Distance, Measurement, and the Ontological Reconstruction of Light: A Discrete Spacetime Framework Based on Topological Self-Trapping, Solid-Angle Probability, and Marker Phase Transitions (Draft Version)

In standard physics, distance is an a priori geometric background, the Born rule is an unquestionable probability axiom, and measurement collapse is an unexplained assumption. Within the ZTD (Marker Ontology) discrete spacetime framework, this paper re-examines and reconstructs the ontological status of the continuum background and the probabilistic-wave hypothesis.We propose and quantitatively formulate a continuous formula for effective measurement distance, L_"eff" =η(M)⋅r, which reduces the establishment of distance to the accumulation of irreversible physical events (effective markers). On this basis, we present an independent measurement-theoretic argument: the question “what is the time of a photon when it has flown half the distance?” is not an epistemological limitation but a category mistake—its three presuppositions (the existence of a “half-way” moment, the identifiability of a “photon in flight,” and the correlatability of coordinate time and proper time) are all unrealizable at the measurement-theoretic level. This argument does not depend on relativity; it relies only on the operational fact that “detection = absorption” (this argument adopts an operationalist measurement-theoretic stance; see §3.3). The same argument applies in parallel to quantum entanglement: “separation before measurement” is likewise not a definable state, rather than “separation exists but we do not know it.”Furthermore, this paper explores the true ontology of the photon: a single photon is not a continuous omnidirectional classical spherical wave, but a “topological self-trapped soliton pipe” generated by nonlinear truncation of the network, with energy locked in the core and not spatially diluted. Combined with the topological closure event, this paper provides an alternative realist picture based on an “omnidirectional solid-angle projection interface” for the physical picture in which a single photon, after crossing ten billion light-years, can still instantly excite a detector, and points out that the Born rule (P=σ/4πr^2) is essentially the geometric projection onto the detector of the transverse coherent scattering cross-section of the soliton’s topological tail in the three-dimensional network. Finally, by analogy with the phase-transition idea of topological defects, this paper argues that: measurement is not wavefunction collapse, but a topological phase transition in which local degrees of freedom of the network are stripped, and markers ultimately solidify into topological records.Keywords: Marker Ontology; discrete asynchronous Poisson network; topological self-trapped soliton; solid-angle projection; topological defect phase transition; time dissipator; topological closure; category mistake