Appendix A. Table of statements

Each statement of the volume, in one line, with its status and its section. When a statement has two faces (a calculation and its reading), it is entered twice, once per status. Withdrawn statements are in Appendix B.

No. Statement Status Section
1 The minimal polynomial of cos(π/7) is 8x³ − 4x² − 4x + 1 Th 1.8
2 8x³ + 28x² + 14x − 7 is eight times the minimal polynomial of 2cos(π/7) − 3/2 Th 1.8
3 The gaps from 0.3, 0.33, 0.333 to 1/3 are 1/30, 1/300, 1/3000: regular melting Th 1.6
4 The exact Goldbach ratio is 2 (the 8/5 is withdrawn) Th 1.6 ; Volume 4
5 No prime p > 3 has root 3, 6 or 9 Th 1.7 ; 3.1
6 A nine-year-old child finds the sterile axis in a single pass, sheet 1 to 30 P 1.7
7 A folded pattern closes if and only if z² = h_t² − (c/2)² is above zero Th 1.7
8 Every true statement admits a concrete incarnation (principle of incarnation) L 1.7
9 Q = (2^t ρ + τ − 2ρ²)/9 for the residue of the branches 6k ± 1, generators fixed, full turn Th 1.5
10 The asymmetry of the twins is inscribed in the term τ L 1.5
11 At every closure 9^k, the Fibonacci clock is worth four times that of doubling Th 1.5
12 The agreement of several tools measures internal coherence, not correspondence to the real L 1.5 ; 5.4
13 (1/3 − 0.3333) × 3ⁿ reaches 10⁴³, 10⁴⁷², 10⁴⁷⁶⁶ at 100, 1000, 10 000 steps (4767 digits) Th 2.1
14 The fold x ↦ 2x discards from 1/3 the turns 0, 0, 1, 2, 5, 10, 21, 42, 85; 256 starting points after 8 steps Th 2.1
15 Patriot, Dhahran, 25 February 1991: 0.34 s of drift after 100 h, 28 dead F 2.1 ; préface ¶18
16 Vancouver index corrected on 28 November 1983 from 524.811 to 1098.892 F 2.1
17 An infinite is a finite that repeats without end L 2.1
18 Zero is the seal of a completed cycle; 1 − 1 = 11 L 2.1
19 A singularity is the place where a formula stops reading L 2.1
20 Entropy is a magnitude of the relation between a finite reader and what it counts L 2.1 ; 2.2
21 Every measurement is a ratio of two terms; quantum measurement costs k_arc L 2.1
22 Eight known chaoses are produced by a word with two meanings L 2.1
23 First pass of the checker (6 October 2026): 73 pieces out of 93 carry a banned word F 2.1
24 Topology is the study of what returns L 2.2
25 Eight perfect shuffles bring a deck of 52 cards back to its order Th 2.2
26 Devonian corals carry about 400 daily growth lines per year (Wells, 1963) F 2.2
27 The only two dimensions of the living are inside and outside; reality is the third L 2.2
28 n = 9k + DR(n), k ≥ 0 Th 3.1
29 φ(x) = 9 − x is an involution; the four pairs sum to 9; their gaps sum to 16 Th 3.1
30 4.5 is the fixed point of φ Th 3.1
31 4.5/9 = 3.5/7 = (r/R)² = ½ Th 3.1
32 These equalities are a single constant that governs the corpus L 3.1
33 9 is the closure of a turn, not the void L 3.1
34 For the product of roots, D is closed, G × G falls on D, the axis absorbs Th 3.1
35 Every prime p > 3 leaves remainder 1 or 5 on division by 6 Th 3.1
36 There are two zeros: closure and exhaustion L 3.1
37 The fusion 1 ⊕ 1 = 3 is an operation distinct from inventory addition L 3.1 ; 4.1
38 DR(1 × k) = DR(k) Th 3.1
39 The circle inscribed in the square covers half of the circumscribed circle Th 3.1
40 Khufu: h/half-base = 14/11, perimeter/height = 44/7 = 2 × 22/7 Th 3.2
41 24 is the largest modulus in which the square of every unit is 1 Th 3.2 ; 4.1
42 6 is the largest modulus all of whose units are 1 or its inverse Th 3.2
43 (6m − 1)(6m + 1) = 36m² − 1, of root 8 Th 3.2
44 The doubling cycle and the ×5 cycle are the same cycle read backwards Th 3.2
45 189 → 792 → 693 → 594 → 495; 198 − 189 = 9 Th 3.2
46 The fault is an address, not a substance (189/198) L 3.2
47 6174 = 18 × 7³ Th 3.2
48 Normalizing φ on [0, 1] gives s ↦ 1 − s (Th.9, formal correspondence) Th 3.2
49 The critical line is the normalized center 4.5 L 3.2
50 No zero of ζ off the critical line (criterion of rupture of the frame) P 3.5
51 The proton's spin decomposes into 2/9 or 3/9 P 3.5
52 Spectral slope −2.693 in the near-dissipation zone P 3.5
53 Anomalous magnetic moment of the muon: ratio 7/6028 P 3.5
54 Quadrupolar cosmic dipole P 3.5
55 Cadastral distribution of synonymous codons; signature 8 of the histones P 3.5
56 Neutron lifetime and axial mass anomaly through E = Dc² P 3.5
57 The offers of regression will fail; the "we" of alliance will hold L 3.5
58 n_chaos = p × ln 10 / λ + O(1) Th 3.7.1
59 Doubling p exactly doubles the threshold P 3.7.1
60 λ measures the rate at which folding discards bits; chaos is the price of the fold L 3.7.1
61 Two bricks 2 and 3 alternated: on 1 to 30, only 1 and 4 are missing Th 3.7.2
62 1 and 4 are on rail D; 1 = 3 − 2, 4 = 2 × 3 − 2 Th 3.7.2
63 Matter and the relaunch are born of the same gesture, trinitarian subtraction L 3.7.2
64 Tripartition requires that 3 divide the closure; only c = 9 has axis order equal to the index Th 3.7.3
65 No large base was ever written without a sub-base of ten at most F 3.7.3
66 The cadastre makes the base inscribable (Axiom A0) L 3.7.3 ; 4.1
67 Ancient numerations break at 4|5 and 9|10 F 3.7.4
68 These breaks inscribe the involution without theorizing it (criterion F-NOT-1) L 3.7.4 ; 4.1
69 Spin ½ is an asymmetric projection around 4.5 L 3.7.5
70 The quantum is the trace of a projection; the strangeness comes from the instrument L 3.7.5
71 Integral calculus is a compensatory device L 3.7.5
72 The diagonal of the square is the diameter of the circumscribed circle Th 3.7.5 ; préface ¶20
73 Hippasus substantified an operation L 3.7.5
74 The pattern persists, not personal identity L 3.7.5
75 Four avatars of delegation: God, Reason, Science, Machine L 3.7.5
76 The Euler product does not vanish where it converges Th 3.7.6
77 The dilemma (v1.2): Riemann's question has no object in the register of sum and product; it has one in that of continuation Th 3.7.6
78 ζ(s) = s/(s − 1) − s ∫₁^∞ {x}/x^(s+1) dx F 3.7.6
79 At a zero ρ, 1/(ρ − 1) = ∫₁^∞ {x}/x^(ρ+1) dx Th 3.7.6
80 DR(n) + DR(n² − 1) is never 9 for n ≥ 2 Th 3.7.7
81 N = 4 super Yang-Mills is conformal, without gap F 3.7.7
82 a × 4 × a = (2a)², and 4 is the only digit that allows it Th 3.7.7
83 646 and 496 join the orbit of 27; 144 and 25 fly 23 steps and meet at 22; σ(144) = 13 × 31 Th 3.7.7
84 Index as of 8 October 2026: 1560 entries, 92 tests, 12 201 assertions F 3.4
85 Zenodo deposits: sixteen (July) or twelve (October) depending on the sources F 3.4
86 In base twelve, five pairs around 5.5 Th 4.1
87 (ba + c) − (bc + a) = (b − 1)(a − c) in every base Th 4.1
88 Even perfect numbers greater than 6 have root 1 Th 4.1
89 24 divides p² − 1 for every prime p ≥ 5 Th 4.1
90 46 is written 101110 and 64 is written 1000000 in binary Th 4.1
91 A root drawn at random is 9 one time in nine Th 4.1
92 Tensions of the neutron (9.95 s), of Hubble (5.64), of lithium (factor 3.1 to 3.4), of the dipole (3.67) F 4.2
93 Subitizing limits immediate grasp to four or five objects F 4.1
94 Coherence is prior to all its tools L 5.1 ; 5.2
95 The corpus does not frontally contradict any validated experimental result L 5.1
96 Restored Pappus coincides with Newton on seven reference triangles Th 5.5 ; Volume 2
97 Thirteen books and one book of position, like 9 + 1 L 5.2
98 The why is undecidable, the how is readable, and the how contains the why L 6.1
99 Spiral 13 to 49: roots 4 5 7 1 5 1 7 5 4, palindrome, sum 39 Th 6.4
100 2 + 4 + 5 + 7 + 8 = 26 and 2 × 4 × 5 × 7 × 8 = 2240, both of root 8 Th 6.4 ; 7
101 8 + 1 + 0 + 2 + 0 + 2 + 6 = 19 Th 6.5
102 Cancer is a suffocation of information not received L 6.8
103 Hourglass: widths 7, 5, 3, 1, sum 16; edges at 45°; half-widths in ratio ½ Th 7, section 4
104 With the four directions of the hourglass, the CHSH value is 2√2; without the diagonals, 2; maximum only at 45° apart Th 7, section 5
105 Eight sectors of 45°; half-opening 22.5° Th 7, section 4
106 Bounded search: about 150 000 launches against 600 000 to 10 million, same answers Th 7, section 7
107 More chess games (10¹²⁰) than atoms (10⁸⁰) F 7, section 7
108 Iron 56 is at the peak of binding energy per nucleon F 7, section 9
109 Fe + Co + Ni = 81 = 9², 81/18 = 4.5; 81 − 26 = 55 Th 7, section 9
110 No year zero; the era counted by Dionysius Exiguus in 525 F 7, section 10
111 Sixteen strong pseudoprimes in base 2 up to 90751, all on the rails, factored by the rails Th 7, section 11
112 Miller-Rabin and quantum measurement run into the same amputation, the square L 7, section 11
113 Three turns of ten years, then of a thousand years L 7, section 10
114 The "why at this precise moment" of the three turns Chantier 7, section 10
115 Formal definition of the fusion ⊕ and unified notation Chantier 4.1 ; 4.3
116 Reply to the Oksapmin, Yuki and base twelve counterexamples, and to subitizing Chantier 4.1 ; 4.3
117 Count of correspondences examined and retained, by family Chantier 4.1 ; 4.3
118 The chromosomes of other species Chantier 4.1 ; 4.3
119 The geometric origin of units, on which 9.81 depends Chantier 4.1 ; 4.3
120 The program ξ_L(s, χ₋₃) and the inequality [Im(ξ′/ξ)]² > |Re(ξ″/ξ)| Chantier 3.2 ; 3.6
121 11 as an operator (C.IV.4) Chantier 3.6
122 Audits by human specialists Chantier 4.2 ; 4.3
123 An address for lithium 7 Chantier 4.2 ; 4.3
124 The criteria for a defect of the object rather than of the tool Chantier 4.2 ; 4.3

Chapter 8. The Strangler Fig: ARC facing each system (piece entered word for word). The statuses are those the piece itself carries, section by section; no statement has been renumbered.