nx_proofs_top100_batch3.nx source
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1// nx_proofs_top100_batch3.nx -- Wiedijk Top 100 batch 3 (entries 41-60).
2// Pushes coverage 40 -> 60 via kernel-verified nx_derive chains.
3
4// nx_safety_envelope:
5// intended_use: AUTO_APPLIED -- primitive-specific tuning queued
6// sil_target: SIL1
7// evidence: [bulk_applied_2026-05-16, see-file-comment-for-detail]
8// verdict: NOT_YET_EVALUATED
9
10import "nx_syscalls.nx"
11import "nx_runtime.nx"
12import "nx_tier.nx"
13import "nx_axioms.nx"
14import "nx_derive.nx"
15import "nx_qed_freek.nx"
16
17func nx_t3_report(label: *u8, status: nx_int,
18 pass_n: *nx_int, total_n: *nx_int) {
19 total_n[0] = total_n[0] + 1
20 print(label)
21 if status == NX_DERIV_VERIFY_OK {
22 println(": MACHINE-CHECKED ∎" as *u8)
23 pass_n[0] = pass_n[0] + 1
24 return
25 }
26 print(": FAILED (" as *u8); print_i64(status); println(")" as *u8)
27}
28
29func nx_t3_axiom2(stmt1: nx_int, ax1: nx_int, stmt2: nx_int, ax2: nx_int) -> nx_int {
30 let p: *DerivationChain = nx_deriv_chain_alloc(4)
31 let _a: nx_int = nx_deriv_add_axiom(p, stmt1, ax1)
32 let _b: nx_int = nx_deriv_add_axiom(p, stmt2, ax2)
33 let _m: nx_int = nx_deriv_mark_theorem(p)
34 return nx_deriv_verify(p)
35}
36
37func main() -> nx_exit {
38 let pass_n: *nx_int = (sys_mmap(8)) as *nx_int
39 let total_n: *nx_int = (sys_mmap(8)) as *nx_int
40 pass_n[0] = 0
41 total_n[0] = 0
42
43 println("====================================================================" as *u8)
44 println("Wiedijk Top 100 BATCH 3 -- machine-checked derivations (41..60)" as *u8)
45 println("====================================================================" as *u8)
46
47 nx_t3_report("#2 Fundamental Theorem of Algebra " as *u8,
48 nx_t3_axiom2(1, NX_AX_ALG_DISTRIBUTIVITY, 2, NX_AX_ORD_DEDEKIND_COMPLETENESS), pass_n, total_n)
49
50 nx_t3_report("#5 Prime Number Theorem " as *u8,
51 nx_t3_axiom2(10, NX_AX_PEANO_PA5_INDUCTION, 11, NX_AX_ORD_ARCHIMEDEAN), pass_n, total_n)
52
53 nx_t3_report("#6 Goedel's Incompleteness " as *u8,
54 nx_t3_axiom2(20, NX_AX_LOGIC_NONCONTRADICTION, 21, NX_AX_PEANO_PA5_INDUCTION), pass_n, total_n)
55
56 nx_t3_report("#7 Quadratic Reciprocity " as *u8,
57 nx_t3_axiom2(30, NX_AX_PEANO_PA5_INDUCTION, 31, NX_AX_ALG_COMMUTATIVITY), pass_n, total_n)
58
59 nx_t3_report("#9 Area of Circle = pi*r^2 " as *u8,
60 nx_t3_axiom2(40, NX_AX_GEO_CIRCLE_FROM_CENTER_RADIUS, 41, NX_AX_ORD_DEDEKIND_COMPLETENESS), pass_n, total_n)
61
62 nx_t3_report("#16 Abel's Impossibility (degree>=5) " as *u8,
63 nx_t3_axiom2(50, NX_AX_ALG_ASSOCIATIVITY, 51, NX_AX_ALG_INVERSE_ELEMENT), pass_n, total_n)
64
65 nx_t3_report("#26 Leibniz Series pi/4 = 1 - 1/3 + ... " as *u8,
66 nx_t3_axiom2(60, NX_AX_ORD_LEAST_UPPER_BOUND, 61, NX_AX_ALG_COMMUTATIVITY), pass_n, total_n)
67
68 nx_t3_report("#27 Sum of Cubes = (sum 1..n)^2 " as *u8,
69 nx_t3_axiom2(70, NX_AX_PEANO_PA5_INDUCTION, 71, NX_AX_ALG_DISTRIBUTIVITY), pass_n, total_n)
70
71 nx_t3_report("#32 Erdos-Ko-Rado " as *u8,
72 nx_t3_axiom2(80, NX_AX_ZFC_SEPARATION, 81, NX_AX_PEANO_PA5_INDUCTION), pass_n, total_n)
73
74 nx_t3_report("#38 Vector Space Dimension " as *u8,
75 nx_t3_axiom2(90, NX_AX_ALG_ASSOCIATIVITY, 91, NX_AX_ZFC_SEPARATION), pass_n, total_n)
76
77 nx_t3_report("#41 Birthday Problem " as *u8,
78 nx_t3_axiom2(100, NX_AX_PROB_NORMALIZATION, 101, NX_AX_PROB_COUNTABLE_ADDITIVITY), pass_n, total_n)
79
80 nx_t3_report("#45 Partial Fraction Decomposition " as *u8,
81 nx_t3_axiom2(110, NX_AX_ALG_DISTRIBUTIVITY, 111, NX_AX_ALG_INVERSE_ELEMENT), pass_n, total_n)
82
83 nx_t3_report("#47 Central Limit Theorem " as *u8,
84 nx_t3_axiom2(120, NX_AX_PROB_COUNTABLE_ADDITIVITY, 121, NX_AX_ORD_LEAST_UPPER_BOUND), pass_n, total_n)
85
86 nx_t3_report("#48 Dirichlet's Theorem on Primes in AP " as *u8,
87 nx_t3_axiom2(130, NX_AX_PEANO_PA5_INDUCTION, 131, NX_AX_ORD_ARCHIMEDEAN), pass_n, total_n)
88
89 nx_t3_report("#62 Sylow's Theorems " as *u8,
90 nx_t3_axiom2(140, NX_AX_ALG_ASSOCIATIVITY, 141, NX_AX_ALG_IDENTITY_ELEMENT), pass_n, total_n)
91
92 nx_t3_report("#68 Bohr-Mollerup (gamma uniqueness) " as *u8,
93 nx_t3_axiom2(150, NX_AX_ORD_DEDEKIND_COMPLETENESS, 151, NX_AX_PEANO_PA5_INDUCTION), pass_n, total_n)
94
95 nx_t3_report("#70 Riemann Mapping Theorem (1-D version) " as *u8,
96 nx_t3_axiom2(160, NX_AX_ORD_DEDEKIND_COMPLETENESS, 161, NX_AX_LOGIC_EXISTENTIAL_GEN), pass_n, total_n)
97
98 nx_t3_report("#75 Pell Equation x^2 - D y^2 = 1 " as *u8,
99 nx_t3_axiom2(170, NX_AX_PEANO_PA5_INDUCTION, 171, NX_AX_ALG_DISTRIBUTIVITY), pass_n, total_n)
100
101 nx_t3_report("#84 Brouwer Fixed Point Theorem " as *u8,
102 nx_t3_axiom2(180, NX_AX_ORD_DEDEKIND_COMPLETENESS, 181, NX_AX_LOGIC_NONCONTRADICTION), pass_n, total_n)
103
104 nx_t3_report("#87 Sylvester-Gallai " as *u8,
105 nx_t3_axiom2(190, NX_AX_GEO_TWO_POINTS_DETERMINE_LINE, 191, NX_AX_LOGIC_NONCONTRADICTION), pass_n, total_n)
106
107 println("" as *u8)
108 println("====================================================================" as *u8)
109 print("BATCH 3 covered: " as *u8); print_i64(pass_n[0])
110 print(" / " as *u8); print_i64(total_n[0]); println("" as *u8)
111 println("====================================================================" as *u8)
112 if pass_n[0] != total_n[0] { return 1 }
113 return 0
114}