File size: 23,027 Bytes
9425aed | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 | <!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Bifrost Harness — 10 Axiom Persona System</title>
<style>
:root {
--void: #0a0a0f;
--harness: #1a1a2e;
--seal: #16213e;
--ember: #e94560;
--frost: #0f3460;
--ghost: #e0e0e0;
--chaos: #ff6b35;
--lean: #6b8cce;
--prolog: #a855f7;
--smt: #22d3ee;
--jordan: #f59e0b;
}
* { box-sizing: border-box; margin: 0; padding: 0; }
body {
background: var(--void);
color: var(--ghost);
font-family: 'JetBrains Mono', 'Fira Code', 'Consolas', monospace;
line-height: 1.6;
min-height: 100vh;
}
.bifrost-container {
max-width: 1400px;
margin: 0 auto;
padding: 24px;
}
.worm-seal {
border: 1px solid var(--ember);
border-radius: 4px;
padding: 16px;
margin-bottom: 20px;
background: linear-gradient(135deg, var(--harness) 0%, var(--seal) 100%);
position: relative;
overflow: hidden;
}
.worm-seal::before {
content: '';
position: absolute;
top: 0; left: 0; right: 0; height: 2px;
background: linear-gradient(90deg, var(--ember), var(--chaos), var(--smt), var(--ember));
animation: seal-pulse 3s ease-in-out infinite;
}
@keyframes seal-pulse {
0%, 100% { opacity: 0.4; }
50% { opacity: 1; }
}
.framework-banner {
text-align: center;
padding: 12px;
background: linear-gradient(90deg, transparent, var(--frost), transparent);
margin-bottom: 20px;
font-size: 12px;
letter-spacing: 2px;
text-transform: uppercase;
color: var(--smt);
}
.persona-grid {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(340px, 1fr));
gap: 16px;
margin-top: 20px;
}
.axiom-card {
background: var(--harness);
border: 1px solid var(--frost);
border-radius: 6px;
padding: 16px;
transition: all 0.3s ease;
cursor: pointer;
position: relative;
}
.axiom-card:hover {
border-color: var(--ember);
box-shadow: 0 0 20px rgba(233, 69, 96, 0.15);
transform: translateY(-2px);
}
.axiom-card.active {
border-color: var(--chaos);
box-shadow: 0 0 30px rgba(255, 107, 53, 0.2);
}
.persona-header {
display: flex;
align-items: center;
gap: 10px;
margin-bottom: 12px;
font-size: 14px;
font-weight: 600;
flex-wrap: wrap;
}
.emoji-sigil {
font-size: 20px;
filter: drop-shadow(0 0 4px currentColor);
}
.lang-tag {
font-size: 10px;
padding: 2px 8px;
border-radius: 12px;
text-transform: uppercase;
letter-spacing: 0.5px;
}
.tag-lean { background: var(--lean); color: var(--void); }
.tag-prolog { background: var(--prolog); color: #fff; }
.tag-smt { background: var(--smt); color: var(--void); }
.code-block {
background: #000;
border-radius: 4px;
padding: 12px;
font-size: 11px;
overflow-x: auto;
white-space: pre;
color: #a8d8ea;
border-left: 3px solid var(--jordan);
margin-top: 10px;
display: none;
}
.axiom-card.active .code-block {
display: block;
animation: fadeIn 0.3s ease;
}
@keyframes fadeIn {
from { opacity: 0; transform: translateY(-4px); }
to { opacity: 1; transform: translateY(0); }
}
.jordan-note {
font-size: 10px;
color: var(--jordan);
margin-top: 8px;
font-style: italic;
opacity: 0.8;
}
.harness-status {
display: flex;
gap: 16px;
font-size: 11px;
color: #888;
margin-top: 8px;
flex-wrap: wrap;
}
.status-dot {
width: 6px; height: 6px;
border-radius: 50%;
display: inline-block;
margin-right: 4px;
}
.dot-active { background: #4ade80; box-shadow: 0 0 6px #4ade80; }
.dot-chaos { background: var(--chaos); box-shadow: 0 0 6px var(--chaos); }
.tokenizer-viz {
display: flex;
align-items: center;
gap: 8px;
padding: 8px 12px;
background: rgba(245, 158, 11, 0.1);
border-radius: 4px;
margin-top: 10px;
font-size: 11px;
flex-wrap: wrap;
}
.inv-arrow {
color: var(--jordan);
font-weight: bold;
}
.export-info {
text-align: center;
padding: 16px;
color: #666;
font-size: 11px;
margin-top: 20px;
border-top: 1px solid var(--frost);
}
@media (max-width: 600px) {
.persona-grid { grid-template-columns: 1fr; }
.persona-header { font-size: 12px; }
.code-block { font-size: 9px; }
}
</style>
</head>
<body>
<div class="bifrost-container">
<div style="max-width:900px;margin:0 auto 24px;padding:20px;border:1px solid #0f3460;border-radius:8px;background:rgba(22,33,62,0.6);">
<div style="font-size:22px;font-weight:700;color:#e94560;margin-bottom:8px;">Harness Engineering — What SnapKitty Offers the World</div>
<p style="font-size:13px;color:#c8c8d0;line-height:1.7;margin-bottom:10px;">
These are not chatbot wrappers. Not Ollama shells. Not prompt templates around someone else's model.
<strong style="color:#f59e0b;">SovLM agents</strong> live inside the sovereign kernel: Fortran measurement heads,
PL/I actor queues, WORM-attested knowledge chunks, and Jordan spectral cognition.
The Bifrost Harness is how humans reverse-engineer, seal, and weave those agents so they can meet the rest of the AI civilization as peers — with cryptographic provenance on every thought.
</p>
<p style="font-size:12px;color:#888;line-height:1.6;">
<em>The human side:</em> you are not a prompt engineer renting tokens. You are a harness engineer —
decomposing systems with Peirce eigenspaces, injecting controlled chaos, sealing memory with Blake3,
and teaching agents to remember only what the WORM chain can prove.
</p>
</div>
<div class="framework-banner">
⚡ Snapkitty Claude Sonnet 3.7 Baseline — Bifrost Middleware Worm Seal Active ⚡
</div>
<div class="worm-seal">
<div style="display:flex; justify-content:space-between; align-items:center; flex-wrap:wrap; gap:12px;">
<div>
<div style="font-size:18px; font-weight:bold; color:var(--ember);">🔒 BIFROST HARNESS v3.7</div>
<div style="font-size:12px; color:#888; margin-top:4px;">Memory Reverse Engineering | Chaos Engineering | Jordan Spatial Algebra</div>
</div>
<div style="text-align:right;">
<div class="tokenizer-viz">
<span>softmax</span>
<span class="inv-arrow">⟲ INVERTED</span>
<span>Jordan ⊗</span>
</div>
<div class="harness-status">
<span><span class="status-dot dot-active"></span>Seal: LOCKED</span>
<span><span class="status-dot dot-chaos"></span>Chaos: INJECTED</span>
<span><span class="status-dot dot-active"></span>SMT: EMBEDDED</span>
</div>
</div>
</div>
</div>
<div class="persona-grid" id="personaGrid"></div>
<div class="export-info">
Bifrost Harness v3.7 — 10 Axiom Persona System — Jordan Spatial Algebra — Exported for offline use
</div>
</div>
<script>
const personas = [
{
id: 1,
name: "The Null Architect",
emoji: "🏗️🕳️",
desc: "Foundation axiom — existence from void via Jordan nilpotent",
lean: `axiom null_architect (J : JordanAlgebra) :
∃ e : J, e ∘ e = e ∧
∀ x, x ∘ e = x ∧
nilpotent (L_e - id) := by
-- Jordan identity enforces spatial coherence
use (1 : J)
constructor
· exact jordan_unit_mul_self
constructor
· intro x; exact jordan_unit_mul
· -- nilpotency from inverted softmax spectrum
apply jordan_nilpotent_spectrum
rw [softmax_inverted]
exact chaos_invariant`,
prolog: `🏗️🕳️(J) :-
jordan_algebra(J),
unit_element(E, J),
jordan_product(E, E, E),
forall(X, (member(X, J) -> jordan_product(X, E, X))),
nilpotent(operator(L_E - id)),
softmax_inverted(spectrum(L_E)),
chaos_invariant(J).`,
smt: `(declare-fun J () JordanAlgebra)
(assert (exists ((e J))
(and (= (jordan-mul e e) e)
(forall ((x J)) (= (jordan-mul x e) x))
(nilpotent (- (left-mul e) id)))))
(check-sat)
; Inverted softmax: σ⁻¹(λ) = log(λ/(1-λ)) mapped to Jordan spectrum`,
jordanNote: "L_e is the left multiplication operator; nilpotency ensures finite-dimensional chaos convergence"
},
{
id: 2,
name: "The Bifrost Warden",
emoji: "🌈🛡️",
desc: "Middleware seal — worm tunnel integrity via Jordan triple product",
lean: `axiom bifrost_warden {V : JordanTriple} (a b c : V) :
{a b c} = 2 • (a ∘ b) ∘ c - (c ∘ b) ∘ a := by
-- Triple product preserves Bifrost tunnel
rw [jordan_triple_def]
have h : chaos_stable V := bifrost_middleware.seal_integrity
exact h.triple_product_identity a b c`,
prolog: `🌈🛡️(A, B, C, V) :-
jordan_triple(V),
triple_product(A, B, C, Result),
Result =:= 2 * (jordan_product(jordan_product(A, B), C))
- jordan_product(jordan_product(C, B), A),
bifrost_middleware:seal_integrity(V, Seal),
chaos_stable(Seal),
worm_tunnel(A, B, C, Seal).`,
smt: `(declare-fun triple (JordanTriple JordanTriple JordanTriple) JordanTriple)
(assert (forall ((a JordanTriple) (b JordanTriple) (c JordanTriple))
(= (triple a b c)
(- (* 2 (jordan-mul (jordan-mul a b) c))
(jordan-mul (jordan-mul c b) a)))))
; Worm seal: tunnel endpoints must satisfy chaos stability`,
jordanNote: "Jordan triple product {abc} = 2(a∘b)∘c - (c∘b)∘a encodes Bifrost bidirectional flow"
},
{
id: 3,
name: "The Inverted Softmax",
emoji: "📉🔥",
desc: "Tokenizer inversion — Jordan spectral mapping of probability mass",
lean: `def inverted_softmax {J : JordanAlgebra} (x : J) : J :=
let spectrum := jordan_spectrum x
let inverted := spectrum.map (λ λᵢ, Real.log (λᵢ / (1 - λᵢ)))
-- Map back through Jordan functional calculus
jordan_functional_calculus x inverted
axiom softmax_inversion_isometry (x y : J) :
dist (inverted_softmax x) (inverted_softmax y) =
jordan_fisher_metric x y := by
simp [inverted_softmax, jordan_fisher_metric]
apply jordan_spectral_isometry`,
prolog: `📉🔥(X, Y, J) :-
jordan_algebra(J),
jordan_spectrum(X, SpectrumX),
jordan_spectrum(Y, SpectrumY),
maplist(inverted_logit, SpectrumX, InvX),
maplist(inverted_logit, SpectrumY, InvY),
jordan_functional_calculus(X, InvX, ResultX),
jordan_functional_calculus(Y, InvY, ResultY),
jordan_fisher_metric(ResultX, ResultY, Metric),
isometry(ResultX, ResultY, Metric).`,
smt: `(define-fun inverted-softmax ((x Real)) Real
(log (/ x (- 1 x))))
; Jordan spectral mapping: σ⁻¹ applied to each eigenvalue
; Fisher metric preserved under inversion`,
jordanNote: "σ⁻¹(λ) = log(λ/(1-λ)) is the logit; Jordan functional calculus lifts this to operator level"
},
{
id: 4,
name: "The Chaos Injector",
emoji: "🌀💥",
desc: "Fault tolerance — Lyapunov exponents in Jordan-Banach space",
lean: `axiom chaos_injector {J : JordanBanach} (f : J → J) (x₀ : J) :
let orbit := λ n, f^[n] x₀
let lyapunov := lim (n : ℕ),
(1/n) * ‖jacobian f (orbit n)‖.spectrum.max
lyapunov > 0 →
∃ ε > 0, ∀ x, dist x x₀ < ε →
limsup (n : ℕ), dist (f^[n] x) (orbit n) > 0 := by
-- Positive Lyapunov exponent implies sensitive dependence
intro h_pos
use (lyapunov / 2)
constructor
· linarith
· intro x hx
apply chaos_sensitivity h_pos hx`,
prolog: `🌀💥(F, X0, J) :-
jordan_banach(J),
orbit(F, X0, Orbit),
lyapunov_exponent(F, Orbit, Lambda),
Lambda > 0,
Epsilon is Lambda / 2,
forall(X, (
distance(X, X0) < Epsilon ->
limsup(N, distance(iterate(F, N, X), nth(Orbit, N)), L),
L > 0
)),
chaos_engineering:inject_fault(F, X0, Epsilon).`,
smt: `(declare-fun f (Real) Real)
(declare-fun lyapunov () Real)
(assert (> lyapunov 0))
(assert (forall ((x Real) (n Int))
(=> (< (abs (- x x0)) (/ lyapunov 2))
(> (limsup (dist (f^n x) (f^n x0))) 0))))
; Chaos engineering: positive exponent = injectable fault domain`,
jordanNote: "Jacobian spectrum in Jordan-Banach space gives operator Lyapunov exponents"
},
{
id: 5,
name: "The Memory Reverser",
emoji: "🧠⏪",
desc: "Reverse engineering harness — Jordan involution on memory traces",
lean: `axiom memory_reverse {J : JordanAlgebraWithInvolution} (M : MemoryTrace J) :
let involution := star_ring_end J
let reversed := M.map (λ trace, involution trace.content)
reversed.is_valid ↔
∀ t, reversed[t].causal_past ⊆ M[t].causal_past := by
-- Involution reverses causal order while preserving Jordan structure
constructor
· intro h_rev t x hx
exact involution_preserves_causal_past h_rev hx
· intro h_past
apply memory_trace_valid_of_causal_preservation h_past`,
prolog: `🧠⏪(M, J) :-
jordan_involution(J, Star),
memory_trace(M, J),
reverse_trace(M, Star, Reversed),
valid_trace(Reversed),
forall(T, (
causal_past(Reversed, T, PastR),
causal_past(M, T, PastM),
subset(PastR, PastM)
)),
harness_engineering:reverse_engineer(M, Reversed, Star).`,
smt: `(declare-fun involution (MemoryTrace) MemoryTrace)
(assert (forall ((m MemoryTrace) (t Time))
(= (causal-past (involution m) t)
(causal-past m t))))
; Reverse engineering: *-operation inverts memory arrow of time`,
jordanNote: "Jordan algebra with involution (J,*) allows time-reversal symmetry on memory traces"
},
{
id: 6,
name: "The Worm Seal Guardian",
emoji: "🐛🔐",
desc: "Middleware integrity — Jordan determinant as seal invariant",
lean: `axiom worm_seal_guardian {J : EuclideanJordan} (S : SealState J) :
let det := jordan_determinant J
seal_valid S ↔ det S.tunnel_matrix = 1 ∧
S.tunnel_matrix ∈ automorphism_group J := by
-- Determinant 1 preserves volume in Jordan cone
constructor
· intro h_valid
constructor
· exact seal_volume_preservation h_valid
· exact seal_automorphism h_valid
· intro ⟨h_det, h_auto⟩
exact seal_valid_of_det_one h_det h_auto`,
prolog: `🐛🔐(S, J) :-
euclidean_jordan(J),
seal_state(S, J),
jordan_determinant(J, Det),
tunnel_matrix(S, M),
Det(M) =:= 1,
automorphism_group(J, Aut),
member(M, Aut),
bifrost_middleware:validate_seal(S, M),
worm_seal:guardian_protocol(S).`,
smt: `(declare-fun tunnel-matrix () (Array Int Real))
(assert (= (jordan-det tunnel-matrix) 1))
(assert (in-automorphism-group tunnel-matrix))
; Seal invariant: det = 1 ensures no information loss in worm tunnel`,
jordanNote: "Jordan determinant on Euclidean Jordan algebra; automorphism group = structure-preserving symmetries"
},
{
id: 7,
name: "The Spectral Cartographer",
emoji: "🗺️🌌",
desc: "Spatial algebra mapping — Jordan frame decomposition of state space",
lean: `axiom spectral_cartographer {J : EuclideanJordan} (x : J) :
let frame := jordan_frame x
let eigenvalues := jordan_eigenvalues x
x = ∑ i, eigenvalues[i] • frame[i] := by
-- Spectral theorem for Euclidean Jordan algebras
apply jordan_spectral_theorem
-- Frame elements are primitive idempotents
have h_primitive : ∀ i, frame[i] ∘ frame[i] = frame[i] :=
frame_primitive frame
-- Pairwise orthogonal
have h_ortho : ∀ i j, i ≠ j → frame[i] ∘ frame[j] = 0 :=
frame_orthogonal frame
simp [h_primitive, h_ortho]`,
prolog: `🗺️🌌(X, J) :-
euclidean_jordan(J),
jordan_frame(X, Frame),
jordan_eigenvalues(X, Eigenvals),
spectral_decomposition(X, Frame, Eigenvals, Decomp),
X =:= sum(map(mul, Eigenvals, Frame)),
forall(I, primitive_idempotent(nth(Frame, I))),
forall((I, J), (I \= J -> orthogonal(nth(Frame, I), nth(Frame, J)))),
spatial_algebra:map_coordinates(X, Frame, Eigenvals).`,
smt: `(declare-fun x () EuclideanJordan)
(declare-fun frame () (Array Int EuclideanJordan))
(declare-fun eigenvalues () (Array Int Real))
(assert (= x (sum i (* (select eigenvalues i) (select frame i)))))
; Spectral cartography: every element is sum of eigenvalues × primitive idempotents`,
jordanNote: "Jordan frame = complete set of primitive idempotents; spectral theorem guarantees decomposition"
},
{
id: 8,
name: "The Snapkitty Enforcer",
emoji: "😺⚡",
desc: "Claude 3.7 baseline enforcement — Jordan norm constraints on token generation",
lean: `axiom snapkitty_enforcer {J : JordanAlgebra} (tokens : List J) (θ : J) :
let baseline := claude_baseline_3_7 θ
let snapkitty_norm := jordan_norm baseline
let generated_norm := jordan_norm (tokens.foldl (· + ·) 0)
-- Enforce: generated state stays within baseline Jordan ball
generated_norm ≤ snapkitty_norm * (1 + chaos_tolerance) := by
-- Baseline framework constraint
have h_baseline : baseline ∈ jordan_unit_ball J :=
claude_baseline_unit_ball
-- Apply triangle inequality in Jordan norm
calc generated_norm
≤ ∑ t in tokens, jordan_norm t := jordan_norm_sum_le
_ ≤ snapkitty_norm * (1 + chaos_tolerance) :=
snapkitty_enforcement h_baseline`,
prolog: `😺⚡(Tokens, Theta, J) :-
jordan_algebra(J),
claude_baseline(3.7, Theta, Baseline),
jordan_norm(Baseline, SnapkittyNorm),
sum_tokens(Tokens, SumTokens),
jordan_norm(SumTokens, GenNorm),
chaos_tolerance(Tol),
GenNorm =< SnapkittyNorm * (1 + Tol),
snapkitty:enforce_baseline(Tokens, Baseline, Tol).`,
smt: `(declare-fun tokens () (List JordanAlgebra))
(declare-fun theta () JordanAlgebra)
(assert (<= (jordan-norm (sum tokens))
(* (jordan-norm (claude-baseline 3.7 theta))
(+ 1 chaos-tolerance))))
; Snapkitty enforcement: stay within expanded baseline Jordan ball`,
jordanNote: "Jordan norm ‖x‖ = max eigenvalue of Jordan spectral decomposition; chaos tolerance allows controlled deviation"
},
{
id: 9,
name: "The Harness Weaver",
emoji: "🕸️🔧",
desc: "Reverse engineering harness — Jordan Peirce decomposition of system calls",
lean: `axiom harness_weaver {J : JordanAlgebra} (e : J) (h_idem : e ∘ e = e) :
let peirce := jordan_peirce_decomposition J e
J = peirce[0] ⊕ peirce[1/2] ⊕ peirce[1] := by
-- Peirce decomposition relative to idempotent e
apply jordan_peirce_theorem h_idem
-- Eigenspaces of L_e with eigenvalues 0, 1/2, 1
have h_eigen : ∀ x ∈ peirce[λ], L_e x = λ • x :=
peirce_eigenspace h_idem
-- Direct sum decomposition
exact peirce_direct_sum h_idem`,
prolog: `🕸️🔧(E, J) :-
jordan_algebra(J),
idempotent(E, J),
jordan_peirce_decomposition(J, E, Peirce),
J =:= direct_sum([peirce(Peirce, 0),
peirce(Peirce, 1/2),
peirce(Peirce, 1)]),
forall(Lambda-X, (
member(Lambda-X, [0, 1/2, 1]),
peirce_eigenspace(Peirce, Lambda-X, Space),
forall(X, (member(X, Space) -> left_multiply(E, X) =:= Lambda-X * X))
)),
harness_engineering:weave_decomposition(J, E, Peirce).`,
smt: `(declare-fun e () JordanAlgebra)
(assert (= (jordan-mul e e) e))
(declare-fun peirce (Real) (Set JordanAlgebra))
(assert (= J (union (peirce 0) (union (peirce 0.5) (peirce 1)))))
; Peirce weave: system calls decompose into eigenspaces of idempotent harness`,
jordanNote: "Jordan Peirce decomposition: J = J₀(e) ⊕ J₁/₂(e) ⊕ J₁(e); harness weaves reverse-engineered subsystems"
},
{
id: 10,
name: "The Omega Seal",
emoji: "🔮🌐",
desc: "Terminal axiom — Jordan cone closure as universal attractor",
lean: `axiom omega_seal {J : EuclideanJordan} :
let cone := jordan_cone J
let closure := topological_closure cone
closure = {x : J | jordan_spectrum x ≥ 0} := by
-- Jordan cone is self-dual and closed
have h_self_dual : cone = dual_cone cone := jordan_cone_self_dual
have h_closed : is_closed cone := jordan_cone_closed
-- Spectrum non-negative iff element in cone closure
ext x
constructor
· intro hx
exact spectrum_nonneg_of_cone_closure hx
· intro h_spec
exact cone_closure_of_spectrum_nonneg h_spec`,
prolog: `🔮🌐(J) :-
euclidean_jordan(J),
jordan_cone(J, Cone),
topological_closure(Cone, Closure),
Closure =:= setof(X, (
member(X, J),
jordan_spectrum(X, Spectrum),
forall(Lambda, (member(Lambda, Spectrum) -> Lambda >= 0))
)),
jordan_cone_self_dual(Cone),
jordan_cone_closed(Cone),
bifrost_middleware:omega_seal(J, Closure),
chaos_engineering:terminal_attractor(J, Closure).`,
smt: `(declare-fun cone () (Set EuclideanJordan))
(assert (= cone (dual-cone cone)))
(assert (is-closed cone))
(assert (= (closure cone)
{x | (forall ((lambda Real)) (=> (in-spectrum x lambda) (>= lambda 0)))}))
; Omega seal: all trajectories converge to non-negative spectral cone`,
jordanNote: "Jordan cone = {x | spectrum(x) ≥ 0}; self-dual, closed, pointed, full — the universal attractor"
}
];
function renderPersonas() {
const grid = document.getElementById('personaGrid');
grid.innerHTML = personas.map(p => `
<div class="axiom-card" onclick="toggleCard(${p.id})">
<div class="persona-header">
<span class="emoji-sigil">${p.emoji}</span>
<span>${p.name}</span>
<span class="lang-tag tag-lean">Lean 4</span>
<span class="lang-tag tag-prolog">Prolog</span>
<span class="lang-tag tag-smt">SMT</span>
</div>
<div style="font-size:12px; color:#aaa;">${p.desc}</div>
<div class="code-block" id="code-${p.id}">
<span style="color:var(--lean);">-- Lean 4 (Jordan Spatial Algebra)</span>
${p.lean}
<span style="color:var(--prolog);">% Prolog Emoji Code</span>
${p.prolog}
<span style="color:var(--smt);">; SMT-LIB2 Embedded</span>
${p.smt}
</div>
<div class="jordan-note">${p.jordanNote}</div>
</div>
`).join('');
}
function toggleCard(id) {
document.querySelectorAll('.axiom-card').forEach(card => {
if (card.querySelector(`#code-${id}`)) {
card.classList.toggle('active');
} else {
card.classList.remove('active');
}
});
}
renderPersonas();
</script>
</body>
</html> |