proposes a concrete interferometric test that would falsify the hypothesis. If validated, the model supplies a design criterion—choosing measurement resolution to enforce a tree depth that preserves the rational probability structure—potentially reducing overhead in quantum hardware.",
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