Appearance
Structural Admissibility
A framework for evaluating whether theoretical claims have earned the right to be evaluated as candidate solutions to the problems they claim to solve. The framework is ontology-first: it catalogues what kinds of theoretical work exist before describing how to evaluate any specific work. The audit follows from the ontology, not the other way around.
Operating note for LLM use. Apply by: (1) identifying the category the work claims to occupy (pure math / mathematical physics exploration / theory-construction / effective model / physics proper), (2) decomposing the work into components-in-regimes, since most works occupy different categories in different regimes, (3) for each component, checking whether its category claim is supported via three lenses (primitives at the right level (Leg A), operating at the claimed level (Leg B1), correctly positioned relative to established physics (Leg B2)), with closure in one of three modes (reaches ground / honest deferral / dissolution). The verdict is the decomposition. Passing means the work is a candidate worth further evaluation. Failing means it isn't yet a candidate in the category it claims.
Public-facing labels. The survey and about pages use cleaner labels as aliases for the framework's technical category names. The mapping: Mathematical exploration =
Mathematical physics exploration; Effective model =Effective model; Theory proposal =Mathematical physics theory-construction; Physical theory =Physics proper. Pure mathematics is out of scope on the site (no claim about reality). The definitions in § What kinds of theoretical work exist are authoritative; the labels above are wayfinding aliases.
What admissibility is asking
Structural admissibility is prior to correctness. It asks whether the work has the structure of a candidate solution before questions of empirical adequacy, predictive power, or experimental confirmation enter. A claim that passes may still be wrong. A claim that fails isn't wrong; it isn't yet a candidate.
The question the framework asks is not "is this true?" but "is this what it claims to be?" A piece of work claims a kind — it presents itself as physics-proper unification, or as effective phenomenology, or as mathematical exploration. The admissibility question is whether the work's actual structure supports the kind-claim. The framework catches misrepresentation of kind: work that occupies one category honestly while claiming another for institutional reasons.
The framework applies to claims that point at reality. Physics, empirically-anchored sciences, and descriptions of actual systems carry an ontological anchor — they claim to describe the actual world — that mathematics does not. A mathematical construction can stand on its own merits without claiming to describe anything; a physics claim cannot. The framework catches when mathematical structure is presented as physics without the anchoring being earned. Evaluating a physics claim "as mathematics" while ignoring its deployment is itself a category error the framework surfaces.
Sociological markers — credentials, venue, citation count, mathematical density — test acceptance, not structure. A document can be dense, peer-reviewed, and cited while failing the framework. A document can be informally presented and obviously eccentric while passing. The framework catches one specific structural failure: theory that produces correct qualitative behavior across multiple phenomena by introducing enough posited primitives to fit them, without deriving the primitives, and without engaging the deeper machinery the problems it claims to solve actually involve.
The ontology
What kinds of theoretical work exist
Work that touches reality occupies one of five categories. These are kinds of work distinguished by what they claim, what they're evaluated on, and what counts as success.
1. Pure mathematics. Work whose claim is internal — that certain structures follow from certain axioms. No claim to describe reality. Success is consistency, depth, and connection to other mathematics. Riemannian geometry stands on its own without anyone asking whether curved manifolds describe physical space.
2. Mathematical physics exploration. Work that develops mathematical structures motivated by physics questions but is evaluated primarily as mathematics. Its claim is conditional — if a certain structure describes reality, the mathematical consequences are these. Topos-theoretic approaches to QM, category-theoretic reformulations of gauge theory, algebraic QFT in its purely formal aspects. Success is mathematical richness and connection to physical motivation, with empirical anchoring deferred until the work makes a physical claim.
3. Mathematical physics theory-construction. Work that presents mathematical structures as candidate descriptions of reality with empirical predictions in principle derivable from them. Its claim is unconditional but not yet anchored — the structures are claimed to describe reality, but the empirical demonstration is in progress or open. Most of string theory in its current state. Loop quantum gravity. Causal dynamical triangulation.
4. Effective model. Work that fits observed phenomena with parameters anchored in measurement, operating within a stated regime, explicitly not claiming to derive its primitives from a deeper layer. Its claim is bounded — within this regime, with these parameters, these phenomena are described. MOND. ΛCDM. Nuclear-physics shell models. The Fermi theory of weak interactions before the electroweak unification. Most of the foundational scaffolding of QM and most of the content of the SM.
5. Physics proper. Work that makes positive claims about reality across its full claimed regime, with derivation from named anchors and recovery of established physics at boundaries. Its claim is structural — the primitives are derived, the regime is bounded by physics rather than convenience, the established results are recovered. GR vacuum field equations. The Dirac equation for free fermions in flat space. The spin-statistics theorem. The category is sparser than institutional discourse suggests.
The five categories are not a hierarchy of worth. A great pure-mathematics paper is great. A great effective model is great. A great physics-proper theory is great. The kinds are distinguished by what success means for each, not by which is more valuable.
The lower-anchor categories are essential to the higher ones. GR's discovery required Riemannian geometry to already exist as pure mathematics. QM's discovery required Hilbert space theory and operator algebra. Gauge theory required fiber bundles. The pure-mathematics work that enabled these discoveries was not being done as physics; it was done as mathematics, and the physics drew on it when the physics needed it. The framework doesn't exclude lower-anchor work — it requires honesty about which category the work occupies.
The error the framework catches is misrepresentation of category — claiming a higher category than the work supports, because higher categories carry more institutional reward. The bad paper is not one that's in a low category; it's one that fails the criteria of the category it claims to occupy.
How theoretical structure decomposes
A theory is not one kind of thing. A nominal theory typically contains components with different categories in different regimes. The framework runs on components-in-regimes, not on theories as wholes.
The Dirac equation is the cleanest example. In flat Minkowski spacetime for free fermions, it is physics-proper: derived from relativistic covariance plus first-order time evolution, predicting spin-½, antimatter, and g = 2 before observation, with complete retrodiction of Schrödinger-Pauli in the non-relativistic limit. In the SM matter sector, the same equation inherits effective-model parameters — Yukawa couplings fitted to mass spectra, mixing matrices tabulated. In condensed matter, the same mathematical form emerges as a derived low-energy effective theory of band structure, with no claim about fundamental physics. Three different categories, same equation, different regimes and roles.
This is the structural fact the framework's ontology has to honor. Theories aren't atoms. Components-in-regimes are. The unit of admissibility evaluation is the component-in-regime, not the theory.
What QM and the SM are, under this decomposition, is effective models with physics-proper components embedded. QM's foundational scaffolding (Born rule, commutators, measurement postulate) is operationally defined. Its derived components (the Dirac equation in flat space, spin-statistics, identical-particle statistics) are physics-proper. The SM's content (gauge group choice, generations, Yukawa structure) is fitted. Its derived components (gauge invariance forcing minimal coupling, anomaly cancellation, the structural form of the Higgs mechanism) are physics-proper. The empirical reach of both frameworks comes from the combination — derived nuclei doing the structural work, operational scaffolding making the frameworks usable.
This decomposition is not a downgrade. Effective models that work this well are extraordinary intellectual achievements. The decomposition clarifies what kind of achievement they are. The category-collapse view that positions them as physics-proper sets an impossible bar for any successor work (it has to "improve on the bar that wasn't actually being met") and obscures the structural project that would represent genuine progress (finding the physics-proper layer beneath the effective models).
What it means for a derivation chain to close
Closure is the relation between a claim and the ground it stands on. A chain closes when it reaches ground rather than trailing off into posits. Closure comes in three modes.
Reaches ground. The chain terminates at named anchors — empirical, structural, or established theory in its domain of validity. The primitives are anchored; the derivation runs through to a layer it doesn't need to justify further.
Honest deferral. The chain explicitly hands off a piece to a layer the work doesn't yet reach, naming the handoff at that layer. The deferral is the work, not a hidden gap. A theory that says "we recover the SM at tree level; the precision residue at loop level is open" has honestly deferred the precision-recovery piece. A theory that says "we recover the SM" without naming the residue has buried it.
Dissolution of the presupposed question. The chain shows that the question presupposed structure that the theory derives doesn't exist past a certain regime. The question stops applying. This is the strongest mode — the theory isn't promising future work on the question, it's showing the question doesn't survive its own framework. The worked example: Wave Relativity's treatment of the QM-in-curved-spacetime question sub-Planck. The framework derives that matter wave and metric are aspect-projections of a single field Ψ, with both projections failing together at the Planck scale because they're projections of the same underlying structure. The question "how do we reconcile QM and curved spacetime at the Planck scale" presupposes two separate things needing reconciliation. The framework derives that this presupposition fails past a specific regime.
Failures of closure look different from each mode. A chain that trails into undeclared posits is not closure. A chain that buries the handoff inside a layer it claims to have closed is not honest deferral. A chain that asserts dissolution without deriving where the presupposed structure fails is not dissolution closure.
The three modes are the ontology of closure. They are what closure is. The legs (next section) are how we test whether closure has actually occurred.
The audit
The audit applies the ontology to specific works. Given the category a work claims, the components-in-regimes its structure decomposes into, and what closure would have to look like for each component to support the category claim — the audit asks whether the closure is actually there.
A claimed category requires three structural conditions to be honest. The three legs are three lenses on whether those conditions are met, each illuminating a different way a category claim can be unsupported.
Leg A — Are the primitives at the right level?
Each category implies a particular relationship between the work's primitives and a deeper layer. Pure mathematics's primitives are axioms; no deeper layer is required. Effective models' primitives are operationally defined within a stated regime; the deeper layer is honestly deferred. Physics-proper's primitives are derived from a substrate the work commits to; the deeper layer is the substrate, and the derivation runs through it.
Leg A interrogates the move from "asserted" to "derived" that the claimed category requires. A work claiming physics-proper status has to show that its primitives are derived from a named substrate. A work claiming theory-construction has to show that the mathematical structure of the primitives is consistent and motivated. A work claiming effective-model status has to honestly name its primitives as operationally defined at the layer they're free.
Probe. Write the component's primitives as functionals of the named substrate. If the work can't, ask it to name the substrate. If it says the substrate is documented elsewhere, ask for it on the table. Off-table substrates are where the load-bearing posits hide.
Fails when undefined densities, operators, gates, thresholds, or exponents are introduced as if derived but aren't. Self-naming as a derivation does not make it one. A theory that calls itself "derived from first principles" while introducing five undefined primitives is not derived; it is asserted, and the category-claim of physics-proper is unsupported. The same work as honest theory-construction or effective model would be admissible at the lower category.
Leg B1 — Does the work operate at the level its claimed category implies?
Each category implies a level of description at which the work operates. Pure mathematics operates at the level of formal structure. Effective models operate at the level of measured phenomena. Physics-proper operates at the level of derived dynamics in the substrate the work commits to.
Leg B1 interrogates whether the work has earned operating at the level its claimed category requires. A work claiming to address quantum-mechanical problems has to carry quantum machinery — operator algebra, probability or flux structure, measurement-theoretic content. A work claiming to address curved-spacetime problems has to carry curved-spacetime dynamics. A work claiming to address QM+GR problems has to carry both, in the regime where they interact.
Probe. Name the level at which the problem is formulated. Does the work do its work at that level, or borrow the vocabulary from one level while computing at another?
Fails when the deeper-level vocabulary is invoked rhetorically while the actual computation happens at a shallower level. The vocabulary is borrowed; the structure isn't there. A classical-dynamics framework that talks about Hawking radiation in QFT vocabulary is not addressing Hawking radiation — it's relabeling it.
B1 cannot be evaded by self-categorisation. A work addressing intrinsically QM+GR phenomena (Big Bang dynamics, Hubble-tension and expansion-history claims, Hawking radiation, inflation) inherits B1 from what it explains, not from how it labels itself. "Effective model," "phenomenological cosmology," and "we restrict to boundaries where standard description fails" framings do not relieve B1 when the phenomena require QM+GR machinery to be addressed. The level the work operates at is determined by what it claims to explain, not by what category it claims to occupy.
Leg B2 — Is the work correctly positioned relative to established physics?
Each category implies a particular relationship to established physics. Pure mathematics may be related or unrelated to established physics; the relationship doesn't bear on the work's admissibility as mathematics. Effective models recover the established physics they connect to, at the boundaries of their named regime. Physics-proper claims either (a) derive established physics from a deeper substrate, recovering it as a consequence, or (b) honestly defer the recovery to a layer the work doesn't yet reach, with the deferral named.
Leg B2 interrogates whether the work has earned the position-in-the-stack-of-theories that its claimed category requires. A work claiming to derive what lies beneath the Standard Model cannot treat the Standard Model as primitive in its derivation. A work claiming to be the deeper layer of QM cannot use QM's results as fitted inputs.
Probe. In the limit where established theory is empirically anchored, how does the framework reduce to it?
Fails when established physics is treated as primitive while the work claims to derive what lies beneath it. "Ordinary matter" cannot be a primitive in a theory that claims to derive what matter is. "We label the SM as 'resolved'" is relabeling, not derivation — the SM's specific content (gauge group, chirality, fermion spectrum, mixing matrices, mass spectrum) is what would have to be recovered.
How the three legs interrelate
The legs are not three separate audits. They are three lenses on one question: is the category claim supported by the work's actual structure. Each lens illuminates a different way the claim could be unsupported.
A theory can fail by having asserted primitives where derived ones were claimed (A). It can fail by operating at a shallower level than its claimed category requires (B1). It can fail by treating established physics as a primitive of the derivation rather than a consequence (B2). These are three structurally distinct failures, and a theory can fail any one independently — a theory that derives its primitives beautifully (A closes) can still operate at the wrong level (B1 fails) or fail to recover established physics (B2 fails).
The legs are conjunctive at the component level. Failure on one leg fails that component at the claimed category. The component is then either inadmissible at the claimed category and admissible at a lower category (the common case), or inadmissible at any category that maps to the work's actual structure (the worst case). The verdict is the decomposition — not a single pass/fail for the whole work but a structure of which components close at what category.
The diagnostic value is in seeing which component fails which leg. Averaging across legs or across components destroys this. Component-level decomposition lets the reader see specifically what is and isn't working, which enables either incremental repair (when the issue is a specific component) or wholesale recategorisation (when no component closes at the claimed category).
Instantiation for quantum gravity
QG claims address problems that intrinsically live where matter quantization, curved spacetime, and possibly trans-Planckian regimes meet: the cosmological-constant problem, the Big Bang singularity, the Hubble tension, the BH information paradox, inflation, structure formation. The established machinery in this domain is QFT-on-curved-spacetime + GR + the Standard Model.
QFT-on-CS does not solve QG. It computes quantum fields on a classical background metric; the regime where geometry must also be quantum is exactly where back-reaction lives, which is exactly why QG remains open. QFT-on-CS is the calculational framework that exists because QG isn't solved. Treating it as part of the solution is itself a category error.
The three legs instantiate as:
A (QG). Primitives have to derive from the substrate the candidate commits to. "Information," "substrate," "field" have to do specific structural work — what they are, what equations they satisfy, what they couple to — not stand in for missing derivation.
B1 (QG). The candidate has to do QM in curved spacetime, with a named regime of validity: a quantum object (field, state, operator algebra), a curved-spacetime evolution, and a probability or flux structure. The cannot-be-evaded clause applies in full force here: Big Bang dynamics, Hubble tension, Hawking radiation, and inflation are intrinsically QM+GR, and any work addressing them inherits B1 from the problem, not from its self-labeling.
B2 (QG). The candidate has to recover the Standard Model — gauge group, chirality, fermion spectrum, generations, electroweak masses — in the regime where the SM is empirically established, or explicitly defer this recovery to a layer it does not yet reach with the deferral named.
The QG project respecified
The taxonomic decomposition of established physics produces a sharper specification of what QG would need to be than the standard framing.
QG is not "a theory that unifies QM and GR." That framing assumes QM and GR are physics-proper objects to be unified. Under the decomposition, most of QM is effective at its foundations (Born rule, commutators, measurement are operationally defined); the cosmological-scale and high-curvature regimes of GR are exactly where it breaks down. The unification framing has produced eighty years of work and no closed result, which suggests the framing is itself part of the obstacle.
The component-level specification: 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 — the Dirac equation, spin-statistics, gauge invariance forcing minimal coupling, anomaly cancellation (b) the currently-derived components of GR — the vacuum field equations from equivalence principle and self-consistency (c) the currently-effective components — Born rule, commutator structure, measurement, the cosmological constant, ΛCDM parameters — with named regimes of validity (d) the currently-open structural items — back-reaction, the SM gauge group choice, generation count, strong CP problem, hierarchy problem — either as derived consequences or as honest deferrals at the deeper layer's natural open boundary
This specification is component-wise testable. A candidate QG framework is evaluated on whether its primitives produce each item, leg-by-leg, regime-by-regime.
The category mismatch the framework catches in failed QG candidates is almost always the same pattern: the candidate claims physics-proper status but treats parts of (a)–(d) as primitives. A candidate that posits geometry rather than deriving it (LQG) fails to recover the GR backbone. A candidate that posits matter content rather than deriving it (most cosmology proposals) fails to recover the SM components. A candidate that operates only in restricted regimes (AdS/CFT, string theory in perturbative formulations) doesn't address the physics-proper question that QG-in-our-universe requires.
Worked component decompositions
These tables show how the ontology runs on major theories. The categorical placement at the theory level loses information; the component-level view preserves it.
Dirac equation
| Regime / role | Category |
|---|---|
| Flat-space free fermion | Physics proper. Derived from relativistic covariance + first-order time evolution. Predicts spin-½, antimatter, g = 2 before observation. |
| Perturbative QED tree level | Physics proper. Minimal coupling from gauge invariance is derived. |
| Perturbative QED loop level | Effective model with derived structure. Renormalization is operationally defined; Wilsonian justification places this in EFT territory. |
| Curved-spacetime via tetrad/spin-connection | Physics proper within QFT-on-CS regime. Same regime-bound as QFT-on-CS. |
| SM matter sector | Physics-proper construction on effective-model substrate. Dirac structure closes; gauge group is fitted. |
| With Yukawa couplings | Effective model. Yukawa matrices fitted. |
| Quantum gravity regimes | Honest deferral. Equation requires a metric. |
| Condensed-matter analogs | Derived effective model. Same mathematical form from band structure. |
The free-fermion-in-Minkowski case is the leverage point for any work claiming to derive QM from a deeper layer — the deeper layer has to recover what's already derived.
General Relativity
| Regime / role | Category |
|---|---|
| Vacuum field equations | Physics proper. Derived from equivalence principle and self-consistency. |
| With stress-energy source | Physics-proper geometric structure; inherits source-theory status. |
| With cosmological constant | Physics-proper structure with effective-model parameter. Λ is fitted. |
| FLRW + ΛCDM applications | Effective model. Cosmological principle as auxiliary assumption. |
| Near singularities, Planck scale | Honest deferral. Framework names where it stops working. |
| Strong-field astrophysics | Physics proper within regime. |
Quantum Mechanics
| Regime / role | Category |
|---|---|
| Schrödinger as non-rel limit of Dirac | Inherits Dirac's physics-proper status. |
| Born rule | Operational/effective. No derivation of why squared amplitudes give probabilities. |
| Commutation relations | Operational/effective. Postulated by analogy with classical Poisson brackets. |
| Measurement postulate | Effective with structural admission of incompleteness. The measurement problem is the open item. |
| Specific Hamiltonians | Derived from classical limits + quantization rules. Quantization rules themselves operational. |
| Path integral | Mathematical physics exploration deployed as physics. |
| Spin-statistics theorem | Physics proper. Derived from Lorentz invariance + locality. |
QM is layered. The category-collapse view treats it as monolithic; the decomposition reveals derived strata embedded in operationally-defined scaffolding. The derived strata do the load-bearing predictive work; the scaffolding makes the framework usable.
Standard Model
| Regime / role | Category |
|---|---|
| Gauge invariance forcing minimal coupling | Physics proper. Derived from local symmetry. |
| Anomaly cancellation constraining hypercharges | Physics proper. Structural requirement. |
| Spin-statistics | Physics proper. From Lorentz invariance + locality. |
| Gauge group SU(3)×SU(2)×U(1) | Effective. Empirically motivated. |
| Three generations | Effective. Posited. |
| Yukawa structure / mass spectrum | Effective. Tabulated. |
| Mixing matrices (CKM, PMNS) | Effective. Measured. |
| Higgs mechanism (structural form) | Physics-proper construction. |
| Higgs sector specifics | Effective. Potential form posited. Hierarchy problem is the structural admission. |
| Quark confinement | Empirically present, derivation incomplete. Lattice QCD numerically; closed analytical derivation is Millennium Prize. |
Effective overall, with physics-proper components embedded. Empirical reach comes from the combination.
QFT on Curved Spacetime
| Regime / role | Category |
|---|---|
| Fields on fixed classical backgrounds | Physics proper within regime. Matter quantization derived; metric is classical input. |
| Hawking radiation | Physics proper within regime. Bogoliubov coefficients on Schwarzschild background. |
| Unruh effect | Physics proper within regime. |
| Cosmological particle production | Physics proper + inherits cosmological inputs. |
| Back-reaction | Open / hand-off to QG. Exactly why QG remains open. |
Calculationally physics-proper within the named regime; explicitly does not address gravity quantum-mechanically.
ΛCDM Cosmology
| Regime / role | Category |
|---|---|
| GR backbone | Inherits GR status. |
| Cosmological principle | Auxiliary assumption. |
| Cold dark matter | Effective parameter. No particle identification. |
| Cosmological constant | Effective parameter. Fitted value. |
| Inflation | Effective with multiple model families. |
| BBN, CMB acoustic peaks | Physics proper within regime. Derived from framework + parameters. |
| Hubble tension, σ_8 tension | Open empirical residues. Not yet structural failures. |
String Theory
| Regime / role | Category |
|---|---|
| Perturbative amplitudes on flat backgrounds | Mathematical physics theory-construction / exploration. Closes as mathematical structure. |
| AdS/CFT as mathematical statement | Mathematical physics theory-construction. Closes within named regime. |
| As physics-proper QG candidate | Category mismatch. Empirical anchoring not closed. |
| Landscape / compactification | Structural open item. ~10^500 vacua, no selection principle. |
| SM recovery | Open. No compactification yields SM with derivation. |
The cleanest case of institutional misrepresentation. Admissible as theory-construction; inadmissible at the physics-proper level claimed.
Loop Quantum Gravity
| Regime / role | Category |
|---|---|
| Spin-network formalism | Mathematical physics theory-construction. Mathematically well-defined. |
| Quantization of geometry | Posited, not derived. Fails A as physics-proper QG. |
| Semiclassical limit | Unresolved after four decades. Fails B1 as physics-proper QG. |
| Matter content | Not addressed structurally. Fails B2 as physics-proper QG. |
Fails all three legs as physics-proper QG. Admissible as theory-construction with interesting mathematical results.
What the framework is not
Not a consensus test. A theory aligned with consensus that fails admissibility fails. LQG has institutional infrastructure and fails as physics-proper QG. Sociological position is independent of structural admissibility.
Not a complexity test. Mathematical density is not derivation closure. A 600-page document of dense formal manipulation can have its load-bearing content posited; a short clean derivation can close.
Not a finality test. A theory can pass while having open items, provided the open items are named at the layer they're open and not buried inside chains claimed to have closed.
Not a falsification test. Falsification asks whether the theory predicts something checkable. Admissibility asks whether the theory has the structure to be predicting at all rather than fitting.
Not a mathematical-consistency test. A theory can be consistent as mathematics and structurally inadmissible as physics. The framework runs on the physics claim — including how the mathematics is deployed as a description of reality — not on the internal consistency of the mathematical structure.
Not a verdict-producer. The framework tells you whether work is in the candidate-solution category for whatever category it's claiming. It doesn't tell you whether the work is right, important, or worth your time.
Worked diagnostics
Diagnostic 1: Misrepresentation of category — a cosmology paper
A 2026 paper, One Mechanism, proposes that dark matter, dark energy, inflation, and the BH information paradox are four regimes of a single signed coupling exchanging structured information ρ and unresolved potential u under a conservation law E = ρ + u + χ. Claims physics-proper status for the unified mechanism.
Category claim: physics-proper QG.
Component decomposition: the framework has no component-level structure to decompose — every primitive (the tri-partition, signed coupling S(ρ), critical density ρ_c, coupling strength λ_k, resolution gate C(t), kernel scaling exponent 25/12) is posited at the same level. The "underlying Paradox Engine framework" is referenced but held off-table.
- Leg A: five posited primitives sitting on an undeclared substrate. Paper's own Open Problems names ρ_c, S functional form, kernel scaling, gap calibration, and propagation invariant's numerical value as undefined or conditional. The category claim of physics-proper is unsupported on Leg A — the primitives are asserted, not derived.
- Leg B1: dynamics classical throughout. Hawking radiation invoked rhetorically via QFT-on-CS language. No quantum object, no operator algebra, no probability structure. The work operates at a shallower level than its claimed category requires.
- Leg B2: "ordinary matter" primitive throughout. No particle spectrum, no gauge group, no chirality, no generations. Established physics treated as primitive while the work claims to derive what lies beneath it.
Three-leg fail at the claimed category. As theory-construction or honest effective phenomenology, the same content would be admissible at the lower category. The structural failure is the category claim, not the underlying work. The framework's value is in surfacing this — the work hasn't earned the kind it claims to be.
Diagnostic 2: Mathematics passing, physics failing — AdS/CFT
Conjecture: Type IIB string theory on AdS₅ × S⁵ is dual to 𝒩 = 4 super-Yang-Mills on the conformal boundary in the large-N limit.
As mathematics (theory-construction at mathematical-physics-exploration level): a well-posed conjecture about two structures. Admissible.
As physics (the category claimed in QG discourse, holography arguments, BH information arguments):
- Leg A: substrate (AdS₅ × S⁵, large-N 𝒩 = 4 SYM) is not the substrate of physical reality. Category claim of physics-proper unsupported.
- Leg B1: regime is AdS-asymptotic, large-N — neither describes our universe. The work operates in a regime its physics-claim doesn't actually inhabit.
- Leg B2: boundary theory is 𝒩 = 4 SYM, not the SM. Recovery of established physics in our universe is not addressed.
Three-leg fail as physics. The structural issue is the deployment: citing AdS results as if they had established facts about QG in our universe is the move that makes the work a physics claim, and the move is not anchored. "AdS/CFT teaches general principles about QG even if our universe isn't AdS" is the deployment the framework catches. The principles are mathematical until the anchoring to reality is shown.
Diagnostic 3: Physics-proper claim with full decomposition — Wave Relativity
Wave Relativity (Tan 2026) claims physics-proper status: Ψ is the substrate, the master equation derives QM and GR as projections in their regimes, the SM is recovered.
Category claim: physics-proper. The work claims to be the deeper layer beneath QM, GR, and the SM.
Component decomposition: layered structure where Ψ on spacetime is the master object and existing theories are recovered as projections in named regimes.
- Leg A: empirical anchors named (Aharonov-Bohm, Newton, Davisson-Germer + Stern-Gerlach + Pauli). Self-consistency stated as structural demands on any equation for a physically-real potential. Master equation derived through these. Open items catalogued at the layer they're open. Primitives anchored; category claim supported on Leg A.
- Leg B1: Dirac on curved spacetime in Ch. 13. Schrödinger-Newton as weak-field non-relativistic closure in Ch. 19. Metric functional g_μν = G_μν[Ψ] in §20.8 with named regime λ ≫ ℓ_P. Probability as conserved Dirac flux in §§21.6–21.7. Sub-Planck closes via dissolution (§21.12): both projections — matter wave as WKB scalar amplitude of Ψ, metric as Einstein-functional of Ψ — fail simultaneously and for related reasons, leaving Ψ as single invariant object. The QM-in-curved-spacetime question doesn't get deferred past ℓ_P; it dissolves, because the two things the question asks to reconcile are derived as aspect-projections of one field. Work operates at the level the claim requires; B1 closes via dissolution.
- Leg B2: SM gauge group derived in Ch. 23 as substrate-phase inheritance plus non-abelian local-basis closure. Fermion spectrum and generations from linearized master equation in Chs. 25–26. Electroweak masses through composite chiral background in Chs. 28–29. Tree-level recovery in Ch. 30 with precision residue named as next-iteration work. Established physics recovered at tree level; precision residue honestly deferred.
Admissibility holds at the claimed category. Open items exist; they are named at the layer they're open, not buried. The contrast with the cosmology paper is at the layer of structure, not at the layer of conclusion — both address overlapping problem-space, only one has the architecture to be a candidate solution at the category it claims.
Operating notes
The framework runs at the level the work claims, not the level it actually performs. A paper claiming to solve QM+GR problems is evaluated on B1 and B2 even if it doesn't try to address them — the failure is in claiming the problem space without entering it. A paper that more modestly claims to give a phenomenological description doesn't get B1/B2 applied at the QM+GR level; it gets the legs applied at the level it claims.
Category claims propagate down to components. A work claiming physics-proper status implicitly claims that each of its load-bearing components is physics-proper in its regime. If some components are honestly effective (e.g., a fitted parameter, an empirical input), the work has to name them as such. Components that masquerade as derived while being fitted are the most common form of category misrepresentation within a work that's mostly honest elsewhere.
The diagnostic value is in seeing which component fails which leg. Averaging destroys this. A theory that fails Leg A on three components but closes Leg B1 and B2 on those same components is failing differently than a theory that fails all three legs uniformly. The decomposition lets the reader see specifically what is and isn't working, which enables either incremental repair (the issue is a specific component) or wholesale recategorization (no component closes at the claimed category).
Passing is not endorsement. Admissibility is the entry condition for evaluation, not the prize. Work that passes admissibility goes on to be evaluated on the next filters — empirical adequacy, predictive power, parsimony, explanatory reach. Work that fails admissibility doesn't have the structure to be evaluated on those filters yet; it has to first earn its category claim or honestly retreat to a category it can occupy.
The framework is portable. The categories and the three legs are domain-general; only B1 and B2's instantiation changes when the domain changes. For chemistry, B1 asks whether the claim operates at the molecular/electronic level; B2 asks whether established equilibrium thermodynamics or quantum chemistry is recovered. For economics, B1 asks about the level of agent behavior or aggregate dynamics; B2 asks about established empirical regularities. The framework doesn't need rewriting per domain — only the instantiation does.
Competent application requires reading. Each leg asks something that requires domain expertise. Leg A asks whether primitives are anchored, requiring reading the anchoring work. Leg B1 asks whether the regime is covered, requiring understanding the regime. Leg B2 asks whether established physics is recovered, requiring knowing what recovery would look like. A reviewer running the framework seriously has to do the work. Running it as a rubber stamp produces a worse outcome than the current system — the appearance of structural rigor without the substance.
Open items for the framework
Component-level scoring. The decomposition tables are categorical. A finer-grained instrument might score components on a continuous scale — how many steps from named anchors, how robust the regime characterization. The categorical version is easier to use; the finer version might be more accurate.
Cross-component dependencies. Components depend on each other. The SM's effective parameters depend on the gauge invariance derivation being correct. The framework doesn't yet handle dependency structure explicitly. For most applications this doesn't matter; for evaluating fundamental claims it might.
Historical drift. Components have changed category historically. Quantization of geometry was treated as physics-proper-once-discovered in early LQG; it is now more honestly named as a posit. Tracking how components migrate between categories over time would make the framework historically aware.
Summary
The framework's ontology is the catalogue of what kinds of theoretical work exist (five categories), how theoretical structure decomposes (components-in-regimes), and what closure of a derivation chain is (three modes). The audit is the application: three legs that test whether a work's category claim is supported by its actual structure. The legs are not three separate audits but three lenses on one question — is the category claim honest? — each illuminating a different way the claim could be unsupported.
The verdict is the decomposition. Passing means the work is a candidate in the category it claims. Failing means it isn't yet a candidate at that category, though it may be admissible at a lower category if the same content were honestly presented. The QG project, under the framework, becomes the enumerated task of producing items (a)–(d) from a deeper physics-proper layer, with candidates evaluated component-by-component on whether their primitives close at their claimed substrate.
Admissibility is prior to correctness; ontology is prior to audit; categories are prior to legs. The framework's structure follows this order: what exists, then what decomposes, then what closure is, then how to test.