Quantum structure follows from refinement-stable bookkeeping, not postulates. Soft selection is forced when corridor-level action ties make hard selection require forbidden tie-break (micro-history) data. The corridor therefore retains all admissible configuration classes and aggregates them using action-only weights. Interference stability pressures a phase-bearing carrier, concatenation stability pressures exponential phase weights, and gauge-meaningful scalar prediction forces quadratic magnitude extraction (the Born slot). No Hilbert axioms, path-integral primitives, or calculus limits are assumed.
Quantum structure follows from refinement-stable bookkeeping, not postulates. Soft selection is forced when corridor-level action ties make hard selection require forbidden tie-break (micro-history) data. The corridor therefore retains all admissible configuration classes and aggregates them using action-only weights. Interference stability pressures a phase-bearing carrier, concatenation stability pressures exponential phase weights, and gauge-meaningful scalar prediction forces quadratic magnitude extraction (the Born slot). No Hilbert axioms, path-integral primitives, or calculus limits are assumed.
A forced-structure derivation of corridor-consistent measurement updating from the Born slot. This preprint extends the Forced Sequence / Corridor program beyond closed evolution. Given the Born extraction rule and the operator corridor (local, linear, norm-preserving closed updates), it derives a refinement-stable conditioning update for registered outcomes: the state updates by normalized outcome filtering under an interface-cut. The paper defines a collapse-class slot by four constraints: (1) Born-consistent outcome weights, (2) coarse-graining invariance (no partition-sensitive tie-break dependence), (3) exhaustiveness as weight preservation at the prediction tier, and (4) single-summary bookkeeping closure at this stage of the series (with mixed-state extensions deferred to composite/open-system corridors).
A forced-structure route from quantization constraints to a Schrödinger-class update law. This preprint continues the Forced Sequence / Corridor program. It derives an operational “local update” corridor that avoids global recomputation, then shows how refinement stability constrains admissible updates into a linear, norm-preserving class with a phase-bearing generator. The result is presented as a structural slot (what must hold under the corridor constraints), not as an assumed physical postulate. Prior papers in the sequence provide the prerequisite corridor objects and invariants.
This paper extends the Forced Sequence / Corridor program to composite systems. After deriving the Born slot, local linear norm-preserving closed evolution (Schrodinger-class slot), and interface-cut conditioning (collapse-class slot), the next forced step is composition: how two subsystem ledgers combine without introducing forbidden tie-break structure. The paper shows that subsystem superposition compatibility, composite superposition closure over product generators, and Born-consistent factorization on product states force a tensor-class product slot for the composite carrier. This yields an entanglement slot: composite summaries need not factor into a single product, and non-factorability is the corridor definition of entanglement. The paper also derives the corridor form of local conditioning in composites: a local outcome registration updates the joint ledger by normalized filtering, changing conditional predictions for the other subsystem as bookkeeping rather than superluminal dynamics. Open-system reductions, density-matrix style bookkeeping, and interaction-generator selection are deferred to the next forced corridors.
Effective open dynamics emerges from compression, not mystery. This paper continues a forcing sequence that derives quantum-formal structure from refinement-stable bookkeeping constraints. Building on prior results (operator corridor, measurement corridor, composite-system corridor, open-system corridor, and open-system update corridor), it shows how a subsystem can exhibit a stable open evolution while the larger ledger evolves by closed norm-preserving updates. The core pressures are: (1) closed-to-open induction (reduction of a closed composite to a subsystem), (2) open-tier no-full-recompute (effective updates cannot depend on unbounded environment history), and (3) time-homogeneous coarse-graining at the effective tier. These pressures drive the effective family of subsystem updates into a Markov/semigroup structure (up to corridor equivalence). Under a stabilized first-order content assumption at the effective tier, the evolution occupies a time-local master-equation slot. Finally, enforcing the already-derived CPTP constraints on the effective semigroup identifies the Lindblad-class (GKSL) generator slot as the conventional representation of the corridor-forced constraint class. The paper is representation-agnostic: it forces the constraint slot and clarifies what is derived versus deferred (conditions for Markov validity, non-Markov regimes, locality and symmetry constraints, and relativistic compatibility).
This paper is Paper 003 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops the Born Ledger: the probability scalarization of Binary Mechanics. Paper 002 derived finite polarized graph histories and the primitive finite amplitude law. In that construction, amplitudes are not assigned to instantaneous graph states, vertices, or hidden local phase registers. Instead, they arise as finite sums of Z4-weighted admissible histories grouped into coarse record classes. The present paper begins from that result and asks what probability ledger is forced once record-disjoint coarse alternatives are required to receive stable nonnegative weights. The central result is a no-fence scalarization theorem: the only admissible nonnegative scalarization of a finite complex record amplitude is its squared modulus. When normalized over an exhaustive record-disjoint partition, this yields the Born-type probability rule. The derivation does not assume Hilbert space, a wavefunction, a measurement postulate, a continuum path integral, primitive probability, or primitive branch selection. Interference appears before probability as cancellation inside finite history amplitudes, and probability appears only as the record-level scalarization of those amplitudes. No fine history is primitively deleted or selected; the ledger assigns weights to record-disjoint coarse alternatives generated from the full admissible finite history structure. The paper therefore supplies the Born-weighting step in the Binary Mechanics construction: finite graph histories first, finite amplitudes second, record ledgers third, normalized probabilities last.
This paper continues a constructive “forced-sequence” program that introduces only representational structure required by earlier residues and refinement-stability constraints. Building on (i) a minimal phase-bearing carrier with a quadratic yield map, (ii) closed evolution as yield-invariant internal update with unitary/antiunitary symmetry pressure, and (iii) refinement corridors that force compressed transport and germ connection fields, the paper isolates the next forced step: refinement-stable closedness. If a transport family represents internal (closed) evolution under arbitrary refinement, then yield preservation must persist at the germ level (the “yield corridor”). Using a tier-based (non-limit) notion of first-order content and an explicit accumulation principle for repeated near-identity composition, the paper derives infinitesimal symmetry pressure: admissible germ generators of closed transport must lie in the infinitesimal symmetry class of the quadratic yield structure. Specializing to the minimal complex-carrier realization, this yields a Hamiltonian corridor: germ generators are constrained to the antiunitary-compatible infinitesimal class underlying norm-preserving phase evolution, without assuming Hilbert space axioms, Schrödinger dynamics, derivatives, or a continuum limit as primitives. Finally, the paper imposes a residue-closure constraint: interaction residues (graded bracket / curvature-tier contributions) must remain admissible under the yield corridor at their proper tier.