Structural Admissibility — QM + GR

Reading note: this page uses the framework's technical category names throughout (Mathematical physics exploration, Mathematical physics theory-construction, Effective model, Physics proper). The public-facing labels on the survey and about pages map as: Mathematical exploration = Mathematical physics exploration; Theory proposal = Mathematical physics theory-construction; the other two carry the same name in both registers. The names below are the load-bearing technical ones; the full framework carries the canonical definitions.

The QM+GR domain is where the taxonomic view of physics does the most work. The category-collapse view treats "theoretical physics" as one bucket; the honest view sees that what gets called "established physics" is largely effective with embedded physics-proper components, and that what gets called "quantum gravity" is mostly theory-construction claiming a category it doesn't occupy.

The framework is ontology-first. The legs are how we test category claims; they are not the framework itself but its application.

What the established frameworks actually are

General Relativity. Vacuum field equations are physics-proper — derived from equivalence principle + self-consistency, completely retrodict Newton in the weak field, predicted Mercury precession, lensing, and gravitational waves before observation. Cosmological constant Λ is effective. FLRW + ΛCDM is effective with the cosmological principle as auxiliary assumption. GR-near-singularities is honest deferral to QG. GR is the closest thing to physics-proper among the established frameworks.

Quantum Mechanics. Effective model with significant physics-proper components embedded. Born rule, commutators, measurement postulate are operationally defined. The Dirac equation (flat-space, free fermion), spin-statistics, identical-particle statistics are physics-proper. The framework's empirical reach comes from the combination — derived nuclei doing predictive work, operational scaffolding making the framework usable.

Standard Model. Same shape as QM. Gauge invariance forcing minimal coupling, anomaly cancellation constraining hypercharges, spin-statistics are physics-proper. Gauge group choice, three generations, Yukawa structure, mixing matrices are effective. Higgs mechanism is physics-proper construction with effective specifics. Predictive reach from derived structural backbone plus fitted content.

QFT on Curved Spacetime. Calculational framework, not a theory of gravity. Matter sector quantization derived; metric is classical input. Back-reaction unresolved — exactly why QG remains open. This is the framework that exists because QG isn't solved; treating it as part of the solution is itself a category error.

What QG actually has to be

QG is not "unify QM and GR." That framing assumes QM and GR are physics-proper objects to be unified. They aren't. Most of QM is effective at its foundations; the cosmological-scale and high-curvature regimes of GR are where it breaks down. The unification framing has produced eighty years of work and no closed result; the framing itself is part of the obstacle.

The taxonomic respecification: QG is the project of identifying the physics-proper layer that produces, as derived consequences from a deeper substrate,

(a) the currently-derived components of QM — Dirac equation, spin-statistics, gauge invariance, anomaly cancellation (b) the currently-derived components of GR — vacuum field equations from equivalence principle + self-consistency (c) the currently-effective components — Born rule, commutators, measurement, cosmological constant, ΛCDM parameters — with named regimes of validity (d) the currently-open structural items — back-reaction, SM gauge group choice, generation count, strong CP, hierarchy problem — either as derived consequences or honest deferrals

This specification is component-wise testable. A candidate QG framework is evaluated on whether its primitives produce each item, lens-by-lens, regime-by-regime.

The audit in the QG regime

Three lenses on whether a candidate's category claim (typically physics-proper QG) is supported by its actual structure.

Leg A — Are the primitives at the right level? Physics-proper QG requires primitives derived from the substrate the candidate commits to. "Information," "substrate," "field" have to do specific structural work — not stand in for missing derivation. If the candidate's primitives are operationally defined or asserted, the physics-proper claim is unsupported.

Leg B1 — Does the work operate at the QM+GR level? Physics-proper QG requires a quantum object (field, state, operator algebra), a curved-spacetime evolution, and a probability or flux structure. B1 cannot be evaded by self-categorisation. Big Bang dynamics, Hubble tension, Hawking radiation, and inflation are intrinsically QM+GR; a work addressing any of these inherits B1 from what it explains. "Effective model" and "boundaries where standard description fails" framings do not relieve B1 when the phenomena require QM+GR machinery.

Leg B2 — Is the work correctly positioned relative to established physics? A candidate claiming to be deeper than the SM must recover SM gauge group, chirality, fermion spectrum, generations, and electroweak masses where the SM is empirically established, or honestly defer the recovery. Treating the SM as primitive while claiming to derive what's beneath it is the category-mismatch B2 catches.

Closure comes in three modes — reaches ground, honest deferral, or dissolution of the presupposed question. Dissolution is the strongest: the framework derives that the question presupposed structure that doesn't exist past a derived boundary, so the question stops applying.

Categorical failure modes the framework catches

Theory-construction claiming physics-proper. String theory's empirical anchoring is open (10^500 vacua, no SM-yielding compactification identified). Admissible as theory-construction; inadmissible at the physics-proper category claimed.

Theory-construction failing all three lenses. LQG quantizes geometry without deriving why geometry is the quantization target (A). Semiclassical limit unresolved after four decades (B1). Matter content not addressed (B2). Admissible as theory-construction with interesting math; not at the physics-proper category claimed.

Mathematics passing, physics failing. AdS/CFT is a well-posed mathematical conjecture (admissible as theory-construction). Deployed as physics-proper QG — substrate isn't reality (A fails), regime isn't our universe (B1 fails), boundary theory isn't the SM (B2 fails). The deployment is what makes the work a physics claim, and the deployment isn't anchored.

Effective phenomenology claiming derivation. A 2026 cosmology paper claims one signed coupling explains DM, DE, inflation, and BH information paradox. Components operationally defined (A fails), classical dynamics with no quantum structure (B1 fails), SM treated as primitive labeled "resolved" (B2 fails). Three-leg fail at the claimed category. The same work as honest theory-construction would be admissible.

Physics-proper claim with full decomposition. Wave Relativity (Tan 2026) derives from three empirical anchors through self-consistency to one master equation (A closes). Dissolves the sub-Planck QM-in-curved-spacetime question because matter wave and metric are derived as aspect-projections of a single field Ψ (B1 closes via dissolution). Recovers SM gauge group, fermion spectrum, generations, and electroweak masses at tree level, with precision residue named (B2 closes with honest deferral). The contrast case for what passing at the physics-proper category looks like.

Operating notes

The framework runs at the level the work claims. A program claiming to address QG problems is evaluated on B1 and B2 even if it never enters those levels — that is the failure.

The diagnostic value is in seeing which component fails which lens, not in averaging. Component-level decomposition lets the reader see specifically what is and isn't working.

Passing is not endorsement. Failing is not refutation. The framework tells you what kind of work the claim actually is, and whether the work is in the category it claims. The next filters (empirical adequacy, predictive power, parsimony) follow after admissibility, not instead of it.