{"id":349,"date":"2025-08-21T14:44:52","date_gmt":"2025-08-21T12:44:52","guid":{"rendered":"https:\/\/qfunity.com\/?page_id=349"},"modified":"2025-08-21T14:44:52","modified_gmt":"2025-08-21T12:44:52","slug":"qfunity-and-c","status":"publish","type":"page","link":"https:\/\/qfunity.com\/index.php\/qfunity-and-c\/","title":{"rendered":""},"content":{"rendered":"\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n    <meta charset=\"UTF-8\">\n    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n    <title>QFunity &#8211; Emergence of Causality, Light, and Information<\/title>\n    <script src=\"https:\/\/polyfill.io\/v3\/polyfill.min.js?features=es6\"><\/script>\n    <script id=\"MathJax-script\" async src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-mml-chtml.js\"><\/script>\n    <style>\n        :root {\n            --primary-color: #1a237e;\n            --secondary-color: #0d47a1;\n            --accent-color: #b71c1c;\n            --light-color: 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var(--primary-color);\n            color: white;\n            padding: 0.6rem 1.2rem;\n            border-radius: 4px;\n            text-decoration: none;\n            margin-top: 2rem;\n            transition: background-color 0.3s;\n        }\n        .back-button:hover {\n            background-color: var(--secondary-color);\n        }\n        @media (max-width: 768px) {\n            .hero h1 {\n                font-size: 1.8rem;\n            }\n            .section-title {\n                font-size: 1.5rem;\n            }\n            .info-table {\n                font-size: 0.9rem;\n            }\n        }\n    <\/style>\n<\/head>\n<body>\n    <section class=\"hero\">\n        <div class=\"container\">\n            <h1>Emergence of Causality, Light, and Information in QFunity<\/h1>\n            <p>A unified framework for the origin of time, causality, the speed of light, and the nature of information<\/p>\n        <\/div>\n    <\/section>\n\n    <section class=\"content-section\">\n        <div class=\"container\">\n            <h2 class=\"section-title\">From Pre-Temporal State to Causal Spacetime<\/h2>\n            \n            <div class=\"theory-principle\">\n                <h3>The Pre-Temporal State (EPT): Absence of Time and Causality<\/h3>\n                <p>The pre-temporal state (EPT) is an acausal, timeless state governed by pure rotation, described by the pre-temporal Hamiltonian:<\/p>\n                <div class=\"equation-box\">\n                    \\[ \\mathcal{H}_{\\text{pre}} = \\int_{\\text{EPT}} \\left[ \\hat{\\mathbb{B}}_\\epsilon, \\hat{\\mathbb{V}}_\\epsilon \\right] \\Psi_{\\text{universe}} \\, d^3x = \\frac{\\hbar}{\\epsilon} \\cdot \\mathcal{R}_{\\text{total}} \\]\n                <\/div>\n                <div class=\"equation-explanation\">\n                    <h4>Interpretation:<\/h4>\n                    <ul>\n                        <li><strong>\\( \\left[ \\hat{\\mathbb{B}}_\\epsilon, \\hat{\\mathbb{V}}_\\epsilon \\right] = 0 \\)<\/strong>: The zero commutator indicates no causal order, with the torsion operator \\( \\hat{\\mathbb{B}}_\\epsilon \\) and fractal potential operator \\( \\hat{\\mathbb{V}}_\\epsilon \\) acting without sequence. See <a href=\"\/index.php\/rotation\">Rotation Details<\/a>.<\/li>\n                        <li><strong>\\( \\mathcal{R}_{\\text{total}} \\)<\/strong>: The total rotational energy, defined as:\n                            \\[ \\mathcal{R}_{\\text{total}} \\equiv \\int_{\\text{EPT}} \\left( \\| \\hat{\\mathbb{T}} \\|^2 + \\| \\hat{\\mathbb{\\Omega}} \\|^2 \\right) d\\mu \\]\n                            where \\( \\hat{\\mathbb{T}} \\sim \\nabla \\hat{\\mathbb{B}}_\\epsilon \\) is the torsion tensor (\\( [\\hat{\\mathbb{T}}] = L^{-1} \\)), \\( \\hat{\\mathbb{\\Omega}} \\sim \\nabla \\hat{\\mathbb{V}}_\\epsilon \\) is the vorticity tensor, and \\( d\\mu \\) is the fractal measure with dimension:\n                            \\[ D_f = 2 + \\frac{\\log(\\epsilon\/\\epsilon_0)}{\\log N} \\]\n                            Here, \\( N \\) is the fractal branching factor, and \\( \\epsilon_0 \\sim \\ell_P \\) is the Planck length reference scale. The fractal volume is:\n                            \\[ V = \\int_{\\text{EPT}} d\\mu \\sim R^{D_f} \\]\n                            The dimension of \\( \\mathcal{R}_{\\text{total}} \\) is \\( [L^{D_f &#8211; 4}] \\), adjusted by fundamental constants to yield energy (\\( M L^2 T^{-2} \\)).<\/li>\n                        <li><strong>\\( \\mathcal{H}_{\\text{pre}} \\)<\/strong>: Analogous to the Wheeler-DeWitt equation, it constrains the EPT state without temporal dynamics, with \\( \\frac{\\hbar}{\\epsilon} \\cdot \\mathcal{R}_{\\text{total}} \\) as the energy eigenvalue.<\/li>\n                    <\/ul>\n                <\/div>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Symmetry Breaking: Birth of Time and Causality<\/h3>\n                <p>The transition from the EPT to spacetime occurs via a symmetry breaking, where the commutator becomes non-zero, as described by the QFunity master equation:<\/p>\n                <div class=\"equation-box\">\n                    \\[ \\lim_{\\epsilon \\to 0^+} \\left[ \\hat{\\mathbb{B}}_\\epsilon \\hat{\\mathbb{V}}_\\epsilon &#8211; \\hat{\\mathbb{V}}_\\epsilon \\hat{\\mathbb{B}}_\\epsilon^2 \\right] \\Psi = \\Lambda \\cdot \\frac{\\Psi}{\\|\\Psi\\|^2 + \\epsilon^2} \\]\n                <\/div>\n                <div class=\"equation-explanation\">\n                    <h4>Mechanism:<\/h4>\n                    <ul>\n                        <li><strong>Critical Threshold<\/strong>: Symmetry breaking occurs when the rotational energy density exceeds the Planck density:\n                            \\[ \\mathcal{E}_{\\text{EPT}} = \\frac{\\mathcal{R}_{\\text{total}}}{V} > \\mathcal{E}_{\\text{crit}} \\sim \\frac{c^7}{\\hbar G^2} \\]\n                        <\/li>\n                        <li><strong>Non-Commutation<\/strong>: The non-zero commutator \\( \\left[ \\hat{\\mathbb{B}}_\\epsilon, \\hat{\\mathbb{V}}_\\epsilon \\right] \\neq 0 \\) establishes a fundamental causal order. See <a href=\"\/index.php\/rotation\">Rotation Details<\/a>.<\/li>\n                        <li><strong>Emergence of Time<\/strong>: Time \\( t \\) emerges as a parameter in the curvature equation:\n                            \\[ \\eta(t) = \\frac{\\mathcal{E}_{\\text{EPT}}(t)}{\\hbar} \\cdot \\int_{-\\infty}^{t} \\omega(\\tau) e^{-i \\frac{\\mathcal{E}_{\\text{Micro}}(\\tau)}{\\hbar} (t &#8211; \\tau)} \\, d\\tau \\]\n                            Here, \\( \\tau \\) is a pseudo-temporal parameter representing fractal complexity levels, with the integral filtering coherent rotational states from the EPT.<\/li>\n                    <\/ul>\n                <\/div>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Emergence of the Speed of Light \\( c \\)<\/h3>\n                <p>The speed of light \\( c \\) emerges as the propagation speed of perturbations in the emergent spacetime, derived by linearizing the master equation around the critical point:<\/p>\n                <div class=\"equation-box\">\n                    \\[ \\left( \\hat{\\mathbb{O}}_1 \\partial_t^2 &#8211; \\hat{\\mathbb{O}}_2 \\nabla^2 \\right) \\delta\\Psi = 0 \\]\n                    \\[ \\hat{\\mathbb{O}}_1 \\equiv \\Lambda \\cdot \\frac{1}{\\hbar \\omega_{\\text{eff}}}, \\quad \\hat{\\mathbb{O}}_2 \\equiv \\frac{\\ell_P^2}{\\hbar} \\]\n                    \\[ c^2 = \\frac{\\text{v.p.}(\\hat{\\mathbb{O}}_2)}{\\text{v.p.}(\\hat{\\mathbb{O}}_1)} = \\frac{\\ell_P^2 \/ \\hbar}{\\Lambda \/ (\\hbar \\omega_{\\text{eff}})} = \\frac{\\ell_P^2 \\omega_{\\text{eff}}}{\\Lambda} \\]\n                    \\[ c = \\frac{\\ell_P \\sqrt{\\omega_{\\text{eff}}}}{\\sqrt{\\Lambda}} \\]\n                    \\[ \\omega_{\\text{eff}} \\sim \\sqrt{\\frac{\\mathcal{E}_{\\text{crit}}}{\\hbar}} \\sim \\frac{c}{\\ell_P} \\]\n                <\/div>\n                <div class=\"equation-explanation\">\n                    <h4>Derivation:<\/h4>\n                    <ul>\n                        <li><strong>Linearization<\/strong>: Perturbing \\( \\Psi = \\Psi_0 + \\delta\\Psi \\) yields a wave equation, with \\( \\hat{\\mathbb{O}}_1 \\) (dimension \\( T^2 \/ (M L^2) \\)) linked to the energy scale of the symmetry breaking and \\( \\hat{\\mathbb{O}}_2 \\) (dimension \\( T \/ M \\)) to the emergent spatial structure.<\/li>\n                        <li><strong>Speed \\( c \\)<\/strong>: If \\( \\Lambda \\sim 1 \\), then \\( c \\approx \\ell_P \\sqrt{\\omega_{\\text{eff}}} \\), recovering the known value when \\( \\omega_{\\text{eff}} \\sim c \/ \\ell_P \\).<\/li>\n                        <li><strong>Metric<\/strong>: The emergent metric defines the causal structure:\n                            \\[ g_{\\mu\\nu}(\\epsilon) = g_{\\mu\\nu}^{GR} + \\frac{\\ell_P^2}{\\epsilon^2} g_{\\mu\\nu}^{\\text{LQG}} + \\alpha&rsquo; \\cdot g_{\\mu\\nu}^{\\text{strings}} \\]\n                            The light cone slope, set by \\( c \\), governs causal information propagation. See <a href=\"\/index.php\/observer\">Observer Details<\/a>.<\/li>\n                    <\/ul>\n                <\/div>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Scale-Dependent Causality<\/h3>\n                <p>The observer\u2019s scale \\( \\epsilon \\) modulates the perception of causality and \\( c \\):<\/p>\n                <div class=\"equation-box\">\n                    <h4>Cosmic Horizon:<\/h4>\n                    \\[ R_{\\text{horizon}} = \\frac{c}{H_0} \\cdot \\sqrt{\\frac{\\epsilon}{\\epsilon_{\\text{cosmic}}}} \\]\n                    \\[ \\epsilon_{\\text{cosmic}} \\sim \\frac{c}{H_0} \\]\n                <\/div>\n                <div class=\"equation-explanation\">\n                    <h4>Superluminal Correlations:<\/h4>\n                    <ul>\n                        <li><strong>Human Observer (\\( \\epsilon \\sim 1 \\, \\text{m} \\))<\/strong>: Horizon \\( R_{\\text{horizon}} \\approx \\frac{c}{H_0} \\approx 14 \\, \\text{Gly} \\).<\/li>\n                        <li><strong>Galactic Observer (\\( \\epsilon \\sim 10^{20} \\, \\text{m} \\))<\/strong>: Smaller horizon leads to apparent superluminal correlations for events within the human-scale horizon.<\/li>\n                    <\/ul>\n                <\/div>\n                <div class=\"equation-box\">\n                    <h4>Quantum Collapse:<\/h4>\n                    \\[ P(\\psi \\to \\phi) = \\frac{|\\langle \\phi | \\psi \\rangle|^2}{|\\langle \\psi | \\psi \\rangle|^2 + \\epsilon_O^2} \\]\n                <\/div>\n                <div class=\"equation-explanation\">\n                    <h4>Planck-Scale Entanglement:<\/h4>\n                    <ul>\n                        <li><strong>Macroscopic Scale (\\( \\epsilon_O \\sim 10^{-3} \\, \\text{m} \\))<\/strong>: Clear collapse, enforcing strict causality.<\/li>\n                        <li><strong>Planck Scale (\\( \\epsilon_O \\sim \\ell_P \\))<\/strong>: No collapse, preserving entanglement and reflecting the acausal EPT. See <a href=\"\/index.php\/zero\">Zero Details<\/a>.<\/li>\n                    <\/ul>\n                <\/div>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Fate of Light Information at Obstacles<\/h3>\n                <p>When a photon encounters an obstacle (e.g., a planet), the fate of its information depends on the interaction:<\/p>\n                <div class=\"equation-explanation\">\n                    <h4>Interaction Types:<\/h4>\n                    <ul>\n                        <li><strong>Absorption<\/strong>: The photon\u2019s energy is converted into heat or chemical energy, localizing and thermalizing its information (direction, frequency, polarization). Most of the original information is lost as a coherent signal.<\/li>\n                        <li><strong>Scattering<\/strong>: The photon\u2019s direction changes (e.g., Rayleigh scattering), preserving but altering information. Frequency and polarization may be modified, leading to corrupted information.<\/li>\n                        <li><strong>Reflection<\/strong>: Information is best preserved, with direction reversed but frequency, phase, and polarization largely maintained (e.g., by a mirror).<\/li>\n                    <\/ul>\n                    <p>Interactions with massive matter involve energy and momentum exchange, degrading the purity of the photon\u2019s information. Light is an excellent information carrier in vacuum but poor through massive matter.<\/p>\n                <\/div>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Neutrinos: Transparent Carriers of Information<\/h3>\n                <p>Neutrinos, interacting only via the weak force and gravity, have an extremely low interaction cross-section:<\/p>\n                <div class=\"equation-explanation\">\n                    <h4>Properties:<\/h4>\n                    <ul>\n                        <li><strong>Low-Energy Neutrinos<\/strong>: Can traverse the Earth or a light-year of lead with near-zero interaction probability.<\/li>\n                        <li><strong>Information Preservation<\/strong>: Neutrino information (flavor, energy, momentum) remains nearly unaltered, making them ideal messengers from dense environments (e.g., stellar cores, supernovae, early universe).<\/li>\n                    <\/ul>\n                <\/div>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Massless Particles and EPT: Guardians of Causal Information<\/h3>\n                <p>Only massless particles (photons, gluons, potentially gravitons) travel at \\( c \\), defining the light cones:<\/p>\n                <div class=\"equation-explanation\">\n                    <h4>Key Points:<\/h4>\n                    <ul>\n                        <li><strong>Causal Information<\/strong>: Particles moving at \\( c \\) are the primary carriers of causally connected information, as they define the light cone structure.<\/li>\n                        <li><strong>EPT Connection<\/strong>: Massless particles are the first excitations of the EPT post-symmetry breaking, with \\( c = \\ell_P \\sqrt{\\omega_{\\text{eff}}} \/ \\sqrt{\\Lambda} \\) inherited from the EPT dynamics. They are manifestations of the emergent causal structure.<\/li>\n                        <li><strong>Neutrinos<\/strong>: With near-zero mass, neutrinos approximate this behavior, carrying near-pristine information from the early universe.<\/li>\n                    <\/ul>\n                <\/div>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Innate vs. Acquired Information<\/h3>\n                <p>QFunity distinguishes two types of information:<\/p>\n                <div class=\"equation-box\">\n                    <h4>Innate Information (EPT):<\/h4>\n                    \\[ \\lim_{\\epsilon \\to 0^+} \\left[ \\hat{\\mathbb{B}}_\\epsilon \\hat{\\mathbb{V}}_\\epsilon &#8211; \\hat{\\mathbb{V}}_\\epsilon \\hat{\\mathbb{B}}_\\epsilon^2 \\right] \\Psi_0 = \\Lambda \\cdot \\frac{\\Psi_0}{\\|\\Psi_0\\|^2} \\]\n                <\/div>\n                <div class=\"equation-explanation\">\n                    <h4>Innate Information:<\/h4>\n                    <ul>\n                        <li><strong>Origin<\/strong>: Encoded in the initial state \\( \\Psi_0 \\) at symmetry breaking, determining fundamental constants (e.g., \\( c \\), \\( \\alpha \\)) and primordial fluctuations (e.g., CMB anisotropies).<\/li>\n                        <li><strong>Carriers<\/strong>: Massless particles (photons, gravitons) and the spacetime metric itself.<\/li>\n                        <li><strong>Example<\/strong>: CMB photon temperature variations \\( \\delta T\/T \\) reflect the primordial state \\( \\Psi_0 \\).<\/li>\n                    <\/ul>\n                <\/div>\n                <div class=\"equation-box\">\n                    <h4>Acquired Information:<\/h4>\n                    \\[ i\\hbar \\frac{\\partial \\Psi(t)}{\\partial t} = \\left( \\hat{\\mathbb{V}}_\\epsilon + \\hat{\\mathbb{B}}_\\epsilon^2 \\right) \\Psi(t) \\]\n                <\/div>\n                <div class=\"equation-explanation\">\n                    <h4>Acquired Information:<\/h4>\n                    <ul>\n                        <li><strong>Origin<\/strong>: Generated by interactions post-symmetry breaking, encoded in the evolving state \\( \\Psi(t) \\).<\/li>\n                        <li><strong>Carriers<\/strong>: Massive matter (electrons, atoms), gravitational waves from dynamic events, and \u00ab\u00a0polluted\u00a0\u00bb light (e.g., stellar spectral lines).<\/li>\n                        <li><strong>Example<\/strong>: Stellar absorption lines reflect the chemical composition and dynamics of stars.<\/li>\n                    <\/ul>\n                <\/div>\n                <table class=\"info-table\">\n                    <tr>\n                        <th>Characteristic<\/th>\n                        <th>Innate Information (EPT)<\/th>\n                        <th>Acquired Information (History)<\/th>\n                    <\/tr>\n                    <tr>\n                        <td><strong>Origin<\/strong><\/td>\n                        <td>Initial state \\( \\Psi_0 \\) at symmetry breaking<\/td>\n                        <td>Evolution of \\( \\Psi(t) \\) via interactions<\/td>\n                    <\/tr>\n                    <tr>\n                        <td><strong>Equation<\/strong><\/td>\n                        <td>Master Equation<\/td>\n                        <td>Generalized Schr\u00f6dinger Equation<\/td>\n                    <\/tr>\n                    <tr>\n                        <td><strong>Carriers<\/strong><\/td>\n                        <td>Massless particles, spacetime<\/td>\n                        <td>Massive matter, gravitational waves, polluted light<\/td>\n                    <\/tr>\n                    <tr>\n                        <td><strong>Nature<\/strong><\/td>\n                        <td>Fundamental constants, primordial spectrum<\/td>\n                        <td>Stellar composition, cosmic structures, DNA<\/td>\n                    <\/tr>\n                    <tr>\n                        <td><strong>Alteration<\/strong><\/td>\n                        <td>Preserved if uninteracted<\/td>\n                        <td>Subject to degradation, thermalization<\/td>\n                    <\/tr>\n                    <tr>\n                        <td><strong>Example<\/strong><\/td>\n                        <td>CMB anisotropies<\/td>\n                        <td>Stellar spectral lines<\/td>\n                    <\/tr>\n                <\/table>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Testable Predictions<\/h3>\n                <p>QFunity\u2019s framework yields observable phenomena:<\/p>\n                <div class=\"equation-explanation\">\n                    <ul>\n                        <li><strong>Superluminal Correlations<\/strong>: Large-scale alignments in the CMB or galaxy distributions may appear acausal at galactic scales (\\( \\epsilon \\sim 10^{20} \\, \\text{m} \\)), testable via CMB anomaly studies or large-scale structure surveys.<\/li>\n                        <li><strong>Planck-Scale Entanglement<\/strong>: Non-locality at \\( \\epsilon \\sim \\ell_P \\), reflecting the acausal EPT, testable in high-energy physics (e.g., LHC anomalies with missing transverse energy) or Casimir effect experiments. See <a href=\"\/index.php\/micro-ept\">Micro-EPT Details<\/a>.<\/li>\n                        <li><strong>Neutrino Information<\/strong>: Neutrinos from supernovae or the early universe carry near-pristine information, testable via neutrino observatories like IceCube.<\/li>\n                    <\/ul>\n                <\/div>\n            <\/div>\n\n            <div class=\"theory-principle\">\n                <h3>Implications for Universes with Different \\( c \\)<\/h3>\n                <p>Different EPT parameters yield varying \\( c&rsquo; \\):<\/p>\n                <div class=\"equation-box\">\n                    \\[ c&rsquo; = \\frac{\\ell_P \\sqrt{\\omega_{\\text{eff}}&rsquo;}}{\\sqrt{\\Lambda}} \\]\n                <\/div>\n                <div class=\"equation-explanation\">\n                    <h4>Interpretation:<\/h4>\n                    <ul>\n                        <li><strong>Higher \\( \\omega_{\\text{eff}}&rsquo; \\)<\/strong>: More energetic symmetry breaking yields \\( c&rsquo; > c \\).<\/li>\n                        <li><strong>Lower \\( \\omega_{\\text{eff}}&rsquo; \\)<\/strong>: Less energetic breaking yields \\( c&rsquo; < c \\).<\/li>\n                        <li><strong>Consequences<\/strong>: Altered fundamental constants (e.g., fine-structure constant) lead to different physical laws, testable in multi-messenger astronomy.<\/li>\n                    <\/ul>\n                <\/div>\n            <\/div>\n\n            <div style=\"text-align: center; margin-top: 3rem;\">\n                <a href=\"\/index.php\/hypotheses\" class=\"back-button\">Back to Hypotheses<\/a>\n            <\/div>\n        <\/div>\n    <\/section>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>QFunity &#8211; Emergence of Causality, Light, and Information Emergence of Causality, Light, and Information in QFunity A unified framework for the origin of time, causality, the speed of light, and the nature of information From Pre-Temporal State to Causal Spacetime The Pre-Temporal State (EPT): Absence of Time and Causality The pre-temporal state (EPT) is an [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-349","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/qfunity.com\/index.php\/wp-json\/wp\/v2\/pages\/349","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qfunity.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/qfunity.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/qfunity.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/qfunity.com\/index.php\/wp-json\/wp\/v2\/comments?post=349"}],"version-history":[{"count":6,"href":"https:\/\/qfunity.com\/index.php\/wp-json\/wp\/v2\/pages\/349\/revisions"}],"predecessor-version":[{"id":356,"href":"https:\/\/qfunity.com\/index.php\/wp-json\/wp\/v2\/pages\/349\/revisions\/356"}],"wp:attachment":[{"href":"https:\/\/qfunity.com\/index.php\/wp-json\/wp\/v2\/media?parent=349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}