We present the Interference-First Reality (IFR) framework, in which physical objectivity is not assumed as primitive but is operationally characterized through the stabilization of observer-induced probability distributions under redundant observation. Within this framework, emergent shared reality is identified with the Fréchet barycenter of an ensemble of observer-induced probability distributions in Jensen-Shannon geometry. A consistency theorem shows that empirical barycenters converge almost surely to their population counterpart as the number of independent observers grows, grounding objectivity in standard metric barycenter theory rather than in additional physical postulates. Alongside this variational construction, we introduce a complementary weighted geometric-overlap estimator and analyze its relation to the barycentric formulation. We instantiate the framework across five physical domains: cosmic microwave background (CMB), heart-rate variability (HRV), JWST spectroscopy, large-scale structure (LSS), and gravitational-wave open data (GWOSC). Across all domains, we find reproducible multi-observer collective summaries, bounded Jensen-Shannon distances consistent with stabilization, and a cross-domain distinguishability hierarchy stable under bootstrap resampling and insensitive to the choice between arithmetic and geometric aggregation. Permutation-based null tests further show that the observed clustering structure exceeds domain-specific random baselines. The empirical scope is nevertheless domain-specific: the GW cross-event comparison mainly reflects observational context and noise geometry, while the JWST case probes structured instrumental heterogeneity within a common observing program rather than independent platforms. Finally, we outline an extension in which time is defined as cumulative informational arc-length between successive stabilized collective states, leaving its full development to a companion study.
We present the Interference-First Reality (IFR) framework, in which physical objectivity is not assumed as primitive but is operationally characterized through the stabilization of observer-induced probability distributions under redundant observation. Within this framework, emergent shared reality is identified with the Fréchet barycenter of an ensemble of observer-induced probability distributions in Jensen-Shannon geometry. A consistency theorem shows that empirical barycenters converge almost surely to their population counterpart as the number of independent observers grows, grounding objectivity in standard metric barycenter theory rather than in additional physical postulates. Alongside this variational construction, we introduce a complementary weighted geometric-overlap estimator and analyze its relation to the barycentric formulation. We instantiate the framework across five physical domains: cosmic microwave background (CMB), heart-rate variability (HRV), JWST spectroscopy, large-scale structure (LSS), and gravitational-wave open data (GWOSC). Across all domains, we find reproducible multi-observer collective summaries, bounded Jensen-Shannon distances consistent with stabilization, and a cross-domain distinguishability hierarchy stable under bootstrap resampling and insensitive to the choice between arithmetic and geometric aggregation. Permutation-based null tests further show that the observed clustering structure exceeds domain-specific random baselines. The empirical scope is nevertheless domain-specific: the GW cross-event comparison mainly reflects observational context and noise geometry, while the JWST case probes structured instrumental heterogeneity within a common observing program rather than independent platforms. Finally, we outline an extension in which time is defined as cumulative informational arc-length between successive stabilized collective states, leaving its full development to a companion study.
We present the Interference-First Reality (IFR) framework, in which physical objectivity is not assumed as primitive but is operationally characterized through the stabilization of observer-induced probability distributions under redundant observation. The emergent shared reality is identified with the Fréchet barycenter in Jensen-Shannon geometry. Framework instantiated across five physical domains: CMB, HRV, JWST spectroscopy, large-scale structure (LSS), and gravitational-wave data (GWOSC). Published in Journal of Applied Mathematics and Physics, 14, 1627-1674 (2026). DOI: 10.4236/jamp.2026.144077
We introduce Interference-First Reality (IFR), a theoretical framework in which physical objectivity is not assumed as a primitive property of the world, but is derived as a stable multi-observer limit of an underlying interference structure. The fundamental object of the theory is a pre-spatiotemporal interference state Ψ defined on an abstract configuration space X, together with a family of operational observer maps projecting Ψ into observer-accessible representation spaces. Agreement between observers is quantified by an information-geometric redundant dispersion functional. Within IFR, objective structures are defined as stable Fréchet-type centers of observer projections, and physical configurations are selected by a variational principle involving interference dynamics, informational curvature, and redundant multi-observer contraction. The parameter λ is not identified with physical time. Instead, temporal order is defined as the ordered succession of stable minima of redundant dispersion, while effective spacetime geometry arises when the underlying information geometry admits a low-dimensional metric representation. The framework derives objectivity, time, space, and gravitation from a single variational structure. Contents of this deposit. Alongside the complete-formulation preprint, the archive contains the consolidated information-geometry module ifr_core, implementing Jensen–Shannon divergence and distance, geometric and arithmetic barycenters, and the redundant-dispersion functional, together with its verification routines, the full set of analysis scripts, and self-configuring ready-to-run launcher packages for Windows, macOS, and a flat code archive. The ifr_core module is byte-identical across all packages and hash-verified, and reproduces all reported JSD/KL values with a maximum numerical discrepancy below 1e-13. The packages are strictly code-only. Data directories contain only .gitkeep or README.md placeholders, and the public re-downloadable datasets used in the analyses, including Planck, GWOSC, JWST/JADES, and PhysioNet, are intentionally excluded from the deposit. Citation. The Concept DOI 10.5281/zenodo.20528552 is the stable DOI to be used for citation and resolves to the most recent version. Each deposit mints a version DOI for archival versioning only; version DOIs should not be used in manuscripts. Peer-reviewed publication. This document is the complete and unified formulation of the IFR framework, subdivided into six parts for peer-reviewed publication in the Journal of Applied Mathematics and Physics (JAMP). The empirical validation referenced here has been published in Bianchi (2025), JAMP 13, 4355–4378, and Bianchi (2026), JAMP 14, 1627–1674. Part I of the series has been published as Bianchi, M. (2026) Interference-First Reality Theory: Foundations and Objectivity, JAMP 14(7), 2735–2772, DOI 10.4236/jamp.2026.147137. Part II is under peer review; Parts III–VI are in preparation for sequential submission.
This paper establishes a local structural bridge between two recently developed information-geometric frameworks for observer-dependent probability representations on finite state spaces. Background. On the parametric side, the partition-adapted framework of Khomyakov (KLEO v3.24.1) defines observer entropy as the Kullback–Leibler divergence between a parametric distribution and the uniform lift of its coarse-graining, and shows that it scales quadratically with the resolution threshold, with a coefficient determined by the Fisher information matrix. On the empirical side, the Interference-First Reality (IFR) framework of Bianchi (2026) identifies multi-observer objectivity with the Fréchet barycenter of observer-induced distributions in the Jensen–Shannon metric, with almost-sure convergence guaranteed by metric barycenter theory. Principal results. The paper derives four main results: 1. Local Metric Bridge Lemma (Section 3): On the open probability simplex, the Jensen–Shannon divergence satisfies the local quadratic expansion D_JS(p ‖ p + εδ) = (ε²/8) I_p(δ) + O(ε³), where the explicit coefficient 1/8 arises from the midpoint structure of the symmetric divergence. 2. Multi-Observer Quadratic Aggregation Theorem (Section 4): For a partition-adapted parametric family satisfying conditions (A1)–(A3) of Khomyakov (KLEO v3.24.1), the empirical Jensen–Shannon Fréchet barycenter of an N-observer ensemble, centered on the within-class neutral locus, exists uniquely for small ε and coincides to leading order with the weighted Fisher–Rao barycenter of the within-class perturbation directions. The minimal Jensen–Shannon dispersion satisfies a quadratic scaling law governed by the within-class block I_ww(θ₀*) of the Fisher information matrix. 3. Leading-order coincidence of estimators (Corollary 6.1): The variational Fréchet minimizer p_F and the closed-form geometric overlap estimator p_G of Bianchi (2026) agree to order O(ε²) in Jensen–Shannon distance within the local regime. 4. Multi-observer Landauer corollary (Corollary 6.6): Under a per-channel irreversibility assumption and an additivity postulate for independent observer channels, the aggregate energetic cost of barycenter formation is bounded below by k_B T times the Jensen–Shannon dispersion. Scope. The bridge is local in ε (the within-class perturbation amplitude) and finite in N (the number of observers). It does not subsume Bianchi's almost-sure N → ∞ consistency theorem nor Khomyakov's ε → 0⁺ quadratic scaling result; it establishes their structural compatibility in the overlapping regime where both apply. The results are specialized to balanced exponential families (softmax), with explicit worked-example coefficients for four- and five-point state spaces. Domain-specific applicability is assessed against the cross-domain distinguishability hierarchy of Bianchi (2026), Table 14, identifying the low-dispersion regime (d_JS ≲ 10⁻² nats) as the primary domain of validity. Keywords: Jensen–Shannon divergence, Kullback–Leibler divergence, Fisher information, Fisher–Rao metric, multi-observer aggregation, Fréchet barycenter, probability simplex, partition-adapted parameterization, observer entropy, information geometry. MSC 2020: 62B10, 94A17, 53B12, 62F12.
This Zenodo record provides the reproducibility package for the published paper “Interference-First Reality: Multi-Observer Emergence of Objectivity and Time from Information Geometry,” published in the Journal of Applied Mathematics and Physics. The deposited material includes the scripts, data products, tables, figures, source files, and supplementary outputs required to reproduce the analyses and results reported in the article. This repository is intended to ensure methodological transparency, facilitate independent verification, and support the reuse and reproducibility of the published research. Note (2026-10). An updated version of the code supplement is available at https://doi.org/10.5281/zenodo.23269851 (record 10.5281/zenodo.17672528, updated version 2026-10). It corrects the selection of the raw GWOSC strain files, now bound to the GPS window of the requested event, and adds the HRV epoch and CMB smoothing observer constructions; all permutation null tests are generated by the released launcher with one statistic, B = 5000 and seed 12345. The observed Jensen–Shannon distances reported in the article are unchanged; the null distributions of the updated version supersede those of this supplement. See CHANGES.md in the updated package.