A meta-scientific framework for classifying the empirical closure status of known physical "laws"/"formula" using independent observational constraints

A meta-scientific framework for classifying the empirical closure status of known physical "laws"/"formula" using independent observational constraints as per ICF method. The gap told us exactly what the next theory needed to do: The deductive structure is a three-step algorithm the ICF framework already defines: Where do independent constraints fail or diverge? (locate the gap) What new quantity would need to become an independent observable to close that gap? (identify what's missing) The next theory must do exactly that , nothing more, nothing less. (the necessary condition) DESCRIPTION This registry provides a comprehensive, systematic classification of 87 fundamental physics formulas across eight major sectors, evaluated strictly by their empirical constraint status. The work applies the Independent-Constraint Framework (ICF), a methodological tool for assessing whether physical relations are sufficiently determined by independent observational measurements. What this Registry contains 1. Master Formula Table (87 formulas) A complete inventory of fundamental relations across: Classical Mechanics (7 formulas) Special Relativity (6 formulas) General Relativity (10 formulas) Gravitational Waves (5 formulas) Quantum Mechanics (7 formulas) Thermodynamics (4 formulas) Nuclear & Particle Physics (4 formulas) Cosmology - ΛCDM (8 formulas) Each entry specifies: Formula name and mathematical expression Domain of validity Number and type of independent empirical constraints ICF status: CLOSED (≥2 independent constraints), PARTIAL, or GAP Empirical verification references 2. Gap Registry (12 entries) A structured classification of all identified gaps in physics, categorized into four types: Type 1 - Measurement Impossibility Gaps where the physical setup prevents observational access by construction (e.g., black hole interior, pre-Big Bang state) Type 2 - Technical Limitation Gaps where measurement is theoretically possible but currently infeasible due to technological constraints (e.g., Hawking radiation detection, single graviton detection, Planck-scale physics) Type 3 - Constraint Conflict Gaps where multiple validated measurement methods produce incompatible results (e.g., H₀ tension at 5σ, S₈ tension at 3σ, lithium abundance problem) Type 4 - Theoretical Incompatibility Gaps where two well-validated theories make contradictory assumptions about the same regime (e.g., quantum mechanics vs. general relativity at the Planck scale) 3. ICF Transition Chain A logical reconstruction of theory succession showing exactly where and why each major theoretical extension was required: Newton → Special Relativity (constraint failure at v/c ≥ 10⁻⁴) Special Relativity → General Relativity (gravity as independent observable) General Relativity boundary (ρ → ρ_Planck) Quantum Mechanics boundary (spacetime becomes dynamical) QM + GR → Quantum Gravity (unresolved) Each transition is documented with: The specific constraint that failed The empirical observation that forced the extension The new observable required by the successor theory ICF proof that the extension was necessary 4. Sector Summary Quantitative overview of constraint status by sector, including total formulas, complete vs. partial vs. missing, and assessment of sector closure. Methodology: The Independent-Constraint Framework (ICF) Core Principle A physical relation is classified as CLOSED only when at least two conceptually independent empirical constraints restrict its free parameters within a specified domain. Independence means the constraints probe different physical aspects or use different measurement techniques. Classification Criteria CLOSED (Complete) ≥2 independent empirical constraints exist Constraints agree within measurement uncertainty Domain of validity clearly defined Status: empirically determined within stated regime PARTIAL GAP Some constraints exist but insufficient for full determination May indicate incomplete measurement coverage or constraint tension GAP (Missing) Zero independent constraints available, OR Fundamental measurement impossibility, OR Constraint conflict that cannot be resolved with existing data What ICF Terminology neans The terms used throughout this work—"closed," "complete," "missing," "gap," "validated", are employed in a strictly procedural and methodological sense related to empirical constraint structure. These terms refer ONLY to: The degree of observational constraint on theoretical relations within specified physical regimes Whether at least two observationally distinct empirical constraints restrict free parameters These terms do NOT imply: Ultimate truth or final completeness Freedom from deeper conceptual limitations Immunity to future empirical revision Metaphysical or ontological claims about reality A relation described as "closed" means constraint sufficiency: at least two independent observational methods restrict its parameters in the stated domain. The word "complete" denotes internal consistency with available constraints, not fundamental completeness. All classifications are provisional, regime-dependent, and subject to revision with new observations, improved measurements, or theoretical advances. Key findings Well-Constrained Sectors Classical mechanics: Fully closed with 3+ independent constraints per formula Special relativity: Fully closed in inertial frames General relativity: Closed for exterior spacetime with 6+ independent constraints (perihelion precession, gravitational lensing, gravitational waves, time dilation, Shapiro delay, frame-dragging) Quantum mechanics: Closed for fixed-background spacetime with 10+ independent constraints Standard Model: Closed with 100+ constraints, >99.99% agreement Critical Tensions H₀ tension (5σ): CMB vs. distance ladder measurements disagree—genuine constraint conflict requiring resolution S₈ tension (3σ): CMB vs. weak lensing clustering amplitude—real discrepancy between independent probes Lithium problem: BBN prediction vs. observation differ by factor 2.5 Fundamental Gaps Quantum gravity: Largest gap in physics—no independent Planck-scale observables exist; QM and GR make contradictory assumptions about time (parameter vs. observable) Black hole interior: Causally inaccessible—zero constraints possible by construction Pre-Big Bang: No causal access to t < 10⁻⁴³ seconds What this Work is not This registry is not: A new physical theory or model A proposal for unification or quantum gravity An attempt to resolve open problems in physics A claim about the ultimate nature of reality Speculation about future theories This registry is: A systematic audit of empirical constraint status A methodological framework for evaluating theoretical closure A historical reconstruction of theory succession based on constraint failure A taxonomy of gaps by their epistemological character A reference tool for understanding where physics stands empirically Intended Audience Philosophers of science: Interested in theory validation, empirical adequacy, and scientific realism Physicists: Seeking clarity on empirical status of different sectors and open problems Historians of physics: Studying theory succession and the logic of theoretical extensions Graduate students: Learning where physics is well-established vs. uncertain Science communicators: Explaining what physics does/doesn't know and why Strict Methodological Commitments No speculation: Only empirically verified constraints are counted No metaphor: Terms like "closed" and "gap" have precise procedural definitions Domain-specific: All claims specify regime of validity Revision-ready: All classifications subject to change with new data Constraint-counting: Status determined by number and independence of observational constraints, not theoretical elegance or simplicity Usage Notes Users of this registry should understand that: ICF status applies only within specified domains (e.g., "v << c", "weak gravity", "ρ < ρ_Planck") "Closed" means constraint sufficiency, not ultimate truth Gaps are classified by epistemological type, not ranked by importance The registry is a snapshot of empirical status as of January 2026 New observations can change any classification Relation to existing Literature This work draws on but differs from: Van Fraassen's empirical adequacy: ICF requires multiple independent constraints, not just observable agreement Theory succession literature (DiSalle, Norton, Friedman): ICF provides quantitative constraint tracking, not just conceptual analysis Physics validation studies: ICF creates comprehensive cross-theory comparison showing exactly where constraints exist/fail No existing work provides a complete formula-by-formula registry with explicit constraint counts and gap taxonomy. Future Extensions This registry could be extended to include: Astrophysical phenomenology (stellar structure, galactic dynamics) Condensed matter physics (superconductivity, quantum Hall effect) Atomic and molecular physics Plasma physics More detailed constraint analysis for each formula (specific experiments, error bars, historical evolution) Citation If you use this registry in your work, please cite: Sahraoui, N. (2026). ICF Formula Registry: Complete History of All Formulas by Sector.