Theory-of-Everything Requirements

Comparative status of the empirical benchmark, string/M-theory, loop quantum gravity, and Lumen.

Method. Status records demonstrated scope, not overall rank. Rows are unweighted.

Establishedvalidated in its working domain Partialsubstantial result, missing closure Proposedmechanism or interpretation Openno current answer

Strongest current result and principal limitation for each requirement.
Required answer	SM + GR + ΛCDMEmpirical benchmark, not one unified theory	String / M-theoryBroad unification programme	Loop quantum gravityQuantum-spacetime programme	Lumen TOECurrent Second Edition claims
1 · Foundations
Fundamental objects and lawWhat exists, and what governs its evolution?	Partial Quantum fields and the metric are explicit, but obey separate frameworks.	Partial Strings and branes unify interactions; the full non-perturbative formulation is incomplete.	Partial Spin networks give quantum geometry; matter is coupled rather than unified.	Partial S³/B⁴ substrate and master operator; the unified field equation is assembled.P01 · P18 · P19
Quantum theory and measurementStates, probabilities, outcomes, and the classical limit.	Established Quantum mechanics and QFT predict outcomes precisely; measurement is a postulate.	Partial Quantum consistency and unitarity are central; measurement is inherited from quantum theory.	Partial Quantum geometry is explicit; the standard measurement framework is assumed.	Partial Equal-amplitude Born weights derived. Unequal-amplitude probabilities and single-outcome selection open.P27 · P28
Origin of the observer and measurementWhy does observation occur, and where does the measuring frame come from?	Open The observer is external and unmodeled; measurement enters only as a postulate.	Open Inherits quantum measurement; the origin of the observer is not addressed.	Open Quantum geometry without an observer model; measurement is assumed from outside.	Partial Observation is foundational: the observer is a frame (the Hopf fiber), not consciousness, and intersubjective coherence between two observers generates the geometry. The measurement axiom and general Born rule remain open.P27 · P41
Spacetime, dimensionality, and timeWhy this arena, signature, locality, and causal structure?	Partial 3+1 Lorentzian spacetime works extraordinarily well but is an input.	Partial Critical dimensions constrain the theory; compactification to our 3+1 vacuum is not unique.	Partial Background-independent quantum geometry; topology and the problem of time remain.	Partial Boundary dimension and Hopf lapse are derived from premises; full spacetime dynamics are not.P08 · P28 · P43
Mathematical and ultraviolet consistencyA complete, anomaly-free theory at every energy.	Partial The SM is renormalizable; quantized GR is only an effective field theory.	Partial Perturbative amplitudes are strongly controlled; general non-perturbative definition is incomplete.	Partial Kinematics are rigorous; dynamics and the correct low-energy limit remain unsettled.	Partial Finite identities are verifier-pinned; UV completion and several proof bridges remain open.P03 · P18 · P40
2 · Observed physics
Quantum gravity and the GR limitQuantize gravity and recover Einstein dynamics.	Partial GR is experimentally established; its quantum completion is absent.	Partial A graviton and low-energy gravity arise naturally; realistic vacuum selection remains unresolved.	Partial GR is quantized non-perturbatively; a convincing full classical limit is still open.	Partial Relativistic lapse is derived; Einstein’s equations are recovered only conditionally, via a horizon-thermodynamic (Jacobson) route, not unconditionally.P17 · P19 · P28
Gauge forces and Higgs breakingWhy U(1)×SU(2)×SU(3), and why electroweak symmetry breaks.	Established The gauge theory and Higgs mechanism are precision-tested; their form is input.	Partial Realistic gauge and Higgs sectors exist in compactifications, without unique selection.	Open Standard gauge fields can be coupled, but their group and breaking are not derived.	Partial Division-algebra assignment reaches the group; hypercharge and Yang-Mills dynamics are incomplete.P06 · P20
Matter, chirality, and three generationsWhy these particles, representations, and family count?	Partial The observed spectrum is encoded; the family count is unexplained.	Partial Chiral three-family models exist; no compactification is uniquely selected.	Open Particle content is normally supplied as matter coupled to quantum geometry.	Partial Three-family count from maximal rank of J₃(O). Peirce mass/mixing assignment closed relative to the self-observation axiom.P06 · P13
Masses, couplings, mixing, and neutrinosCalculate the dimensionless parameters rather than merely fit them.	Partial Values are measured inputs; minimal SM neutrinos are massless.	Partial Yukawa and neutrino mechanisms exist but depend on vacuum and moduli choices.	Open Not derived by the core programme.	Partial Many numerical relations are testable; some are fitted, conditional, or already retracted.P06 · P12 · P13
3 · Cosmic regime
Black holes, singularities, and informationMicrostates, entropy, evaporation, and the final state.	Partial Classical holes and semiclassical thermodynamics work; singularities and information remain open.	Partial Microstate entropy is derived for important special classes; generic astrophysical closure remains.	Partial Area spectra, entropy, and singularity-resolution models exist; complete dynamics remain.	Proposed Compression and self-lensing provide a picture, not a black-hole microstate derivation.P17
Early universe and baryogenesisInitial state, inflation or bounce, perturbations, and matter excess.	Partial ΛCDM plus inflation fits observations; inflaton, initial state, and baryogenesis are unsettled.	Partial Many inflation, reheating, and baryogenesis constructions exist; none is uniquely selected.	Partial Loop cosmology supplies bounce and perturbation models with quantization ambiguities.	Proposed Breath/cycle and seeding mechanisms exist; a precision primordial history is not closed.P14 · P15 · P37
Precision cosmologyBBN yields, CMB acoustic peaks, structure growth, and cluster lensing.	Established Primordial abundances, CMB acoustic spectrum, large-scale growth, and cluster lensing fitted within ΛCDM.	Partial Model-dependent early-universe and dark-sector constructions; no unique end-to-end precision cosmology.	Partial Primordial perturbation models; no unique BBN-to-cluster calculation.	Open Predictions for tilt and tensor ratio. No recombination or transfer function, BBN yield calculation, derived matter power spectrum, or cluster-scale lensing result.P14 · P37 · P38 · P39
The arrow of timeWhy a thermodynamic and cosmological direction from time-symmetric laws?	Partial Microscopic laws are time-symmetric; the low-entropy initial condition is assumed, not explained.	Open No unique account of the initial low-entropy state.	Partial Loop-cosmology bounce models exist; the entropy arrow across the bounce is unsettled.	Proposed Time is read as the witness-relative ordering of a timeless, reversible substrate; the arrow is observer-side, not a fundamental law.P08 · P43
Dark matter and galaxy dynamicsIdentity plus quantitative behavior from galaxies to large-scale structure.	Partial Cold dark matter fits broad structure data; its particle identity is unknown.	Proposed Axions, moduli, and hidden sectors supply candidates, not a unique prediction.	Open No standard dark-matter identity follows from the core theory.	Partial Kernel/hidden-branch halo is SPARC-tested; its physical closure premise remains conditional.P38 · P39 · SPARC
Dark energy, expansion, and H₀Acceleration’s scale, evolution, and present expansion rate.	Partial ΛCDM fits much of cosmology; vacuum scale and Hubble tension are unexplained.	Proposed de Sitter and quintessence models face control, selection, and initial-condition challenges.	Open Cosmological models exist, but no accepted unique dark-energy or H₀ result follows.	Partial Λ₀ matches the present density at 0.94σ (derived, not fit). The live tension is confined to dark-energy evolution — DESI prefers an evolving w over the corpus’s constant Λ₀ — and H₀ is anchor-limited.P32 · P37 · P39
4 · Scientific closure
Precision recovery of known physicsReproduce the tested Standard Model, GR, and cosmology in their domains.	Established The benchmark: enormous precision across particle, gravitational, and cosmological observations.	Partial Can yield SM-like effective theories and GR; our exact low-energy vacuum is not recovered uniquely.	Partial Promising semiclassical calculations; full GR plus Standard Model recovery is incomplete.	Partial Verified numerical matches. Incomplete: Einstein dynamics, unequal-amplitude Born probabilities, outcome selection, hypercharge, and key couplings.P19 · P20 · P40
Novel falsifiable predictionsResults fixed before measurement that distinguish the framework.	Established Many historical predictions succeeded; few unexplained parameters are themselves predicted.	Partial Individual models predict signatures; few are generic to the whole framework.	Proposed Planck-scale and cosmological signatures are studied; none has confirmed the theory.	Partial Pre-committed neutrino, dark-sector, and cosmology tests; decisive outcomes remain pending.P06 · P39 · P40
Parameter economy and uniquenessWhy this solution, with no hidden fitting freedom?	Open Particle and cosmological parameters are measured rather than explained.	Open The large vacuum landscape prevents a unique low-energy selection.	Partial Economical gravitational input, but dynamics and quantization choices remain.	Partial Compact geometric seed with broad reuse; reverse-engineered and empirical anchors remain.P18 · P35 · P36
Naturalness and fine-tuningWhy aren’t the vacuum energy and electroweak scale catastrophically fine-tuned?	Open The cosmological constant (~10¹²⁰) and the Higgs mass are the sharpest fine-tuning problems, unexplained.	Proposed A landscape with anthropic selection is offered; no derivation singles out the observed values.	Open Not addressed by the core programme.	Open Lumen does not develop a naturalness account. Its zero-parameter architecture and geometric Λ₀ (not a vacuum energy) are structurally relevant, but the corpus does not connect them to the fine-tuning problem.P32 · P36
Reproducibility and independent validationPublic calculations, adversarial review, and experimental replication.	Established Independently reproduced worldwide across theory and experiment.	Partial Vast peer-reviewed formal literature; no direct empirical validation of the framework.	Partial Large peer-reviewed formal programme; no direct empirical validation.	Partial Public papers, verifiers, and repair ledger; independent peer review and replication remain open.P40

Scope. A partial cell may contain exact results alongside unresolved dependencies. Other programmes, including asymptotic safety and causal sets, are not included.

External basis. CERN: Standard Model scope and gaps · Marchesano, Shiu & Weigand: Standard Model from string theory · Strominger & Vafa: black-hole microstates · Rovelli: Loop Quantum Gravity review · Agullo, Wang & Wilson-Ewing: loop cosmology and observations.

Lumen basis. Current Second Edition pages and their linked verifier output. Editorial synthesis dated 29 June 2026; it is not an independent ranking or peer-review verdict.