Appendix A: Table of statements

Every numbered statement of the volume, with its title, its status and its chapter. The title summarizes the statement in one line; the full text is in the chapter.

No. Statement Status Chapter
É1.1 The relational state L 1
É1.2 The measurement protocol with a reading variable Th 1
É1.3 The update is not a signal L 1
É1.4 The pair and its reader L 1
É1.5 E(a, b) = −cos θ Th 1
É1.6 The pure-sign protocol gives S = 4
É1.7 The nine one-symbol quantities Th 1
É1.8 The involution and the constant Th 1
É1.9 The universal fold Th 1
É1.10 Lemma A, the spectral norm Th 1
É1.11 Lemma B, the gain of the diagonal Th 1
É1.12 Lemma C, the universal projection cost Th 1
É1.13 The decomposition of the bound Th 1
É1.14 From factorization to mechanism L 1
É1.15 The geometric mean of the ceilings Th 1
É1.16 The fold between the classical and the formal L 1
É1.17 The two circles Th 1
É1.18 The quantum world fills the maximum as the inner circle fills the outer one L 1
É1.19 The operative meaning of the ceiling L 1
É1.20 No-signaling Th 1
É1.21 The Born rule as geometric compression L 1
É1.22 Entanglement as inversion pair L 1
É1.23 The minimum of the relation L 1
É1.24 What is instantaneous and what is bounded L 1
É1.25 The universality of projection Chantier 1
É1.26 What the model does not do L 1
É1.27 F1, the exact cosine P 1
É1.28 F2, the exact bound P 1
É1.29 F3, the margins P 1
É1.30 F4, the universality of k P 1
É1.31 F5, the two properties of primes Th 1
É1.32 The discipline of the double derivation L 1
É1.33 A.1, the constant k Th 1
É1.34 A.2, the ceiling 2√2 Th 1
É1.35 A.3, the geometric mean of the ceilings Th 1
É1.36 What the three tables establish L 1
É1.37 The geometry of the hourglass Th 1
É1.38 The four directions of the hourglass are the Tsirelson settings Th 1
É1.39 Without the diagonals, the classical bound Th 1
É1.40 The maximum requires the 45° gap Th 1
É1.41 The drawing and the bound L 1
É1.42 S/4 = r/R = √k Th 1
É1.43 Non-locality as grammar L 1
É1.44 The degree of entanglement as position Chantier 1
É2.1 P1, relational priority L 2
É2.2 P2, zero topological distance L 2
É2.3 P3, no ontological randomness L 2
É2.4 P4, structural closure L 2
É2.5 Isotropy as symmetry L 2
É2.6 The topological order T_sys L 2
É2.7 Randomness as projection residue L 2
É2.8 Determinism without superdeterminism L 2
É2.9 The update as memory, not as signal L 2
É2.10 Lorentz invariance L 2
É2.11 Why no operator L 2
É2.12 The echo of the closure L 2
É2.13 The two chambers and their gap Th 2
É2.14 The 3 as ternary invariant L 2
É2.15 The off-center pivot Th 2
É2.16 Spin 1/2 as position L 2
É2.17 The scale of the gap Th 2
É2.18 A discrete scale between matter and relation L 2
É2.19 Entanglement as shared position L 2
É2.20 Antiparallel reflection is the only admissible update Th 2
É2.21 Corollary: determinism Th 2
É2.22 Four frameworks L 2
É2.23 The February criteria P 2
É2.24 The non-standard relational configurations Chantier 2
É2.25 The February conclusion L 2
É3.1 The problem and the four traditions F 3
É3.2 The common presupposition L 3
É3.3 P0, the relational genesis (principle of the wave) L 3
É3.4 P1, relational primacy L 3
É3.5 P2, zero topological distance L 3
É3.6 P3, epistemic randomness L 3
É3.7 P4, structural quantization L 3
É3.8 P5, operative completeness L 3
É3.9 The sequence in six stations L 3
É3.10 Structure precedes geometry L 3
É3.11 The generative engine: the 1 is born of the 3, and the 3 of the stretched 1 L 3
É3.12 Definition: the wave as product of tension L 3
É3.13 Frequency, amplitude, nodes, zeros L 3
É3.14 Superposition and Schrödinger's cat L 3
É3.15 Definition: measurement as binding L 3
É3.16 The passage is invertible L 3
É3.17 The principle of triadic completion L 3
É3.18 The continuity of measurement L 3
É3.19 The roots of the squares at the center Th 3
É3.20 Inversion as elevation L 3
É3.21 Definition: the degree of binding L 3
É3.22 Three graded observations L 3
É3.23 No quantum-classical boundary L 3
É3.24 The standing 1 and the lying 1 L 3
É3.25 The Fourier transform generates a cycle of order 4 F 3
É3.26 Duality as rotation by π/2 L 3
É3.27 Why projection takes place L 3
É3.28 k as cost of the inversion L 3
É3.29 This is not the Zeh and Zurek program under another name L 3
É3.30 Unitarity L 3
É3.31 What triggers the inversion L 3
É3.32 Consciousness is not required L 3
É3.33 The comparative table L 3
É3.34 F1, the graded outcomes P 3
É3.35 F2, the passage rate depends on the direction of the binding P 3
É3.36 F3, the conservation of information P 3
É3.37 F4, the roots in spectral transitions Chantier 3
É3.38 F5, no irreducible discontinuity P 3
É3.39 What the piece does not claim L 3
É3.40 Five open questions Chantier 3
É4.1 The Robertson bound Th 4
É4.2 The Copenhagen reading F 4
É4.3 The reading by projection L 4
É4.4 The arithmetic derivations of k Th 4
É4.5 The geometric path Th 4
É4.6 The path through π Th 4
É4.7 Seven appearances of the factor 1/2 Th 4
É4.8 A single explanation for seven L 4
É4.9 The extended table L 4
É4.10 The unavoidable question L 4
É4.11 Half of the angular information L 4
É4.12 The Flatland tax L 4
É4.13 The canonical relation F 4
É4.14 The non-commutativity of projections L 4
É4.15 The double decomposition of uncertainty L 4
É4.16 The image of the pixel L 4
É4.17 P1, saturation at the Planck scale P 4
É4.18 P1 bis, conforming instruments P 4
É4.19 P2, the universality of k P 4
É4.20 P3, no energy non-conservation in the tunnel P 4
É4.21 The geometry of observation mistaken for the nature of the real L 4
É4.22 A determinism of structure, not of prediction L 4
É4.23 A third position L 4
É5.1 The epistemic protocol of v2.0 L 5
É5.2 Theorem 1, unitarity: nothing is lost Th 5
É5.3 Theorem 2, exponential attenuation Th 5
É5.4 Theorem 3, Hartman saturation Th 5
É5.5 What is contested and what is not F 5
É5.6 Reading 1, the switch L 5
É5.7 The two contact constants frame unity Th 5
É5.8 Reading 2, the complete signature of the switch L 5
É5.9 Decay as subtraction of the two half-rails Th 5
É5.10 Reading 3, the corrected projection law L 5
É5.11 Reading 4, no energy debt L 5
É5.12 Reading 5, Hartman without paradox L 5
É5.13 Theorem 4, frustrated total reflection Th 5
É5.14 Reading 6, frustrated reflection exhibits reading 3 L 5
É5.15 Prediction 1, discrimination on Hartman P 5
É5.16 Prediction 2, no stochasticity intrinsic to the switch P 5
É5.17 Prediction 3, the recovery scale P 5
É5.18 The three falsification conditions P 5
É5.19 Erratum 1: the circular projection law of v1.0 L 5
É5.20 Erratum 2: the framing of v1.0 L 5
É5.21 What is replaced in the piece on Heisenberg L 5
É5.22 There is no forbidden region L 5
É6.1 The statuses declared by the piece L 6
É6.2 The dimension of h Th 6
É6.3 Nature discretizes action in areas L 6
É6.4 Two quantities of the same dimension Th 6
É6.5 Theorem 2.1, the half-integer area Th 6
É6.6 Theorem 2.2, the integer increment Th 6
É6.7 Invariance over twenty-six orders of magnitude Th 6
É6.8 The joints between the numbers L 6
É6.9 Theorem 3.1, the structure of the four pairs Th 6
É6.10 The cross of bipolarization L 6
É6.11 Reading 4.1, the order of traversal L 6
É6.12 The safeguard L 6
É6.13 Theorem 5.1 of the source, the trapezoid encodes depth L 6
É6.14 The six compressions Th 6
É6.15 Liouville's theorem F 6
É6.16 Theorem 6.1 of the source, the invariance of area under deformation L 6
É6.17 The falsification criterion of section 6 P 6
É6.18 The recomposition of the cell Th 6
É6.19 Two readings of the half L 6
É6.20 Reading 7.1, the two halves cross at the joint L 6
É6.21 The half is invisible to any differential reading Th 6
É6.22 Reading 7.2, the position of the half L 6
É6.23 The external constraint: the Casimir force P 6
É6.24 Reading 8.1, the factor 1/2 of the bound is k L 6
É6.25 What this reading does not assert L 6
É6.26 Reading 9.1, requalification and not suppression L 6
É7.1 (i) The frame Th 7
É7.2 (ii) The inversion pairs Th 7
É7.3 (iii) The barycenter Th 7
É7.4 (iv) The axis Th 7
É7.5 (v) The diagonal Th 7
É7.6 (vi) The invariance of the pairs: multiplication never separates the partners Th 7
É7.7 Positions are contingent; pairs are structural L 7
É7.8 (vii) The 9 governs at the three levels Th 7
É7.9 The witness rail L 7
É7.10 The theorem of the two names Th 7
É7.11 A single position read from both ends L 7
É7.12 The double turn of the spinor F 7
É7.13 The property belongs to the binding L 7
É7.14 Spin 1/2 as embodied involution L 7
É7.15 The angles of the polygons Th 7
É7.16 The spin crisis F 7
É7.17 The visible and the hidden L 7
É7.17 bis The empty nucleus carries both L 7
É7.17 ter No spin without chirality, and a single turn L ; F 7
É7.17 quater How the double turn entered physics F ; L 7
É7.18 Confinement F 7
É7.19 The same signature as the axis L 7
É7.20 The gauge decomposition F 7
É7.21 The closure holds back the 1 so that the 8 bind L 7
É7.22 The mass of the proton comes from the binding F 7
É7.23 P0 realized L 7
É7.24 The discriminating test P 7
É7.25 The collapse clause P 7
É7.26 The separation of facts and readings L 7
É7.27 What is missing is the grammar L 7
É8.1 The cascade of six decisions L 8
É8.2 The variant of Principia relationalis L 8
É8.3 The axioms of the alternative L 8
É8.4 "Theorem 4": ħ is a resolution L 8
É8.5 The proposed derivation and its weakness L 8
É8.6 The consequences L 8
É8.7 Exact discretization at the Planck scale P 8
É8.8 "Theorem 5": Heisenberg's 1/2 is k L 8
É8.9 "Theorem 6": the photon is a state interval L 8
É8.10 The double slit and the film L 8
É8.11 The discrete transitions of photon counting P 8
É8.12 The Higgs mechanism and its questions F 8
É8.13 "Theorem 7": mass as topological memory L 8
É8.14 "Theorem 8": dark matter as hidden memory L 8
É8.15 The v1 predictions on mass P 8
É8.15 bis The origin of the term 117 Th, L 8
É8.16 NGC 3198, P to received P 8
É8.17 The Hubble tension, P to received P 8
É8.18 Dark energy as relaxation L 8
É8.19 The complexity of the spectrum F 8
É8.20 "Theorem 9": two topological parameters, k and D L 8
É8.21 No fourth generation P 8
É8.22 The classification table, recalculated Th 8
É8.23 Quarks as geometric corners L 8
É8.24 Gluons as tension L 8
É8.25 The neutron as supersaturated proton L 8
É8.26 The proton-electron unification L 8
É8.27 The parsimony table L 8
É8.28 "Theorem 10": finite sufficiency L 8
É8.29 No experiment beyond the alphabet P 8
É8.30 "Theorem 11": measurement as geometric projection L 8
É8.31 The three pillars of Copenhagen L 8
É8.32 Bell's theorem reread, without being contested L 8
É8.33 The Tsirelson bound, from prediction to theorem Th 8
É8.34 The master table, with the statuses of this volume L 8
É8.35 The inverted cascade L 8
É8.36 The note on 22/7 L 8
É8.37 The position L 8
É8.38 The three criteria of fall P 8
É9.1 A corrupted mathematical grid L 9
É9.2 The ontological inversion L 9
É9.3 The six crimes and the six principles L 9
É9.4 The generative engine L 9
É9.5 Pillar I: completeness and the triple convergence L 9
É9.6 The numbers of the cosmic breathing Th 9
É9.7 Pillar II: the cosmic breathing and the genesis of space L 9
É9.8 The arithmetic of salt and iron Th 9
É9.9 Pillar III: the birth of iron L 9
É9.10 Pillar IV: quantum ontology L 9
É9.11 Pillar V: chaos eradicated and the illusion of dark matter L 9
É9.12 Pillar VI: the matryoshka atom L 9
É9.13 The ontological sequence as engine of everything L 9
É9.14 The table of crossed constants L 9
É9.15 The architecture that protects itself L 9
É9.16 The predictions of Principia, domain by domain P 9
É9.17 A single mathematics L 9
É9.18 The method: the observation of numbers L 9
É9.19 The ten articles of February 2026 F 9
É10.1 The atom redefined L 10
É10.2 Completeness does not divide by two L 10
É10.3 Duality as aspect L 10
É10.4 The self-coding of the root Th 10
É10.5 Numbers are self-coded L 10
É10.6 The immortality of the 9 L 10
É10.7 The doll of 25 L 10
É10.8 The physical atom inherits the structure L 10
É10.9 The infinite expansion as refusal L 10
É10.10 The arithmetic of fission, corrected Th 10
É10.11 The conservation of the root is that of the count L 10
É10.12 The principle of the full turn L 10
É10.13 Energy as stored tension L 10
É10.14 The illusion of infinite divisibility L 10
É10.15 The illusion of the inner void L 10
É10.16 Democritus resolved L 10
É10.17 The accelerator as hammer L 10
É10.18 The conservation of the root of the nucleon number P 10
É10.19 The complete products P 10
É10.20 The refusal of division P 10
É10.21 No ultimate particle P 10
É10.22 The relation is immortal L 10
É11.1 The received framework F 11
É11.2 The diagnosis: the integral is amnesiac L 11
É11.3 "Theorem 1.1": the landscape as amnesia L 11
É11.4 The six axioms of the April piece L 11
É11.5 496 is perfect Th 11
É11.6 Perfection as least tension L 11
É11.7 "Theorem 2.1": the uniqueness of 496 L 11
É11.8 The mirror and the gradient Th 11
É11.9 The barycenter 595 Th 11
É11.10 The two cycles in the gradient L 11
É11.11 The string as mirror relation L 11
É11.12 The fixed point of the mirror Th 11
É11.13 The motionless axis L 11
É11.14 Theorem 3.5: the barycenter is always a palindrome Th 11
É11.15 A law of involution L 11
É11.16 Theorem 3.6: the tension quantum 99 Th 11
É11.17 Quantization as theorem L 11
É11.18 The chirality of the gradient Th 11
É11.19 The sealed string Th 11
É11.20 One involutive grammar, two instances L 11
É11.21 The refutation criteria of the sealing P 11
É11.22 The non-closure of SU(n) Th 11
É11.23 The count of dimensions Th 11
É11.24 The six ratios and the six gaps Th 11
É11.25 The six dimensions as six ratios L 11
É11.26 The two cycles and the quarter turn Th 11
É11.27 The square born of the bricks L 11
É11.28 The pairs 22-23 and 31-32 Th 11
É11.29 The + 1 turns the structure into an assembly L 11
É11.30 The reading rule L 11
É11.31 The eight pieces L 11
É11.32 Theorem 6: the string of the perfect has no inverse Th 11
É11.33 The closure forbids the inverse and imposes the mirror L 11
É11.34 Theorem 7: the 64 and the families 46/64, 496/694 Th 11
É11.35 Theorem 9: the string is 5, 6, 7 at all its levels Th 11
É11.36 Theorem 10: the count 64 Th 11
É11.37 Theorem 11: the paving of equilibrium Th 11
É11.38 The names of the rows L 11
É11.39 Theorem 12: on the axis, doubling is inverting Th 11
É11.40 Theorem 13: three doublings make the inverse, six make the turn, 64 is the return Th 11
É11.41 Theorem 14: the axis restored from the wings Th 11
É11.42 G.1, the vocabulary: mirror and inverse L 11
É11.43 G.2, the polynomial of the heptagon Th 11
É11.44 G.3, the status of Prediction 6.3 L 11
É11.45 What the rewriting closes L 11
É11.46 The rule of the head and the legs L 11
É11.47 The grammar yields the ratio, not the head L 11
É11.48 First contact: the count of generations P 11
É11.49 Second contact: the two lifetimes of the neutron P 11
É11.50 Third contact: the dipoles by tracer Chantier 11
É11.51 Prediction 6.1, uniqueness F 11
É11.52 Prediction 6.2, the collapse of the landscape P 11
É11.53 Prediction 6.3, the dimensional structure L 11
É11.54 Prediction 6.4, the universality of the gradient Chantier 11
É11.55 Prediction 6.5, the ratio 3/2 Th 11
É11.56 Prediction 6.6, the non-closure of SU(n) Th 11
É11.57 The right head with the wrong tool L 11
É12.1 Einstein's sentence F 12
É12.2 The inversion of the sentence and its consequences L 12
É12.3 E = Dc² L 12
É12.4 The three simultaneous conditions L 12
É12.5 Activation is binary; density is not L 12
É12.6 The difference from integrated information L 12
É12.7 The decomposition of D L 12
É12.8 The interface and the axis L 12
É12.9 "Theorem 3.4": first-order equivalence L 12
É12.10 Mass is conserved; density is enriched L 12
É12.11 The trinitarian subtraction L 12
É12.12 Lavoisier preserved and extended L 12
É12.13 Nucleosynthesis as enrichment L 12
É12.14 Channel 1, direct violation P 12
É12.15 Channel 2, the signed systematic residue P 12
É12.16 The MIT-NIST test F 12
É12.17 Channel 3, galactic rotation curves P 12
É12.18 Channel 4 (a), the neutron lifetime: corrected P 12
É12.19 Channel 4 (b), the axial mass anomaly of the nucleon P 12
É12.20 Access through the archives L 12
É12.21 General relativity read in density gradients Chantier 12
É12.22 The status of research program L 12
É13.1 The theorem of Pappus F 13
É13.2 The regular polygon around one of its sides Th 13
É13.3 The arbitrary triangle around one of its sides Th 13
É13.4 The equilateral triangle, where k operates pure L 13
É13.5 The arbitrary polygon, and the limit that remains L 13
É13.6 Arbitrary precision in a closed algebra L 13
É13.7 Solid mechanics as recovery L 13
É13.8 The protocol of generalization P 13
É13.9 Four consequences of the amputation L 13
É13.10 Three and a half centuries above the amputation L 13
É13.11 The cadastral table of the 92 elements Th 13
É13.12 Mendeleev's fold L 13
É13.13 The Ni-Co-Fe triad Th 13
É13.14 The peak of nuclear stability F 13
É13.15 The extremum at position 81 L 13
É13.16 The number 945 Th 13
É13.17 The cosmic descent 945 → 3 Chantier 13
É13.18 The numbers of the couple Th 13
É13.19 The two constants F 13
É13.20 The positions of the couple L 13
É13.21 The three regimes of the couple L 13
É13.22 The two values of the formula Th 13
É13.23 The two measured values F 13
É13.24 The meter of 1791 F 13
É13.25 Planetary gravity as structure L 13
É13.26 Nuclear gravity as binding energy L 13
É13.27 Every planet Chantier 13
É13.28 The LIEM proposition L 13
É13.29 The four projections L 13
É13.30 The cadastral tetrahedron L 13
É13.31 The matter-antimatter asymmetry L 13
É13.32 The dipole of the cosmic background F 13
É13.33 The quadrupole of the four pairs P 13
É13.34 The anomaly as the source reports it F 13
É13.35 The ratio 7/6028 Th 13
É13.36 The reading of a_μ as a closed ratio Chantier 13
É13.37 Why a closed ratio would matter L 13
É13.38 Re(s) = 1/2 = k, and the seven derivations L 13
É13.39 The posture of the cadastral carrier in physics L 13
É13.40 The five open protocols of the book, with their statuses L 13