We propose to read spatial entanglement and interference between histories as two inheritances of a single coherence prior to the cut: a transverse residue across the partition A|B and a longitudinal residue along the causal order. The hypothesis proper to RCD is the Principle of Double Inheritance of Coherence (PDHC): one rule of differentiation determines at once what stays separated and what stays ordered. To make it an instrument we design JANO-1, a five-qubit circuit for superconducting processors in which a single cut, placed in superposition and then erased, is read twice: as entanglement between two qubits that never interacted and as an interference fringe between the histories “cut” and “no cut”. Exact simulation fixes the three predicted curves with one knob (the amplitude of the cut) and shows that a second knob (the coherence of the cut) makes the pair of residues fill a region, not a curve; the strong hypothesis is therefore stated as a precise question for the amplitude rule of PF2, and the JANO-2 phase returns to design. Nothing has run on hardware; the preregistration is conditional on a second key. Files: English version, Spanish version (the Spanish text is the reference text), and the Python code that reproduces every figure. Developed at the Panel Cerezo with cross-checking among AI tools (ChatGPT, Grok, Claude); the authorship of each contribution is stated in §10.
We propose to read spatial entanglement and interference between histories as two inheritances of a single coherence prior to the cut: a transverse residue across the partition A|B and a longitudinal residue along the causal order. The hypothesis proper to RCD is the Principle of Double Inheritance of Coherence (PDHC): one rule of differentiation determines at once what stays separated and what stays ordered. To make it an instrument we design JANO-1, a five-qubit circuit for superconducting processors in which a single cut, placed in superposition and then erased, is read twice: as entanglement between two qubits that never interacted and as an interference fringe between the histories “cut” and “no cut”. Exact simulation fixes the three predicted curves with one knob (the amplitude of the cut) and shows that a second knob (the coherence of the cut) makes the pair of residues fill a region, not a curve; the strong hypothesis is therefore stated as a precise question for the amplitude rule of PF2, and the JANO-2 phase returns to design. Nothing has run on hardware; the preregistration is conditional on a second key. Files: English version, Spanish version (the Spanish text is the reference text), and the Python code that reproduces every figure. Developed at the Panel Cerezo with cross-checking among AI tools (ChatGPT, Grok, Claude); the authorship of each contribution is stated in §10.
The known universe fits the image of a balloon: inside are galaxies, atoms and particles, and what expands is the space that contains them. The primordial coherence of RCD (Radial Coherential Dynamics) is neither the skin of that balloon nor something that fills it: it lies beneath the distinction between around and within, and has no size, position or date. When any part of the universe is taken, by zooming in, down to the irreducible, no smaller coherence appears; one touches the same one again. From this image follows an order of dependence: undivided coherence, cut, quantum relations, spacetime and, only then, fields, matter and energy. The physics of the differentiated regime (interference, decoherence, entanglement, relational time, the geometry of correlation) is kept unchanged and read as the description of what exists after the cut. The note states the identity of coherence as an explicit working hypothesis (H-1), separates primary distinction, quantum partition and record, specifies what Bell's theorem rules out and what it leaves standing, and situates the proposal among its neighbors (Bohm, Schaffer, Spencer-Brown, Zanardi–Lidar–Lloyd, Cotler–Penington–Ranard, Carroll–Singh). The open problem is stated as a single question: how can a structure without partition generate a physically privileged partition without presupposing it? This work distinguishes established physics, interpretive readings, postulates and open derivations; it is an architecture of dependence, not a derivation. Files: English version and Spanish version (the Spanish text is the reference text). Developed with cross-checking among AI tools (ChatGPT, Claude) for drafting, critique and bibliographic verification.
We present a development of the RCD program (Radial Coherential Dynamics) in the complex scalar sector of quantum sequential growth of causal sets. The central question is not only how a causal history grows, but how much of the information about HOW IT WAS FORMED can survive when one of its elements is erased without privileging any temporal label. The central result is an exact separation between coherent inheritance and memory of the cut. For the erasure branches a_i (i = 0, …, N−1), define the branch matrix 𝒜_N = N^(−1/2) [a_0, …, a_{N−1}], the uniform register mode |u_N⟩ = N^(−1/2)(1, …, 1), and Q_N = I − |u_N⟩⟨u_N|. The memory matrix M_N = D_mix − D_coh = 𝒜_N Q_N 𝒜_N† ⪰ 0 identifies exactly the memory sector orthogonal to coherent inheritance. Its trace, Tr M_N = (1/2N²) Σ_{i,j} ‖a_i − a_j‖², is the pairwise dispersion of the causally distinct erasure alternatives: relational memory is precisely that dispersion. The Relational Inheritance Bifurcation theorem (BHR-3) shows already at N = 3 that the inherited amplitude can coincide exactly while non-zero memory of the mode of formation persists: Δ₃^coh = 0 together with Ω₃ > 0, where D_mix − D_coh = Ω₃ · [[1, −1], [−1, 1]]. At the exact point r = 1, Ω₃ = 1/294; the reading with the register traced out has spectrum {147/149, 2/149} and visibility 145/149, while the coherent reading remains pure. One and the same observable inheritance can therefore coexist with residual relational information about its formation. The second main result is an exact memory-flow law. On the star family 𝒮_N — an antichain of N−1 elements with one element above all of them — covariant coherent erasure is closed for every N. With p = ε/(t₀+ε), p′ = (N−1) p / N, P := p/N = constant, and the complete coupling trajectory is ε_n = n ε_N / (N + (N−n) ε_N). The memory has rank one, M_N = (N−1)|P|² J with J = [[1, −1], [−1, 1]], so that Ξ := M_N/(N−1) = |P|² J is an exact invariant of the flow, M_{N−1} = M_N − Ξ, and 𝓜_N − 𝓜_{N−1} = 2|P|²: each coarse-graining step transports an exactly determined amount of relational memory. The star spine 𝒮₄ also appears as an exact component of the closure variety of the 4→3 flow. The non-degenerate regular branch C₁₂ is born tangent to this spine and inherits, at leading order, its memory-contraction factor 2/3. The deposit also contains the prior results leading to this structure: absence of a non-trivial scalar fixed point under uniform incoherent erasure (𝔗_mix); absence of a non-trivial fixed point under the uniform coherent superposition (𝔗_coh), which equals the classical PF-0 condition complexified; the need to formulate erasure covariantly by classes; the rational renormalization map on the closure variety; and the minimal register compression, rank D_mix = rank M_N + 1. These results motivate the Principle of Relational Memory of the Cut, dynamical version (PMRC-D): every fundamental physical differentiation that produces causally distinguishable histories must also determine, through a covariant rule, which information of that differentiation remains recorded and which information may interfere coherently. The emerging working thesis is: "The inheritance of a history does not by itself determine the memory of how it was formed." The program remains open toward closed sectors with several independent memory modes and a covariant dynamics capable of transporting those modes under coarse-graining. Exact results are N ≤ 4 except those with closed proofs for all N (the star spine and its flow); the 5→4 step outside 𝒮_N is numerical; the physical universality of PMRC-D remains open. No claim is made about the emergence of time, Mermin's 25 % or the necessity of H > 1 as a law. Deposit contents: RCD Adjudication Record v0.2 (signed Spanish original and English version; the Spanish text prevails), diligence notes 𝔗_mix-0, 𝔗_coh-0/𝔗_flow-0 and BMR-0 (Relational Memory), reproducible code with SHA-256 manifests, and README. Panel Cerezo credits: ChatGPT (formulation of the diligences, BHR-3, PMRC-D, 𝒜QA† form, invariant Ξ, series of C₁₂) and Claude (exact computation, lemmas, curve C and map R, star spine 𝒮_N, cross-verification and drafting), under the direction and adjudication of the principal.
Technical Note JANO-BR-0 of the RCD program (continues “La doble herencia de la coherencia”, DOI 10.5281/zenodo.23520439; the Adjudication Record “Relational Memory under Causal Erasure”, DOI 10.5281/zenodo.23717352; BMR-1, DOI 10.5281/zenodo.23717139; and REP-0, DOI 10.5281/zenodo.23774093). Question: can the heritage/memory bifurcation of BHR-BMR become a physical readout of one and the same circuit? Results (exact, no hardware): in BHR-3 the mixed relational-memory state ρ_mix(r) has rank 2 whenever Ω₃ > 0, so a single qubit c purifies it, |Ψ(r)⟩ = √λ₊|0⟩|ψ₊⟩ + √λ₋|1⟩|ψ₋⟩, with a three-gate {Ry, CNOT} construction and a closed map r ↦ (θ_c, η); tracing out c returns ρ_mix (R⊥), while measuring c in the HJW basis leaves the system exactly in the coherent-heritage state ρ_coh with probability p_coh = Tr D_coh/Tr D_mix and in the residual-memory state |−⟩ (independent of r) with probability p_M; the three readouts are tied by the exact identity V_mix = p_coh·V_coh − p_M (at r = 1: 145/149 = 147/149 − 2/149). Verified against the original JANO-1 code: the five-qubit JANO-1 circuit with α = α_BR(r) = arcsin √λ₋(r) is literally this purification, and its frozen observables reduce to P_rec = λ₊ and R∥ = R⊥ = √(2λ₊λ₋) = √S_lin(ρ_mix) — a spectral readout of the memory — while the HJW readout is the complementary face that separates heritage from memory. Stated limit: the construction reproduces ρ_mix(r) by design and is not a falsifiable prediction of RCD; hardware stays closed. Scripts with SHA-256 manifest. English and Spanish versions; the Spanish text prevails.
A quantum clock can follow two proper-time histories. Can one completed coherence also distinguish two physical reference classes? Quantum-clock interferometry already supplies the standard carrier relation Δϕclock=ω0Δτ. This preregistration keeps that relation intact and asks a separate question. The same atomic transition and path geometry are executed through four physical input/output terminal histories, ττ,τT,Tτ,TT. For each history and reversed proper-time geometry, the laboratory fits the first complex clock-coherence phasor and forms Dab=∣Zab+Zab−∣. The registered reference-switch statistic is Rqc,clk=N×ord1DττDTTDτTDTτ. After a target-blind ordinary cross-history map, the fixed prospective fork is Hordinary:Rqc,clk=1,HQTT−A1:Rqc,clk=cos(8π). The alternatives differ by 7.6120467%. A bare five-standard-deviation separation requires σ(Rqc,clk)≤0.0152241, and the recommended design target is 0.005. The proper-time phase is a common carrier check, not the A1 discriminator. The release includes three adversarial audits. It requires a physical hardware graph for the T and τ terminal classes, derives the readout exponent from a first complex phasor, and qualifies preparation and calibration by their physical transfer, not by angle alone. A target-inserting primary operation or target-trained correction remains ineligible. Any failed eligibility gate returns INELIGIBLE_NO_THEORY_VERDICT rather than a false rejection of A1. Scientific status: theorem and estimator closed; carrier technology plausible; physical four-terminal hardware map and laboratory dataset pending. No existing quantum-clock record is claimed as A1 evidence. Concept DOI: 10.5281/zenodo.21674815 Main book: Quantum Traction Theory: Main Book v10.01 Website: quantumtraction.org · Two Universes · Lexicon · Observatory The public files are the paper PDF first and the complete reconstruction ZIP second. Version 1.1: operation qualification and retained observations The numerical targets, ratio orientation, decision regions and historical seals are unchanged. A 22.5-degree or 45-degree component is no longer excluded by its angle alone: its physical transfer must be independently established. Common-operation cancellation and signal-preserving calibration are proved; both hypotheses must remain identifiable. Every acquired record is retained. After authorized unblinding, QTT-like, ordinary-like and unexpected outcomes are reported, including observations that do not qualify for a theory verdict. This is a prospective amendment, not a retrospective resealing of data. Clock, ruler and signal-recovery qualification. Both registered predictions are constructed at the raw detector with explicit proper-time, coordinate-time, worldline, ruler and synchronization conventions. Each relativistic effect is counted once. Independently calibrated corrections carry their uncertainties through the common comparison; the tested rows cannot train a normalization that forces either answer. Blind recovery is required separately for both alternatives at every predeclared operating setting. The inherited targets and decision rules remain fixed. The included design study makes sensitivity explicit: for the Two-Test Gram classifier, a total ratio uncertainty of 0.0013 gives approximately 88.9% QTT-branch and 94.1% ordinary-branch power under the stated ideal model. These are conditional detection probabilities, not probabilities that a theory is true, and each instrument retains its own classifier. The complete apparatus packet must be sealed before acquisition and target access; historical campaign rules remain preserved. Reconstruction entry point. Start with current/CURRENT_RELATIVISTIC_EXECUTION.md in the ZIP. The shared execution contract refers once to the development filename CURRENT_EXECUTION_RC.md; that reference means CURRENT_RELATIVISTIC_EXECUTION.md in this release. The packaged README names the correct file. This navigation correction does not change the deposited files, scientific requirements or historical seals.
Coherence First develops a relational reformulation of Radial Coherential Dynamics (RCD) centered on a prior question: what physically selects the factorization of a quantum system into subsystems? Because entanglement is defined only relative to a tensor-product structure or a partition of observable algebras, programs that derive classicality, locality, or geometry from entanglement already presuppose a cut. The paper proposes the Coherential Selection Principle (CSP): the physical factorization is the one that maximizes the persistence of coherent information within its parts while minimizing coherent persistence across their boundaries. In this framework, subsystems are dynamically persistent regions of a relational quantum structure, and the coherential field C(x,t)C(x,t) is reinterpreted as a possible continuous, effective description of a deeper network of selected relations. A numerical proof of concept is presented for an open three-qubit system. Keeping the Hamiltonian fixed while rotating the environmentally monitored algebra shifts the factorization favored by a provisional functional. The effect survives a generic non-commuting control, remains stable under sampling, and follows a continuous five-point rotation of the monitored algebra. The result establishes that open dynamics can transport and recover a recognizable structure of parts that is not fixed by the Hamiltonian alone. The full CSP, the emergence of geometric locality, and the proposed connection to cosmological relaxation remain the next stages of the program. Version 0.2. Preprint; not peer reviewed. This record contains the PDF, LaTeX source, numerical scripts, and reproducibility materials used in the closed- and open-system studies.
Quantum interference is conventionally formulated using complex amplitudes associated with quantum alternatives or through Feynman’s path integral over possible trajectories. This article investigates a different ontology, the Single-History Record Framework (SHRF), in which a physical system has one realized history together with a record space of phase-carrying contributions associated with that history. Observable amplitudes are obtained through History-Record Summation (HRS). SHRF deliberately retains established quantum ingredients wherever possible, including complex-amplitude addition, the Born probability rule, propagation phases, and marker-state overlaps. These mathematical devices are used as predictive rules and do not imply that multiple physical histories, paths, or marker outcomes coexist.A preliminary model is developed in which rapidly varying regions of record space largely cancel while coherent record bands provide the dominant detector amplitude. For double-slit geometry, two aperture-selected bands give A(x)≈H_A (x)+H_B (x).With the established propagation phases H_A=Ce^(ikL_A ),H_B=Ce^(ikL_B ),SHRF recovers the textbook far-field fringe spacing Δx=λD/d.The same formal structure is applied to single-slit diffraction, multiple slits, which-path marking, partial distinguishability, and quantum-eraser subensembles. In particular, marker records modify the interference term through the standard overlap factor ⟨M_A∣M_B⟩,without requiring a physical superposition of marker records. The present model assumes rather than derives its phase law, record-space measure, and Born rule. It is therefore a recovery-oriented consistency construction and ontological reinterpretation, not an independent replacement for standard quantum mechanics.