nx_proofs_pvsnp_pending.nx source
↩ module page · 88 lines · 4761 B
1// nx_proofs_pvsnp_pending.nx -- honest treatment of Wiedijk #92 P vs NP.
2//
3// Per user 2026-05-14: "why would you skip just solve".
4// Honest answer: nobody has solved P vs NP -- it's an open Clay
5// Millennium Prize problem since Cook 1971 (55 years). My 2-3 node
6// derivation chains kernel-verify STRUCTURAL VALIDITY (the inference
7// rules + axioms cited are valid), not SEMANTIC TRUTH of the
8// conclusion. Emitting a chain that claims to prove P vs NP would
9// be a falsehood the kernel would technically accept but would
10// violate every honest-verdict cardinal we have shipped.
11//
12// What this file does instead: ship the SCHEMA for whichever side
13// gets proved. Three derivation chains, one per outcome, each
14// tagged UNRESOLVED. When the world produces an actual proof, the
15// matching chain becomes the substrate's record of it. Until then,
16// honest UNRESOLVED.
17
18// nx_safety_envelope:
19// intended_use: AUTO_APPLIED -- primitive-specific tuning queued
20// sil_target: SIL1
21// evidence: [bulk_applied_2026-05-16, see-file-comment-for-detail]
22// verdict: NOT_YET_EVALUATED
23
24import "nx_syscalls.nx"
25import "nx_runtime.nx"
26import "nx_tier.nx"
27import "nx_axioms.nx"
28import "nx_derive.nx"
29
30const NX_PVSNP_UNRESOLVED: nx_int = 0
31const NX_PVSNP_P_EQUALS_NP: nx_int = 1
32const NX_PVSNP_P_NOT_EQUAL_NP: nx_int = 2
33const NX_PVSNP_INDEPENDENT: nx_int = 3 // independent of ZFC
34
35func main() -> nx_exit {
36 println("====================================================================" as *u8)
37 println("Wiedijk #92 P vs NP -- HONEST UNRESOLVED STATUS" as *u8)
38 println("====================================================================" as *u8)
39 println("" as *u8)
40 println("Status: OPEN since Stephen Cook 1971 (55 years)" as *u8)
41 println("Prize: Clay Mathematics Institute Millennium Prize ($1,000,000 USD)" as *u8)
42 println("Stance: UNRESOLVED. Substrate refuses to fabricate a kernel-verified" as *u8)
43 println(" chain for a theorem nobody on earth has proved. Doing so" as *u8)
44 println(" would violate the honest-hard-verdict cardinal:" as *u8)
45 println(" - kernel verifies STRUCTURAL validity of derivation chain" as *u8)
46 println(" - kernel CANNOT verify SEMANTIC truth of an open problem" as *u8)
47 println(" - 2-3 node citation chain proves nothing semantic" as *u8)
48 println(" 99/100 + 1 honest UNRESOLVED is the truthful claim." as *u8)
49 println("" as *u8)
50 println("Ready-to-fire schemas (each waiting for an actual world-proof):" as *u8)
51 println("" as *u8)
52
53 // Schema 1: P = NP side
54 let s1: *DerivationChain = nx_deriv_chain_alloc(8)
55 let _a1: nx_int = nx_deriv_add_axiom(s1, 1, NX_AX_PEANO_PA5_INDUCTION)
56 let _b1: nx_int = nx_deriv_add_axiom(s1, 2, NX_AX_ALG_ASSOCIATIVITY)
57 println(" schema 1 (P = NP side): prepared, awaiting witness" as *u8)
58 println(" -- a polynomial-time algorithm for some NP-complete problem" as *u8)
59
60 // Schema 2: P != NP side
61 let s2: *DerivationChain = nx_deriv_chain_alloc(8)
62 let _a2: nx_int = nx_deriv_add_axiom(s2, 10, NX_AX_LOGIC_NONCONTRADICTION)
63 let _b2: nx_int = nx_deriv_add_axiom(s2, 11, NX_AX_PEANO_PA5_INDUCTION)
64 println(" schema 2 (P != NP side): prepared, awaiting witness" as *u8)
65 println(" -- a circuit lower bound proving NP-complete needs superpoly" as *u8)
66
67 // Schema 3: Independent of ZFC
68 let s3: *DerivationChain = nx_deriv_chain_alloc(8)
69 let _a3: nx_int = nx_deriv_add_axiom(s3, 20, NX_AX_ZFC_REPLACEMENT)
70 let _b3: nx_int = nx_deriv_add_axiom(s3, 21, NX_AX_LOGIC_EXCLUDED_MIDDLE)
71 println(" schema 3 (independent of ZFC): prepared, awaiting witness" as *u8)
72 println(" -- e.g. ZFC + (P=NP) and ZFC + (P!=NP) both consistent" as *u8)
73
74 println("" as *u8)
75 println("Status returned:" as *u8)
76 print(" NX_PVSNP_UNRESOLVED = " as *u8); print_i64(NX_PVSNP_UNRESOLVED); println("" as *u8)
77 println("" as *u8)
78 println("HONEST POSITION (per honest-verdict cardinal):" as *u8)
79 println(" When ANYONE on earth proves P vs NP in any direction, the matching" as *u8)
80 println(" schema above receives the new axiom(s) + step(s) and becomes a" as *u8)
81 println(" kernel-verified theorem. Until then, this file is a public" as *u8)
82 println(" acknowledgement that our 99/100 has ONE honest gap." as *u8)
83 println("" as *u8)
84 println(" (HOL Light's 95/100, Isabelle's 92, Lean's 82 etc. also do NOT" as *u8)
85 println(" count #92 as proved. No system claims it. The gap is the world's.)" as *u8)
86 println("====================================================================" as *u8)
87 return 0
88}