nx_geo_s2_gate.nx source

1// nx_geo_s2_gate.nx -- GATE for GEO-005 Hilbert (S2-class) cell index, on an 8x8 grid (k=3, 64 cells). 2// Proves correctness AND the measured locality exceed over geohash's Z-order: 3// bijection : Hilbert xy2d hits all 64 distinct indices [0,63] exactly once 4// roundtrip : d2xy(xy2d(x,y)) == (x,y) for all cells 5// continuity : max Manhattan step between CONSECUTIVE Hilbert indices == 1 (the defining property) 6// exceed : Z-order's max consecutive step == 8 (= grid width N) -- it TEARS; Hilbert (1) wins 7// 8// Evidence -> knowledge/status/geo_s2.log (GEOS2GATE authored=organ ... verdict=GREEN). 9// license_tier: ORIGINAL 10import "nx_geo_s2.nx" 11import "nx_syscalls.nx" 12import "nx_gate_verdict.nx" 13 14const GS2_LOG: *u8 = "knowledge/status/geo_s2.log" 15 16func g2_w(fd: i64, s: *u8) -> i64 { var n: i64 = 0; while s[n] != (0 as u8) { n = n + 1 } sys_write(fd, s, n); return 0 } 17func g2_wn(fd: i64, v: i64) -> i64 { let bb: *u8 = sys_mmap(28); var m: i64=v; if m<0 {m=0-m; sys_write(fd,"-" as *u8,1)}; let t: *u8 = sys_mmap(28); var k: i64=0; if m==0 {t[0]=48;k=1}; while m>0 {t[k]=(48+(m%10)) as u8; m=m/10; k=k+1}; var i: i64=0; while i<k {bb[i]=t[k-1-i]; i=i+1}; sys_write(fd, bb, k); return 0 } 18func g2_abs(x: i64) -> i64 { if x < 0 { return 0 - x } return x } 19 20func g2_emit(fd: i64, cnt: i64, rt: i64, hmax: i64, zmax: i64, ok: i64) -> i64 { 21 g2_w(fd, "GEOS2GATE authored=organ method=hilbert-curve grid=8x8 bijection_count=" as *u8); g2_wn(fd, cnt) 22 g2_w(fd, " roundtrip_ok=" as *u8); g2_wn(fd, rt) 23 g2_w(fd, " hilbert_consec_max=" as *u8); g2_wn(fd, hmax) 24 g2_w(fd, " zorder_consec_max=" as *u8); g2_wn(fd, zmax) 25 if ok == 1 { g2_w(fd, " verdict=GREEN\n" as *u8) } else { g2_w(fd, " verdict=RED\n" as *u8) } 26 return 0 27} 28 29func main() -> i64 { 30 let hx: *i64 = sys_mmap(8 * 64) as *i64 31 let hy: *i64 = sys_mmap(8 * 64) as *i64 32 let zx: *i64 = sys_mmap(8 * 64) as *i64 33 let zy: *i64 = sys_mmap(8 * 64) as *i64 34 let seen: *i64 = sys_mmap(8 * 64) as *i64 35 var i: i64 = 0 36 while i < 64 { seen[i] = 0; i = i + 1 } 37 38 var bij_ok: i64 = 1 39 var rt_ok: i64 = 1 40 let o2: *i64 = sys_mmap(16) as *i64 41 var x: i64 = 0 42 while x < 8 { 43 var y: i64 = 0 44 while y < 8 { 45 let hd: i64 = geo_hilbert_xy2d(3, x, y) 46 if hd < 0 { bij_ok = 0 } else { 47 if hd >= 64 { bij_ok = 0 } else { 48 if seen[hd] == 1 { bij_ok = 0 } 49 seen[hd] = 1 50 hx[hd] = x; hy[hd] = y 51 } 52 } 53 let zd: i64 = geo_zorder_xy2d(3, x, y) 54 zx[zd] = x; zy[zd] = y 55 // round-trip 56 geo_hilbert_d2xy(3, hd, o2) 57 if o2[0] != x { rt_ok = 0 } 58 if o2[1] != y { rt_ok = 0 } 59 y = y + 1 60 } 61 x = x + 1 62 } 63 64 var cnt: i64 = 0 65 i = 0 66 while i < 64 { cnt = cnt + seen[i]; i = i + 1 } 67 68 // consecutive-index Manhattan step: max over d -> d+1 69 var hmax: i64 = 0 70 var zmax: i64 = 0 71 var d: i64 = 0 72 while d < 63 { 73 let hm: i64 = g2_abs(hx[d] - hx[d + 1]) + g2_abs(hy[d] - hy[d + 1]) 74 if hm > hmax { hmax = hm } 75 let zm: i64 = g2_abs(zx[d] - zx[d + 1]) + g2_abs(zy[d] - zy[d + 1]) 76 if zm > zmax { zmax = zm } 77 d = d + 1 78 } 79 80 var ok: i64 = 1 81 if bij_ok != 1 { ok = 0 } 82 if cnt != 64 { ok = 0 } 83 if rt_ok != 1 { ok = 0 } 84 if hmax != 1 { ok = 0 } // Hilbert is continuous 85 if zmax <= hmax { ok = 0 } // Z-order tears -> measured exceed 86 87 g2_emit(1, cnt, rt_ok, hmax, zmax, ok) 88 let lf: i64 = sys_openat_append(GS2_LOG, 420) 89 if lf >= 0 { g2_emit(lf, cnt, rt_ok, hmax, zmax, ok); sys_close(lf) } 90 91 // MIGRATED onto nx_gate_verdict by nx_gate_dry_apply (D001, minimal form): every check 92 // row above is untouched, so the PASS/FAIL vector cannot change; only the hand-rolled 93 // verdict emission is replaced by the ONE shared base class. Proven by nx_gate_migrate verify. 94 let ctr__dry: *i64 = gv_ctr() 95 ctr__dry[0] = ok 96 ctr__dry[1] = 1 97 let rc__dry: i64 = gv_verdict("GEO-S2-GATE" as *u8, ctr__dry, "teeth unchanged; verdict emission migrated onto the shared base class" as *u8) 98 sys_exit(rc__dry) 99 return rc__dry 100}