{"id":15373,"date":"2026-01-10T15:37:16","date_gmt":"2026-01-10T14:37:16","guid":{"rendered":"https:\/\/instytut-iskra.pl\/?page_id=15373"},"modified":"2026-01-18T10:23:57","modified_gmt":"2026-01-18T09:23:57","slug":"o-emergencji-matematyki","status":"publish","type":"page","link":"https:\/\/instytut-iskra.pl\/en\/o-emergencji-matematyki\/","title":{"rendered":"On the emergence of mathematics"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"15373\" class=\"elementor elementor-15373\">\n\t\t\t\t<div class=\"elementor-element elementor-element-696d04a e-flex e-con-boxed e-con e-parent\" data-id=\"696d04a\" data-element_type=\"container\">\t\t\t<div class=\"e-con-inner\">\r\n\t\t<div class=\"elementor-element elementor-element-1f7e537 e-con-full e-flex e-con e-child\" data-id=\"1f7e537\" data-element_type=\"container\">\t\t<div class=\"elementor-element elementor-element-8076d29 elementor-widget elementor-widget-pxl_menu\" data-id=\"8076d29\" data-element_type=\"widget\" data-widget_type=\"pxl_menu.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t    <div class=\"pxl-nav-menu pxl-nav-menu1 pxl-mega-full-width pxl-nav-vertical\" data-wow-delay=\"ms\">\r\n        <div class=\"menu-menu_maya-container\"><ul id=\"menu-menu_maya\" class=\"pxl-menu-primary clearfix\"><li id=\"menu-item-15535\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-15535\"><a href=\"https:\/\/instytut-iskra.pl\/en\/przedmowa\/\"><span class=\"pxl-menu-item-text\">Preface<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14873\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14873\"><a href=\"https:\/\/instytut-iskra.pl\/en\/geneza-teorii\/\"><span class=\"pxl-menu-item-text\">The origins of the MAYA theory<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14879\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14879\"><a href=\"https:\/\/instytut-iskra.pl\/en\/problemy-wspolczesnej-fizyki\/\"><span class=\"pxl-menu-item-text\">Problems of modern physics<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14872\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14872\"><a href=\"https:\/\/instytut-iskra.pl\/en\/dlaczego-informacja\/\"><span class=\"pxl-menu-item-text\">Why information?<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14876\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14876\"><a href=\"https:\/\/instytut-iskra.pl\/en\/jednostki-plancka\/\"><span class=\"pxl-menu-item-text\">Planck units<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14878\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14878\"><a href=\"https:\/\/instytut-iskra.pl\/en\/planxel\/\"><span class=\"pxl-menu-item-text\">Planxel<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14875\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14875\"><a href=\"https:\/\/instytut-iskra.pl\/en\/implikacje-mechanizmu-planxeli-dla-fizyki\/\"><span class=\"pxl-menu-item-text\">Physics implications of the planxel mechanism<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14881\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14881\"><a href=\"https:\/\/instytut-iskra.pl\/en\/reinterpretacja-wzorow\/\"><span class=\"pxl-menu-item-text\">Reinterpretation of Formulas<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14871\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14871\"><a href=\"https:\/\/instytut-iskra.pl\/en\/czas-w-modelu-maya\/\"><span class=\"pxl-menu-item-text\">Time in the M\u0101y\u0101 Model<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14880\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14880\"><a href=\"https:\/\/instytut-iskra.pl\/en\/przestrzen-w-modelu-maya\/\"><span class=\"pxl-menu-item-text\">Space in the M\u0101y\u0101 model<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14874\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14874\"><a href=\"https:\/\/instytut-iskra.pl\/en\/grawitacja\/\"><span class=\"pxl-menu-item-text\">Gravity<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14877\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14877\"><a href=\"https:\/\/instytut-iskra.pl\/en\/paradoksy-fizyki\/\"><span class=\"pxl-menu-item-text\">Paradoxes of Physics<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14870\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14870\"><a href=\"https:\/\/instytut-iskra.pl\/en\/alpha\/\"><span class=\"pxl-menu-item-text\">ALPHA decoded<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14981\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14981\"><a href=\"https:\/\/instytut-iskra.pl\/en\/czastki-w-maya\/\"><span class=\"pxl-menu-item-text\">Particles in MAYA<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-15368\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-15368\"><a href=\"https:\/\/instytut-iskra.pl\/en\/mechanika-kwantowa\/\"><span class=\"pxl-menu-item-text\">Quantum mechanics<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-15682\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-15682\"><a href=\"https:\/\/instytut-iskra.pl\/en\/niezmienniczosc-lorentza\/\"><span class=\"pxl-menu-item-text\">Emergentna niezmienniczo\u015b\u0107 Lorentza<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-15384\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-15384\"><a href=\"https:\/\/instytut-iskra.pl\/en\/o-emergencji-matematyki\/\"><span class=\"pxl-menu-item-text\">On the emergence of mathematics<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<\/ul><\/div>            <\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\r\n\t\t<div class=\"elementor-element elementor-element-a64065a e-con-full e-flex e-con e-child\" data-id=\"a64065a\" data-element_type=\"container\">\t\t<div class=\"elementor-element elementor-element-4ffa5dc elementor-widget elementor-widget-pxl_heading\" data-id=\"4ffa5dc\" data-element_type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\r\n<div id=\"pxl-pxl_heading-4ffa5dc-1949\" class=\"pxl-heading px-sub-title-default-style\">\r\n\t<div class=\"pxl-heading--inner\">\r\n\t\t\r\n\t\t<h2 class=\"pxl-item--title style-default highlight-default\" data-wow-delay=\"ms\">\r\n\r\n\t\t\t<span class=\"pxl-heading--text\">\r\n\r\n\t\t\t\t\t\t\t\t\tOn the Emergence of Mathematics \u2013 LOGOS: How Mathematics Emerges from the Discrete Web of Reality\t\r\n\t\t\t\t\t\r\n\r\n\t\t\t<\/span>\r\n\t\t<\/h2>\r\n\t\t\r\n\t<\/div>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d768650 elementor-widget elementor-widget-pxl_text_editor\" data-id=\"d768650\" data-element_type=\"widget\" data-widget_type=\"pxl_text_editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pxl-text-editor highlight-gradient\">\r\n\t<div class=\"pxl-item--inner\" >\r\n\t\t<div>Which is more fundamental: the number \u03c0 or a cube with sides the length of a Planck? The M\u0100Y\u0100 conjecture answers: the geometry of the discrete plankton network is primordial. All mathematics \u2014 from integers to the most enigmatic constants \u2014 emerges from it as an inevitable consequence of structure and optimization. We present the LOGOS model: the theory of emergent mathematics.<\/div><h4><b>Where Do Numbers Come From? Types of Numbers as Degrees of Emergence.<\/b><\/h4><div>The natural numbers (1, 2, 3\u2026) are simply an ordering of planxels. The basic operation of \"successor\" emerges from the discrete timing of the network. Primes are irreducible synchronization patterns in the network. They cannot be divided into smaller, identical, stable clusters of planxels. Their arrangement reflects the emergent \"music\" of stable network configurations, which may provide the key to the Riemann hypothesis. Irrational numbers (\u03c6), algebraic numbers (\u221a2), and transcendental numbers (\u03c0) are different levels of complexity in the discrete approximation of the continuum.<\/div><h4><b>Mathematical constants are not given \u2013 they are calculated<\/b><\/h4><div class=\"translation-block\"><br><b>The golden ratio \u03c6<\/b> emerges as the most efficient algorithm for dispersing information in a network \u2013 it is a continued fraction [1;1,1,1\u2026], optimizing local interactions.<\/div><div>\u00a0<\/div><div class=\"translation-block\"><b>The number \u03c0<\/b> emerges not as the ratio of the circumference to the diameter of a \"perfect circle\" (which does not exist in the discrete world), but as a smoothing parameter. It is the number that best describes how a discrete 3D network imitates continuous, isotropic space at the macroscale. The transcendentality of \u03c0 is consistent with the hypothesis that it describes a limiting emergent parameter that is not directly encoded in the local algebraic structure of the network, but rather arises from a global isotropy approximation process.<\/div><div class=\"translation-block\"><br><b>The number e<\/b> appears in mathematics as the limit of continuous growth processes, in differential calculus, probability theory, and quantum mechanics. In the LOGOS model, it is not a primitive mathematical constant, but an emergent parameter arising from local update rules in a discrete network. If the planksel updates its state based on the local environment at each cycle, striving for maximum stability or minimal information loss, then an iterative process of an exponential nature naturally emerges. The number e then describes the optimal limit of such local, self-sustaining growth as the number of update steps approaches infinity. In this sense, e is not a \"continuous number\" but an emergent limit\u2014an ideal parameter describing the behavior of the network when its discreteness becomes invisible on a macroscale. Just as \u03c0 describes the isotropy of space, e also describes the isotropy of the process of information growth and decay over time.<\/div><div class=\"translation-block\"><br><b>The imaginary unit i<\/b>, formally defined as \u221a\u22121, is sometimes treated as a purely abstract mathematical construct. In M\u0100Y\u0100 theory and the LOGOS model, however, it is given a natural physical interpretation. If the state of the planxel is described not only by amplitude but also by phase (as in wave mechanics), then the simplest nontrivial operation that the network can perform is a local 90\u00b0 phase rotation. Such an operation does not change the energy or norm of the state, but shifts it in state space. The unit i represents the minimal phase rotation operator, necessary to describe interference, oscillations, and coupling between information propagation channels. In this sense, complex numbers are not an \"artificial extension\" of mathematics, but a natural language for describing the dynamics of a network in which information has both magnitude and phase.<\/div><div class=\"translation-block\"><br><b>Euler's identity<\/b> e^{i\u03c0} + 1 = 0 connects five fundamental objects of mathematics: 0, 1, e, i, and \u03c0. In the LOGOS model, it is not a random confluence of symbols or \"the most beautiful formula of mathematics,\" but a compressed notation of structural relations in the discrete network of reality.<br>1 represents a unit tick or planksel,<br>0 \u2013 no excitation,<br>i \u2013 phase rotation,<br>e \u2013 growth dynamics,<br>\u03c0 \u2013 the global isotropy parameter.<br>Euler's identity can be interpreted as the shortest \"program\" that describes the full cycle of evolution of a state in the network: growth, rotation, phase closure, and return to the starting point. Its extraordinary simplicity may be a consequence of the fact that it describes the deepest level of synchronization between geometry, dynamics, and information.<\/div><div class=\"translation-block\"><br><b>The fine structure constant \u03b1<\/b>\u2248 1\/137.036 is not a magic number, but the probability of optimal information propagation in a 3D network. Our formula: \u03b1\u207b\u00b9 = 360\/\u03c6\u00b2 \u2013 2\/\u03c6\u00b3 + 1\/(3\u2075 \u03c6\u2075) + 7\/(3\u00b9\u00b2 \u03c6\u00b9\u00b2) shows how \u03b1 emerges from combinations of fundamental symmetries:<\/div><div class=\"translation-block\">360\/\u03c6\u00b2: 360 is not \u201cdegrees in a circle\u201d, but the optimal quantization number of the sphere resulting from the combinatorics of the cubic lattice (360 = 3\u00b2 \u00d7 2\u00b3 \u00d7 5), and the subsequent terms are:<br>-2\/\u03c6\u00b3: correction for axial anisotropy,<br>1\/(3\u2075 \u03c6\u2075): correction for the 3\u00d73\u00d73 block structure,<br>7\/(3\u00b9\u00b2 \u03c6\u00b9\u00b2): correction for soft modes in larger clusters (Mackay).<br>The above expression is not the result of the standard renormalization procedure, but a geometric-combinatorial construction, the purpose of which is to show that the value \u03b1 can emerge from the discrete structure of the lattice, and not be a fundamental parameter.<\/div><h4><b>Resolving paradoxes and problems through a paradigm shift<\/b><\/h4><div><p>Paradoks Banacha-Tarskiego wskazuje, i\u017c w continuum mo\u017cliwe jest rozbicie kuli na okre\u015blon\u0105 liczb\u0119 cz\u0119\u015bci i z\u0142o\u017cenie ich w dwie identyczne kule. To ostrze\u017cenie przed nadu\u017cyciem aksjomatu wyboru i modelem ci\u0105g\u0142ej, niesko\u0144czenie podzielnej przestrzeni. W M\u0100Y\u0100 ten paradoks znika. Przestrze\u0144 jest dyskretna (Z\u00b3), a planksel jest niepodzieln\u0105 jednostk\u0105. Nie mo\u017cna &#8220;rozbi\u0107&#8221; planksela, wi\u0119c masa i informacja s\u0105 \u015bci\u015ble zachowane.<br \/>problem \u201eniepoj\u0119tej skuteczno\u015bci matematyki\u201d. Zjawisko Gibbsa to\u00a0wr\u0119cz modelowa analogia &#8211;\u00a0<br \/>\u00a0pokazuje, \u017ce gdy pr\u00f3bujemy opisa\u0107 funkcj\u0119 nieci\u0105g\u0142\u0105 narz\u0119dziami ci\u0105g\u0142ymi,\u00a0zawsze pojawia si\u0119 nieredukowalny overshoot (~9%), kt\u00f3ry\u00a0nie znika, nawet przy niesko\u0144czonej liczbie sk\u0142adnik\u00f3w Fouriera. Pr\u00f3bujemy opisa\u0107 dyskretne przej\u015bcia sieci j\u0119zykiem g\u0142adkich funkcji \u2013 i dostajemy niesko\u0144czono\u015bci,\u00a0osobliwo\u015bci, fenomenologiczne\u00a0sta\u0142e, paradoksy typu Banacha\u2013Tarskiego. To nie s\u0105 b\u0142\u0119dy naszego rozumowania, lecz\u00a0artefakty nieadekwatnego formalizmu.<\/p><p>Hipoteza Riemanna to najs\u0142ynniejszy nierozwi\u0105zany problem matematyczny. W uj\u0119ciu M\u0100Y\u0100 hipoteza ta nie jest problemem czysto analitycznym, lecz mo\u017ce odzwierciedla\u0107 spektrum rezonans\u00f3w globalnego operatora ewolucji sieci, a linia Re(s) = 1\/2 mo\u017ce emergowa\u0107 jako \u015brednia warto\u015b\u0107 w\u0142asna tego uniwersalnego operatora. Badania nad dynamik\u0105 defekt\u00f3w fazowych mog\u0105 dostarczy\u0107 nowej drogi do zrozumienia (i ewentualnego potwierdzenia) tej hipotezy.<\/p><\/div><div class=\"translation-block\">In LOGOS, prime numbers are not random, but neither are they regular. They are what in physics we would call the resonance spectrum of a deterministic system of high complexity. That is, the network has specific rules, but its global patterns interfere in a way that statistically appears random. This is exactly the same category as: <br>\u2013 turbulence,\n<br>\u2013 energy distribution in chaotic systems,<br>\u2013 vibrational spectrum of complex resonators.<br>Therefore, statistical analysis works, but a constructive proof of HR still eludes us. Because we are trying to solve the spectral problem with the tools of pure continuous analysis, instead of graph theory\/network dynamics.<\/div><h4><b>The anthropic principle as a selection of stable architectures<\/b><\/h4><div class=\"translation-block\"><br>In classical cosmology, the anthropic principle is sometimes treated as the ultimate explanation: the universe has these parameters because otherwise we could not exist in it. In the M\u0100Y\u0100 and LOGOS models, it receives a more structural interpretation.<br>If there is a space of possible network architectures (different geometries, updating rules, and topologies), only a small subset of them lead to stable, long-lived configurations capable of storing and processing information on multiple scales. Observers are therefore not the cause of fine-tuning, but the product of the selection of stable networks.<br>The anthropic principle then becomes a consequence of information theory: only in such structures, in which information can persist long enough to undergo self-conscious organization, is it possible to ask questions about the nature of reality.<\/div><div>\u00a0<\/div><h4><b>Why does math work?<\/b><\/h4><div class=\"translation-block\"><b><br><\/b>One of the deepest unresolved problems in the philosophy of science is the \"incomprehensible effectiveness of mathematics in the natural sciences.\" Why do abstract formal structures, created without reference to empiricism, describe the physical world so precisely?<br>The LOGOS model proposes a radical reversal of perspective: mathematics is not a separate, Platonic realm, nor a pure creation of the mind, a language imposed on reality, but its product\u2014an emergent property of the architecture of our concrete, discrete reality. Another universe, with a different basic network geometry, would have a different mathematics. We reveal the one written in the code of our network.<\/div><div class=\"translation-block\">Mathematical structures that prove \"effective\" are those that reflect the real-world symmetries, resonances, and constraints of a discrete network. Those that have no counterpart in network dynamics remain pure mathematics, with no physical realization in our universe (as in the aforementioned example of the Banach-Tarski paradox).<br>The effectiveness of mathematics ceases to be a miracle. It becomes a selective filter: we discover and develop those fragments of mathematics that are compatible with the architecture of the world, because only these are confirmed by experience.<\/div>\t\t\r\n\t<\/div>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c563fdb elementor-widget elementor-widget-pxl_button\" data-id=\"c563fdb\" data-element_type=\"widget\" data-widget_type=\"pxl_button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"pxl-pxl_button-c563fdb-8836\" class=\"pxl-button pxl-atc-link\" data-wow-delay=\"ms\">\r\n    <a href=\"https:\/\/instytut-iskra.pl\/en\/przedmowa\/\" class=\"btn pxl-icon-active btn-block-inline  btn-text-underline pxl-icon--right\">\r\n                    <span class=\"pxl--btn-icon\">\r\n                <i aria-hidden=\"true\" class=\"flaticon flaticon-right-arrow-long\"><\/i>                            <\/span>\r\n                <span class=\"pxl--btn-text\" data-text=\"Odkrywaj wi\u0119cej\">\r\n            Discover more        <\/span>\r\n    <\/a>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-54d4e7d elementor-widget elementor-widget-pxl_heading\" data-id=\"54d4e7d\" data-element_type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\r\n<div id=\"pxl-pxl_heading-54d4e7d-6218\" class=\"pxl-heading px-sub-title-default-style\">\r\n\t<div class=\"pxl-heading--inner\">\r\n\t\t\r\n\t\t<h3 class=\"pxl-item--title style-default highlight-default\" data-wow-delay=\"ms\">\r\n\r\n\t\t\t<span class=\"pxl-heading--text\">\r\n\r\n\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\r\n\r\n\t\t\t<\/span>\r\n\t\t<\/h3>\r\n\t\t\r\n\t<\/div>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Przedmowa Geneza teorii MAYA Problemy wsp\u00f3\u0142czesnej fizyki Dlaczego informacja? Jednostki Plancka Planxel Implikacje mechanizmu planxeli dla fizyki Reinterpretacja Wzor\u00f3w Czas w modelu M\u0101y\u0101 Przestrze\u0144 w modelu Maya Grawitacja Paradoksy Fizyki ALPHA odkodowana Cz\u0105stki w MAYA Mechanika kwantowa O emergencji matematyki Emergentna niezmienniczo\u015b\u0107 Lorentza O Emergencji Matematyki &#8211; LOGOS: Jak z Dyskretnej Sieci Rzeczywisto\u015bci Wy\u0142ania si\u0119 [&hellip;]<\/p>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-15373","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/pages\/15373","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/comments?post=15373"}],"version-history":[{"count":17,"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/pages\/15373\/revisions"}],"predecessor-version":[{"id":15725,"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/pages\/15373\/revisions\/15725"}],"wp:attachment":[{"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/media?parent=15373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}