SCBE-AETHERMOORE Patent Figures
FIG. 1: SCBE 14-Layer Pipeline Block Diagram
+-----------------------------------------------------------------------------+
| SCBE 14-LAYER PIPELINE |
+-----------------------------------------------------------------------------+
| |
| +-------+ +-------+ +-------+ +-------+ +-------+ |
| | L1 |-->| L2 |-->| L3 |-->| L4 |-->| L5 | |
| |Context| |Realify| |Weight | |Poincare| |Mobius | |
| |Acquire| |C^D->R^2D| |G^{1/2}| |Embed | |Stabil.| |
| +-------+ +-------+ +-------+ +-------+ +-------+ |
| | | |
| v v |
| c(t) in C^D u in B^n_{1-e} |
| |
| +-------+ +-------+ +-------+ +-------+ +-------+ |
| | L6 |-->| L7 |-->| L8 |-->| L9 |-->| L10 | |
| |Breath | |Phase | |Realm | |Spectral| |Spin | |
| | b(t) | |Q*(a+u)| |Distance| |Coherence| |Coherence| |
| +-------+ +-------+ +-------+ +-------+ +-------+ |
| | | | | |
| v v v v |
| diffeomorphism d* = min d_H S_spec in[0,1] C_spin in[0,1] |
| |
| +-------+ +-------+ +-------+ +-------+ |
| | L11 |-->| L12 |-->| L13 |-->| L14 | |
| | Trust | |Harmonic| |Composite| |Audio | |
| | tau | |H(d*,R) | | Risk' | |Coherence| |
| +-------+ +-------+ +-------+ +-------+ |
| | | | | |
| v v v v |
| tau in [0,1] R^{(d*)^2} Risk'->Decision S_audio in[0,1] |
| |
+-----------------------------------------------------------------------------+
|
v
+-------------------------------+
| CRYPTOGRAPHIC ENVELOPE |
| AES-256-GCM |
| + Fail-to-Noise Output |
+-------------------------------+
FIG. 2: Dataflow Diagram - Computed Values Between Layers
+--------------------------------------------------------------------------+
| DATA FLOW THROUGH PIPELINE |
+--------------------------------------------------------------------------+
INPUT OUTPUT
| |
v v
+-----+ +-----+ +-----+ +-----+ +-----+ +-----------------+
|c(t) |--->|x(t) |--->|x_G |--->| u_0 |--->| u_s |--->| u_b (breathing) |
|C^D | |R^2D | |R^2D | |B^n | |B^n | | B^n |
+-----+ +-----+ +-----+ +-----+ +-----+ +--------+--------+
|
v
+-------------------------------------------------------------------------+
| |
| +---------+ +---------+ +---------+ |
| | u_p |<--------| u_b | | d* | |
| | (phase) | | |-------->| realm | |
| | B^n | | | |distance | |
| +----+----+ +---------+ +----+----+ |
| | | |
| v v |
| +-------------------------------------------------------------+ |
| | COHERENCE EXTRACTION | |
| | +---------+ +---------+ +---------+ +---------+ | |
| | | S_spec | | C_spin | | tau | | S_audio | | |
| | | [0,1] | | [0,1] | | [0,1] | | [0,1] | | |
| | +----+----+ +----+----+ +----+----+ +----+----+ | |
| +-------+------------+------------+------------+--------------+ |
| | | | | |
| +------------+-----+------+------------+ |
| v |
| +-----------------+ |
| | Risk_base | |
| | = Sum w_i(1-coh)| |
| +--------+--------+ |
| | |
| v |
| +-----------------+ +-----------------+ |
| | Risk' |<-----| H(d*, R) | |
| | = Risk_base * H | | = R^{(d*)^2} | |
| +--------+--------+ +-----------------+ |
| | |
+-----------------------------+-------------------------------------------+
v
+-----------------+
| DECISION |
| ALLOW/QUARANTINE|
| /DENY |
+-----------------+
FIG. 3: Verification-Order Flowchart (Cheapest Reject First)
+------------------+
| REQUEST ARRIVES |
+--------+---------+
|
v
+------------------+
| 1. TIMESTAMP | O(1)
| SKEW CHECK |
+--------+---------+
|
+------------+------------+
| |
PASS v FAIL v
| +------------------+
| | FAIL-TO-NOISE |
| | OUTPUT |
| +------------------+
v
+------------------+
| 2. REPLAY GUARD | O(1) amortized
| CHECK |
+--------+---------+
|
+------------+------------+
| |
PASS v FAIL v
| +------------------+
| | FAIL-TO-NOISE |
| +------------------+
v
+------------------+
| 3. NONCE PREFIX | O(1)
| VALIDATION |
+--------+---------+
|
+--------+--------+
| |
PASS v FAIL v
| +------------------+
| | FAIL-TO-NOISE |
| +------------------+
v
+------------------+
| 4. CONTEXT | O(n)
| COMMITMENT |
+--------+---------+
|
+--------+--------+
| |
v FAIL v
| +------------------+
| | FAIL-TO-NOISE |
| +------------------+
v
+------------------+
| 5-8. HYPERBOLIC | O(n) to O(n log n)
| PROCESSING |
+--------+---------+
|
v
+------------------+
| 9. RISK | O(1)
| DECISION |
+--------+---------+
|
+----+----+------------+
| | |
v v v
ALLOW QUARANTINE DENY
| | |
v v v
+-------+ +-------+ +------------------+
|CREATE | |CREATE | | FAIL-TO-NOISE |
|ENVELOPE| |ENVELOPE| | OUTPUT |
| | |+AUDIT | +------------------+
+-------+ +-------+
FIG. 4: Context Commitment and HKDF Key Derivation
+-------------------------------------------------------------------------+
| CONTEXT COMMITMENT & KEY DERIVATION |
+-------------------------------------------------------------------------+
+-----------------------------+
| CONTEXT c(t) |
| c = (c_1, ..., c_D) |
| c_k = a_k * e^{i*phi_k}|
+--------------+--------------+
|
v
+-----------------------------+
| JCS CANONICALIZE |
| (deterministic ordering) |
+--------------+--------------+
|
v
+-----------------------------+
| SHA-256 HASH |
| H(canonical_context) |
+--------------+--------------+
|
v
+-----------------------------+
| CONTEXT COMMITMENT |
| commitment = H(c) |
+--------------+--------------+
|
+--------------+--------------+
| |
v v
+---------------------+ +---------------------+
| STORED IN AAD | | HKDF DERIVATION |
| canonical_body_hash| | |
+---------------------+ | IKM = master_key |
| salt = commitment |
| info = "scbe-v1" |
+----------+----------+
|
v
+---------------------+
| DERIVED KEY |
| 256-bit AES key |
+---------------------+
FIG. 5: Poincare Ball Embedding with Clamping Operator
+-------------------------------------------------------------------------+
| POINCARE BALL EMBEDDING (A4) |
+-------------------------------------------------------------------------+
EUCLIDEAN SPACE R^n
+-----------------------------+
| |
| x |
| *---------------------->|
| | |
| | ||x|| can be any |
| | positive value |
| | |
+-----+-----------------------+
|
| Psi_alpha(x) = tanh(alpha*||x||) * x/||x||
|
v
+-----------------------------+
| POINCARE BALL B^n |
| |
| .---. |
| / * \ |
| | u | |
| | ||u||<1| |
| \ / |
| '---' |
| |
| Unit ball boundary |
+-----------------------------+
|
| Pi_eps(u) = (1-eps)*u/||u|| if ||u|| > 1-eps
|
v
+-----------------------------+
| CLAMPED SUB-BALL |
| B^n_{1-eps} |
| |
| .---. |
| / * \ |
| | u_c | |
| |<=1-eps| |
| \ / |
| '---' |
| [safety margin] |
+-----------------------------+
CLAMPING GUARANTEES:
* ||u|| <= 1 - eps_ball (always strictly inside ball)
* Denominators in hyperbolic formulas never approach zero
* Numerical stability under adversarial inputs
FIG. 6: Breathing Transform (Diffeomorphism)
+-------------------------------------------------------------------------+
| BREATHING TRANSFORM T_breath(u; b) - AXIOM A6 |
| |
| WARNING: THIS IS A DIFFEOMORPHISM, NOT AN ISOMETRY |
+-------------------------------------------------------------------------+
FORMULA: T_breath(u; b) = tanh(b * artanh(||u||)) * u/||u||
+---------------------------------------------------------------------+
| |
| b < 1 (CONTRACTION) b = 1 (IDENTITY) b > 1 (EXPANSION) |
| |
| .---. .---. .---. |
| / \ / \ / \ |
| | *-->* | | * | | *<--* | |
| | u u_b | | u | | u_b u | |
| | | | | | | |
| \ / \ / \ / |
| '---' '---' '---' |
| |
| Points move Points stay Points move |
| toward center in place toward edge |
| |
+---------------------------------------------------------------------+
RADIAL SCALING BEHAVIOR:
+---------------------------------------------------------------------+
| |
| new_r | |
| 1.0 + / b=2.0 |
| | / |
| 0.8 + / |
| | / / b=1.0 (identity) |
| 0.6 + / / |
| | / / |
| 0.4 + / / |
| | / / \ b=0.5 |
| 0.2 + / / |
| | / / |
| 0.0 +--------+----+--------------------------------------------> |
| 0 0.2 0.4 0.6 0.8 1.0 old_r |
| |
+---------------------------------------------------------------------+
CRITICAL PROPERTY:
+---------------------------------------------------------------------+
| d_H(T_breath(u), T_breath(v)) != d_H(u, v) when b != 1 |
| |
| The breathing transform CHANGES hyperbolic distances. |
| It is a smooth bijection (diffeomorphism) but NOT distance- |
| preserving (not an isometry). |
+---------------------------------------------------------------------+
FIG. 7: Phase Transform (Isometry)
+-------------------------------------------------------------------------+
| PHASE TRANSFORM T_phase(u) - AXIOM A7 |
| |
| THIS IS AN ISOMETRY (DISTANCE-PRESERVING) |
+-------------------------------------------------------------------------+
FORMULA: T_phase(u) = Q * (a (+) u)
where:
(+) = Mobius addition
Q = orthogonal rotation matrix in O(n)
a = phase shift vector in B^n
+---------------------------------------------------------------------+
| |
| STEP 1: MOBIUS ADDITION STEP 2: ROTATION |
| |
| .---. .---. |
| / \ / \ |
| | * | a (+) u | * | Q * v |
| | u | --------> | v | --------> |
| | * a | | | |
| \ / \ / |
| '---' '---' |
| |
| Hyperbolic translation Euclidean rotation |
| (preserves d_H) (preserves d_H) |
| |
+---------------------------------------------------------------------+
MOBIUS ADDITION FORMULA (A5):
+---------------------------------------------------------------------+
| |
| (1 + 2<u,v> + ||v||^2) * u + (1 - ||u||^2) * v |
| u (+) v = ------------------------------------------------ |
| 1 + 2<u,v> + ||u||^2 * ||v||^2 |
| |
+---------------------------------------------------------------------+
ISOMETRY PROPERTY:
+---------------------------------------------------------------------+
| d_H(T_phase(u), T_phase(v)) = d_H(u, v) ALWAYS |
| |
| The phase transform PRESERVES hyperbolic distances. |
| This is crucial for realm distance computation after phase. |
+---------------------------------------------------------------------+
FIG. 8: Hyperbolic Distance Computation
+-------------------------------------------------------------------------+
| HYPERBOLIC DISTANCE d_H(u, v) - AXIOM A5 |
+-------------------------------------------------------------------------+
FORMULA:
2 * ||u - v||^2
d_H(u, v) = arcosh( 1 + --------------------------------- )
(1 - ||u||^2) * (1 - ||v||^2)
WITH DENOMINATOR FLOOR:
denom = max( (1 - ||u||^2) * (1 - ||v||^2), eps^2 )
+---------------------------------------------------------------------+
| |
| POINCARE BALL VISUALIZATION |
| |
| .-----------. |
| / \ |
| / \ |
| | * | |
| | / \ | |
| | / \ | |
| | / \ | |
| | * * | |
| | u v | |
| | | |
| \ / |
| \ / |
| '-----------' |
| |
| Geodesic (shortest path) curves toward boundary |
| |
+---------------------------------------------------------------------+
DISTANCE PROPERTIES:
+---------------------------------------------------------------------+
| |
| 1. SYMMETRY: d_H(u, v) = d_H(v, u) |
| |
| 2. NON-NEGATIVE: d_H(u, v) >= 0 |
| |
| 3. IDENTITY: d_H(u, u) = 0 |
| |
| 4. TRIANGLE: d_H(u, w) <= d_H(u, v) + d_H(v, w) |
| |
| 5. BOUNDARY: d_H -> infinity as points approach boundary |
| |
+---------------------------------------------------------------------+
DENOMINATOR FLOOR GUARANTEE:
+---------------------------------------------------------------------+
| |
| The eps^2 floor ensures: |
| - No division by zero when points near boundary |
| - Bounded output even under adversarial inputs |
| - Numerical stability in floating-point arithmetic |
| |
+---------------------------------------------------------------------+
FIG. 9: Coherence Signal Extraction
+-------------------------------------------------------------------------+
| COHERENCE SIGNAL EXTRACTION |
| All outputs bounded in [0, 1] |
+-------------------------------------------------------------------------+
+---------------------------------------------------------------------+
| |
| INPUT SIGNALS COHERENCE OUTPUTS |
| |
| +-------------+ +-------------+ |
| | FFT Spectrum| -----------------> | S_spec | |
| | (frequency) | Energy ratio | [0, 1] | |
| +-------------+ with eps floor +-------------+ |
| |
| +-------------+ +-------------+ |
| | Phase Angles| -----------------> | C_spin | |
| | (phasors) | Mean magnitude | [0, 1] | |
| +-------------+ |Sum e^{i*th}|/N +-------------+ |
| |
| +-------------+ +-------------+ |
| | Hopfield | -----------------> | tau | |
| | Energy | Normalized | [0, 1] | |
| +-------------+ energy +-------------+ |
| |
| +-------------+ +-------------+ |
| | Audio Phase | -----------------> | S_audio | |
| | Stability | Hilbert-based | [0, 1] | |
| +-------------+ coherence +-------------+ |
| |
+---------------------------------------------------------------------+
SPECTRAL COHERENCE (S_spec):
+---------------------------------------------------------------------+
| |
| sum of top-k FFT magnitudes |
| S_spec = ---------------------------------- |
| total FFT energy + eps |
| |
| High S_spec = energy concentrated in few frequencies (coherent) |
| Low S_spec = energy spread across spectrum (incoherent) |
| |
+---------------------------------------------------------------------+
SPIN COHERENCE (C_spin):
+---------------------------------------------------------------------+
| |
| | Sum_{k=1}^{N} e^{i * theta_k} | |
| C_spin = ------------------------------------ |
| N |
| |
| High C_spin = phases aligned (coherent) |
| Low C_spin = phases random (incoherent) |
| |
+---------------------------------------------------------------------+
BEHAVIORAL TRUST (tau):
+---------------------------------------------------------------------+
| |
| tau = sigmoid(-E_hopfield / temperature) |
| |
| where E_hopfield = -0.5 * x^T * W * x |
| |
| High tau = low energy state (stable attractor) |
| Low tau = high energy state (unstable) |
| |
+---------------------------------------------------------------------+
AUDIO COHERENCE (S_audio):
+---------------------------------------------------------------------+
| |
| S_audio = mean phase stability via Hilbert transform |
| |
| High S_audio = stable phase relationships |
| Low S_audio = phase instability |
| |
+---------------------------------------------------------------------+
FIG. 10: Composite Risk Functional with Harmonic Amplification
+-------------------------------------------------------------------------+
| COMPOSITE RISK FUNCTIONAL - AXIOM A12 |
+-------------------------------------------------------------------------+
RISK COMPUTATION PIPELINE:
+---------------------------------------------------------------------+
| |
| COHERENCE SIGNALS WEIGHTS RISK_BASE |
| |
| d_tri -----> w_d * d_tri ----+ |
| | |
| 1-C_spin ----> w_c * (1-C_spin) ---+ |
| | |
| 1-S_spec ----> w_s * (1-S_spec) ---+---> Risk_base = Sum |
| | |
| 1-tau -----> w_tau * (1-tau) ---+ |
| | |
| 1-S_audio ---> w_a * (1-S_audio) --+ |
| |
| CONSTRAINT: w_d + w_c + w_s + w_tau + w_a = 1 |
| All weights >= 0 |
| |
+---------------------------------------------------------------------+
HARMONIC AMPLIFICATION:
+---------------------------------------------------------------------+
| |
| H(d*, R) = R^{(d*)^2} |
| |
| H | |
| | * |
| 10 + * |
| | * |
| 8 + * |
| | * |
| 6 + * |
| | * |
| 4 + * |
| | * |
| 2 + * |
| | * |
| 1 +----*---+------+------+------+------+------+------+----> d* |
| 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 |
| |
| Near realm (d* small): H approx 1 (no amplification) |
| Far from realm (d* large): H grows exponentially |
| |
+---------------------------------------------------------------------+
FINAL RISK:
+---------------------------------------------------------------------+
| |
| Risk' = Risk_base * H(d*, R) |
| |
| - Risk_base in [0, 1] (bounded by weight sum = 1) |
| - H >= 1 (amplification factor) |
| - Risk' in [0, infinity) but bounded for clamped states |
| |
+---------------------------------------------------------------------+
FIG. 11: Three-State Decision Partitioning
+-------------------------------------------------------------------------+
| THREE-STATE DECISION PARTITIONING |
+-------------------------------------------------------------------------+
DECISION THRESHOLDS:
+---------------------------------------------------------------------+
| |
| Risk' | |
| | |
| 1.0 + - - - - - - - - - - - - - - - - - - - - - - - - - - - |
| | |
| | +--------------------------------------------------+ |
| theta_2 | DENY | |
| (0.67) + | Risk' >= theta_2 | |
| | | - Block request | |
| | | - Output fail-to-noise | |
| | | - Log to secure audit | |
| | +--------------------------------------------------+ |
| | |
| | +--------------------------------------------------+ |
| theta_1 | QUARANTINE | |
| (0.33) + | theta_1 <= Risk' < theta_2 | |
| | | - Allow with audit flag | |
| | | - Create envelope with audit_flag=true | |
| | | - Enhanced monitoring | |
| | +--------------------------------------------------+ |
| | |
| | +--------------------------------------------------+ |
| 0.0 + | ALLOW | |
| | | Risk' < theta_1 | |
| | | - Normal operation | |
| | | - Create envelope | |
| | | - Standard logging | |
| | +--------------------------------------------------+ |
| | |
+---------------------------------------------------------------------+
DECISION FLOW:
+---------------------------------------------------------------------+
| |
| +----------+ |
| | Risk' | |
| +----+-----+ |
| | |
| +--------------+--------------+ |
| | | | |
| v v v |
| Risk'<theta_1 theta_1<=Risk' Risk'>=theta_2 |
| | <theta_2 | |
| v v v |
| +-------+ +----------+ +-------+ |
| | ALLOW | |QUARANTINE| | DENY | |
| +---+---+ +----+-----+ +---+---+ |
| | | | |
| v v v |
| +--------+ +----------+ +-------------+ |
| |Create | |Create | |Fail-to-Noise| |
| |Envelope| |Envelope | |Output | |
| | | |+AuditFlag| | | |
| +--------+ +----------+ +-------------+ |
| |
+---------------------------------------------------------------------+
FIG. 12: Fail-to-Noise Output Behavior
+-------------------------------------------------------------------------+
| FAIL-TO-NOISE OUTPUT BEHAVIOR |
| All failures produce indistinguishable outputs |
+-------------------------------------------------------------------------+
FAILURE MODES (ALL PRODUCE IDENTICAL OUTPUT):
+---------------------------------------------------------------------+
| |
| FAILURE TYPE