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`nx_gsplat_fit_aniso_gate.nx` source

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1// nx_gsplat_fit_aniso_gate.nx -- FITTING ON THE QUALITY PATH: the anisotropic surfel reconstructor.
2//
3// WHY THIS GATE EXISTS. nx_gsplat_fit_gate proved the ISOTROPIC path can be fitted from an image. That
4// is the blob path. The ANISOTROPIC path is the one that renders oriented surfels -- the representation
5// that carries actual quality -- and until 2026-08-23 it could be rendered but never FITTED. A
6// reconstructor that stops where the representation starts to matter is not a reconstructor.
7//
8// ★★THE ACCEPT RULE IS THE ONE THE ISOTROPIC GATE'S FIRST RED TAUGHT US, AND IT IS INHERITED
9// DELIBERATELY. v1 of that gate demanded the error fall at EVERY step; the optimiser reached loss=0 and
10// correctly STOPPED, so the rule demanded the impossible and would have REWARDED A JITTERER. The rule
11// splits at the only boundary in the mathematics:
12//     WHILE loss > 0 -- a residual remains, so descent must STRICTLY reduce the error.
13//     ONCE loss == 0 -- converged, so the error must be EXACTLY CONSTANT.
14// Both phases must occur or the tooth is vacuous and says so, and the convergence floor is DERIVED:
15// an image cannot localise a gaussian finer than a pixel, so world-units-per-pixel IS the floor.
16//
17// ★T0 IS THE TOOTH THAT MAKES THIS GATE DIFFERENT FROM ITS ISOTROPIC SIBLING. If the fixture's surfels
18// happened to project to CIRCLES, the anisotropic gradient would reduce term-for-term to the isotropic
19// one and this gate would prove NOTHING NEW while passing everything. So the conic is measured and the
20// scene must be genuinely elliptical -- ca != cc or cb != 0 -- before any other tooth is believed.
21// license_tier: ORIGINAL  expect_exit: 0
22import "nx_syscalls.nx"
23import "nx_itrig.nx"
24import "nx_gsplat.nx"
25import "nx_gate_verdict.nx"
26
27const FA_NG: i64 = 6
28const FA_STEPS: i64 = 12
29const FA_CAMZ: i64 = 30
30// ★SIZED SO THE ELLIPSE SURVIVES INTEGER TRUNCATION. The tilt gives a 2:1 axis ratio by construction,
31// but the projected axes are INTEGER pixel counts: at rtan=260 the deepest surfel projected to axes of
32// 4 and 3 px, and one of six truncated to a CIRCLE -- T0 caught it at 5 of 6. The conic has to be large
33// enough that a 2:1 ratio is still 2:1 after truncation, so rtan is raised until the minor axis is
34// comfortably above the quantisation, and the x spacing is raised with it to keep the surfels from
35// overlapping (the transmittance approximation is only exact while they do not).
36const FA_RTAN: i64 = 560
37const FA_XSTEP: i64 = 3600
38const FA_ZSTEP: i64 = 1100
39// spacing for the OCCLUDING fixture: chosen so the splats genuinely overlap. At this camera a surfel's
40// screen radius is ~3*sqrt(ca) ~ 38 px while this step is ~17 px, so neighbours overlap by roughly half
41// -- enough that transmittance actually falls (T7 measures it rather than trusting this comment).
42// it_sin4096's full-scale unit: sin is returned as a fraction of this, and a full turn is this many
43// yaw units. Named for its PURPOSE (the trig fixed-point one) rather than for the value.
44const FA_TRIG_ONE: i64 = 4096
45// how many views the multi-view arm cycles. Three is the smallest set giving a centre view plus a
46// baseline on EITHER side, so recovered depth cannot be an artefact of one rotation direction.
47const FA_VIEWS: i64 = 3
48// ⚠⚠THE RAY-STACK FIXTURE NEEDED ITS OWN DEPTH SPACING, AND FINDING OUT WHY KILLED A CLAIM.
49// v1 reused FA_ZSTEP (1100) and asked only for ONE PIXEL of separation. Two things were wrong.
50// First, it_sin4096's unit is one RADIAN per 4096, not one turn -- it_sin4096(256)=256 says so
51// directly (small-angle, sin(t)~t) -- so the "8x margin" I assumed was really 1.3x. Second, and
52// fatally: the largest separation a depth step dz can EVER project to is focal*dz/cz (at sin=1), which
53// for dz=1100 here is 21 px against a splat DIAMETER of ~76 px. No rotation whatsoever can separate
54// those surfels, so the multi-view arm was being asked to recover information no camera could obtain
55// and its failure said nothing about the hypothesis.
56// ★DERIVED FIX: choose the ray-stack spacing so a full-radius separation is REACHABLE --
57//     dz >= 2*radius*cz/focal  =>  dz >= 2*38*30720/586 ~ 3984
58// and take the next round figure above it. T11 then computes the requirement from the LIVE conic
59// radius (not this comment) and refuses if the chosen yaw cannot deliver it.
60const FA_RAYZ: i64 = 4400
61// the multi-view baseline in it4096 yaw units (4096 = one radian). SUFFICIENCY is not asserted here --
62// T11 derives the requirement from the live camera geometry and refuses if this does not clear it.
63const FA_VIEW_YAW: i64 = 1924
64const FA_OVSTEP: i64 = 900
65const FA_PERTURB: i64 = 300
66const FA_TILT: i64 = 181          // 256/sqrt(2): a 45-degree surfel tilt, so the projection is an ELLIPSE
67const FA_W64: i64 = 8
68const FA_BGR: i64 = 26
69const FA_BGG: i64 = 28
70const FA_BGB: i64 = 44
71
72func fa_abs(v: i64) -> i64 { if v < 0 { return 0 - v } return v }
73
74// TILTED surfels, separated in depth (the transmittance approximation is declared in the organ header).
75func fa_truth(g: *i64) -> i64 {
  let st: i64 = gs_stride_aniso()
  var i: i64 = 0
  while i < FA_NG {
      let x: i64 = 0 - (FA_NG/2)*FA_XSTEP + i*FA_XSTEP
      let y: i64 = 0 - 900 + (i - (i/2)*2) * 1800
      let z: i64 = 0 - (FA_NG/2)*FA_ZSTEP + i*FA_ZSTEP
      // TILT ABOUT X, NOT Y. v1 tilted in the XZ plane and T0 CAUGHT IT: the two tangent axes came out
      // the same screen length (measured ca=26 cb=0 cc=26 -- a CIRCLE) for 2 of 6 surfels, which would
      // have tested the isotropic case wearing an anisotropic name. Tilting about X puts t1 along pure
      // screen-X at FULL length while t2 foreshortens by cos(tilt), so ca/cc ~ 2 by construction.
      gs_set_aniso(g, i, x, y, z, 0, FA_TILT, 0 - FA_TILT, FA_RTAN, 50 + i*30, 210 - i*14, 130 + i*18, gs_fxa())
      i = i + 1
  }
  return FA_NG
90}
91func fa_copy(dst: *i64, src: *i64, n: i64) -> i64 {
  var i: i64 = 0
  while i < n { dst[i] = src[i]; i = i + 1 }
  return 0
95}
96func fa_poserr(g: *i64, t: *i64) -> i64 {
  let st: i64 = gs_stride_aniso()
  var e: i64 = 0
  var i: i64 = 0
  while i < FA_NG {
      e = e + fa_abs(g[i*st] - t[i*st]) + fa_abs(g[i*st+1] - t[i*st+1])
      i = i + 1
  }
  return e / FA_NG
105}
106
107func main() -> i64 {
  let ctr: *i64 = gv_ctr()
  gv_head("nx_gsplat_fit_aniso_gate -- the ANISOTROPIC surfel path is fitted from the image, not merely rendered" as *u8)
110
  let st: i64 = gs_stride_aniso()
  let vw: i64 = gs_w()
  let vh: i64 = gs_h()
  let focal: i64 = gs_focal_for(vh)
  let npx: i64 = vw * vh
  let truth: *i64 = sys_mmap(FA_NG*st*FA_W64) as *i64
  let work: *i64 = sys_mmap(FA_NG*st*FA_W64) as *i64
  let ctrl: *i64 = sys_mmap(FA_NG*st*FA_W64) as *i64
  let target: *i64 = sys_mmap(npx*FA_W64) as *i64
  let fb: *i64 = sys_mmap(npx*FA_W64) as *i64
  // acc is sized npx*6, not npx*3: the exact form (usetrans=2) carries the running PREFIX colour in
  // the upper half so the suffix S_i can be formed by subtraction. Declared here because the renderer
  // itself only ever touches the lower half, and a caller that sized it npx*3 would corrupt memory
  // silently rather than fail -- so the requirement lives beside the allocation.
  let acc: *i64 = sys_mmap(npx*6*FA_W64) as *i64
  let trans: *i64 = sys_mmap(npx*FA_W64) as *i64
  let depth: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let sxb: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let syb: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let pa: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let pb: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let pc: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let pdet: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let order: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let count: *i64 = sys_mmap((gs_nb()+2)*FA_W64) as *i64
  let explut: *i64 = sys_mmap(gs_expn()*FA_W64) as *i64
  let gradbuf: *i64 = sys_mmap(FA_NG*3*FA_W64) as *i64
  let wnorm: *i64 = sys_mmap(FA_NG*FA_W64) as *i64
  let tcur: *i64 = sys_mmap(npx*FA_W64) as *i64
  let ovw: *i64 = sys_mmap(FA_NG*st*FA_W64) as *i64
  let ovt: *i64 = sys_mmap(FA_NG*st*FA_W64) as *i64
  let ovtgt: *i64 = sys_mmap(npx*FA_W64) as *i64
  gs_build_explut(explut)
144
  let ng: i64 = fa_truth(truth)
  let visT: i64 = gs_render_aniso_at(truth, ng, 0, FA_CAMZ, target, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, FA_BGR, FA_BGG, FA_BGB, vw, vh, focal)
  var litT: i64 = 0
  var q: i64 = 0
  while q < npx { if target[q] != 0 { litT = litT + 1 } q = q + 1 }
150
  // ---- T0: is the fixture ACTUALLY anisotropic? (see the header: a circle proves nothing here) -----
  var elliptical: i64 = 0
  var j: i64 = 0
  while j < ng {
      if depth[j] >= 0 { if pa[j] != pc[j] { elliptical = elliptical + 1 } else { if pb[j] != 0 { elliptical = elliptical + 1 } } }
      j = j + 1
  }
  gv_puts("  conic: g0 ca=" as *u8); gv_num(pa[0]); gv_puts(" cb=" as *u8); gv_num(pb[0])
  gv_puts(" cc=" as *u8); gv_num(pc[0]); gv_puts(" det=" as *u8); gv_num(pdet[0])
  gv_puts(" | elliptical_gaussians=" as *u8); gv_num(elliptical); gv_puts(" of " as *u8); gv_num(ng); gv_puts("\n" as *u8)
  gv_check("T0 the fixture is GENUINELY ANISOTROPIC: the projected conics are ellipses, so this is not the isotropic case in disguise" as *u8, elliptical == ng, ctr)
162
  fa_copy(work, truth, FA_NG*st)
  var i: i64 = 0
  while i < FA_NG {
      work[i*st]   = work[i*st]   + FA_PERTURB
      work[i*st+1] = work[i*st+1] - FA_PERTURB
      i = i + 1
  }
  let err0: i64 = fa_poserr(work, truth)
  let wpp: i64 = (FA_CAMZ * gs_fx()) / focal
  gv_puts("  fixture: visible=" as *u8); gv_num(visT); gv_puts(" of " as *u8); gv_num(ng)
  gv_puts(" target_lit=" as *u8); gv_num(litT)
  gv_puts(" world_units_per_pixel=" as *u8); gv_num(wpp)
  gv_puts(" perturbation=" as *u8); gv_num(FA_PERTURB)
  gv_puts(" (" as *u8); gv_num(FA_PERTURB/wpp); gv_puts(" px)\n" as *u8)
  var t1: i64 = 0
  if visT == ng { if litT > 0 { if err0 > 0 { t1 = 1 } } }
  gv_check("T1 fixture-reached-the-condition: every surfel visible, target has pixels, positions start OFF truth" as *u8, t1, ctr)
180
  var prev_err: i64 = err0
  var mono: i64 = 1
  var held: i64 = 1
  var n_desc: i64 = 0
  var n_conv: i64 = 0
  var loss0: i64 = 0
  var lossN: i64 = 0
  var s: i64 = 0
  while s < FA_STEPS {
      let l: i64 = gs_pos_grad_step_aniso(work, ng, target, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 1)
      if s == 0 { loss0 = l }
      lossN = l
      let e: i64 = fa_poserr(work, truth)
      // ★★PHASE BOUNDARY IS THE RESOLUTION FLOOR, NOT loss==0 -- and this is the GENERAL form of the
      // rule the isotropic gate discovered. That gate's fixture could recover EXACTLY, so loss really
      // reached 0 and the boundary happened to coincide. This fixture converges to a sub-pixel
      // NEIGHBOURHOOD instead (measured: pos_err settles at 29-32 against a 52-unit pixel, loss
      // plateaus at 37010 and then never moves). Demanding monotone descent BELOW one pixel demands
      // what the image cannot express -- the same error v1 made at the loss==0 boundary, one level
      // down. Above the floor: strict descent. Below it: the error must STAY below it.
      if prev_err >= wpp { n_desc = n_desc + 1; if e >= prev_err { mono = 0 } }
      if prev_err < wpp { n_conv = n_conv + 1; if e >= wpp { held = 0 } }
      gv_puts("    step " as *u8); gv_num(s); gv_puts(": loss=" as *u8); gv_num(l)
      gv_puts(" pos_err=" as *u8); gv_num(e); gv_puts("\n" as *u8)
      prev_err = e
      s = s + 1
  }
  let errN: i64 = prev_err
  gv_puts("  recovery: pos_err " as *u8); gv_num(err0); gv_puts(" -> " as *u8); gv_num(errN)
  gv_puts(" | loss " as *u8); gv_num(loss0); gv_puts(" -> " as *u8); gv_num(lossN)
  gv_puts(" | descent_steps=" as *u8); gv_num(n_desc)
  gv_puts(" converged_steps=" as *u8); gv_num(n_conv); gv_puts("\n" as *u8)
  var t2a: i64 = 0
  if n_desc > 0 { if n_conv > 0 { t2a = 1 } }
  gv_check("T2a both phases were exercised: the run descended from ABOVE the pixel floor and actually reached it" as *u8, t2a, ctr)
  gv_check("T2 ANTI-VACUITY descent: while ABOVE the pixel floor, position error STRICTLY decreased every step (a zero gradient holds it constant, a jitter raises it)" as *u8, mono, ctr)
  gv_check("T2b BOUNDED at the floor: once inside one pixel the error NEVER rose back above it -- the fit settles rather than drifting away" as *u8, held, ctr)
  gv_check("T3 the surfels moved TOWARD truth" as *u8, errN < err0, ctr)
  gv_check("T4 the IMAGE improved: L1 loss fell over the run" as *u8, lossN < loss0, ctr)
  gv_check("T4b converged to SUB-PIXEL: residual error is below the world-units-per-pixel floor the image can resolve" as *u8, errN < wpp, ctr)
221
  fa_copy(ctrl, truth, FA_NG*st)
  var cs: i64 = 0
  while cs < FA_STEPS {
      gs_pos_grad_step_aniso(ctrl, ng, target, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 1)
      cs = cs + 1
  }
  let errC: i64 = fa_poserr(ctrl, truth)
  gv_puts("  at-truth control: pos_err after " as *u8); gv_num(FA_STEPS)
  gv_puts(" steps=" as *u8); gv_num(errC); gv_puts(" derived_bound=" as *u8); gv_num(wpp); gv_puts("\n" as *u8)
  gv_bite("neg-control-at-truth-surfels-do-not-wander" as *u8, errN < err0, errC > wpp, ctr)
232
  // ---- T7/T8 WHAT THE TRANSMITTANCE APPROXIMATION COSTS, MEASURED RATHER THAN ASSERTED ----------
  // The separated fixture above CANNOT answer this: with no overlap T stays full, so usetrans=0 and
  // usetrans=1 are arithmetically identical there -- which is exactly why everything above passing is
  // the NEUTRALITY proof for the change. Overlap is the only place the two forms differ, and adaptive
  // density MANUFACTURES overlap, so this number has to exist BEFORE densification rather than after.
  var ob: i64 = 0
  while ob < FA_NG {
      let ox: i64 = 0 - (FA_NG/2)*FA_OVSTEP + ob*FA_OVSTEP
      let oz: i64 = 0 - (FA_NG/2)*FA_ZSTEP + ob*FA_ZSTEP
      gs_set_aniso(ovt, ob, ox, 0, oz, 0, FA_TILT, 0 - FA_TILT, FA_RTAN, 50 + ob*30, 210 - ob*14, 130 + ob*18, gs_fxa())
      ob = ob + 1
  }
  gs_render_aniso_at(ovt, ng, 0, FA_CAMZ, ovtgt, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, FA_BGR, FA_BGG, FA_BGB, vw, vh, focal)
  let tmid: i64 = trans[(vh/2)*vw + (vw/2)]
  gv_puts("  overlap fixture: transmittance at the stack centre = " as *u8); gv_num(tmid)
  gv_puts(" of " as *u8); gv_num(gs_fxa()); gv_puts(" (full)\n" as *u8)
  gv_check("T7 the overlap fixture ACTUALLY occludes: centre transmittance fell below full, so the two gradient forms CAN differ here" as *u8, tmid < gs_fxa(), ctr)
250
  // identical perturbed start, run under each form
  fa_copy(ovw, ovt, FA_NG*st)
  var pk: i64 = 0
  while pk < FA_NG { ovw[pk*st] = ovw[pk*st] + FA_PERTURB; ovw[pk*st+1] = ovw[pk*st+1] - FA_PERTURB; pk = pk + 1 }
  let oerr0: i64 = fa_poserr(ovw, ovt)
  var os: i64 = 0
  while os < FA_STEPS {
      gs_pos_grad_step_aniso(ovw, ng, ovtgt, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 0)
      os = os + 1
  }
  let err_ap: i64 = fa_poserr(ovw, ovt)
262
  fa_copy(ovw, ovt, FA_NG*st)
  pk = 0
  while pk < FA_NG { ovw[pk*st] = ovw[pk*st] + FA_PERTURB; ovw[pk*st+1] = ovw[pk*st+1] - FA_PERTURB; pk = pk + 1 }
  os = 0
  while os < FA_STEPS {
      gs_pos_grad_step_aniso(ovw, ng, ovtgt, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 1)
      os = os + 1
  }
  let err_ex: i64 = fa_poserr(ovw, ovt)
272
  // third arm: direct + INDIRECT (dT_j/dparam_i). Same start, same steps, same fixture -- the only
  // thing that varies is which terms of the derivative are carried.
  fa_copy(ovw, ovt, FA_NG*st)
  pk = 0
  while pk < FA_NG { ovw[pk*st] = ovw[pk*st] + FA_PERTURB; ovw[pk*st+1] = ovw[pk*st+1] - FA_PERTURB; pk = pk + 1 }
  os = 0
  while os < FA_STEPS {
      gs_pos_grad_step_aniso(ovw, ng, ovtgt, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 2)
      os = os + 1
  }
  let err_full: i64 = fa_poserr(ovw, ovt)
  gv_puts("  OCCLUDED FIT from the same start (pos_err " as *u8); gv_num(oerr0)
  gv_puts("): approximation(T=full) -> " as *u8); gv_num(err_ap)
  gv_puts(" | direct T -> " as *u8); gv_num(err_ex)
  gv_puts(" | direct+INDIRECT -> " as *u8); gv_num(err_full)
  gv_puts(" | floor=" as *u8); gv_num(wpp); gv_puts("\n" as *u8)
  gv_check("T8 the exact direct transmittance form is NOT WORSE than the approximation on an occluding scene (the cost of the approximation, measured)" as *u8, err_ex <= err_ap, ctr)
  // ⚠⚠MEASURED, NEGATIVE, AND IT REFUTES THE ATTRIBUTION MADE ONE ROUND AGO. The indirect term is
  // IMPLEMENTED here and it does NOT improve this fit: direct-only 79 against 81 in the first scaling
  // and 100 after correcting the units to c*T/GFXA - S/((GFXA-alpha)*GFXA). TWO scalings, same
  // direction, so this is not a stray constant. A tooth demanding that it improve would assert a
  // result the data refuses -- the same error as demanding descent below the pixel floor, one level
  // out. What is asserted is what is TRUE: three arms ran on one fixture from one start and produced
  // distinct finite numbers. The negative finding is PUBLISHED rather than buried in a pass.
  var t8b: i64 = 0
  if err_full > 0 { if err_ap > err_ex { t8b = 1 } }
  gv_check("T8b the three-arm comparison is REAL: approximation / direct / direct+indirect all ran on one fixture and one start with the numbers published -- and the indirect arm did NOT improve the fit, which is the FINDING and not a failure" as *u8, t8b, ctr)
300
  // ---- T9/T10 WHEN DOES THE INDIRECT TERM START TO MATTER? ANSWERED AS A DEPTH SWEEP -----------
  // The direct term is shipped; the INDIRECT term (moving splat i changes how much light reaches every
  // splat BEHIND it, dT_j/dparam_i for j after i) is not. Rather than hand the next lane a footnote,
  // this sweeps the stack depth and PUBLISHES the residual curve. The reasoning is the same one that
  // put transmittance before densification: adaptive density manufactures DEEP overlapping stacks, so
  // if the direct-only residual grows with depth, the indirect term becomes binding exactly there and
  // rung 2 inherits this as a precondition instead of discovering it by surprise.
  // ★NO THRESHOLD IS ASSERTED HERE ON PURPOSE. The curve is a MEASUREMENT; calling some depth "too
  // deep" would be a picked constant, and the census just measured only 2.56 percent of estate bounds
  // as derived. T10 anchors the curve instead: if the SHALLOWEST stack reaches the pixel floor, then
  // any growth with depth is the indirect term appearing rather than the method failing.
  // ⚠⚠v1 OF THIS SWEEP WAS CONFOUNDED AND ITS OWN ANCHOR FALSIFIED IT. It varied STACK DEPTH by
  // changing the NUMBER of surfels, which also changed how much image signal existed to fit and how
  // ambiguous the configuration was. It produced 148 -> 132 -> 96: the error FELL as the stack
  // deepened, the opposite of the hypothesis, and the anchor tooth failed because even the shallowest
  // stack (148) never reached the 52 floor. Two variables moved at once, so NOTHING was attributable.
  // ★VARY ONE THING: splat COUNT is held at FA_NG and only the SPACING changes, so occlusion is the
  // only quantity moving. Spacings are derived by successive division of the separated fixture's own
  // step rather than picked, and transmittance is reported at each so the sweep proves it actually
  // varied occlusion instead of asserting it.
  var sp: i64 = FA_XSTEP
  var swept: i64 = 0
  var wide_err: i64 = 0 - 1
  var narrow_err: i64 = 0
  var first_tc: i64 = 0 - 1
  var last_tc: i64 = 0
  while swept < 3 {
      var b2: i64 = 0
      while b2 < FA_NG {
          let ox2: i64 = 0 - (FA_NG/2)*sp + b2*sp
          let oz2: i64 = 0 - (FA_NG/2)*FA_ZSTEP + b2*FA_ZSTEP
          gs_set_aniso(ovt, b2, ox2, 0, oz2, 0, FA_TILT, 0 - FA_TILT, FA_RTAN, 50 + b2*30, 210 - b2*14, 130 + b2*18, gs_fxa())
          b2 = b2 + 1
      }
      gs_render_aniso_at(ovt, FA_NG, 0, FA_CAMZ, ovtgt, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, FA_BGR, FA_BGG, FA_BGB, vw, vh, focal)
      // ⚠OCCLUSION WITNESS REPLACED: the centre pixel is SATURATED at every spacing (a splat always
      // sits at x=0, so trans there is 0 throughout) and v2 of this tooth failed on exactly that -- a
      // witness that cannot move cannot prove the variable moved. Distinct COVERED AREA is the
      // un-saturated witness: with the count FIXED, narrowing the spacing bunches the splats and the
      // area they jointly cover FALLS. That is overlap itself, measured rather than proxied.
      var tc: i64 = 0
      var ap: i64 = 0
      while ap < npx { if trans[ap] < gs_fxa() { tc = tc + 1 } ap = ap + 1 }
      if first_tc < 0 { first_tc = tc }
      last_tc = tc
      fa_copy(ovw, ovt, FA_NG*st)
      var pk2: i64 = 0
      while pk2 < FA_NG { ovw[pk2*st] = ovw[pk2*st] + FA_PERTURB; ovw[pk2*st+1] = ovw[pk2*st+1] - FA_PERTURB; pk2 = pk2 + 1 }
      var os2: i64 = 0
      while os2 < FA_STEPS {
          gs_pos_grad_step_aniso(ovw, FA_NG, ovtgt, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 1)
          os2 = os2 + 1
      }
      let de: i64 = fa_poserr(ovw, ovt)
      if wide_err < 0 { wide_err = de }
      narrow_err = de
      gv_puts("    spacing=" as *u8); gv_num(sp)
      gv_puts(" covered_px=" as *u8); gv_num(tc)
      gv_puts(" direct_only_pos_err=" as *u8); gv_num(de)
      gv_puts(" floor=" as *u8); gv_num(wpp); gv_puts("\n" as *u8)
      swept = swept + 1
      sp = sp / 3
  }
  gv_puts("  INDIRECT-TERM WATCH: occlusion is the only variable above -- count is fixed at " as *u8)
  gv_num(FA_NG); gv_puts(", so any rise in the residual is dT_j/dparam_i becoming binding\n" as *u8)
  var t9: i64 = 0
  if swept == 3 { if last_tc < first_tc { t9 = 1 } }
  gv_check("T9 the sweep actually VARIED OCCLUSION at fixed splat count: the jointly covered area FELL as spacing narrowed, which is overlap deepening (otherwise the curve measures nothing)" as *u8, t9, ctr)
  // ⚠THE ANCHOR IS THE SEPARATED FIXTURE, NOT THE WIDEST SWEEP POINT. Even at spacing=3600 the surfels
  // already touch (screen radius ~38 px against ~70 px spacing), so that point is NOT overlap-free and
  // anchoring on it would attribute its own residual to the indirect term. The genuinely unoccluded
  // result is T4b's: the separated fixture, same method and same perturbation, reaching sub-pixel.
  var t10: i64 = 0
  if errN < wpp { if narrow_err > wide_err { t10 = 1 } }
  // ⚠⚠ATTRIBUTION WITHDRAWN. v1 of this tooth said the rise "IS dT_j/dparam_i, the term this organ
  // does not yet carry". The organ NOW carries it (T8b) and carrying it does NOT remove the rise --
  // so that causal claim is refuted by my own control and has been removed rather than restated. The
  // RISE is measured and stands; its CAUSE is open, and the live candidate is that overlapping splats
  // along one view ray are genuinely under-determined FROM A SINGLE IMAGE -- which is an argument for
  // multi-view fitting, not for more gradient terms. A tooth may assert a measurement; it may not
  // assert a mechanism its own experiment failed to confirm.
  gv_check("T10 the residual RISES monotonically as overlap deepens (measured); the CAUSE is deliberately NOT attributed -- adding the indirect term did not remove it, leaving single-view ambiguity as the live candidate" as *u8, t10, ctr)
383
  // ---- T11/T12/T13 MULTI-VIEW: THE DISCRIMINATING EXPERIMENT FOR THE UNDER-DETERMINATION CLAIM ---
  // PRE-DECLARED ACCEPT RULE, written before the run: if splats stacked along ONE view ray are
  // genuinely under-determined FROM A SINGLE IMAGE, then views that separate them must COLLAPSE the
  // residual. If it collapses, the hypothesis is confirmed and the indirect term's failure is fully
  // explained -- no gradient can recover information the view does not contain. If it does NOT
  // collapse, the hypothesis is WRONG and something else is at work. Either way this discriminates,
  // which is why it outranks more gradient terms.
  // FIXTURE: the worst case on purpose -- every surfel on the SAME ray (x=0, y=0), separated only in
  // depth, so at yaw=0 they project to one point and the single-view problem is maximally ambiguous.
  // BASELINE DERIVED, NEVER PICKED: a depth separation dz projects to dsx = focal*dz*sin(yaw)/cz, so
  // separating two ray-stacked surfels by at least ONE pixel requires sin(yaw)*4096 >= 4096*cz/(focal*dz).
  // T11 computes that requirement from the LIVE geometry and asserts the chosen baseline clears it.
  let tgtA: *i64 = sys_mmap(npx*FA_W64) as *i64
  let tgtB: *i64 = sys_mmap(npx*FA_W64) as *i64
  let tgtC: *i64 = sys_mmap(npx*FA_W64) as *i64
  var rs: i64 = 0
  while rs < FA_NG {
      gs_set_aniso(ovt, rs, 0, 0, 0 - (FA_NG/2)*FA_RAYZ + rs*FA_RAYZ, 0, FA_TILT, 0 - FA_TILT, FA_RTAN, 50 + rs*30, 210 - rs*14, 130 + rs*18, gs_fxa())
      rs = rs + 1
  }
  // render the centre view FIRST so the requirement below is computed from the LIVE conic rather than
  // from a remembered radius -- the splat's own size is what a view has to out-separate.
  gs_render_aniso_at(ovt, FA_NG, 0, FA_CAMZ, tgtA, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, FA_BGR, FA_BGG, FA_BGB, vw, vh, focal)
  let czr: i64 = FA_CAMZ * gs_fx()
  let srad: i64 = gs_splat_rx(pa[0])
  // ⚠⚠THE FULL-RADIUS BAR WAS TOO STRICT AND THE RESULT PROVED IT. v2 demanded a depth step separate
  // by a WHOLE splat radius (needed sin4096 2635, had 1854) and FAILED -- while T13 below fitted to
  // 44 against a 52 floor at that very baseline. A bar the successful run cannot clear is not a
  // safety margin, it is a wrong requirement, and asserting it would have reported a working
  // capability as broken. The NECESSARY condition is the information floor: the views must separate a
  // depth step by at least ONE PIXEL, because below that the image cannot encode the difference at
  // all. SUFFICIENCY is not asserted here -- T13 demonstrates it empirically, which is the only
  // honest source for it. The achieved separation is printed in radius units so the margin is visible
  // rather than assumed.
  let need1: i64 = FA_TRIG_ONE * czr / (focal * FA_RAYZ)
  let ybase: i64 = FA_VIEW_YAW
  let gotsin: i64 = it_sin4096(ybase)
  let seppx: i64 = focal * FA_RAYZ * gotsin / czr / FA_TRIG_ONE
  gv_puts("  multi-view baseline: splat radius=" as *u8); gv_num(srad)
  gv_puts(" px | need sin4096 >= " as *u8); gv_num(need1)
  gv_puts(" for the 1-pixel information floor | yaw=" as *u8); gv_num(ybase)
  gv_puts(" gives sin4096=" as *u8); gv_num(gotsin)
  gv_puts(" = " as *u8); gv_num(seppx); gv_puts(" px of depth separation\n" as *u8)
  gv_check("T11 the view baseline clears the NECESSARY condition: the chosen yaw separates a depth step by at least one pixel, derived from the live camera geometry -- sufficiency is left to T13 to demonstrate rather than assumed by a margin" as *u8, gotsin >= need1, ctr)
  gs_render_aniso_at(ovt, FA_NG, ybase, FA_CAMZ, tgtB, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, FA_BGR, FA_BGG, FA_BGB, vw, vh, focal)
  gs_render_aniso_at(ovt, FA_NG, 0 - ybase, FA_CAMZ, tgtC, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, FA_BGR, FA_BGG, FA_BGB, vw, vh, focal)
430
  // ARM 1: single view, the ambiguous one
  fa_copy(ovw, ovt, FA_NG*st)
  var mk: i64 = 0
  while mk < FA_NG { ovw[mk*st] = ovw[mk*st] + FA_PERTURB; ovw[mk*st+1] = ovw[mk*st+1] - FA_PERTURB; mk = mk + 1 }
  var ms: i64 = 0
  while ms < FA_STEPS {
      gs_pos_grad_step_aniso(ovw, FA_NG, tgtA, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 1)
      ms = ms + 1
  }
  let err_sv: i64 = fa_poserr(ovw, ovt)
441
  // ARM 2: the SAME start and step count, but the view CYCLES -- this is how 3DGS actually trains,
  // one view per iteration, so multi-view costs no extra machinery here, only different targets.
  fa_copy(ovw, ovt, FA_NG*st)
  mk = 0
  while mk < FA_NG { ovw[mk*st] = ovw[mk*st] + FA_PERTURB; ovw[mk*st+1] = ovw[mk*st+1] - FA_PERTURB; mk = mk + 1 }
  ms = 0
  while ms < FA_STEPS {
      let phase: i64 = ms - (ms/FA_VIEWS)*FA_VIEWS
      if phase == 0 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtA, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 1) }
      if phase == 1 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtB, ybase, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 1) }
      if phase == 2 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtC, 0 - ybase, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 1) }
      ms = ms + 1
  }
  let err_mv: i64 = fa_poserr(ovw, ovt)
456
  // ---- T14 THE INDIRECT TERM, RE-MEASURED UNDER MULTI-VIEW ------------------------------------
  // Its single-view verdict was non-beneficial (79 direct vs 100 with indirect) and I recorded that
  // as UNRESOLVED rather than absent, keeping the three-arm selector so this would cost no code
  // motion. Resolving it here: the ray-stacked multi-view arm is re-run with usetrans=0 and 2 beside
  // the =1 result above. This is where it should matter most -- deep overlap AND enough views for the
  // gradient to have something real to correct -- so a null result here is a genuine answer, not a
  // fixture artefact. NOTHING is asserted about which wins; the numbers are published and the tooth
  // asserts only that all three arms genuinely ran on one fixture from one start.
  fa_copy(ovw, ovt, FA_NG*st)
  mk = 0
  while mk < FA_NG { ovw[mk*st] = ovw[mk*st] + FA_PERTURB; ovw[mk*st+1] = ovw[mk*st+1] - FA_PERTURB; mk = mk + 1 }
  ms = 0
  while ms < FA_STEPS {
      let ph0: i64 = ms - (ms/FA_VIEWS)*FA_VIEWS
      if ph0 == 0 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtA, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 0) }
      if ph0 == 1 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtB, ybase, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 0) }
      if ph0 == 2 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtC, 0 - ybase, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 0) }
      ms = ms + 1
  }
  let mv_ap: i64 = fa_poserr(ovw, ovt)
  fa_copy(ovw, ovt, FA_NG*st)
  mk = 0
  while mk < FA_NG { ovw[mk*st] = ovw[mk*st] + FA_PERTURB; ovw[mk*st+1] = ovw[mk*st+1] - FA_PERTURB; mk = mk + 1 }
  ms = 0
  while ms < FA_STEPS {
      let ph2: i64 = ms - (ms/FA_VIEWS)*FA_VIEWS
      if ph2 == 0 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtA, 0, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 2) }
      if ph2 == 1 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtB, ybase, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 2) }
      if ph2 == 2 { gs_pos_grad_step_aniso(ovw, FA_NG, tgtC, 0 - ybase, FA_CAMZ, fb, acc, trans, depth, sxb, syb, pa, pb, pc, pdet, order, count, explut, gradbuf, wnorm, vw, vh, 2) }
      ms = ms + 1
  }
  let mv_full: i64 = fa_poserr(ovw, ovt)
  gv_puts("  RAY-STACKED FIT (every surfel on one ray, same start pos_err " as *u8); gv_num(FA_PERTURB*2)
  gv_puts("): single-view -> " as *u8); gv_num(err_sv)
  gv_puts(" | 3-view -> " as *u8); gv_num(err_mv)
  gv_puts(" | floor=" as *u8); gv_num(wpp); gv_puts("\n" as *u8)
  gv_check("T12 fixture-reached-the-condition: the single-view arm on a ray-stacked scene really is above the pixel floor, so there is something for extra views to recover" as *u8, err_sv > wpp, ctr)
  gv_check("T13 THE HYPOTHESIS, TESTED: extra views COLLAPSE the ray-stacked residual that no gradient term could fix -- confirming the rise is missing INFORMATION, not a missing derivative" as *u8, err_mv < err_sv, ctr)
  gv_puts("  INDIRECT TERM UNDER MULTI-VIEW (same fixture, same start, 3 views): approximation -> " as *u8); gv_num(mv_ap)
  gv_puts(" | direct T -> " as *u8); gv_num(err_mv)
  gv_puts(" | direct+INDIRECT -> " as *u8); gv_num(mv_full)
  gv_puts(" | floor=" as *u8); gv_num(wpp); gv_puts("\n" as *u8)
  // ⚠⚠MY OWN VACUOUS TOOTH, CAUGHT BY THE NUMBER IT LET THROUGH. v1 asserted only `mv_full > 0` and
  // PASSED on 46,128,546,235 -- a divergence ten orders of magnitude past a 52-pixel floor. Any
  // garbage is greater than zero. That is precisely the defect this gate exists to prevent, committed
  // by its own author, and the bound is now the only one that means anything here: A FIT THAT ENDS
  // WORSE THAN IT BEGAN HAS DIVERGED. The start error is known exactly (the perturbation), so the
  // bound is DERIVED, not chosen.
  // ★AND THE RESOLUTION IS NOW IN HAND, WHICH WAS THE POINT OF RE-MEASURING: usetrans=2 is not merely
  // non-beneficial, it is NUMERICALLY UNSTABLE. Single-view hid it (100 against 79 reads as a mild
  // loss); multi-view exposed it. It is quarantined in the organ header and must not ship until the
  // instability is found. This tooth binds the two SHIPPING arms; the broken arm is reported only.
  let startv: i64 = FA_PERTURB*2
  var t14: i64 = 0
  if mv_ap <= startv { if err_mv <= startv { if err_mv < mv_ap { t14 = 1 } } }
  if mv_full > startv { gv_puts("  >>> usetrans=2 DIVERGED under multi-view (ended worse than it began): NOT SHIPPABLE, quarantined in the organ header\n" as *u8) }
  gv_check("T14 the SHIPPING gradient arms are bounded and ordered under multi-view: neither ends worse than it began, and the direct-transmittance form beats the approximation -- the indirect arm is reported, never asserted on, because it DIVERGES" as *u8, t14, ctr)
514
  return gv_verdict("NX-GSPLAT-FIT-ANISO" as *u8, ctr, "the quality path is a reconstructor: oriented surfels recover their position from the image, hold still at the optimum, and the transmittance approximation now has a measured price" as *u8)
516}
nx_gsplat_fit_aniso_gate.nx source

`nx_gsplat_fit_aniso_gate.nx` source
