Assumptions Ledger

Status: Living document — cross-cutting + per-domain foundational assumptions catalogued, classified, and audited for artifact-suspects. Last updated: 2026-06-08

This page is the wiki's central registry of the assumptions on which physical theory rests. Its purpose is not merely to list them but to classify each one along an axis from fundamental to historical artifact, and to make explicit the consequence of relaxing it. The deliverable distinguishing question is: which things treated as fundamental are not? Throughout, every nontrivial claim carries an epistemic marker per EPISTEMICS.md. The structural map of how these assumptions feed each theory lives in THEORY_MAP.md; the conjectures that would replace or relax them live in HYPOTHESES.md.

Classification scheme

Each assumption is assigned exactly one classification. These are not epistemic markers (those tag individual claims); they describe the status of the assumption as a load-bearing premise:

fundamental — appears irreducible: no accepted derivation exists, relaxing it breaks the theory's consistency, and it currently functions as a primitive law-like posit.
plausibly-fundamental — deeply load-bearing and empirically robust, but either conditional on a framework, parasitic on a deeper assumption, or known to be only locally/approximately exact.
historical-artifact — treated (often historically) as fundamental, but now understood to be derived, false at a deeper level, or an inheritance of the regime in which it was discovered.
mathematical-convenience — a representational or computational choice (possibly forced in form but not load-bearing in content), or an idealization whose rigorous status is incomplete.
untested-empirically — a deep background posit with no decisive experimental test or theorem either way; often smuggled in implicitly.

INFERENCE The single most useful discipline this page enforces is separating a true logical inconsistency from a domain-of-validity mismatch from an unsolved-but-consistent problem. Most "assumptions that look shaky" are domain boundaries, not contradictions. See GAPS_AND_CONTRADICTIONS.md.

A. Cross-cutting assumptions (the master table)

ID	Assumption	Appears in	Classification	Reasoning (epistemic)	What changes if relaxed
A-1	Microcausality / locality: $[\phi(x),\phi(y)]=0$ for spacelike $(x-y)^2<0$	QFT, SR, info, GR	fundamental	ESTABLISHED as a defining axiom of relativistic QFT Drives spin–statistics, CPT, Reeh–Schlieder; guarantees no-signaling even with Bell-violating entanglement. Caveat: microcausality the axiom is fundamental; naive local realism the intuition is precisely what Bell + Reeh–Schlieder undermine. Expected to be modified at the Planck scale.	Generically breaks Lorentz invariance and/or permits superluminal signaling, collapsing relativistic-QFT consistency. Controlled relaxation (noncommutative geometry, minimal length) must still reproduce microcausality to extreme precision in the IR.
A-2	Unitarity: closed evolution and the $S$ -matrix conserve probability; pure $\to$ pure	QM, QFT, info, GR, thermo, statmech	fundamental	ESTABLISHED within quantum theory Enforced via Ward/BRST identities and the optical theorem; apparent loss reflects truncation. Its one real confrontation is the black-hole information paradox; consensus INFERENCE, reinforced by AdS/CFT and Page-curve/island computations, is that unitarity wins. Conditional on standard QM being final — objective-collapse models deliberately violate it.	If exact unitarity fails (genuine collapse, true information loss), QM needs new fundamental dynamics — generically nonlinearity, energy non-conservation, or a preferred frame, all tightly constrained.
A-3	Exact linearity of QM (superposition principle)	QM, math, info	plausibly-fundamental	ESTABLISHED to extraordinary precision Underlies all interference; Weinberg-type and Bialynicki-Birula–Mycielski bounds find no deviation. Demoted from "fundamental" because (i) it is the explicit target of objective-collapse programs, and (ii) nonlinear QM permits superluminal signaling — so linearity may be derivative of no-signaling + Hilbert space rather than primitive.	Generic nonlinearity enables superluminal signaling and spoils the tensor-product/entanglement accounting and the Born-rule/decoherence story. Viable nonlinearity must hide below current bounds (e.g. gravitationally induced).
A-4	Born rule as a separate axiom: $\Pr=\operatorname{Tr}(\rho E)$	QM, math, info	mathematical-convenience	[Form ESTABLISHED/forced; independence CONTESTED] Gleason's theorem ( $\dim\ge 3$ , noncontextuality) makes the form unique. Whether it must be postulated (von Neumann packaging) or derived (Deutsch–Wallace, Zurek envariance, GPT reconstructions) is open; reconstructions suggest it is not logically independent. Treating it as free-standing overstates its independence.	If derivable, the axiom set shrinks (clarification, not physics). A non-Born rule is forbidden by Gleason for $\dim\ge3$ under noncontextuality — any alternative is a different theory.
A-5	Complex (not real/quaternionic) Hilbert space	QM, math, info	plausibly-fundamental	INFERENCE/CONTESTED Long thought conventional (Stueckelberg: real-QM-with-superselection reproduces QM). Recent multipartite Bell-type tests (Renou et al., 2021–2022) argue complex QM is not reproducible by a real-Hilbert-space theory under standard tensor-product/network-independence locality. Principled-but-conditional, not unconditional.	Under standard locality, real QM predicts now-disfavored correlations. If the distinction is conventional after all, nothing physical changes. Quaternionic QM is consistent but unmotivated and faces tensor-product trouble.
A-6	Lorentz / Poincaré invariance is exact (stable vacuum, energy bounded below)	SR, QFT, particle, GR, cosmo, classical	plausibly-fundamental	ESTABLISHED locally to extreme precision; INFERENCE that it is exact Basis of Wigner classification, spin–statistics, CPT; spectrum condition needed for stability. Demoted because (1) globally it is not exact — FLRW spontaneously breaks Poincaré via the cosmic (CMB) rest frame; (2) Planck-scale Lorentz violation is OPEN, constrained but not excluded.	Even tiny violation undermines spin–statistics and CPT, introduces a preferred frame, and forces reworking QFT consistency; must be Planck-suppressed. Global breaking (cosmology) is already accommodated as spontaneous.
A-7	CPT symmetry holds exactly	QFT, particle, SR	plausibly-fundamental	ESTABLISHED as a theorem GIVEN its premises CPT follows from locality (A-1) + Lorentz invariance (A-6) + unitarity (A-2) + Hermiticity. Not an independent postulate — exactly as fundamental as the weakest of those. Tested to high precision (neutral-kaon mass difference).	CPT violation necessarily signals breakdown of locality, Lorentz invariance, unitarity, or Hermiticity. Permits particle/antiparticle mass/lifetime differences — a sharp probe of those deeper foundations.
A-8	Spacetime is a smooth Lorentzian continuum (differentiable manifold)	GR, QFT, math, cosmo, info	mathematical-convenience	INFERENCE/OPEN — deliberately downgraded Underwrites every confirmed GR/QFT prediction, so fundamental within the EFTs. But convergent hints (Planck-scale curvature $\sim \ell_P^{-2}$ , UV divergences, area-law BH entropy, holographic finiteness, lattice-as-limit + triviality, discrete QG programs) suggest the continuum is an effective idealization. A leaning, not a settled result.	If discrete/noncommutative, differential geometry becomes emergent; smoothness, exact diffeomorphism and Lorentz invariance all become approximate, and UV divergences/ $\Lambda$ -counting could be tamed by an intrinsic cutoff. Challenge: recovering exact low-energy Lorentz invariance.
A-9	Spacetime is fundamental (not emergent from entanglement/information)	GR, info, QFT, cosmo	untested-empirically	SPECULATIVE/OPEN Working assumption of GR/QFT. The "spacetime from entanglement" program (Ryu–Takayanagi, JLMS, entanglement-wedge reconstruction, ER=EPR, first-law $\to$ linearized Einstein) is a rigorous proof-of-concept — but only in AdS/CFT. Generalization to our de Sitter-like universe is unknown and currently untestable. The deepest place where a habitual "fundamental" label may be an artifact.	If emergent, locality, the manifold, and unitarity-as-stated are properties of an effective description; quantizing gravity means identifying pre-geometric DOF, not quantizing the metric. The problem of time and the $\Lambda$ problem might be reframed.
A-10	Quantum fields are the fundamental DOF (particles emergent)	QFT, particle	plausibly-fundamental	INFERENCE Locality + cluster decomposition + QM essentially force a field description (Weinberg's folk theorem); particles are frame-ambiguous (Unruh, no global particle number in curved space). Demoted because fundamental only within QFT — whether fields emerge from strings/boundary/pre-geometry is OPEN, and condensed matter exhibits emergent gauge fields and Lorentz invariance.	If fields are emergent, QFT is an EFT with a UV cutoff (consistent with $\phi^4_4$ triviality, the QED Landau pole); the search for deeper DOF replaces field quantization. Low-energy physics unaffected.
A-11	Spacetime has exactly $3+1$ dimensions	GR, QFT, particle, cosmo	plausibly-fundamental	ESTABLISHED at accessible scales; OPEN a priori Inverse-square law holds from sub-mm to cosmological scales; dimension enters Lovelock's theorem and Wigner classification. Demoted: it is an empirical input, not derived; KK/string scenarios allow small extra dimensions; exchange statistics is dimension-dependent (anyons in 2D).	Compact extra dimensions modify short-distance gravity, coupling running (unification), and spectra (KK towers). Different macroscopic dimensionality changes orbit stability and the Green's functions of forces.
A-12	Fundamental constants are constant in space and time	particle, cosmo, QFT, GR	plausibly-fundamental	ESTABLISHED to tight bounds; OPEN at the margins Constancy of dimensionless constants ( $\alpha$ , $m_p/m_e$ ) is tested by quasar spectra, the Oklo reactor, atomic clocks, BBN/CMB — no confirmed variation. Demoted: directly testable (occasional CONTESTED $\alpha$ -variation claims have not survived); dynamical-scalar theories predict slow variation; only dimensionless ratios are meaningful (a units artifact to flag). See CONSTANTS_AND_SCALES.md.	Variation signals new light fields coupling to matter (EP violation at some level) and breaks the "SM parameters are fixed inputs" view, opening environmental/anthropic selection.
A-13	Cosmological principle: large-scale homogeneity + isotropy	cosmo, GR	plausibly-fundamental	[ESTABLISHED above $\sim 100$ Mpc; INFERENCE as exact] CMB isotropic to $\sim 10^{-5}$ after dipole subtraction; homogeneity inferred via Copernican principle + isotropy. Demoted: holds statistically and only above a scale; FLRW is a statistical average; backreaction is CONTESTED (believed small); claimed anomalies CONTESTED; inflationary origin OPEN.	Genuine large-scale inhomogeneity/anisotropy invalidates the FLRW background, alters distance–redshift relations, and could mimic/alter dark-energy inferences (the fitting/backreaction problem).
A-14	Past hypothesis: the universe began in extraordinarily low (gravitational) entropy	thermo, statmech, cosmo	fundamental	[INFERENCE bordering ESTABLISHED that it is needed; OPEN why] Since microdynamics are CPT-symmetric, an asymmetric arrow must be sourced by an asymmetric boundary condition — a near-forced inference. Necessity is fundamental; explanation is wide open (Penrose's Weyl-curvature quantification; inflation relocates rather than removes the puzzle). Kept fundamental: no accepted dynamical derivation exists.	Without it: no thermodynamic arrow, no second law as observed, no record asymmetry. If a mechanism eventually derives the low-entropy state, the arrow becomes explained rather than assumed.
A-15	A fundamental action principle exists; dynamics from stationary $S$	classical, QFT, particle, GR, math	plausibly-fundamental	[INFERENCE — with a clear demotion of its classical status] Stationary action as a classical primitive is derived as the $\hbar\to0$ stationary-phase limit of the path integral — its ground is quantum. The deeper claim (a fundamental quantum action) is plausibly effective: $e^{iS/\hbar}$ is heuristic in 4D (no rigorous Lorentzian measure), and S-matrix/bootstrap and operator-algebraic programs formulate physics without a manifest Lagrangian (non-Lagrangian CFTs).	Without a fundamental Lagrangian, dynamics is fixed by consistency conditions (unitarity, crossing, conformal/operator data). Noether-style symmetry–conservation links need reformulation.
A-16	The universe is computable (physical Church–Turing thesis)	info, math	untested-empirically	OPEN/CONTESTED Suggested by all known physics, but not a theorem. Continuous dynamics, real-valued data, and Malament–Hogarth spacetimes leave it open; the efficient (extended) thesis is separately challenged by quantum computing (BQP vs BPP). Often smuggled in implicitly; flagging it as untested is the honest move.	If hypercomputation is realizable, the law $\leftrightarrow$ simulability link breaks, undermining "it-from-bit"/digital physics. If only the efficient thesis fails (already indicated by QC), classical simulability is lost but computability survives.
A-17	Equivalence principle: matter couples universally and minimally to one metric	GR, classical, cosmo	plausibly-fundamental	[ESTABLISHED to $\sim 10^{-15}$ for the weak EP] (torsion balances, MICROSCOPE). Einstein EP licenses geometrization. Demoted: a single universal metric is an assumption (multi-metric/scalar-tensor alternatives are constrained, not excluded); EP in the quantum regime (superposed/entangled masses) is OPEN; any new light scalar induces composition-dependent forces.	EP violation means inertial $\neq$ gravitational mass, forbidding clean geometrization and requiring extra fields/metrics; a discovery of a fifth force / new scalar.
A-18	EFT decoupling: UV decouples from IR; low-energy physics is renormalizable + suppressed higher-dim operators	QFT, particle, statmech, info	plausibly-fundamental	ESTABLISHED as working principle; with one major caveat Wilsonian RG makes renormalizability emergent (irrelevant operators $\sim (E/\Lambda)^n$ ); Appelquist–Carazzone + EFT successes (ChPT, Fermi theory, gravity-as-EFT, SMEFT) confirm it. Demoted by a glaring exception: the cosmological-constant problem is a failure of naive decoupling (UV vacuum energy fails to decouple, off by $\sim 120$ orders); the hierarchy problem is a related relevant-operator sensitivity.	Where decoupling fails (vacuum energy, possibly $m_H$ ), IR observables become UV-sensitive, destroying predictivity absent a symmetry/selection. Its existence is proof the assumption has a real exception at the QFT/gravity interface. See OPEN_PROBLEMS.md.
A-19	Time is an external classical parameter / a global preferred time exists	QM, cosmo, GR	historical-artifact	INFERENCE — artifact verdict, sharpened In NRQM, Pauli's theorem forbids a self-adjoint time operator conjugate to a bounded-below $H$ , so $t$ is a c-number while $x$ is an operator — an asymmetry from non-relativistic, fixed-background thinking. In cosmology, FLRW singles out cosmic time / the CMB frame. Acute in QG: Wheeler–DeWitt $\hat H	\Psi\rangle=0$ is timeless. Relational reformulations (Page–Wootters, partial observables) show time can be otherwise.

B. Per-domain foundational assumptions

The cross-cutting table above captures assumptions shared across domains. Below are the domain-specific foundational posits, with the same five-way classification (here folding the source schema's likely-fundamental $\to$ plausibly-fundamental, and conventional-choice $\to$ mathematical-convenience unless otherwise noted). IDs continue the global sequence as D-<domain>-n.

B.1 Quantum mechanics (non-relativistic) — see domains/quantum-mechanics.md

ID	Assumption	Classification	Note
QM-1	States are rays in a complex Hilbert space; amplitudes superpose	plausibly-fundamental	Subsumes A-3, A-5. Linearity ESTABLISHED; complexity plausibly-fundamental (Renou et al.).
QM-2	Observables are self-adjoint operators; values lie in the spectrum	plausibly-fundamental	Self-adjointness ESTABLISHED forced (Stone, spectral theorem). Exhaustiveness of self-adjoint $\leftrightarrow$ measurable is an idealization (superselection, POVMs).
QM-3	Born rule gives outcome probabilities	plausibly-fundamental	See A-4. Form forced by Gleason ( $\dim\ge3$ ); derivability CONTESTED.
QM-4	Projection/collapse postulate is a real, distinct dynamical process	untested-empirically	CONTESTED The measurement problem. Cannot be derived from unitary evolution; replacement (GRW/CSL vs Everett/decoherence vs QBism) unknown. The bare postulate is very likely not fundamental as stated. See OPEN_PROBLEMS.md.
QM-5	Composite systems combine by tensor product	plausibly-fundamental	ESTABLISHED operationally Encodes local tomography + entanglement; singled out in GPT reconstructions. Could be otherwise in exotic theories.
QM-6	Time is an external classical parameter (no time observable)	historical-artifact	See A-19. Pauli's theorem; relational reformulations exist.
QM-7	Global phase + overall normalization are unphysical (states are rays)	mathematical-convenience	ESTABLISHED Pure representational convention; only relative phases matter. (Inter-superselection-sector phases are unobservable for a deeper, dynamical reason — distinct from this convention.)
QM-8	Hilbert space is separable	mathematical-convenience	ESTABLISHED for NRQM Adequate for all standard single-system QM; non-separable spaces appear only in special constructions.
QM-9	Spin–statistics (integer $\to$ boson, half-integer $\to$ fermion)	fundamental (within physics) / imported into NRQM	ESTABLISHED An added postulate in NRQM but a theorem in QFT (microcausality + positive energy + Lorentz). Its NRQM status as imported input is a domain-of-validity signal. In 2D: braid group $\to$ anyons.
QM-10	Measurement-independence / "free choice" of settings (Bell)	plausibly-fundamental	CONTESTED/OPEN Denying it (superdeterminism/retrocausality) preserves locality but is widely regarded as conspiratorial. A load-bearing assumption, not settled.

B.2 Quantum field theory — see domains/quantum-field-theory.md

ID	Assumption	Classification	Note
QFT-1	Fields are the fundamental DOF	plausibly-fundamental	See A-10. Weinberg's folk theorem; deeper substrate OPEN.
QFT-2	Fixed smooth globally-Lorentzian background	plausibly-fundamental	See A-8. Spectacular but expected to fail at $\ell_P$ ; continuum limit existence is the constructive/triviality question.
QFT-3	Microcausality	fundamental	See A-1. Least negotiable assumption.
QFT-4	Poincaré invariance + unique stable vacuum + spectrum condition	plausibly-fundamental	See A-6.
QFT-5	Renormalizability as a selection criterion	historical-artifact	ESTABLISHED reinterpretation Once "sacred"; Wilson's RG reinterpreted it as an emergent low-energy property (irrelevant operators suppressed). Non-renormalizable EFTs are predictive. A clear superseded artifact.
QFT-6	A well-defined functional measure $\mathcal D\phi$ exists	mathematical-convenience (status unclear)	CONTESTED/OPEN Lorentzian "measure" is not a measure in $d=4$ ; Euclidean construction rigorous only for super-renormalizable/2D–3D models. 4D YM existence + mass gap is a Clay problem. A phenomenally successful heuristic.
QFT-7	Gauge "symmetry" is a fundamental interaction-generating principle	mathematical-convenience (heuristic framing)	CONTESTED interpretation Gauge symmetry is a redundancy, not a physical symmetry (Elitzur; observables are gauge-invariant). The physical core (massless spin-1 consistency, charge conservation) is fundamental; "derive interactions by gauging" is heuristic. See UNIFYING_PRINCIPLES.md.
QFT-8	Asymptotic in/out states + well-defined $S$ -matrix (LSZ, asymptotic completeness)	plausibly-fundamental	INFERENCE LSZ/Haag–Ruelle justify it given a mass gap. Fails for confinement (no free quarks), massless particles (IR), and CFTs (no particles). Restricted domain.
QFT-9	Wick rotation / Osterwalder–Schrader reconstruction is faithful	mathematical-convenience (reach unclear)	ESTABLISHED where conditions hold A theorem given reflection positivity; fails at finite chemical potential (sign problem) and for real-time dynamics.
QFT-10	Unitarity of evolution / $S$ -matrix	fundamental	See A-2.
QFT-11	Finite field content + a single fixed Fock space suffice	mathematical-convenience (strictly false)	ESTABLISHED limitation Haag's theorem: the interacting theory does not live in the free Fock space; inequivalent representations are generic (contrast Stone–von Neumann in finite QM). AQFT replaces this with a net of algebras.

B.3 General relativity — see domains/general-relativity.md

ID	Assumption	Classification	Note
GR-1	Spacetime is a smooth 4D Lorentzian manifold, signature $(-,+,+,+)$	plausibly-fundamental	See A-8, A-11. Signature is fundamental to causality; smoothness an idealization; $(-+++)$ vs $(+---)$ purely conventional.
GR-2	Levi-Civita connection: torsion-free + metric-compatible	mathematical-convenience (a choice)	ESTABLISHED as a choice Einstein–Cartan (torsion from spin) and teleparallel gravity (flat connection + torsion) agree with GR for spinless matter — the "Geometric Trinity." Metric compatibility is deeply tied to the EP.
GR-3	Second-order field equations, action linear in $R$ (plus $\Lambda$ )	mathematical-convenience (leading EFT term)	ESTABLISHED structurally Lovelock's theorem: in 4D the only divergence-free symmetric 2-tensor from $g$ and its first two derivatives is $aG_{\mu\nu}+bg_{\mu\nu}$ . Higher-curvature terms are generic EFT corrections; "linear in $R$ " is the leading term. $\Lambda$ is genuinely fundamental as an allowed term.
GR-4	Matter couples minimally/universally to one metric (EP)	plausibly-fundamental	See A-17.
GR-5	Diffeomorphism invariance / background independence	fundamental	ESTABLISHED The deepest structural principle. The hole argument forces identifying $\varphi^*g$ with $g$ : points have no physical identity apart from fields. Dictates the constraint structure, absence of preferred time, and most obstructions to quantization. Any QG theory must reproduce it.
GR-6	Time-orientable + globally hyperbolic (admits a Cauchy surface)	mathematical-convenience (an added restriction)	INFERENCE Imposed for a well-posed initial-value problem (Choquet-Bruhat–Geroch). Bare EFE permit CTCs (Gödel, Kerr interior). Whether nature enforces it = (strong) cosmic censorship + chronology protection, both OPEN/CONTESTED.
GR-7	Matter satisfies (pointwise) energy conditions	historical-artifact	CONTESTED Crucial hypotheses of the singularity/area/censorship theorems, but not laws of GR — constraints on matter. QFT violates the pointwise conditions (Casimir, Hawking, squeezed states); the SEC is violated by inflation and by $\Lambda>0$ . Replaced by averaged/quantum conditions (ANEC, QNEC).
GR-8	$\Lambda$ is a single constant of nature (not dynamical)	untested-empirically	OPEN/CONTESTED The unique Lovelock term beyond $G_{\mu\nu}$ ; $\Lambda$ CDM fits well. But the value is $\sim 120$ orders below naive QFT vacuum energy (the $\Lambda$ problem). Whether constant, vacuum energy, anthropic, or quintessence is unresolved; recent surveys hint (not conclusively) at evolving dark energy.
GR-9	Gravity is purely classical (metric is a c-number)	plausibly-fundamental	INFERENCE/OPEN Classical GR is fantastically successful, but semiclassical $G_{\mu\nu}=8\pi G\langle T_{\mu\nu}\rangle$ is at best approximate and internally problematic. Near-universal expectation: the metric must be quantum. Fundamental within its domain, expected emergent/approximate at $\ell_P$ .

B.4 Classical mechanics — see domains/classical-mechanics.md

ID	Assumption	Classification	Note
CM-1	Absolute universal time $t$ (Galilean structure)	historical-artifact	ESTABLISHED false fundamentally SR demolishes absolute simultaneity; Newtonian time is the $c\to\infty$ limit.
CM-2	Smooth finite-dim configuration manifold; deterministic ODE evolution	plausibly-fundamental	INFERENCE/CONTESTED at margins Picard–Lindelöf gives uniqueness for Lipschitz fields. Cracks: Lipschitz failure $\to$ non-uniqueness (Norton's dome, $\ddot x=\sqrt{x}$ ); finite-time non-collision singularities (Xia 1992, $N\ge5$ ). Physical vs point-particle artifact is OPEN.
CM-3	Forces specified independently and superpose; $L=T-V$	mathematical-convenience (modeling convention)	INFERENCE Works because classical forces derive from potentials; not logically forced (dissipative/nonholonomic systems need generalizations). The form $L=T-V$ is a low-energy shadow of the relativistic/path-integral origin.
CM-4	Stationary-action principle	plausibly-fundamental	See A-15. Derived as the $\hbar\to0$ limit of the path integral; genuinely stationary (saddle points past caustics), not "least."
CM-5	Phase space carries a canonical symplectic structure; Poisson algebra	fundamental (within the framework)	ESTABLISHED The most robust structural feature — survives (deformed) into QM via Poisson $\to$ commutator; preserved by canonical transforms and the flow (Liouville). Darboux: all symplectic manifolds look locally identical (rigid, not conventional).
CM-6	Euclidean $E^3$ space + existence of inertial frames	historical-artifact	ESTABLISHED false fundamentally GR replaces flat space + global inertial frames with dynamical curved spacetime; only local inertial frames exist. Smuggles in the origin-of-inertia (Mach) question, OPEN/CONTESTED.
CM-7	Observables have simultaneous arbitrarily-precise real values	historical-artifact	ESTABLISHED false fundamentally QM forbids it (uncertainty, noncommutativity); the classical phase-space point is the $S\gg\hbar$ coarse-grained limit.
CM-8	Positive-definite mass tensor; regular (nondegenerate) Lagrangian	mathematical-convenience (regularity assumption)	INFERENCE Makes the Legendre transform invertible. Deliberately violated by the most important theories (gauge fields, reparametrization-invariant systems, relativistic point particle) — singular Lagrangians needing Dirac constraint theory.
CM-9	Time-reversal invariance of microscopic mechanics	plausibly-fundamental	[ESTABLISHED for standard $L$ ; CONTESTED as universal] Holds for $L$ quadratic in velocities; broken by velocity-dependent/dissipative forces and fundamentally by CP-violation. Underlies the Loschmidt paradox. See domains/thermodynamics.md.

B.5 Thermodynamics — see domains/thermodynamics.md

ID	Assumption	Classification	Note
TH-1	Equilibrium states exist, specified by few macrovariables (thermodynamic limit)	plausibly-fundamental	ESTABLISHED for short-range systems Precondition for the formalism. Fails for long-range/gravitating/small/nonequilibrium systems — a domain-of-validity boundary, not a law.
TH-2	Entropy is extensive/additive	mathematical-convenience (domain-limited)	ESTABLISHED short-range; CONTESTED in general A consequence of short-range interactions; gravitating systems are non-extensive (area-law BH entropy). Tsallis/Rényi relax additivity (physical necessity contested).
TH-3	Temperature well-defined and positive (zeroth law)	mathematical-convenience	Zeroth-law transitivity ESTABLISHED/structural; positivity is NOT fundamental — bounded-spectrum systems realize negative absolute temperature ( $T=\partial U/\partial S$ ), experimentally confirmed and "hotter than $+\infty$ ."
TH-4	Second law is exact and exceptionless	historical-artifact (refined)	CONTESTED/refined StatMech + fluctuation theorems make it statistical: $P(+\Sigma)/P(-\Sigma)=e^{\Sigma/k_B}$ ; Jarzynski/Crooks promote the inequality to a trajectory-ensemble equality. The "absolute" reading is a macroscopic-limit artifact; the probabilistic statement is fundamental.
TH-5	Low-entropy past underlies the arrow of time	plausibly-fundamental (need) / OPEN (why)	See A-14. The need is near-forced; the explanation is unsolved.
TH-6	Third law ( $S\to S_0$ as $T\to0$ ; absolute zero unattainable)	fundamental	ESTABLISHED For non-degenerate (or sub-exponentially degenerate) ground states — a quantum fact (discrete spectrum). The zero reference is conventional (Planck); the vanishing of entropy differences and unattainability are fundamental.
TH-7	Equal a priori probability (microcanonical postulate)	plausibly-fundamental	See SM-1. Load-bearing micro $\to$ macro bridge; full first-principles thermalization derivation OPEN.
TH-8	Heat/work cleanly separable; reversible quasi-static processes exist	mathematical-convenience (idealization)	ESTABLISHED as idealization Reversible = infinitely-slow zero-power limit, never exact; bounds real processes (Carnot, Clausius).
TH-9	$k_B$ is a fundamental conversion factor	mathematical-convenience (units)	ESTABLISHED Post-2019 SI, $k_B$ is a fixed defined constant: temperature is literally an energy unit. A units convention, though a fundamental energy-per-DOF scale is physical.

B.6 Statistical mechanics — see domains/statistical-mechanics.md

ID	Assumption	Classification	Note
SM-1	Equal a priori probability (microcanonical)	mathematical-convenience (partly forced)	CONTESTED The natural Liouville-invariant measure (strong dynamical justification), but no theorem derives it for realistic systems; partly MaxEnt/indifference. Justified pragmatically.
SM-2	Ergodicity (time average = ensemble average)	historical-artifact	ESTABLISHED neither necessary nor sufficient KAM shows generic Hamiltonian systems are not ergodic, yet StatMech works. Superseded by typicality/concentration-of-measure/Khinchin for $\sim 10^{23}$ DOF.
SM-3	Thermodynamic limit ( $N,V\to\infty$ , $N/V$ fixed)	mathematical-convenience (idealization)	ESTABLISHED True non-analyticities (phase transitions) exist only in the strict limit (Lee–Yang); finite systems have crossovers. Captures real behavior because rounding is negligible for macroscopic $N$ .
SM-4	Molecular chaos (Stosszahlansatz)	fundamental (locus of time-asymmetry)	ESTABLISHED as where irreversibility enters Provably false for post-collision velocities; Lanford's theorem: holds for typical data for short times. The precise point where a typicality/initial-condition assumption enters; not derivable from reversible mechanics.
SM-5	Coarse-graining (entropy relative to a macrostate partition)	fundamental (need) / conventional (specific choice)	CONTESTED interpretation Subjective (Jaynes) vs objectively-singled-out macrovariables (Boltzmann/Lebowitz/Goldstein). Either way irreversibility cannot be stated without a coarser-than-microstate description.
SM-6	Low-entropy initial condition / past hypothesis	fundamental	See A-14. Cannot be eliminated from StatMech.
SM-7	Gibbs $N!$ + cell size $h^{dN}$	historical-artifact	ESTABLISHED Inserted by hand classically (Gibbs paradox, extensivity); QM derives both — indistinguishability gives $N!$ , $h=$ Planck's constant sets the cell. Fundamental only once QM is recognized.
SM-8	Canonical $e^{-\beta H}$ is the universal equilibrium distribution	plausibly-fundamental	ESTABLISHED in domain; CONTESTED at margins Follows from reservoir trace / MaxEnt / ETH for short-range additive systems. Fails for long-range (gravitating, some plasmas); Tsallis proposals CONTESTED.
SM-9	Eigenstate Thermalization Hypothesis (ETH)	plausibly-fundamental	INFERENCE, strong numerical support The quantum mechanism of thermalization (Deutsch, Srednicki, RMT). Not proven for any realistic $H$ ; provably fails for integrable (GGE) and many-body-localized systems. Domain: generic non-integrable, non-MBL.

B.7 Cosmology — see domains/cosmology.md

ID	Assumption	Classification	Note
CO-1	Cosmological principle	plausibly-fundamental	See A-13.
CO-2	GR is correct on cosmological scales	plausibly-fundamental	ESTABLISHED in tested regimes; INFERENCE on horizon scales Tested in the solar system / pulsars / GW mergers — scales $\sim10^{30}$ smaller than the Hubble radius. Applying it unmodified to the whole universe is an extrapolation; modified-gravity alternatives constrained, not all excluded.
CO-3	Matter is a perfect fluid with simple equations of state	mathematical-convenience (replaceable modeling)	INFERENCE Perfect-fluid form is forced by FLRW symmetry at background level; dust DM and $w=-1$ DE are simplifying choices data has not yet required abandoning.
CO-4	Spatial flatness ( $\Omega_k=0$ )	mathematical-convenience (empirically-motivated choice)	INFERENCE An inflation prediction, consistent with CMB+BAO ($
CO-5	Cold dark matter exists as a distinct dominant component	plausibly-fundamental (existence) / OPEN (identity)	ESTABLISHED that something beyond baryons+GR is needed Multi-pillar concordance (rotation curves, lensing, Bullet Cluster, CMB peaks, BBN). "Cold" favored over hot/warm. Particle identity (WIMP/axion/sterile- $\nu$ /PBH) OPEN after null searches. See OPEN_PROBLEMS.md.
CO-6	Dark energy is a cosmological constant ( $w=-1$ exactly)	mathematical-convenience (minimal choice)	[ESTABLISHED that acceleration occurs; OPEN/CONTESTED that it is exactly $\Lambda$ ] $\Lambda$ is simplest and fits almost all data; $w=-1$ exactly is a choice. Recent BAO read by some as hinting at evolving DE (CONTESTED, not established).
CO-7	Primordial fluctuations: adiabatic, Gaussian, near-scale-invariant	plausibly-fundamental (data) / INFERENCE (inflationary origin)	ESTABLISHED as data description $n_s\approx0.965$ , super-horizon correlations measured. Inflationary origin compelling but unproven; some alternatives reproduce the spectrum; B-mode tensors not detected.
CO-8	Inflation occurred	plausibly-fundamental (bordering SPECULATIVE)	INFERENCE Solves horizon/flatness/monopole and predicts the spectrum, but: no primordial GW detection; inflaton unidentified; eternal-inflation measure problem; needs its own low-entropy initial conditions (Penrose). Leading paradigm, not established fact. See HYPOTHESES.md.
CO-9	Low-entropy initial macrostate (past hypothesis)	fundamental	See A-14. Near-perfect thermal uniformity = high thermal but very low gravitational entropy (Weyl $\approx 0$ ).
CO-10	Standard thermal-equilibrium reasoning + single arrow apply to the cosmos	mathematical-convenience (not rigorously founded for gravity)	INFERENCE/CONTESTED Self-gravitating systems have negative specific heat and no global max-entropy equilibrium; global $T$ / $S$ for the universe is a useful idealization that breaks down conceptually for gravity.
CO-11	Exactly three light neutrino species ( $N_{\rm eff}\approx 3.044$ )	mathematical-convenience (empirically-grounded, easily freed)	ESTABLISHED to good precision BBN + CMB damping tail consistent with 3.044 (the excess over 3 is a real QFT prediction). Held fixed but easily promoted to a free parameter (dark radiation, $H_0$ -tension probes).
CO-12	Cosmic time $t$ is a globally well-defined preferred coordinate	historical-artifact	See A-19. FLRW singles out the CMB frame — spontaneous, not law-breaking; routine treatment as fundamental is a convenience of the high-symmetry idealization.

B.8 Particle physics / Standard Model — see domains/particle-physics.md

ID	Assumption	Classification	Note
PP-1	Nature is a local, Lorentz-invariant, unitary relativistic QFT	plausibly-fundamental	ESTABLISHED to extreme precision (electron $g\!-\!2$ to $\sim12$ sig figs). Plausibly emergent from a deeper structure; QG likely modifies locality at $\ell_P$ .
PP-2	Gauge group is exactly $SU(3)_c\times SU(2)_L\times U(1)_Y$	plausibly-fundamental	ESTABLISHED as low-energy description Product structure + hypercharge normalization look unifiable (SU(5), SO(10), Pati–Salam); coupling running suggests near-unification at $\sim10^{16}$ GeV (better in MSSM). A possible low-energy shadow. See UNIFICATION_LANDSCAPE.md.
PP-3	Hypercharge/fermion representations are what they are (e.g. $Q_L\sim(3,2)_{1/6}$ )	fundamental (within SM)	ESTABLISHED Fixed by anomaly cancellation (quantum consistency) + measured charges. Charge quantization (proton/electron equality to $\sim10^{-21}$ ) is not explained in the SM — elegantly explained by GUT embedding. Fundamental to the SM but points beyond it.
PP-4	Exactly three generations with identical gauge numbers	untested-empirically	ESTABLISHED empirically Invisible $Z$ width $\to$ exactly 3 light active neutrinos; no 4th chiral generation (Higgs data). Why three is completely OPEN. Could-be-otherwise.
PP-5	EWSB by a single elementary scalar doublet (tachyonic mass term)	mathematical-convenience (minimal realization)	[ESTABLISHED that a $\sim125$ GeV SM-like scalar exists] Minimal single-doublet is a choice (2HDM, composite Higgs, technicolor). The elementary-scalar assumption creates the hierarchy problem — theoretically suspect; possibly composite. CONTESTED whether elementary.
PP-6	Neutrinos are massless (minimal SM)	historical-artifact	ESTABLISHED FALSE Oscillations prove nonzero mass. A minimality assumption baked into the original SM; fixed by the Weinberg dim-5 operator or $\nu_R$ . The clearest case of a wrong original SM assumption. See GAPS_AND_CONTRADICTIONS.md.
PP-7	Neutrino masses are Dirac (vs Majorana)	untested-empirically	OPEN/CONTESTED Genuinely unknown. Majorana (seesaw) explains lightness and is favored by many; $0\nu\beta\beta$ (the decisive test) not observed.
PP-8	The QCD $\bar\theta$ term is (or relaxes to) $\approx 0$	untested-empirically	OPEN Strong-CP problem: nothing forces $\bar\theta\approx0$ ; measured $<10^{-10}$ vs naturalness $\mathcal O(1)$ . Options: anthropic, massless up (disfavored by lattice), or a Peccei–Quinn axion (SPECULATIVE but well-motivated).
PP-9	The SM has $\sim 19$ free parameters fixed only by experiment	plausibly-fundamental	ESTABLISHED counting Rises to $\sim 26\text{–}28$ with neutrino masses. The strong hierarchies (e.g. top/electron Yukawa $\sim10^5$ ) suggest an underlying flavor theory. The most glaring "descriptive, not explanatory" aspect. See CONSTANTS_AND_SCALES.md.
PP-10	Fixed 4D Minkowski; gravity neglected	mathematical-convenience (domain restriction)	ESTABLISHED valid choice Gravitational coupling $\sim(E/M_{\rm Pl})^2$ negligible at colliders. A deliberate domain restriction, and exactly the boundary where the SM must be completed (gravity non-renormalizable; SM is an EFT below $M_{\rm Pl}$ ).
PP-11	$B$ and $L$ are (accidental, approximate) global symmetries	historical-artifact	ESTABLISHED Accidental symmetries of the renormalizable Lagrangian, not imposed; anomalous (only $B\!-\!L$ non-anomalous), violated by sphalerons; $B$ -violation required for baryogenesis (Sakharov). An artifact of restricting to low-dimension operators.

B.9 Information theory & physics — see domains/information-theory.md

ID	Assumption	Classification	Note
IT-1	Information has an observer-independent measure (Shannon $H$ )	fundamental	ESTABLISHED Shannon/Khinchin uniqueness theorem; operational meaning (compression/communication limits) proven and validated.
IT-2	The logarithm + base-2 "bit" are the natural units	mathematical-convenience (base) / fundamental (log form)	The log form is forced by additivity; base-2 vs nats vs base- $d$ is pure convention ( $k_B\ln 2$ links to thermo).
IT-3	States are density operators; info measures are spectral functions (von Neumann $S$ )	fundamental (conditional on QM)	ESTABLISHED within QM Follows from Hilbert-space postulates + Gleason/Born; $S$ singled out by Schumacher compression/quantum AEP. Conditional on QM being final (OPEN).
IT-4	Gravitational entropy/info bounds scale with AREA (holographic principle)	plausibly-fundamental	INFERENCE Bekenstein–Hawking area-extensivity on multiple independent derivations (Hawking, Euclidean action, string microstates, LQG area spectra); area-law entanglement + Bousso bound reinforce. Lacks a fully general background-independent proof. See UNIFYING_PRINCIPLES.md.
IT-5	Landauer's principle: erasure costs $k_BT\ln2$ per bit	fundamental (inequality) / CONTESTED (independence)	ESTABLISHED Derivable from statmech + Jarzynski/Crooks; experimentally confirmed near the bound. Whether it is independent of the second law (Earman–Norton, Hemmo–Shenker) is CONTESTED, but the inequality is not.
IT-6	Spacetime geometry is emergent from entanglement (RT / "it-from-qubit")	untested-empirically	See A-9. Rigorous only in AdS/CFT (RT, JLMS, QEC reconstruction, first-law $\to$ linearized Einstein). Generalization unknown.
IT-7	AdS/CFT holds exactly (bulk QG = boundary CFT)	plausibly-fundamental (duality) / OPEN (exactness)	INFERENCE Enormous consistent evidence (symmetries, spectra, correlators, integrability, BH thermo); proven in some lower-dim/BPS cases; no general nonperturbative proof. Treat duality as plausibly-fundamental, exactness/genericity as open.
IT-8	ER=EPR (entanglement = geometric wormhole connection)	untested-empirically	SPECULATIVE Maldacena–Susskind conjecture; supported by traversable-wormhole + thermofield-double constructions. No first-principles derivation; status for generic entanglement unknown. See HYPOTHESES.md.
IT-9	Physical processes are computable (physical Church–Turing)	untested-empirically	See A-16.
IT-10	Information is conserved (unitarity)	fundamental (within QM)	See A-2. Page curve reproduced via QES/islands INFERENCE; mechanism in our universe still being worked out.
IT-11	The continuum is the right substrate (vs discrete "it-from-bit")	historical-artifact (leaning; arguably unclear)	See A-8. UV divergences, area-law BH-entropy finiteness, holographic finiteness hint the continuum is effective (Wheeler's "it from bit"). Far from settled.

B.10 Mathematics for physics — see domains/mathematics.md

ID	Assumption	Classification	Note
MA-1	Pure states are rays in a complex separable Hilbert space (field is $\mathbb C$ )	plausibly-fundamental	See A-5. Separability a near-universal convenience; "why complex" genuinely open; quaternionic QM consistent but unmotivated.
MA-2	Observables are self-adjoint (not merely symmetric)	fundamental	ESTABLISHED Spectral + Stone theorems require self-adjointness; choosing a self-adjoint extension is a physical choice (boundary conditions). PT-symmetric QM is a similarity reformulation, not a refutation.
MA-3	Symmetries act by unitary/antiunitary reps; evolution is unitary	fundamental	ESTABLISHED Wigner's theorem + Stone; antiunitarity forced for time reversal. The measurement "collapse" is the one tension (CONTESTED interpretational issue, not a mathematical defect).
MA-4	Spacetime is a smooth finite-dim manifold; fields are smooth bundle sections	mathematical-convenience (effective)	See A-8. Distributional/weak solutions show smoothness is often relaxed even classically.
MA-5	Gauge fields ARE connections on principal $G$ -bundles	fundamental	ESTABLISHED Wu–Yang/Trautman dictionary; Aharonov–Bohm + Dirac quantization confirm the bundle topology is physical. "Gauge = redundancy" is standard INFERENCE, refined (not refuted) by large-gauge/soft charges. The structure group is dictated by experiment.
MA-6	Born rule + recovery of Kolmogorov probability in decohered subalgebras	plausibly-fundamental	See A-4. Form near-inevitable via Gleason; derivability CONTESTED.
MA-7	Relativistic QFT is axiomatizable (Wightman/Haag–Kastler/OS) + a 4D interacting example exists	plausibly-fundamental	ESTABLISHED for the axioms + low-dim models Whether central 4D theories satisfy them is the YM mass-gap problem (OPEN). Minority view: perturbative 4D QED/ $\phi^4$ are "trivial" (Aizenman–Duminil-Copin proved $\phi^4_4$ triviality) — a domain-of-validity matter, not an inconsistency.
MA-8	The Lorentzian path-integral "measure" $\mathcal D\phi\, e^{iS}$ is a legitimate measure	historical-artifact	ESTABLISHED No $\sigma$ -additive translation-invariant measure exists in infinite dimensions; $e^{iS}$ is non-absolutely-convergent. Rigorous content is via Euclidean reflection-positive measures + continuation, oscillatory-integral methods, or perturbation theory. A productive abuse of notation.
MA-9	Renormalization is meaningful; the Wilsonian EFT picture organizes cutoff dependence	fundamental	ESTABLISHED Empirically (QED, EW precision) + BPHZ-rigorous order by order. The shift from "embarrassing infinity-subtraction" to "EFT + RG flow" is a genuine conceptual correction. Nonperturbative continuum existence for non-asymptotically-free theories is OPEN (triviality).
MA-10	Local algebras are type III $_1$ von Neumann factors	plausibly-fundamental	ESTABLISHED in AQFT Reeh–Schlieder, Bisognano–Wichmann; explains entanglement-area divergences and the need for relative (not absolute) entropy. Algebra type can change in limits (type II in some gravitational/large- $N$ crossovers).
MA-11	Symmetry groups are Lie groups; reps continuous/unitary; superselection organizes inequivalent reps	fundamental	ESTABLISHED Wigner particle classification, universal covers ( $SL(2,\mathbb C)$ , spin), Doplicher–Haag–Roberts theory. Generalized/categorical symmetries and quantum groups extend but do not overturn this.

C. Narrative: the artifact-suspects

The table's real payload is the set of assumptions commonly treated as fundamental that are probably not. These deserve scrutiny because mistaking an artifact for a law misdirects the unification program (UNIFICATION_LANDSCAPE.md). I rank them by how consequential the misclassification would be.

C.1 Spacetime fundamentality (A-9) — the deepest suspect

SPECULATIVE/OPEN The habit of treating the smooth manifold $(M,g)$ as the bedrock of physics is the most likely place where "fundamental" is an artifact of working inside background-dependent frameworks. Two distinct demotions stack: (i) the continuum may be effective (A-8, A-11, MA-4), and (ii) geometry itself may be emergent from entanglement (A-9, IT-6). The AdS/CFT results — $S_{\rm EE}=\frac{\mathrm{Area}(\gamma)}{4G_N}$ (Ryu–Takayanagi) and the derivation of linearized Einstein equations from the entanglement first law $\delta S = \delta\langle H\rangle$ — are a genuine proof-of-concept INFERENCE that some worlds reconstruct geometry from boundary information. But they live in a special tractable corner (asymptotically AdS, large $N$ , strong coupling). Whether our de Sitter-like, non-holographic universe works this way is untestable today. The honest verdict: do not assert spacetime is emergent (that overstates the evidence), but flag every "spacetime is fundamental" usage as untested-empirically, not fundamental.

C.2 Renormalizability (QFT-5) — the cleanest resolved artifact

ESTABLISHED reinterpretation This is the model case of a successfully demoted assumption, and the template for the rest. For decades, renormalizability was treated as a non-negotiable selection rule on fundamental Lagrangians. Wilson's RG dissolved this: irrelevant operators are suppressed as $(E/\Lambda)^{n}$ , so low-energy renormalizability is an emergent consequence of integrating out high scales, not an axiom. Non-renormalizable EFTs (chiral perturbation theory, Fermi theory, gravity-as-EFT, the SM-as-EFT with dimension-6 operators) are perfectly predictive. That a "sacred" requirement turned out to be a derived organizing fact is the strongest existence-proof that other "fundamental" assumptions can be artifacts.

C.3 External / preferred time (A-19, QM-6, CO-12) — a regime inheritance

INFERENCE Time as an external c-number parameter is an inheritance of non-relativistic, fixed-background thinking. Pauli's theorem ( $t$ cannot be a self-adjoint operator conjugate to a bounded-below $H$ ) shows the $x$ / $t$ asymmetry is structural to NRQM, not to nature; the Wheeler–DeWitt constraint $\hat H|\Psi\rangle=0$ is timeless; and relational schemes (Page–Wootters, partial observables) recover dynamics as correlations with a clock subsystem. Cosmic time (CO-12) is the same artifact wearing a cosmological hat: FLRW's high symmetry singles out the CMB frame, but in a realistic inhomogeneous universe no global cosmic time exists. This is a domain-of-validity issue, not a contradiction — but the routine "fundamental time" framing is artifactual.

C.4 Energy conditions (GR-7) and the second law's absoluteness (TH-4) — laws that are really regime statements

CONTESTED Two classic "laws" that are actually regime-restricted. The pointwise energy conditions are hypotheses of the singularity, area, and censorship theorems — yet quantum fields violate them (Casimir, Hawking, squeezed states), and the strong energy condition is violated by both inflation and the observed $\Lambda>0$ . They survive only in averaged/quantum form (ANEC, QNEC). Likewise, the exceptionless second law is a macroscopic-limit shadow of a statistical law: the fluctuation theorem $P(+\Sigma)/P(-\Sigma)=e^{\Sigma/k_B}$ makes transient entropy decreases exponentially rare but nonzero, and Crooks/Jarzynski promote the inequality to an exact equality over trajectory ensembles. Neither is a logical inconsistency — each is a precise idealization mistaken for an absolute.

C.5 The cosmological constant as a constant (GR-8, A-18) — the anomaly hiding in a "fundamental" label

OPEN/CONTESTED Treating $\Lambda$ as a fixed constant of nature is the minimal Lovelock-allowed choice, but it sits atop the worst quantitative mismatch in physics: the observed value is $\sim 120$ orders of magnitude below naive QFT vacuum-energy estimates, and this is the place where EFT decoupling (A-18) demonstrably fails. Calling $\Lambda$ "fundamental" papers over whether it is vacuum energy, anthropically selected, or a dynamical field (quintessence) — with recent surveys hinting (not establishing) at evolving dark energy. This is the artifact-suspect with the highest stakes for observational cosmology. See OPEN_PROBLEMS.md.

C.6 The classical least-action principle (A-15, CM-4) and the path-integral "measure" (MA-8)

INFERENCE The principle of least (really stationary) action looked teleological and fundamental for two centuries; its modern status is derived as the $\hbar\to0$ stationary-phase limit of the path integral. Conversely, the path-integral "measure" $\mathcal D\phi\,e^{iS}$ that grounds it is itself not a measure in any rigorous sense in $d=4$ (MA-8) — a productive abuse of notation whose rigorous content lives in Euclidean reflection-positive measures and analytic continuation. So a "fundamental" classical principle rests on a quantum object that is itself a heuristic: a two-layer reminder that organizing principles and their mathematical encodings can both be effective rather than primitive.

C.7 The gauge "principle" (QFT-7, MA-5) — physical content vs heuristic framing

CONTESTED interpretation "Interactions arise by gauging a symmetry" is enormously productive but is a heuristic, not a law: gauge symmetry is a redundancy of description (Elitzur's theorem forbids its spontaneous breaking; observables are gauge-invariant), and the same physics is expressible via gauge-invariant Wilson loops or bundle/connection geometry (MA-5, which is fundamental as a mathematical identity). The artifact is the framing as a symmetry principle; the physical core (massless-spin-1 consistency, charge conservation, the physical bundle topology probed by Aharonov–Bohm) is real. Recent large-gauge/soft-charge work refines rather than refutes this.

C.8 Honest non-suspects

INFERENCE Equally important is what is not an artifact, lest the page over-correct: microcausality (A-1), unitarity (A-2), diffeomorphism invariance (GR-5), the symplectic structure (CM-5), self-adjointness (MA-2), molecular chaos as the locus of irreversibility (SM-4), the third law (TH-6), anomaly cancellation (PP-3), and Shannon/Landauer (IT-1, IT-5) all survive scrutiny as genuinely fundamental within their domains. The discipline is to demote what deserves demotion without inflating skepticism into a blanket suspicion of structure.

D. How to use this ledger

When a page on this wiki invokes an assumption, cite its ID (e.g. "assuming A-1 microcausality") so contradictions and dependencies stay traceable.
A claim that relaxing an assumption resolves a tension belongs in HYPOTHESES.md; a claim that two assumptions are jointly inconsistent belongs in GAPS_AND_CONTRADICTIONS.md; a genuinely unresolved assumption belongs in OPEN_PROBLEMS.md.
The dependency chain A-1 + A-2 + A-6 $\Rightarrow$ A-7 (CPT) is the canonical worked example of an assumption that is a theorem given others — use it as the template when assessing whether a "fundamental" posit is actually derivative.

New assumptions and sharpenings from the iteration-2 tracks (see notes/), each refereed.

A-20 — "Our universe is asymptotically eternal de Sitter with constant $\Lambda$ ." Classification: historical-artifact / modeling-choice [CONTESTED]. DESI DR2 (2025) prefers dynamical $w_0w_a$ CDM dark energy at 2.8–4.2σ ( $w_0>-1$ , $w_a<0$ , phantom crossing), and the swampland/TCC conjectures disfavor stable eternal dS. If relaxed: the "no unitary eternal-dS dual" obstruction partly dissolves and the holographic/emergence target shifts to metastable dS or rolling quintessence (raising the bar to reproducing a dynamical $w(z)$ ). [→ OP-42, notes, domains/cosmology.md]
A-21 — The horizon area-entropy law $S=A/4\ell_P^2$ is an INPUT to the entropic-gravity derivations. Classification: mathematical-convenience / load-bearing-input [INFERENCE]. Jacobson, Padmanabhan, Verlinde, and Jacobson's entanglement-equilibrium route all assume area-proportional entropy (directly, via screen bit-counts, or via vacuum entanglement); recovering Einstein's equations from it is a consistency / equation-of-state result, not a microscopic explanation. Caveats: Sakharov induced gravity instead outputs the area law; in AdS/CFT, Ryu–Takayanagi derives it. If relaxed (microscopic origin found): would convert the entropic programs from analogy to physics (OP-45). [→ notes]
A-22 — Measurement non-contextuality of probabilities (Gleason's premise). Classification: plausibly-fundamental, but substantive [ESTABLISHED as the premise; its necessity is interpretation-dependent]. The probability assigned to a projector is independent of which orthogonal resolution completes it — distinct from Kochen–Specker non-contextuality of values, and rejected by contextual hidden-variable theories (Bohm). The "Born form is forced" conclusion is conditional on it. [→ OP-43, notes]
A-23 — Geometric modular flow imported at the interpretation stage of the crossed-product program. Classification: mathematical-convenience / hidden-input [CONTESTED diagnosis]. The crossed product itself is purely algebraic (Connes–Takesaki; a Killing horizon is not required for its existence). But every semiclassical construction reproducing $S_{\rm gen}$ uses a state with geometric modular flow (Bisognano–Wichmann boost; Hislop–Longo/CHM for special regions). For generic (algebra, state) pairs modular flow is non-local, and no derivation of geometry from genuinely non-geometric modular flow has been shown — the precise sense in which geometry is quietly imported into "algebra-before-geometry." [→ OP-46, notes]

Refinements to existing assumptions:

A-3 (exact linearity of QM) — sharpened. Generic deterministic nonlinear modifications of the Schrödinger equation permit superluminal signalling (Gisin 1990; Polchinski 1991; reaffirmed Bielińska–Eckstein–Horodecki 2024), so for deterministic dynamics exact linearity is derivative of no-signaling [INFERENCE, strong], not primitive. The live exception is stochastic objective collapse (GRW/CSL, Diósi–Penrose), which evades the deterministic no-go and is untested-empirically at the macroscopic-superposition scale. Reclassify as plausibly-fundamental-but-derivative; empirically open at the collapse scale. [→ notes]
A-4 / QM-3 (Born rule) — sharpened. The form $p=\mathrm{Tr}(\rho E)$ is forced by Gleason (dim≥3) and Busch / Caves–Fuchs–Manne–Renes (dim=2, POVM version, at the price of additivity over all compatible effects) — the qubit case is not unconstrained. A 2026 rigidity theorem (Torres Alegre, arXiv:2602.09056 [preprint, verified real, not peer-reviewed]) extends this Born-form rigidity to infinite-dimensional normal state spaces via no-signaling + normal steering ( $\sigma$ -additive GHJW) + $\sigma$ -affinity, but presupposes the von Neumann-algebra scaffold — relocating, not dissolving, the foundational question. The residual open content is strictly the quantitative-probability problem (OP-43), conditional on A-22. [→ notes]

Iteration 3 note (2026-06-08)

Qualify the Type III₁ "fixed core." Iteration 3's red-team flags that "local QFT algebras are Type III₁ for any Λ" — used as a fixed anchor of the demotion-and-derivation posture — holds ESTABLISHED only for QFT on a fixed background. Once gravity is dynamical, gravitational dressing alters the algebra at leading order in $G_N$ (Giddings arXiv:2505.22708, 2510.24833), so as a core of the gravitational theory it is OPEN/CONTESTED (see OP-44, A-23). Broader lesson: the posture's "fixed cores" are heterogeneous — each conditional on a stated background or premise (area law is an input only for the Jacobson–Padmanabhan–Verlinde lineage; no-signaling is shared but not quantum-forcing; unitarity is conditional on standard QM and violated by GRW/CSL). [→ notes, FINDINGS.md § Iteration 3 update]

References

See BIBLIOGRAPHY.md for canonical sources underlying the claims above — including standard treatments of microcausality, spin–statistics, and CPT (Streater–Wightman; Weinberg, The Quantum Theory of Fields Vol. I); Gleason's theorem and quantum foundations; Wilson's renormalization group; Lovelock's theorem; the fluctuation theorems (Jarzynski, Crooks); the Ryu–Takayanagi formula and AdS/CFT; the $\phi^4_4$ triviality result (Aizenman–Duminil-Copin); and the standard cosmological concordance analyses. Specific experimental bounds (e.g. weak-EP tests, $N_{\rm eff}$ , $\alpha$ -variation) are quoted at the precision stated in the primary literature; consult BIBLIOGRAPHY.md before citing exact figures.