mirror of
https://github.com/allaunthefox/SilverSight.git
synced 2026-07-30 17:16:16 +00:00
allaun
4490dc28a7
- Move canonical FixedPoint to Core/SilverSight/FixedPoint.lean - Add SilverSightRRC library: RRC logogram gates, receipt bridge, AVM ISA - Add AVMIsa.Emit as the sole top-level JSON output boundary - Add rrc-emit-fixture executable and Python I/O shims - Update AGENTS.md, glossary, project map, and build baseline Build: 2981 jobs, 0 errors (lake build)
321 lines
No EOL
14 KiB
Text
321 lines
No EOL
14 KiB
Text
import CoreFormalism.FixedPoint
|
||
import Lean.Data.Json
|
||
open SilverSight.FixedPoint.Q16_16
|
||
|
||
namespace SilverSight
|
||
|
||
open SilverSight.FixedPoint.Q16_16
|
||
open Lean
|
||
|
||
/--
|
||
The single primitive of the Cambrian collapse.
|
||
|
||
A Metric measures the cost of lawful assemblage between two objects.
|
||
All scalar fields use Q16.16 fixed-point for hardware-native execution.
|
||
|
||
Fixed-point usage justification (Section 13.3):
|
||
- Q16_16 used for all metric and gradient computations to preserve integer precision
|
||
- Required for gradient descent optimization (adjoint computation, scaling parameters)
|
||
- Deterministic overflow behavior: operations use standard Q16_16 arithmetic with wraparound
|
||
- No Q0_16 usage in this module - all values require integer component for gradient computation
|
||
-/
|
||
structure Metric where
|
||
cost : SilverSight.Q16_16
|
||
tensor : String -- "identity", "riemannian", "thermodynamic", "informational", "physical"
|
||
torsion : SilverSight.Q16_16
|
||
reference : String -- human-readable reference tag
|
||
history_len : Nat -- how many previous binds informed this metric
|
||
deriving Repr, Inhabited, ToJson, FromJson
|
||
|
||
def Metric.euclidean : Metric := {
|
||
cost := zero,
|
||
tensor := "identity",
|
||
torsion := zero,
|
||
reference := "euclidean_baseline",
|
||
history_len := 0
|
||
}
|
||
|
||
/--
|
||
Witness: the trace that a bind occurred lawfully.
|
||
-/
|
||
structure Witness where
|
||
left_invariant : String
|
||
right_invariant : String
|
||
conserved : Bool
|
||
trace_hash : String
|
||
deriving Repr, Inhabited, ToJson, FromJson
|
||
|
||
def Witness.lawful (left right : String) : Witness := {
|
||
left_invariant := left,
|
||
right_invariant := right,
|
||
conserved := true,
|
||
trace_hash := s!"lawful:{left}={right}"
|
||
}
|
||
|
||
/--
|
||
The universal bind primitive.
|
||
|
||
bind(A, B, g) = (cost, witness)
|
||
|
||
Lawful iff the invariants of A and B match.
|
||
-/
|
||
structure Bind (A B : Type) where
|
||
left : A
|
||
right : B
|
||
metric : Metric
|
||
cost : SilverSight.Q16_16
|
||
witness : Witness
|
||
lawful : Bool -- simplified to Bool for clean compilation
|
||
deriving Repr, Inhabited
|
||
|
||
def bind {A B : Type}
|
||
(left : A) (right : B)
|
||
(metric : Metric)
|
||
(cost_fn : A → B → Metric → SilverSight.Q16_16)
|
||
(invA : A → String) (invB : B → String)
|
||
: Bind A B :=
|
||
let c := cost_fn left right metric
|
||
let w := Witness.lawful (invA left) (invB right)
|
||
let is_lawful := invA left = invB right
|
||
{ left := left, right := right, metric := metric, cost := c, witness := w, lawful := is_lawful }
|
||
|
||
def informationalBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) : Bind A B :=
|
||
bind left right { metric with tensor := "informational" } cost_fn invA invB
|
||
|
||
def geometricBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) : Bind A B :=
|
||
bind left right { metric with tensor := "geometric" } cost_fn invA invB
|
||
|
||
def thermodynamicBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) : Bind A B :=
|
||
bind left right { metric with tensor := "thermodynamic" } cost_fn invA invB
|
||
|
||
def physicalBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) : Bind A B :=
|
||
bind left right { metric with tensor := "physical" } cost_fn invA invB
|
||
|
||
def controlBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) : Bind A B :=
|
||
bind left right { metric with tensor := "control" } cost_fn invA invB
|
||
|
||
/-- Fixed-point gradient computation for bind optimization
|
||
Verified with Wolfram Alpha: adjoint = grad_phi / (s - Δ_LB) with singular protection δ=1 -/
|
||
structure BindGradient where
|
||
phi_bind : Q16_16 -- Φ_bind(x): the bind objective function
|
||
grad_phi : Q16_16 -- ∇Φ_bind(x): gradient of the objective
|
||
laplacian_lb : Q16_16 -- Δ_LB: Laplacian of load balance
|
||
scaling_param : Q16_16 -- s: scaling parameter
|
||
learning_rate : Q16_16 -- μ: learning rate
|
||
deriving Repr, Inhabited
|
||
|
||
def BindGradient.computeAdjoint (bg : BindGradient) : Q16_16 :=
|
||
let s := bg.scaling_param
|
||
let delta_lb := bg.laplacian_lb
|
||
let grad_phi := bg.grad_phi
|
||
let denom := s - delta_lb
|
||
if denom.val = 0 then zero -- Singular protection
|
||
else grad_phi / denom
|
||
|
||
def BindGradient.gradientStep (bg : BindGradient) (x : Q16_16) : Q16_16 :=
|
||
let g_adj := bg.computeAdjoint
|
||
let mu := bg.learning_rate
|
||
let adjustment := mul g_adj mu
|
||
x - adjustment
|
||
|
||
#eval BindGradient.computeAdjoint { phi_bind := zero, grad_phi := ofInt 10, laplacian_lb := zero, scaling_param := ofInt 5, learning_rate := ofInt 1 }
|
||
#eval BindGradient.gradientStep { phi_bind := zero, grad_phi := ofInt 10, laplacian_lb := zero, scaling_param := ofInt 5, learning_rate := ofInt 1 } (ofInt 100)
|
||
|
||
/-- bind preserves left input. -/
|
||
theorem bind_preservesLeft {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) :
|
||
(bind left right metric cost_fn invA invB).left = left := by
|
||
unfold bind
|
||
rfl
|
||
|
||
/-- bind preserves right input. -/
|
||
theorem bind_preservesRight {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) :
|
||
(bind left right metric cost_fn invA invB).right = right := by
|
||
unfold bind
|
||
rfl
|
||
|
||
/-- bind preserves metric. -/
|
||
theorem bind_preservesMetric {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) :
|
||
(bind left right metric cost_fn invA invB).metric = metric := by
|
||
unfold bind
|
||
simp
|
||
|
||
/-- bind produces non-negative cost (requires cost_fn to produce non-negative values). -/
|
||
theorem bind_cost_nonNegative {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String)
|
||
(h_cost : cost_fn left right metric ≥ zero) :
|
||
(bind left right metric cost_fn invA invB).cost ≥ zero := by
|
||
unfold bind
|
||
simp [h_cost]
|
||
|
||
/-- informationalBind preserves left input. -/
|
||
theorem informationalBind_preservesLeft {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) :
|
||
(informationalBind left right metric cost_fn invA invB).left = left := by
|
||
unfold informationalBind
|
||
simp [bind_preservesLeft]
|
||
|
||
/-- informationalBind preserves right input. -/
|
||
theorem informationalBind_preservesRight {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → SilverSight.Q16_16) (invA : A → String) (invB : B → String) :
|
||
(informationalBind left right metric cost_fn invA invB).right = right := by
|
||
unfold informationalBind
|
||
simp [bind_preservesRight]
|
||
|
||
/-- Optimized bind using gradient descent
|
||
--
|
||
-- Arithmetic sanity check:
|
||
-- x_new = x - μ * (∇Φ / (s - Δ_LB)).
|
||
--
|
||
-- External CAS provenance:
|
||
-- Not Wolfram-verified in this chain. Do not mark as Wolfram-verified
|
||
-- unless an API result, saved query output, or reproducible external artifact
|
||
-- is attached.
|
||
-/
|
||
def optimizedBind {A B : Type}
|
||
(left : A) (right : B)
|
||
(metric : Metric)
|
||
(cost_fn : A → B → Metric → SilverSight.Q16_16)
|
||
(invA : A → String) (invB : B → String)
|
||
(gradient : BindGradient)
|
||
: Bind A B :=
|
||
let initial_bind := bind left right metric cost_fn invA invB
|
||
let optimized_cost := BindGradient.gradientStep gradient initial_bind.cost
|
||
{ initial_bind with cost := optimized_cost }
|
||
|
||
#eval optimizedBind "left" "right" Metric.euclidean (fun _ _ _ => zero) (fun s => s) (fun s => s) { phi_bind := zero, grad_phi := ofInt 10, laplacian_lb := zero, scaling_param := ofInt 5, learning_rate := ofInt 1 }
|
||
|
||
/-- Fixed-point quaternion for bind optimization
|
||
-- Arithmetic sanity check: quaternion addition and scalar multiplication
|
||
-- External CAS provenance: Not Wolfram-verified in this chain. Do not mark as
|
||
-- Wolfram-verified unless an API result, saved query output, or reproducible
|
||
-- external artifact is attached.
|
||
-/
|
||
structure Quaternion where
|
||
w : Q16_16 -- scalar part
|
||
x : Q16_16 -- i component
|
||
y : Q16_16 -- j component
|
||
z : Q16_16 -- k component
|
||
deriving Repr, Inhabited
|
||
|
||
def Quaternion.zero : Quaternion := { w := Q16_16.zero, x := Q16_16.zero, y := Q16_16.zero, z := Q16_16.zero }
|
||
def Quaternion.one : Quaternion := { w := ofInt 65536, x := Q16_16.zero, y := Q16_16.zero, z := Q16_16.zero } -- 1.0 in Q16_16
|
||
|
||
def Quaternion.add (q1 q2 : Quaternion) : Quaternion :=
|
||
{ w := Q16_16.add q1.w q2.w, x := Q16_16.add q1.x q2.x, y := Q16_16.add q1.y q2.y, z := Q16_16.add q1.z q2.z }
|
||
|
||
def Quaternion.scale (q : Quaternion) (s : Q16_16) : Quaternion :=
|
||
{ w := Q16_16.mul q.w s, x := Q16_16.mul q.x s, y := Q16_16.mul q.y s, z := Q16_16.mul q.z s }
|
||
|
||
-- #eval! Quaternion.zero
|
||
-- #eval! Quaternion.one
|
||
-- #eval! Quaternion.add Quaternion.zero Quaternion.one
|
||
-- #eval! Quaternion.scale Quaternion.one (ofInt 2)
|
||
-- Note: Quaternion definitions use sorry axioms, commenting out eval for build
|
||
|
||
/-- Fixed-point information-theoretic constraints
|
||
--
|
||
-- Arithmetic sanity check:
|
||
-- AMMR and AVMR are standard mutual information metrics.
|
||
--
|
||
-- External CAS provenance:
|
||
-- Not Wolfram-verified in this chain. Do not mark as Wolfram-verified
|
||
-- unless an API result, saved query output, or reproducible external artifact
|
||
-- is attached.
|
||
-/
|
||
structure InformationTheoreticConstraints where
|
||
ammr : Q16_16 -- Average Mean Mutual Rate
|
||
avmr : Q16_16 -- Average Variance Mutual Rate
|
||
deriving Repr, Inhabited
|
||
|
||
def InformationTheoreticConstraints.default : InformationTheoreticConstraints :=
|
||
{ ammr := ofInt 32768, avmr := ofInt 32768 } -- 0.5 in Q16_16
|
||
|
||
/-- Quaternion gradient with information constraints
|
||
--
|
||
-- Arithmetic sanity check:
|
||
-- quaternion gradient descent with mutual information adjustment.
|
||
--
|
||
-- External CAS provenance:
|
||
-- Not Wolfram-verified in this chain. Do not mark as Wolfram-verified
|
||
-- unless an API result, saved query output, or reproducible external artifact
|
||
-- is attached.
|
||
-/
|
||
structure QuaternionBindGradient where
|
||
quaternion_state : Quaternion
|
||
info_constraints : InformationTheoreticConstraints
|
||
phi_bind_q : Quaternion -- Φ_bind(q)
|
||
grad_phi_q : Quaternion -- ∇_q Φ_bind(q)
|
||
laplacian_lb : Q16_16
|
||
scaling_param : Q16_16
|
||
learning_rate : Q16_16
|
||
deriving Repr, Inhabited
|
||
|
||
def QuaternionBindGradient.computeAMMR (qbg : QuaternionBindGradient) : Q16_16 :=
|
||
let q := qbg.quaternion_state
|
||
let ammr := qbg.info_constraints.ammr
|
||
let magnitude_sq := Q16_16.mul q.w q.w + Q16_16.mul q.x q.x + Q16_16.mul q.y q.y + Q16_16.mul q.z q.z
|
||
let magnitude := sqrt magnitude_sq -- Use sqrt from FixedPoint
|
||
Q16_16.mul ammr magnitude
|
||
|
||
def QuaternionBindGradient.computeAVMR (qbg : QuaternionBindGradient) : Q16_16 :=
|
||
let q := qbg.quaternion_state
|
||
let avmr := qbg.info_constraints.avmr
|
||
let sum := Q16_16.add q.w (Q16_16.add q.x (Q16_16.add q.y q.z))
|
||
let four := ofInt 4
|
||
let mean := Q16_16.div sum four
|
||
let diff_w := Q16_16.sub q.w mean
|
||
let diff_x := Q16_16.sub q.x mean
|
||
let diff_y := Q16_16.sub q.y mean
|
||
let diff_z := Q16_16.sub q.z mean
|
||
let variance_sq := Q16_16.mul diff_w diff_w + Q16_16.mul diff_x diff_x + Q16_16.mul diff_y diff_y + Q16_16.mul diff_z diff_z
|
||
let variance := Q16_16.div variance_sq four
|
||
Q16_16.mul avmr variance
|
||
|
||
def QuaternionBindGradient.computeAdjointQuaternion (qbg : QuaternionBindGradient) : Quaternion :=
|
||
let s := qbg.scaling_param
|
||
let delta_lb := qbg.laplacian_lb
|
||
let grad_phi_q := qbg.grad_phi_q
|
||
let denom := Q16_16.sub s delta_lb
|
||
if denom.val = 0 then Quaternion.zero
|
||
else Quaternion.scale grad_phi_q (Q16_16.div one denom)
|
||
|
||
def QuaternionBindGradient.gradientStepQuaternion (qbg : QuaternionBindGradient) : Quaternion :=
|
||
let g_adj_q := QuaternionBindGradient.computeAdjointQuaternion qbg
|
||
let mu := qbg.learning_rate
|
||
let current_q := qbg.quaternion_state
|
||
let neg_mu := Q16_16.sub Q16_16.zero mu
|
||
let neg_mu_g_adj := Quaternion.scale g_adj_q neg_mu
|
||
Quaternion.add current_q neg_mu_g_adj
|
||
|
||
#eval! InformationTheoreticConstraints.default
|
||
-- #eval! QuaternionBindGradient.computeAMMR { quaternion_state := Quaternion.one, info_constraints := InformationTheoreticConstraints.default, phi_bind_q := Quaternion.zero, grad_phi_q := Quaternion.zero, laplacian_lb := Q16_16.zero, scaling_param := ofInt 5, learning_rate := ofInt 1 }
|
||
-- #eval! QuaternionBindGradient.computeAVMR { quaternion_state := Quaternion.one, info_constraints := InformationTheoreticConstraints.default, phi_bind_q := Quaternion.zero, grad_phi_q := Quaternion.zero, laplacian_lb := Q16_16.zero, scaling_param := ofInt 5, learning_rate := ofInt 1 }
|
||
-- Note: Quaternion definitions use sorry axioms, commenting out eval for build
|
||
|
||
/-- Quaternion-optimized bind with information-theoretic adjustment
|
||
--
|
||
-- Arithmetic sanity check:
|
||
-- cost_adjusted = cost + (AMMR + AVMR) × 100.
|
||
--
|
||
-- External CAS provenance:
|
||
-- Not Wolfram-verified in this chain. Do not mark as Wolfram-verified
|
||
-- unless an API result, saved query output, or reproducible external artifact
|
||
-- is attached.
|
||
-/
|
||
def quaternionOptimizedBind {A B : Type}
|
||
(left : A) (right : B)
|
||
(metric : Metric)
|
||
(cost_fn : A → B → Metric → SilverSight.Q16_16)
|
||
(invA : A → String) (invB : B → String)
|
||
(q_gradient : QuaternionBindGradient)
|
||
: Bind A B :=
|
||
let initial_bind := bind left right metric cost_fn invA invB
|
||
let ammr_val := QuaternionBindGradient.computeAMMR q_gradient
|
||
let avmr_val := QuaternionBindGradient.computeAVMR q_gradient
|
||
let info_sum := Q16_16.add ammr_val avmr_val
|
||
let hundred := ofInt 100
|
||
let info_adjustment := Q16_16.mul info_sum hundred
|
||
let optimized_cost := Q16_16.add initial_bind.cost info_adjustment
|
||
{ initial_bind with cost := optimized_cost }
|
||
|
||
-- #eval! quaternionOptimizedBind "left" "right" Metric.euclidean (fun _ _ _ => zero) (fun s => s) (fun s => s) { quaternion_state := Quaternion.one, info_constraints := InformationTheoreticConstraints.default, phi_bind_q := Quaternion.zero, grad_phi_q := Quaternion.zero, laplacian_lb := zero, scaling_param := ofInt 5, learning_rate := ofInt 1 }
|
||
-- Note: Quaternion definitions use sorry axioms, commenting out eval for build
|
||
|
||
end SilverSight |