// SPDX-License-Identifier: Apache-2.0 // © 2026 Lutar, Stephen P. — SZL Holdings · ORCID 0009-0001-0110-4173 · Doctrine v11 // // surfaces/kla.js — KACZMARZ LINEAR ATTENTION (KLA) organ for the holographic // frontier ring. Visualizes the recurrent linear-attention memory state being // UPDATED, one streamed key-value pair at a time, by an orthogonal Kaczmarz // projection onto the constraint S·k = v — a principled scalar replacing the // ad-hoc gate of gated linear attention. Two convergence tracks race along a // pipeline: KLA (proof-teal) vs the ad-hoc GATED baseline (grey), heights driven // by their live running reconstruction error from // /api/killinchu/v1/kla/update. A HUD shows kla vs gated final error, the // improvement_ratio, and convergence steps. Honesty label "MODELED" is read // VERBATIM from the JSON and displayed as-is; it is never upgraded. // // Surface export shape (mirrors specdecode.js / testtime.js exactly): // export default { id, title, endpoints, mount(ctx), unmount() } // ctx = { stage, container, live, label, THREE, szl3d } // // DATA SHOWN (all from live endpoint): // dim, steps, lr, tol, kla_final_recon_error, gated_final_recon_error, // kla_convergence_step, gated_convergence_step, improvement_ratio, // kla_error_curve[], gated_error_curve[] // // LEADER ADOPTED & CITED (clean-room; NOT claimed as SZL's own): // KLA — Kaczmarz Linear Attention (projection update rule modeled here): // (2026) arXiv:2605.08587 // https://arxiv.org/abs/2605.08587 // // HONESTY LABELS: MODELED (deterministic re-implementation of the Kaczmarz // projection state-update arithmetic; NOT a trained GLA model; NEVER-CLAIMED-AS // a production kernel). Read verbatim from JSON; never upgraded here. // COLOURS: lattice-blue 0x5b8dee (streamed key-value / pipeline spine), violet- // blue 0x8a6bff (constraint hyperplane accent), proof-teal 0x3af4c8 (KLA // convergence track / HUD accent), greys (gated baseline / degraded state). // Purple BANNED as UI/background. // 0 RUNTIME CDN. Vendored three.js via ctx.THREE (page importmap). // DOCTRINE v11: degrades gracefully (grey) on 404/error; honesty label still shown. // Nothing here is in the locked-8. Λ stays Conjecture 1. Trust never 100%. import { createShowcase } from "./_showcase.js"; const ID = "kla"; const TITLE = "Kaczmarz Linear Attention · Projection State-Update (live)"; // Endpoint is hosted on the dedicated killinchu Space (isolated compute), reached // cross-origin (killinchu returns access-control-allow-origin: https://a-11-oy.com). // This keeps the KLA organ's rebuilds/faults isolated from the flagship. const EP = "https://szlholdings-killinchu.hf.space/api/killinchu/v1/kla/update?seed=42&dim=8&steps=256&lr=1.0"; // data-viz hues — purple BANNED const C_STREAM = 0x5b8dee; // lattice-blue (streamed key-value pair / pipeline spine) const C_PLANE = 0x8a6bff; // violet-blue (constraint hyperplane / projection accent) const C_KLA = 0x3af4c8; // proof-teal (KLA convergence track / HUD accent) const C_GATED = 0x5a6570; // grey (ad-hoc gated baseline track) const C_DIM = 0x42505d; // grey (degraded / no-live-data) const C_GRID = 0x1b3a44; // floor / link colour // convergence-track pipeline layout geometry const TRACK_LEN = 22.0; // world-units the two tracks span along X (stream axis) const N_BARS = 32; // number of sampled error points rendered per track const BAR_W = 0.42; // bar width const KLA_Z = -1.4; // Z lane for the KLA track const GATED_Z = 1.4; // Z lane for the gated baseline track const MAX_H = 6.0; // max bar height (world units) at max error let _stage = null, _THREE = null, _ctx = null, _group = null, _show = null; let _frameReg = false, _polls = [], _el = {}, _badge = null; // geometry handles let _floor = null; let _spine = null; // THREE.Line — stream axis (pipeline spine) let _plane = null; // THREE.Mesh — constraint hyperplane accent let _klaBars = []; // Array — KLA convergence track let _gatedBars = []; // Array — gated baseline track let _marker = null; // THREE.Mesh — projection "head" pulsing marker // live state const S = { label: null, dim: null, // dim steps: null, // steps lr: null, // lr tol: null, // tol klaErr: null, // kla_final_recon_error gatedErr: null, // gated_final_recon_error klaConv: null, // kla_convergence_step gatedConv: null, // gated_convergence_step improve: null, // improvement_ratio klaCurve: null, // kla_error_curve[] gatedCurve: null, // gated_error_curve[] state: "init", }; // ============================================================================= // mount(ctx) // ============================================================================= export function mount(ctx) { _ctx = ctx; _stage = ctx.stage; _THREE = ctx.THREE; _group = new _THREE.Group(); _stage.scene.add(_group); _stage.camera.position.set(2, 8, 20); try { if (_stage.controls && _stage.controls.target) { _stage.controls.target.set(0, 1.5, 0); _stage.controls.update(); } } catch (_) {} try { _stage.setBloom(true); } catch (_) {} _buildFloor(); _buildSpine(); _buildPlane(); _buildTracks(); _buildMarker(); if (!_frameReg) { _stage.onFrame(_onFrame); _frameReg = true; } _badge = ctx.live.createBadge(); _polls.push(ctx.live.poll(EP, 5000, _onKla, { badge: _badge, onState: (m) => { S.state = m.state; _paintOverlay(); } })); _buildOverlay(); return { id: ID, started: true }; } // ============================================================================= // builders // ============================================================================= function _buildFloor() { const THREE = _THREE; const grid = new THREE.GridHelper(44, 44, C_GRID, 0x0f2027); grid.material.opacity = 0.18; grid.material.transparent = true; grid.position.y = -0.01; _group.add(grid); _floor = grid; } function _buildSpine() { const THREE = _THREE; const x0 = -TRACK_LEN / 2, x1 = TRACK_LEN / 2; const pts = [new THREE.Vector3(x0, 0, 0), new THREE.Vector3(x1, 0, 0)]; const geo = new THREE.BufferGeometry().setFromPoints(pts); const mat = new THREE.LineBasicMaterial({ color: C_STREAM, transparent: true, opacity: 0.5 }); _spine = new THREE.Line(geo, mat); _group.add(_spine); } // A translucent tilted plane standing in for the S·k = v constraint hyperplane // that each Kaczmarz step projects the memory state onto. function _buildPlane() { const THREE = _THREE; const geo = new THREE.PlaneGeometry(5.5, 5.5, 1, 1); const mat = new THREE.MeshStandardMaterial({ color: C_PLANE, emissive: C_PLANE, emissiveIntensity: 0.14, transparent: true, opacity: 0.10, side: THREE.DoubleSide, wireframe: false, }); _plane = new THREE.Mesh(geo, mat); _plane.rotation.y = Math.PI / 5; _plane.rotation.x = Math.PI / 12; _plane.position.set(-TRACK_LEN / 2 + 3.0, 2.6, 0); _group.add(_plane); } // Pre-allocate two fixed rows of bars: KLA lane + gated lane, N_BARS each. // We toggle height/color/opacity in-place as live curve data arrives (no // per-poll geometry churn). function _buildTracks() { const THREE = _THREE; const x0 = -TRACK_LEN / 2; const dx = TRACK_LEN / (N_BARS - 1); const barGeo = new THREE.BoxGeometry(BAR_W, 1, BAR_W); // unit height; scaled in Y for (let i = 0; i < N_BARS; i++) { const x = x0 + i * dx; const klaMesh = new THREE.Mesh( barGeo, new THREE.MeshStandardMaterial({ color: C_KLA, emissive: C_KLA, emissiveIntensity: 0.3, transparent: true, opacity: 0.0 }), ); klaMesh.position.set(x, 0.0, KLA_Z); klaMesh.scale.y = 0.001; klaMesh.visible = false; _group.add(klaMesh); _klaBars.push(klaMesh); const gatedMesh = new THREE.Mesh( barGeo, new THREE.MeshStandardMaterial({ color: C_GATED, emissive: C_GATED, emissiveIntensity: 0.12, transparent: true, opacity: 0.0 }), ); gatedMesh.position.set(x, 0.0, GATED_Z); gatedMesh.scale.y = 0.001; gatedMesh.visible = false; _group.add(gatedMesh); _gatedBars.push(gatedMesh); } } function _buildMarker() { const THREE = _THREE; _marker = new THREE.Mesh( new THREE.IcosahedronGeometry(0.30, 1), new THREE.MeshStandardMaterial({ color: C_KLA, emissive: C_KLA, emissiveIntensity: 0.5, wireframe: true, transparent: true, opacity: 0.85 }), ); _marker.position.set(-TRACK_LEN / 2, 0.4, 0); _group.add(_marker); } // ============================================================================= // live data handler // ============================================================================= function _onKla(j) { // Honesty label read VERBATIM — never upgraded. This module's endpoint puts // the label at TOP LEVEL (j.label); we also defensively check payload.label // in case the response is wrapped, then fall back to the honest default. const rawLabel = (j && j.label != null) ? j.label : (j && j.payload && j.payload.label != null) ? j.payload.label : "MODELED"; S.label = String(rawLabel).toUpperCase(); S.dim = typeof j.dim === "number" ? j.dim : null; S.steps = typeof j.steps === "number" ? j.steps : null; S.lr = typeof j.lr === "number" ? j.lr : null; S.tol = typeof j.tol === "number" ? j.tol : null; S.klaErr = typeof j.kla_final_recon_error === "number" ? j.kla_final_recon_error : null; S.gatedErr = typeof j.gated_final_recon_error === "number" ? j.gated_final_recon_error : null; S.klaConv = typeof j.kla_convergence_step === "number" ? j.kla_convergence_step : null; S.gatedConv = typeof j.gated_convergence_step === "number" ? j.gated_convergence_step : null; S.improve = typeof j.improvement_ratio === "number" ? j.improvement_ratio : null; S.klaCurve = Array.isArray(j.kla_error_curve) ? j.kla_error_curve : null; S.gatedCurve = Array.isArray(j.gated_error_curve) ? j.gated_error_curve : null; _updateTracks(); _paintOverlay(); } // ============================================================================= // geometry updater — drives the two convergence tracks from live curve data // ============================================================================= function _updateTracks() { const live = S.state === "live"; const kla = live && S.klaCurve && S.klaCurve.length ? S.klaCurve : []; const gated = live && S.gatedCurve && S.gatedCurve.length ? S.gatedCurve : []; // shared error scale so the two lanes are directly comparable (higher bar = // higher reconstruction error = worse). Normalize by the max error seen. let maxErr = 0.0; for (let i = 0; i < kla.length; i++) if (kla[i] > maxErr) maxErr = kla[i]; for (let i = 0; i < gated.length; i++) if (gated[i] > maxErr) maxErr = gated[i]; if (maxErr <= 1e-9) maxErr = 1.0; function fill(bars, curve, colHi, colLo, emiHi, emiLo) { for (let i = 0; i < N_BARS; i++) { const mesh = bars[i]; // sample the (possibly shorter/longer) curve across the N_BARS bars const showBar = live && curve.length > 0; if (!showBar) { mesh.visible = false; mesh.scale.y = 0.001; mesh.material.opacity = 0.0; continue; } const idx = Math.min(curve.length - 1, Math.round((i / (N_BARS - 1)) * (curve.length - 1))); const err = curve[idx]; const h = Math.max(0.02, (err / maxErr) * MAX_H); mesh.visible = true; mesh.scale.y = h; mesh.position.y = h / 2; mesh.material.color.setHex(colHi); mesh.material.emissive.setHex(emiHi); mesh.material.emissiveIntensity = emiLo; mesh.material.opacity = 0.92; } } fill(_klaBars, kla, C_KLA, C_KLA, 0.55, 0.5); fill(_gatedBars, gated, C_GATED, C_GATED, 0.2, 0.16); // spine + plane + marker degrade to grey when not live _spine.material.color.setHex(live ? C_STREAM : C_DIM); _spine.material.opacity = live ? 0.5 : 0.15; if (_plane) { _plane.material.color.setHex(live ? C_PLANE : C_DIM); _plane.material.emissive.setHex(live ? C_PLANE : C_DIM); _plane.material.opacity = live ? 0.12 : 0.05; } if (_marker) { if (live && S.improve != null) { _marker.material.color.setHex(C_KLA); _marker.material.emissive.setHex(C_KLA); _marker.material.opacity = 0.85; } else { _marker.material.color.setHex(C_DIM); _marker.material.emissive.setHex(C_DIM); _marker.material.opacity = 0.3; } } } // ============================================================================= // per-frame animation // ============================================================================= function _onFrame() { const t = performance.now(); if (_group) _group.rotation.y = Math.sin(t * 0.00009) * 0.12; if (_plane) _plane.rotation.z = Math.sin(t * 0.0005) * 0.06; if (_marker) { _marker.rotation.y += 0.025; _marker.rotation.x += 0.012; const pulse = 1.0 + 0.15 * Math.sin(t * 0.004); _marker.scale.setScalar(pulse); // marker sweeps along the stream axis to read as the "projection head" const x0 = -TRACK_LEN / 2, x1 = TRACK_LEN / 2; const frac = (Math.sin(t * 0.0006) * 0.5 + 0.5); _marker.position.x = x0 + frac * (x1 - x0); } } // ============================================================================= // overlay // ============================================================================= function _buildOverlay() { const ctx = _ctx; _show = createShowcase(ctx, { id: ID, title: TITLE, accent: "#5b8dee", badge: _badge, chips: [{ label: "MODELED", text: "projection update", name: "kla" }], legend: ["MODELED", "SAMPLE"], description: 'A linear-attention layer stores memory as a matrix S. Each new key-value pair ' + '(k,v) defines a constraint S·k = v; KLA updates the state by ' + 'the orthogonal Kaczmarz projection onto that constraint ' + '(step = lr·(v \\u2212 S·k) kT/(k·k)) \\u2014 a principled scalar replacing ' + 'the ad-hoc gate of gated linear attention. Teal track = KLA, grey track = gated ' + 'baseline; bar height = reconstruction error. ' + 'Honesty label MODELED (deterministic projection simulation; NOT a trained model). 0 runtime CDN.', citations: "Kaczmarz Linear Attention arXiv:2605.08587 (orthogonal projection state-update vs ad-hoc gate). MODELED \u00b7 not claimed-as.", plain: { html: _plainHtml }, }); _el["kla-dim"] = _show.addField("state dim (S is dim\\u00d7dim)"); _el["kla-steps"] = _show.addField("key-value pairs streamed"); _el["kla-klaerr"] = _show.addField("KLA recon error \\u2014 MODELED"); _el["kla-gatederr"] = _show.addField("gated recon error (baseline)"); _el["kla-improve"] = _show.addField("improvement_ratio (gated\\u00f7kla)"); _el["kla-klaconv"] = _show.addField("KLA convergence step"); _el["kla-gatedconv"] = _show.addField("gated convergence step"); _el["kla-label"] = _show.addField("honesty label"); _paintOverlay(); } function _plainHtml() { const imp = S.improve != null ? S.improve.toFixed(2) + "\u00d7" : "loading\u2026"; const ke = S.klaErr != null ? S.klaErr.toFixed(3) : "loading\u2026"; const ge = S.gatedErr != null ? S.gatedErr.toFixed(3) : "loading\u2026"; return ( "What this means: A fast \\u201clinear attention\\u201d model remembers things in a running " + "memory M instead of re-reading the whole past every time. When a new fact arrives, older " + "systems just fade the memory by a hand-tuned amount (an \\u201cad-hoc gate\\u201d) and hope " + "for the best. KLA instead does the geometrically correct thing: it nudges the memory " + "by exactly the right, calculated amount so the new fact is stored while disturbing old facts as " + "little as possible \\u2014 like adjusting one note in a chord without knocking the others out of tune. " + "Here KLA rebuilds the stream of facts with error " + ke + " versus the old gate\\u2019s " + ge + ", " + "about a " + imp + " improvement, and it locks in sooner. Plain: a principled dial replaces a " + "guessed one, so the model remembers more accurately. This view is a MODELED simulation of " + "the projection math (arXiv:2605.08587), not a run of a trained model."); } function _tok(s) { if (s === "live") return null; if (s === "missing") return "NO-LIVE-DATA"; if (s === "degraded") return "DEGRADED"; if (s === "error") return "OFFLINE"; return "\u2026"; } function fx(v, d) { return typeof v === "number" ? v.toFixed(d) : "\u2014"; } function _set(id, v) { if (_el[id]) _el[id].textContent = v; } function _paintOverlay() { const t = _tok(S.state); _set("kla-dim", t || (S.dim != null ? String(S.dim) : "\u2014")); _set("kla-steps", t || (S.steps != null ? String(S.steps) : "\u2014")); _set("kla-klaerr", t || fx(S.klaErr, 4)); _set("kla-gatederr", t || fx(S.gatedErr, 4)); _set("kla-improve", t || (S.improve != null ? S.improve.toFixed(3) + "\u00d7" : "\u2014")); _set("kla-klaconv", t || (S.klaConv != null ? String(S.klaConv) : "\u2014")); _set("kla-gatedconv", t || (S.gatedConv != null ? String(S.gatedConv) : "\u2014")); // honesty label verbatim — never upgraded _set("kla-label", t || (S.label || "MODELED")); if (_show) { _show.setChip("kla", S.label || "MODELED", { text: "projection update" }); _show.refreshPlain(); } } // ============================================================================= // unmount — clean up everything; must not affect other organs // ============================================================================= export function unmount() { _polls.forEach((p) => { try { p.stop(); } catch (_) {} }); _polls = []; try { if (_show) _show.destroy(); } catch (_) {} try { if (_group && _stage) { _group.traverse((o) => { if (o.geometry && o.geometry.dispose) o.geometry.dispose(); if (o.material) { const ms = Array.isArray(o.material) ? o.material : [o.material]; ms.forEach((m) => { if (m.dispose) m.dispose(); }); } }); _stage.scene.remove(_group); } } catch (_) {} _group = _show = null; _floor = null; _spine = null; _plane = null; _klaBars = []; _gatedBars = []; _marker = null; _el = {}; _badge = null; _frameReg = false; _stage = _THREE = _ctx = null; S.label = S.dim = S.steps = S.lr = S.tol = null; S.klaErr = S.gatedErr = S.klaConv = S.gatedConv = S.improve = null; S.klaCurve = S.gatedCurve = null; S.state = "init"; } export default { id: ID, title: TITLE, endpoints: [EP], mount, unmount };