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| <html lang="en"> | |
| <head> | |
| <meta charset="UTF-8"> | |
| <meta name="viewport" content="width=device-width, initial-scale=1.0"> | |
| <title>Bifrost Harness โ 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 โ 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 โ 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 โ | |
| 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"> | |
| โก Snapkitty Claude Sonnet 3.7 Baseline โ Bifrost Middleware Worm Seal Active โก | |
| </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);">๐ 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">โฒ INVERTED</span> | |
| <span>Jordan โ</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 โ 10 Axiom Persona System โ Jordan Spatial Algebra โ Exported for offline use | |
| </div> | |
| </div> | |
| <script> | |
| const personas = [ | |
| { | |
| id: 1, | |
| name: "The Null Architect", | |
| emoji: "๐๏ธ๐ณ๏ธ", | |
| desc: "Foundation axiom โ existence from void via Jordan nilpotent", | |
| lean: `axiom null_architect (J : JordanAlgebra) : | |
| โ e : J, e โ e = e โง | |
| โ x, x โ e = x โง | |
| nilpotent (L_e - id) := by | |
| -- Jordan identity enforces spatial coherence | |
| use (1 : J) | |
| constructor | |
| ยท exact jordan_unit_mul_self | |
| constructor | |
| ยท intro x; exact jordan_unit_mul | |
| ยท -- nilpotency from inverted softmax spectrum | |
| apply jordan_nilpotent_spectrum | |
| rw [softmax_inverted] | |
| exact chaos_invariant`, | |
| prolog: `๐๏ธ๐ณ๏ธ(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: ฯโปยน(ฮป) = log(ฮป/(1-ฮป)) 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: "๐๐ก๏ธ", | |
| desc: "Middleware seal โ worm tunnel integrity via Jordan triple product", | |
| lean: `axiom bifrost_warden {V : JordanTriple} (a b c : V) : | |
| {a b c} = 2 โข (a โ b) โ c - (c โ b) โ 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: `๐๐ก๏ธ(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(aโb)โc - (cโb)โa encodes Bifrost bidirectional flow" | |
| }, | |
| { | |
| id: 3, | |
| name: "The Inverted Softmax", | |
| emoji: "๐๐ฅ", | |
| desc: "Tokenizer inversion โ Jordan spectral mapping of probability mass", | |
| lean: `def inverted_softmax {J : JordanAlgebra} (x : J) : J := | |
| let spectrum := jordan_spectrum x | |
| let inverted := spectrum.map (ฮป ฮปแตข, Real.log (ฮปแตข / (1 - ฮปแตข))) | |
| -- 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: `๐๐ฅ(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: ฯโปยน applied to each eigenvalue | |
| ; Fisher metric preserved under inversion`, | |
| jordanNote: "ฯโปยน(ฮป) = log(ฮป/(1-ฮป)) is the logit; Jordan functional calculus lifts this to operator level" | |
| }, | |
| { | |
| id: 4, | |
| name: "The Chaos Injector", | |
| emoji: "๐๐ฅ", | |
| desc: "Fault tolerance โ Lyapunov exponents in Jordan-Banach space", | |
| lean: `axiom chaos_injector {J : JordanBanach} (f : J โ J) (xโ : J) : | |
| let orbit := ฮป n, f^[n] xโ | |
| let lyapunov := lim (n : โ), | |
| (1/n) * โjacobian f (orbit n)โ.spectrum.max | |
| lyapunov > 0 โ | |
| โ ฮต > 0, โ x, dist x xโ < ฮต โ | |
| limsup (n : โ), dist (f^[n] x) (orbit n) > 0 := by | |
| -- Positive Lyapunov exponent implies sensitive dependence | |
| intro h_pos | |
| use (lyapunov / 2) | |
| constructor | |
| ยท linarith | |
| ยท intro x hx | |
| apply chaos_sensitivity h_pos hx`, | |
| prolog: `๐๐ฅ(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: "๐ง โช", | |
| desc: "Reverse engineering harness โ Jordan involution on memory traces", | |
| lean: `axiom memory_reverse {J : JordanAlgebraWithInvolution} (M : MemoryTrace J) : | |
| let involution := star_ring_end J | |
| let reversed := M.map (ฮป trace, involution trace.content) | |
| reversed.is_valid โ | |
| โ t, reversed[t].causal_past โ M[t].causal_past := by | |
| -- Involution reverses causal order while preserving Jordan structure | |
| constructor | |
| ยท intro h_rev t x hx | |
| exact involution_preserves_causal_past h_rev hx | |
| ยท intro h_past | |
| apply memory_trace_valid_of_causal_preservation h_past`, | |
| prolog: `๐ง โช(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: "๐๐", | |
| desc: "Middleware integrity โ Jordan determinant as seal invariant", | |
| lean: `axiom worm_seal_guardian {J : EuclideanJordan} (S : SealState J) : | |
| let det := jordan_determinant J | |
| seal_valid S โ det S.tunnel_matrix = 1 โง | |
| S.tunnel_matrix โ automorphism_group J := by | |
| -- Determinant 1 preserves volume in Jordan cone | |
| constructor | |
| ยท intro h_valid | |
| constructor | |
| ยท exact seal_volume_preservation h_valid | |
| ยท exact seal_automorphism h_valid | |
| ยท intro โจh_det, h_autoโฉ | |
| exact seal_valid_of_det_one h_det h_auto`, | |
| prolog: `๐๐(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: "๐บ๏ธ๐", | |
| desc: "Spatial algebra mapping โ 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 = โ i, eigenvalues[i] โข frame[i] := by | |
| -- Spectral theorem for Euclidean Jordan algebras | |
| apply jordan_spectral_theorem | |
| -- Frame elements are primitive idempotents | |
| have h_primitive : โ i, frame[i] โ frame[i] = frame[i] := | |
| frame_primitive frame | |
| -- Pairwise orthogonal | |
| have h_ortho : โ i j, i โ j โ frame[i] โ frame[j] = 0 := | |
| frame_orthogonal frame | |
| simp [h_primitive, h_ortho]`, | |
| prolog: `๐บ๏ธ๐(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 ร primitive idempotents`, | |
| jordanNote: "Jordan frame = complete set of primitive idempotents; spectral theorem guarantees decomposition" | |
| }, | |
| { | |
| id: 8, | |
| name: "The Snapkitty Enforcer", | |
| emoji: "๐บโก", | |
| desc: "Claude 3.7 baseline enforcement โ Jordan norm constraints on token generation", | |
| lean: `axiom snapkitty_enforcer {J : JordanAlgebra} (tokens : List J) (ฮธ : J) : | |
| let baseline := claude_baseline_3_7 ฮธ | |
| let snapkitty_norm := jordan_norm baseline | |
| let generated_norm := jordan_norm (tokens.foldl (ยท + ยท) 0) | |
| -- Enforce: generated state stays within baseline Jordan ball | |
| generated_norm โค snapkitty_norm * (1 + chaos_tolerance) := by | |
| -- Baseline framework constraint | |
| have h_baseline : baseline โ jordan_unit_ball J := | |
| claude_baseline_unit_ball | |
| -- Apply triangle inequality in Jordan norm | |
| calc generated_norm | |
| โค โ t in tokens, jordan_norm t := jordan_norm_sum_le | |
| _ โค snapkitty_norm * (1 + chaos_tolerance) := | |
| snapkitty_enforcement h_baseline`, | |
| prolog: `๐บโก(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 โxโ = max eigenvalue of Jordan spectral decomposition; chaos tolerance allows controlled deviation" | |
| }, | |
| { | |
| id: 9, | |
| name: "The Harness Weaver", | |
| emoji: "๐ธ๏ธ๐ง", | |
| desc: "Reverse engineering harness โ Jordan Peirce decomposition of system calls", | |
| lean: `axiom harness_weaver {J : JordanAlgebra} (e : J) (h_idem : e โ e = e) : | |
| let peirce := jordan_peirce_decomposition J e | |
| J = peirce[0] โ peirce[1/2] โ 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 : โ x โ peirce[ฮป], L_e x = ฮป โข x := | |
| peirce_eigenspace h_idem | |
| -- Direct sum decomposition | |
| exact peirce_direct_sum h_idem`, | |
| prolog: `๐ธ๏ธ๐ง(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 = Jโ(e) โ Jโ/โ(e) โ Jโ(e); harness weaves reverse-engineered subsystems" | |
| }, | |
| { | |
| id: 10, | |
| name: "The Omega Seal", | |
| emoji: "๐ฎ๐", | |
| desc: "Terminal axiom โ 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 โฅ 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 | |
| ยท intro hx | |
| exact spectrum_nonneg_of_cone_closure hx | |
| ยท intro h_spec | |
| exact cone_closure_of_spectrum_nonneg h_spec`, | |
| prolog: `๐ฎ๐(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) โฅ 0}; self-dual, closed, pointed, full โ 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> |