Observational Illusions in Cosmology: On the Interpretive Divide between Measurement and Existence in Standard Cosmology

{"Modern":[0],"standard":[1,269],"cosmology":[2,270],"constructs":[3],"cosmological":[4,140,359],"entities,":[5],"histories,":[6],"and":[7,60,130,186,196,257,275,297,306,386,416,627,716,718],"ontologies":[8],"from":[9,105,258,361,482,568],"observational":[10],"data":[11],"through":[12],"the":[13,28,36,40,46,50,55,61,68,82,92,98,110,124,136,147,175,183,187,208,226,239,245,266,293,298,315,331,337,342,345,349,352,356,372,395,410,423,429,444,449,455,459,466,470],"chain":[14,69,241],"O_obs":[15],"→":[16,18,20,248,250],"I_ana":[17,247],"I_theo":[19,249],"O_ont.":[21,64],"The":[22,78,170,368,391,434],"present":[23,125,369],"paper":[24,126,335,370],"does":[25,143,474],"not":[26,85,144,475,542,601,680,748],"question":[27],"reliability":[29],"of":[30,39,88,114,138,149,174,223,301,330,348,354,399,405,451,458,775],"observations.":[31],"What":[32],"it":[33,200,262],"questions":[34],"is":[35,70,84,201,230,263,336,465],"systematic":[37],"conflation":[38],"four":[41],"levels":[42],"in":[43,67,81,121,193,244,339,497,520,524,539,550,554,558,565,574,588,592,607,615,619,623,647,659,669,673,681,687,744,749],"this":[44,400,437],"chain:":[45],"raw":[47],"observable":[48,158],"O_obs,":[49],"analytically":[51],"processed":[52],"quantity":[53,58,142],"I_ana,":[54],"theoretically":[56],"interpreted":[57],"I_theo,":[59],"ontological":[62,267],"conclusion":[63],"Each":[65],"arrow":[66],"an":[71,86,101,384],"independent":[72],"operation":[73],"carrying":[74],"its":[75,233],"own":[76],"assumptions.":[77],"illusion":[79,87,93],"named":[80],"title":[83],"observation":[89],"itself,":[90],"but":[91],"that":[94,106,207,265,409,472],"one":[95],"can":[96],"read":[97],"ontology":[99],"sustaining":[100],"observed":[102],"relation":[103],"directly":[104],"relation.":[107],"Building":[108],"on":[109,438],"Tier-2":[111,205,260,278,316,346,397],"axiomatic":[112],"foundation":[113],"Operatiology":[115],"(Japanese:":[116],"Sousa":[117],"Genron,":[118],"操作原論)":[119],"established":[120,192,264,344],"prior":[122],"work,":[123],"advances":[127],"three":[128],"claims":[129],"establishes":[131,408],"them":[132],"as":[133,203,232,311,443,480],"theorems.":[134,333],"First,":[135],"existence":[137,148],"a":[139,150,204,340,439],"structural":[141,332],"logically":[145],"entail":[146,476],"corresponding":[151],"local":[152],"material":[153],"substance:":[154],"for":[155,178,469,495,518,522,537,552,556,563,572,586,590,605,617,621,657,667,671,742],"any":[156],"Tier-3":[157,234,283,320,379],"Q,":[159],"Q_obs":[160],"⇏":[161],"∃N":[162],"∈":[163],"Nec(S):":[164],"(Q":[165],"↔":[166],"N)":[167],"(Proposition":[168],"4.1).":[169],"specific":[171],"failure":[172],"modes":[173],"Nec(S)":[176,209,411,456,768],"conditions":[177,210,412,457,769],"WIMP":[179],"dark":[180],"matter":[181],"candidates,":[182],"inflaton":[184],"field,":[185],"Big":[188],"Bang":[189],"singularity":[190],"are":[191,252,309,322,381,770],"Lemma":[194],"4.2":[195],"Theorem":[197,220,402],"4.3.":[198],"Second,":[199],"proved":[202],"theorem":[206,398],"contain":[211,419],"no":[212,420],"reference":[213,421],"to":[214,272,388,422,428],"operational":[215,430],"separation":[216,431],"K_op":[217,452,764],"(Lemma":[218],"5.3,":[219],"5.4:":[221],"K_op-Independence":[222],"Structural":[224,406,776],"Necessity);":[225],"Uniform":[227],"Fidelity":[228],"Correspondence":[229],"derived":[231,358],"projection":[235],"(Corollary":[236],"5.5).":[237],"Third,":[238],"analytical":[240,389],"assumptions":[242],"embedded":[243],"arrows":[246],"O_ont":[251],"formally":[253],"decomposed":[254],"(Propositions":[255],"7.1–7.3),":[256],"their":[259],"non-supportedness":[261],"interpretations":[268],"attaches":[271],"\\"early,\\"":[273],"\\"dark,\\"":[274],"\\"far\\"":[276,473],"lack":[277],"ground":[279,468],"(Theorems":[280],"8.1–8.3).":[281],"Existing":[282],"observations":[284],"—":[285,308,413,418],"JWST":[286],"massive":[287],"galaxies":[288],"at":[289],"z":[290],">":[291],"10,":[292],"persistent":[294],"Hubble":[295],"tension,":[296],"successive":[299],"non-detections":[300],"WIMPs":[302],"by":[303,383],"LZ,":[304],"XENONnT,":[305],"PandaX-4T":[307],"reclassified":[310],"correspondences":[312],"consistent":[313],"with":[314,363,766],"structure.":[317],"Three":[318],"genuine":[319],"predictions":[321],"derived.":[323],"Four":[324],"Python":[325],"codes":[326],"provide":[327],"computational":[328],"illustrations":[329],"This":[334,464],"third":[338],"trilogy:":[341],"first":[343],"definition":[347],"universe":[350],"via":[351],"uniqueness":[353],"𝒪_adm;":[355],"second":[357],"observables":[360],"M₃(ℂ)":[362],"zero":[364],"freely":[365],"chosen":[366],"parameters.":[367],"addresses":[371],"inverse":[373],"direction:":[374],"what":[375],"happens":[376],"after":[377],"those":[378],"projections":[380],"received":[382],"observer":[385,424,445],"subjected":[387],"interpretation.":[390],"following":[392],"code":[393,435],"illustrates":[394],"central":[396],"paper.":[401],"5.4":[403,773],"(K_op-Independence":[404,774],"Necessity)":[407,777],"Dist,":[414],"Clos,":[415],"Irr":[417],"state":[425,441,446],"s₀":[426,447],"or":[427],"K_op(s₀,":[432],"T).":[433],"demonstrates":[436],"finite":[440],"space:":[442],"varies,":[448],"value":[450],"changes,":[453],"while":[454],"target":[460],"T":[461,509,551,642,721],"remain":[462],"invariant.":[463],"algebraic":[467],"claim":[471],"\\"information-poor.\\"":[477],"import":[478,484,570],"numpy":[479],"np":[481],"collections":[483],"defaultdict":[485],"def":[486,505,636],"build_state_space(n_states,":[487],"seed=42):":[488],"rng":[489],"=":[490,493,500,510,513,516,529,533,545,548,561,578,581,584,597,610,613,630,643,652,655,665,676,692,697,700,703,709,714,722,752],"np.random.RandomState(seed)":[491],"ops":[492,504,555,620,699],"[]":[494],"_":[496],"range(4):":[498],"p":[499],"rng.permutation(n_states)":[501],"ops.append(p)":[502],"return":[503,632,649,689,694],"compute_nec_conditions(T_indices,":[506],"ops,":[507,639,711,755],"n_states):":[508],"set(T_indices)":[511,644],"dist":[512,544,715],"True":[514,562,585],"T_list":[515],"list(T)":[517],"i":[519,587],"range(len(T_list)):":[521],"j":[523,591],"range(i+1,":[525,593],"len(T_list)):":[526],"s,":[527,595],"sp":[528,596],"T_list[i],":[530],"T_list[j]":[531],"distinguished":[532],"any(op[s]":[534,602],"!=":[535,603],"op[sp]":[536,604],"op":[538,553,606,618,672],"ops)":[540],"if":[541,600,625,645,678,685,746],"distinguished:":[543],"False":[546,611,631],"clos":[547,717],"all(op[s]":[549,614],"s":[557,622,668],"T)":[559],"irr":[560,629,635,708,719],"size":[564],"range(1,":[566,660],"len(T)):":[567],"itertools":[569],"combinations":[571],"subset":[573],"combinations(T_list,":[575],"size):":[576],"sub":[577,616],"set(subset)":[579],"sub_list":[580],"list(sub)":[582],"sub_dist":[583,609,626],"range(len(sub_list)):":[589],"len(sub_list)):":[594],"sub_list[i],":[598],"sub_list[j]":[599],"ops):":[608],"sub_clos":[612],"sub)":[624],"sub_clos:":[628],"dist,":[633,706],"clos,":[634,707],"compute_kop(s0,":[637,753],"T_indices,":[638],"n_states,":[640],"max_depth=6):":[641],"s0":[646,743,747],"T:":[648,688],"0":[650],"visited":[651],"{s0}":[653,656],"frontier":[654,691],"depth":[658,690],"max_depth":[661],"+":[662],"1):":[663],"next_frontier":[664,693],"set()":[666],"frontier:":[670],"ops:":[674],"ns":[675,679,686],"op[s]":[677],"visited:":[682],"visited.add(ns)":[683],"next_frontier.add(ns)":[684],"float('inf')":[695],"n_states":[696],"8":[698],"build_state_space(n_states)":[701],"T_target":[702],"[2,":[704],"3]":[705],"compute_nec_conditions(T_target,":[710],"n_states)":[712,756],"nec":[713],"print(f\\"Target":[720],"{T_target}\\")":[723],"print(f\\"Nec(S)":[724,729],"conditions:":[725],"Dist={dist},":[726],"Clos={clos},":[727],"Irr={irr}\\")":[728],"satisfied:":[730],"{nec}\\")":[731],"print()":[732,762],"print(f\\"{'Observer":[733],"s0':<14}":[734],"{'K_op(s0,T)':<14}":[735],"{'Dist(T)':<10}":[736],"{'Clos(T)':<10}":[737],"{'Irr(T)'}\\")":[738],"print(\\"-\\"":[739],"*":[740],"60)":[741],"range(n_states):":[745],"T_target:":[750],"kop":[751],"T_target,":[754],"print(f\\"{s0:<14}":[757],"{kop:<14}":[758],"{dist:<10}":[759],"{clos:<10}":[760],"{irr}\\")":[761],"print(\\"RESULT:":[763],"varies":[765],"s0;":[767],"invariant.\\")":[771],"print(\\"Theorem":[772],"illustrated.\\")":[778]}

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-15
DOI
https://doi.org/10.5281/zenodo.22770725
Primary Topic
Relativity and Gravitational Theory
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
preprint

Observational Illusions in Cosmology: On the Interpretive Divide between Measurement and Existence in Standard Cosmology

T.O.
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

Observational Illusions in Cosmology: On the Interpretive Divide between Measurement and Existence in Standard Cosmology

T.O.
preprint en

Abstract

Modern standard cosmology constructs cosmological entities, histories, and ontologies from observational data through the chain O_obs → I_ana → I_theo → O_ont. The present paper does not question the reliability of observations. What it questions is the systematic conflation of the four levels in this chain: the raw observable O_obs, the analytically processed quantity I_ana, the theoretically interpreted quantity I_theo, and the ontological conclusion O_ont. Each arrow in the chain is an independent operation carrying its own assumptions. The illusion named in the title is not an illusion of observation itself, but the illusion that one can read the ontology sustaining an observed relation directly from that relation. Building on the Tier-2 axiomatic foundation of Operatiology (Japanese: Sousa Genron, 操作原論) established in prior work, the present paper advances three claims and establishes them as theorems. First, the existence of a cosmological structural quantity does not logically entail the existence of a corresponding local material substance: for any Tier-3 observable Q, Q_obs ⇏ ∃N ∈ Nec(S): (Q ↔ N) (Proposition 4.1). The specific failure modes of the Nec(S) conditions for WIMP dark matter candidates, the inflaton field, and the Big Bang singularity are established in Lemma 4.2 and Theorem 4.3. Second, it is proved as a Tier-2 theorem that the Nec(S) conditions contain no reference to operational separation K_op (Lemma 5.3, Theorem 5.4: K_op-Independence of Structural Necessity); the Uniform Fidelity Correspondence is derived as its Tier-3 projection (Corollary 5.5). Third, the analytical chain assumptions embedded in the arrows I_ana → I_theo → O_ont are formally decomposed (Propositions 7.1–7.3), and from their Tier-2 non-supportedness it is established that the ontological interpretations standard cosmology attaches to "early," "dark," and "far" lack Tier-2 ground (Theorems 8.1–8.3). Existing Tier-3 observations — JWST massive galaxies at z > 10, the persistent Hubble tension, and the successive non-detections of WIMPs by LZ, XENONnT, and PandaX-4T — are reclassified as correspondences consistent with the Tier-2 structure. Three genuine Tier-3 predictions are derived. Four Python codes provide computational illustrations of the structural theorems. This paper is the third in a trilogy: the first established the Tier-2 definition of the universe via the uniqueness of 𝒪_adm; the second derived cosmological observables from M₃(ℂ) with zero freely chosen parameters. The present paper addresses the inverse direction: what happens after those Tier-3 projections are received by an observer and subjected to analytical interpretation. The following code illustrates the central Tier-2 theorem of this paper. Theorem 5.4 (K_op-Independence of Structural Necessity) establishes that the Nec(S) conditions — Dist, Clos, and Irr — contain no reference to the observer state s₀ or to the operational separation K_op(s₀, T). The code demonstrates this on a finite state space: as the observer state s₀ varies, the value of K_op changes, while the Nec(S) conditions of the target T remain invariant. This is the algebraic ground for the claim that "far" does not entail "information-poor." import numpy as np from collections import defaultdict def build_state_space(n_states, seed=42): rng = np.random.RandomState(seed) ops = [] for _ in range(4): p = rng.permutation(n_states) ops.append(p) return ops def compute_nec_conditions(T_indices, ops, n_states): T = set(T_indices) dist = True T_list = list(T) for i in range(len(T_list)): for j in range(i+1, len(T_list)): s, sp = T_list[i], T_list[j] distinguished = any(op[s] != op[sp] for op in ops) if not distinguished: dist = False clos = all(op[s] in T for op in ops for s in T) irr = True for size in range(1, len(T)): from itertools import combinations for subset in combinations(T_list, size): sub = set(subset) sub_list = list(sub) sub_dist = True for i in range(len(sub_list)): for j in range(i+1, len(sub_list)): s, sp = sub_list[i], sub_list[j] if not any(op[s] != op[sp] for op in ops): sub_dist = False sub_clos = all(op[s] in sub for op in ops for s in sub) if sub_dist and sub_clos: irr = False return dist, clos, irr def compute_kop(s0, T_indices, ops, n_states, max_depth=6): T = set(T_indices) if s0 in T: return 0 visited = {s0} frontier = {s0} for depth in range(1, max_depth + 1): next_frontier = set() for s in frontier: for op in ops: ns = op[s] if ns not in visited: visited.add(ns) next_frontier.add(ns) if ns in T: return depth frontier = next_frontier return float('inf') n_states = 8 ops = build_state_space(n_states) T_target = [2, 3] dist, clos, irr = compute_nec_conditions(T_target, ops, n_states) nec = dist and clos and irr print(f"Target T = {T_target}") print(f"Nec(S) conditions: Dist={dist}, Clos={clos}, Irr={irr}") print(f"Nec(S) satisfied: {nec}") print() print(f"{'Observer s0':<14} {'K_op(s0,T)':<14} {'Dist(T)':<10} {'Clos(T)':<10} {'Irr(T)'}") print("-" * 60) for s0 in range(n_states): if s0 not in T_target: kop = compute_kop(s0, T_target, ops, n_states) print(f"{s0:<14} {kop:<14} {dist:<10} {clos:<10} {irr}") print() print("RESULT: K_op varies with s0; Nec(S) conditions are invariant.") print("Theorem 5.4 (K_op-Independence of Structural Necessity) illustrated.")

Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.