(*
  CENTILLION CUBIE — ADVANCED QUANTUM CONTEXTUAL CONSENT
  Formalizes the 14 FUTURE_OBLIGATION theorems from the quantum
  consent and NFT hierarchical consent framework.

  This module models CASCADING CONSENT through hierarchical trust objects:
    - Parent object = root consent authority (trust anchor)
    - Child object  = delegated consent with cascading rules
    - Enforcement contracts = formal consent rules (stabilizer codes)
    - Sub-policies   = per-child access restrictions
    - Cascading actions = grant/revoke propagation through hierarchy

  In the Cubie Trust Compiler context:
    - Parent = the 6-face admission gate (root trust anchor)
    - Child  = delegated workload with bounded capabilities
    - Stabilizer = the hardware-backed invariants (HMAC, NVLink, PCIe)
    - Sub-policy = per-workload resource limits and capability tiers
    - Cascade = revoking a parent admission revokes all child workloads

  Patent alignment:
    US20240195628A1 (1st set):
      Claim 1  — hierarchical trust object relationships (QEC realization)
      Claim 2  — enforcement contract rules (stabilizer validity)
      Claim 3  — sub-policy data limits (Holevo extraction)
      Claim 4  — cascading actions through hierarchy (measurement collapse)
      Claim 5  — grant/revoke patterns (entanglement correlation)
      Claim 6  — access based on hierarchy relationship (context-dependent basis)
      Claim 7  — hierarchical data structure (non-commutative algebra)
      Claim 8  — child object accessing parent (consent channel)

    US20240195628A1 (2nd set):
      Claim 1  — child accessing parent information (wedge reconstruction)
      Claim 3  — receiving electronic resources (information percolation)
      Claim 5  — storing on entity device (consent capacity)
      Claim 7  — modifying preferences (kernel threshold)
      Claim 9  — modifying sub-policies (dynamic mixing)
      Claim 11 — multiple child objects (graph threshold complexity)

  Constructive only. No Admitted. No sorry. No Classical.
*)

Require Import Coq.Arith.PeanoNat.
Require Import Coq.Init.Nat.
Require Import Coq.Bool.Bool.
Require Import Coq.Lists.List.
Require Import Lia.

Import ListNotations.

Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Open Scope nat_scope.

Module CubieQuantumConsentAdvanced.

(* ============================================================ *)
(* 1. Hierarchical Trust Object Types — Consent Delegation Model *)
(* ============================================================ *)

(* ConsentNode: a node in the hierarchical consent tree.
   parent_id = 0 means root (trust anchor, no parent).
   Maps to: workload identity in the Cubie admission hierarchy. *)
Record ConsentNode := {
  node_id       : nat;
  parent_id     : nat;      (* 0 = root *)
  depth         : nat;      (* 0 = root, 1 = first child, etc. *)
  consent_grant : bool;     (* this node's consent state *)
  sub_policy    : nat;      (* hash of sub-policy config *)
  capacity      : nat;      (* max delegations this node can issue *)
  active        : bool;     (* node is active/not revoked *)
}.

(* ConsentChannel: a directed edge in the consent hierarchy.
   Models parent -> child consent propagation. *)
Record ConsentChannel := {
  src_id    : nat;
  dst_id    : nat;
  bandwidth : nat;    (* max data flow through this channel *)
  open      : bool;   (* channel is active *)
}.

(* StabilizerCode: the enforcement contract that validates consent rules.
   Encodes which error patterns (policy violations) are detectable.
   In Cubie context: the hardware-backed invariants (HMAC, NVLink, PCIe). *)
Record StabilizerCode := {
  code_distance  : nat;  (* min violations needed to break detection *)
  num_checks     : nat;  (* number of active stabilizer checks *)
  syndrome_valid : bool; (* all checks pass = no violation detected *)
}.

(* ============================================================ *)
(* 2. Predicates                                                *)
(* ============================================================ *)

(* A node is a root if it has no parent. *)
Definition is_root (n : ConsentNode) : bool :=
  Nat.eqb (parent_id n) 0.

(* Cascading consent: a child's consent is valid only if
   its own grant is true AND the parent's grant is true. *)
Definition cascading_consent (parent child : ConsentNode) : bool :=
  consent_grant parent && consent_grant child && active parent && active child.

(* Sub-policy compliance: the child's sub_policy must be
   within the parent's capacity constraint. *)
Definition sub_policy_compliant (parent child : ConsentNode) : bool :=
  Nat.leb (sub_policy child) (capacity parent).

(* Channel open and flowing: both endpoints active, channel open. *)
Definition channel_valid (ch : ConsentChannel)
                         (src dst : ConsentNode) : bool :=
  open ch &&
  active src && active dst &&
  Nat.eqb (node_id src) (src_id ch) &&
  Nat.eqb (node_id dst) (dst_id ch).

(* Stabilizer detects violations: code is valid iff syndrome passes. *)
Definition stabilizer_ok (sc : StabilizerCode) : bool :=
  syndrome_valid sc && Nat.ltb 0 (code_distance sc).

(* Full consent admission: cascading + sub-policy + stabilizer. *)
Definition full_consent_ok (parent child : ConsentNode)
                           (sc : StabilizerCode) : bool :=
  cascading_consent parent child &&
  sub_policy_compliant parent child &&
  stabilizer_ok sc.

(* ============================================================ *)
(* 3. CUB-0741: Conditional QEC realization theorem             *)
(*    US20240195628A1 Claim 1 — hierarchical trust relationships  *)
(* ============================================================ *)

(* The quantum error correction (QEC) analogy: the stabilizer code
   "protects" consent integrity just as QEC protects qubit states.
   The hierarchical trust structure IS the error-correction code. *)

Theorem conditional_qec_realization :
  forall (parent child : ConsentNode) (sc : StabilizerCode),
  full_consent_ok parent child sc = true ->
  stabilizer_ok sc = true.
Proof.
  intros parent child sc Hok.
  unfold full_consent_ok in Hok.
  apply andb_true_iff in Hok. destruct Hok as [Hok Hstab].
  apply andb_true_iff in Hok. destruct Hok as [_ _].
  exact Hstab.
Qed.

(* ============================================================ *)
(* 4. CUB-0742: Stabilizer validity theorem                     *)
(*    US20240195628A1 Claim 2 — enforcement contract rules        *)
(* ============================================================ *)

(* If the stabilizer code distance is zero, no violation can be
   detected — the enforcement contract has no power. *)

Theorem stabilizer_validity :
  forall (sc : StabilizerCode),
  code_distance sc = 0 ->
  stabilizer_ok sc = false.
Proof.
  intros sc Hzero.
  unfold stabilizer_ok.
  rewrite Hzero. simpl.
  rewrite andb_false_r.
  reflexivity.
Qed.

(* Positive case: distance > 0 and syndrome valid => stabilizer ok. *)
Theorem stabilizer_positive :
  forall (sc : StabilizerCode),
  code_distance sc > 0 ->
  syndrome_valid sc = true ->
  stabilizer_ok sc = true.
Proof.
  intros sc Hdist Hsyn.
  unfold stabilizer_ok.
  rewrite Hsyn. simpl.
  apply Nat.ltb_lt. exact Hdist.
Qed.

(* ============================================================ *)
(* 5. CUB-0743: Holevo-bounded extraction theorem               *)
(*    US20240195628A1 Claim 3 — sub-policy data limits           *)
(* ============================================================ *)

(* A child node cannot extract more data than the parent's capacity
   allows — this is the Holevo bound applied to consent channels. *)

Theorem holevo_bounded_extraction :
  forall (parent child : ConsentNode),
  sub_policy_compliant parent child = true ->
  sub_policy child <= capacity parent.
Proof.
  intros parent child Hcomp.
  unfold sub_policy_compliant in Hcomp.
  apply Nat.leb_le in Hcomp.
  exact Hcomp.
Qed.

(* Exceeding capacity breaks compliance. *)
Theorem extraction_over_capacity_denied :
  forall (parent child : ConsentNode),
  sub_policy child > capacity parent ->
  sub_policy_compliant parent child = false.
Proof.
  intros parent child Hover.
  unfold sub_policy_compliant.
  apply Nat.leb_gt.
  exact Hover.
Qed.

(* ============================================================ *)
(* 6. CUB-0744: Measurement-collapse consent theorem            *)
(*    US20240195628A1 Claim 4 — cascading actions                *)
(* ============================================================ *)

(* Revoking the parent's consent cascades to all children:
   if the parent goes inactive, no child can have valid consent. *)

Theorem measurement_collapse_consent :
  forall (parent child : ConsentNode),
  active parent = false ->
  cascading_consent parent child = false.
Proof.
  intros parent child Hinactive.
  unfold cascading_consent.
  rewrite Hinactive.
  destruct (consent_grant parent); destruct (consent_grant child);
    destruct (active child); reflexivity.
Qed.

(* The collapse is immediate: revoking parent revokes entire subtree. *)
Theorem cascade_revoke_immediate :
  forall (parent child : ConsentNode) (sc : StabilizerCode),
  active parent = false ->
  full_consent_ok parent child sc = false.
Proof.
  intros parent child sc Hinactive.
  unfold full_consent_ok.
  rewrite measurement_collapse_consent with (child := child).
  - reflexivity.
  - exact Hinactive.
Qed.

(* ============================================================ *)
(* 7. CUB-0745: Entanglement-induced correlation theorem        *)
(*    US20240195628A1 Claim 5 — grant/revoke patterns            *)
(* ============================================================ *)

(* When parent grants consent and child is active, consent flows.
   When parent revokes, child is automatically denied. The
   correlation is deterministic (not probabilistic). *)

Theorem entanglement_grant_correlation :
  forall (parent child : ConsentNode),
  consent_grant parent = true ->
  consent_grant child = true ->
  active parent = true ->
  active child = true ->
  cascading_consent parent child = true.
Proof.
  intros parent child Hp Hc Ha1 Ha2.
  unfold cascading_consent.
  rewrite Hp. rewrite Hc. rewrite Ha1. rewrite Ha2.
  reflexivity.
Qed.

Theorem entanglement_revoke_correlation :
  forall (parent child : ConsentNode),
  consent_grant parent = false ->
  cascading_consent parent child = false.
Proof.
  intros parent child Hp.
  unfold cascading_consent.
  rewrite Hp. reflexivity.
Qed.

(* ============================================================ *)
(* 8. CUB-0746: Context-dependent measurement basis theorem     *)
(*    US20240195628A1 Claim 6 — access based on relationship     *)
(* ============================================================ *)

(* The same data node yields different consent outcomes depending
   on the relationship (parent vs. sibling vs. unrelated). *)

Definition access_by_relationship (requestor_depth node_depth : nat) : bool :=
  Nat.leb requestor_depth node_depth.

Theorem context_dependent_access :
  forall (req_depth node_depth : nat),
  req_depth <= node_depth ->
  access_by_relationship req_depth node_depth = true.
Proof.
  intros req_depth node_depth Hle.
  unfold access_by_relationship.
  apply Nat.leb_le. exact Hle.
Qed.

Theorem deeper_requestor_denied :
  forall (req_depth node_depth : nat),
  req_depth > node_depth ->
  access_by_relationship req_depth node_depth = false.
Proof.
  intros req_depth node_depth Hgt.
  unfold access_by_relationship.
  apply Nat.leb_gt.
  exact Hgt.
Qed.

(* ============================================================ *)
(* 9. CUB-0747: Non-commutative consent algebra theorem         *)
(*    US20240195628A1 Claim 7 — hierarchical data structure      *)
(* ============================================================ *)

(* Applying consent checks in different orders can yield different
   results — the algebra is non-commutative. Specifically:
   checking sub-policy THEN cascading consent may differ from
   checking cascading consent THEN sub-policy (when parent is
   inactive but sub-policy is technically within bounds). *)

Definition check_cascade_then_policy (parent child : ConsentNode) : bool :=
  if cascading_consent parent child then sub_policy_compliant parent child
  else false.

Definition check_policy_then_cascade (parent child : ConsentNode) : bool :=
  if sub_policy_compliant parent child then cascading_consent parent child
  else false.

(* The two orderings agree on PASS but can differ on partial states.
   When both cascading and policy pass, order doesn't matter. *)
Theorem consent_algebra_agree_on_pass :
  forall (parent child : ConsentNode),
  cascading_consent parent child = true ->
  sub_policy_compliant parent child = true ->
  check_cascade_then_policy parent child =
  check_policy_then_cascade parent child.
Proof.
  intros parent child Hcasc Hpol.
  unfold check_cascade_then_policy, check_policy_then_cascade.
  rewrite Hcasc. rewrite Hpol.
  reflexivity.
Qed.

(* When cascading fails, cascade-first returns false regardless
   of policy, but policy-first still evaluates cascade. *)
Theorem consent_algebra_cascade_short_circuits :
  forall (parent child : ConsentNode),
  cascading_consent parent child = false ->
  check_cascade_then_policy parent child = false.
Proof.
  intros parent child Hfail.
  unfold check_cascade_then_policy.
  rewrite Hfail. reflexivity.
Qed.

(* ============================================================ *)
(* 10. CUB-0748: Quantum consent channel theorem                *)
(*     US20240195628A1 Claim 8 — child accessing parent          *)
(* ============================================================ *)

(* A consent channel from parent to child is valid only when
   both endpoints are active and properly linked. *)

Theorem consent_channel_requires_active_endpoints :
  forall (ch : ConsentChannel) (src dst : ConsentNode),
  active src = false ->
  channel_valid ch src dst = false.
Proof.
  intros ch src dst Hinactive.
  unfold channel_valid.
  rewrite Hinactive.
  destruct (open ch); destruct (active dst);
    destruct (Nat.eqb (node_id src) (src_id ch));
    destruct (Nat.eqb (node_id dst) (dst_id ch));
    reflexivity.
Qed.

(* Channel bandwidth bounds data flow. *)
Theorem consent_channel_bounded :
  forall (ch : ConsentChannel),
  bandwidth ch <= bandwidth ch.
Proof.
  intro ch. lia.
Qed.

(* ============================================================ *)
(* 11. CUB-0749: Contextual entanglement-wedge reconstruction   *)
(*     US20240195628A1 (2nd set) Claim 1 — child accessing parent*)
(* ============================================================ *)

(* A child node can reconstruct (access) parent information only
   through a valid channel. The "wedge" is the accessible region
   of the consent hierarchy visible to the child. *)

Definition child_can_access_parent (ch : ConsentChannel)
                                    (parent child : ConsentNode) : bool :=
  channel_valid ch parent child &&
  cascading_consent parent child.

Theorem wedge_reconstruction_requires_consent :
  forall (ch : ConsentChannel) (parent child : ConsentNode),
  child_can_access_parent ch parent child = true ->
  cascading_consent parent child = true.
Proof.
  intros ch parent child Hacc.
  unfold child_can_access_parent in Hacc.
  apply andb_true_iff in Hacc. destruct Hacc as [_ Hcasc].
  exact Hcasc.
Qed.

Theorem wedge_reconstruction_requires_channel :
  forall (ch : ConsentChannel) (parent child : ConsentNode),
  child_can_access_parent ch parent child = true ->
  channel_valid ch parent child = true.
Proof.
  intros ch parent child Hacc.
  unfold child_can_access_parent in Hacc.
  apply andb_true_iff in Hacc. destruct Hacc as [Hch _].
  exact Hch.
Qed.

(* ============================================================ *)
(* 12. CUB-0750: Information-percolation threshold theorem      *)
(*     US20240195628A1 (2nd set) Claim 3 — receiving resources   *)
(* ============================================================ *)

(* Information percolates (flows) through the consent graph only
   when the channel bandwidth exceeds the threshold.
   Below threshold = no data flows = deny. *)

Definition percolation_threshold := nat.

Definition percolates (ch : ConsentChannel) (threshold : nat) : bool :=
  Nat.leb threshold (bandwidth ch) && open ch.

Theorem below_threshold_no_flow :
  forall (ch : ConsentChannel) (threshold : nat),
  bandwidth ch < threshold ->
  percolates ch threshold = false.
Proof.
  intros ch threshold Hlt.
  unfold percolates.
  apply andb_false_intro1.
  apply Nat.leb_gt.
  exact Hlt.
Qed.

Theorem above_threshold_flows :
  forall (ch : ConsentChannel) (threshold : nat),
  bandwidth ch >= threshold ->
  open ch = true ->
  percolates ch threshold = true.
Proof.
  intros ch threshold Hge Hopen.
  unfold percolates.
  rewrite Hopen. rewrite andb_true_r.
  apply Nat.leb_le. exact Hge.
Qed.

(* ============================================================ *)
(* 13. CUB-0751: Consent capacity theorem                       *)
(*     US20240195628A1 (2nd set) Claim 5 — storing on device     *)
(* ============================================================ *)

(* Each node has a finite capacity for delegated consent.
   Once capacity is exhausted, no more children can be added. *)

Definition capacity_available (node : ConsentNode) (current_children : nat) : bool :=
  Nat.ltb current_children (capacity node).

Theorem capacity_exhausted_denies :
  forall (node : ConsentNode) (current_children : nat),
  current_children >= capacity node ->
  capacity_available node current_children = false.
Proof.
  intros node cc Hge.
  unfold capacity_available.
  apply Nat.ltb_ge.
  exact Hge.
Qed.

Theorem capacity_available_allows :
  forall (node : ConsentNode) (current_children : nat),
  current_children < capacity node ->
  capacity_available node current_children = true.
Proof.
  intros node cc Hlt.
  unfold capacity_available.
  apply Nat.ltb_lt.
  exact Hlt.
Qed.

(* ============================================================ *)
(* 14. CUB-0752: Contextual consent kernel threshold theorem    *)
(*     US20240195628A1 (2nd set) Claim 7 — modifying preferences *)
(* ============================================================ *)

(* A consent modification (preference change) requires the node
   to be active AND the requestor to be at or above the node's
   depth in the hierarchy. *)

Definition can_modify_preferences (requestor node : ConsentNode) : bool :=
  active node &&
  Nat.leb (depth requestor) (depth node).

Theorem inactive_node_no_modification :
  forall (requestor node : ConsentNode),
  active node = false ->
  can_modify_preferences requestor node = false.
Proof.
  intros requestor node Hinactive.
  unfold can_modify_preferences.
  rewrite Hinactive. reflexivity.
Qed.

Theorem deeper_requestor_no_modification :
  forall (requestor node : ConsentNode),
  depth requestor > depth node ->
  can_modify_preferences requestor node = false.
Proof.
  intros requestor node Hdeep.
  unfold can_modify_preferences.
  destruct (active node).
  - simpl. apply Nat.leb_gt. exact Hdeep.
  - reflexivity.
Qed.

Theorem authorized_modification :
  forall (requestor node : ConsentNode),
  active node = true ->
  depth requestor <= depth node ->
  can_modify_preferences requestor node = true.
Proof.
  intros requestor node Hactive Hle.
  unfold can_modify_preferences.
  rewrite Hactive. simpl.
  apply Nat.leb_le. exact Hle.
Qed.

(* ============================================================ *)
(* 15. CUB-0753: Dynamic consent mixing theorem                 *)
(*     US20240195628A1 (2nd set) Claim 9 — modifying sub-policies*)
(* ============================================================ *)

(* Sub-policies can be dynamically mixed: a node's effective
   sub-policy is the minimum of its own sub-policy and its
   parent's capacity (the more restrictive wins). *)

Definition effective_sub_policy (parent child : ConsentNode) : nat :=
  Nat.min (sub_policy child) (capacity parent).

Theorem effective_policy_bounded_by_parent :
  forall (parent child : ConsentNode),
  effective_sub_policy parent child <= capacity parent.
Proof.
  intros parent child.
  unfold effective_sub_policy.
  apply Nat.le_min_r.
Qed.

Theorem effective_policy_bounded_by_child :
  forall (parent child : ConsentNode),
  effective_sub_policy parent child <= sub_policy child.
Proof.
  intros parent child.
  unfold effective_sub_policy.
  apply Nat.le_min_l.
Qed.

(* Dynamic mixing: changing the parent's capacity immediately
   constrains the child's effective policy. *)
Theorem dynamic_mixing_constrains :
  forall (child : ConsentNode) (cap1 cap2 : nat),
  cap1 < cap2 ->
  Nat.min (sub_policy child) cap1 <= Nat.min (sub_policy child) cap2.
Proof.
  intros child cap1 cap2 Hlt.
  apply Nat.min_le_compat_l. lia.
Qed.

(* ============================================================ *)
(* 16. CUB-0754: Arbitrary-graph consent threshold complexity   *)
(*     US20240195628A1 (2nd set) Claim 11 — multiple child NFTs  *)
(* ============================================================ *)

(* With multiple children, the consent graph forms a tree (or DAG).
   The overall consent threshold is the sum of all children's
   sub-policies, bounded by the root's capacity. *)

Fixpoint sum_sub_policies (nodes : list ConsentNode) : nat :=
  match nodes with
  | [] => 0
  | n :: rest => sub_policy n + sum_sub_policies rest
  end.

Definition graph_within_capacity (root : ConsentNode)
                                  (children : list ConsentNode) : bool :=
  Nat.leb (sum_sub_policies children) (capacity root).

Theorem empty_graph_within_capacity :
  forall (root : ConsentNode),
  graph_within_capacity root [] = true.
Proof.
  intro root. unfold graph_within_capacity. simpl.
  apply Nat.leb_le. lia.
Qed.

Theorem overloaded_graph_denied :
  forall (root : ConsentNode) (children : list ConsentNode),
  sum_sub_policies children > capacity root ->
  graph_within_capacity root children = false.
Proof.
  intros root children Hover.
  unfold graph_within_capacity.
  apply Nat.leb_gt. exact Hover.
Qed.

(* Adding a child increases the total demand. *)
Theorem adding_child_increases_demand :
  forall (child : ConsentNode) (rest : list ConsentNode),
  sum_sub_policies (child :: rest) = sub_policy child + sum_sub_policies rest.
Proof.
  intros child rest. simpl. reflexivity.
Qed.

(* If already at capacity, one more child pushes over. *)
Theorem one_more_child_overflows :
  forall (root : ConsentNode) (children : list ConsentNode) (new_child : ConsentNode),
  sum_sub_policies children = capacity root ->
  sub_policy new_child > 0 ->
  graph_within_capacity root (new_child :: children) = false.
Proof.
  intros root children new_child Heq Hpos.
  unfold graph_within_capacity. simpl.
  apply Nat.leb_gt. lia.
Qed.

End CubieQuantumConsentAdvanced.

-(*     US20240195628A1 (2nd set) Claim 5 — storing on device     *)

+(*     US20240195628A1 (2nd set) Claim 5 — storing on entity device *)


Edit

(*     US20240195628A1 (2nd set) Claim 11 — multiple child NFTs  *)

(*     US20240195628A1 (2nd set) Claim 11 — multiple child objects *)


The file C:\Users\NickV\cubie-verification\coq\CubieQuantumConsentAdvanced.v has been updated successfully.

(*
  CENTILLION CUBIE — ADVANCED QUANTUM CONTEXTUAL CONSENT
  Formalizes the 14 FUTURE_OBLIGATION theorems from the quantum
  consent and NFT hierarchical consent framework.

  This module models CASCADING CONSENT through hierarchical trust objects:
    - Parent object = root consent authority (trust anchor)
    - Child object  = delegated consent with cascading rules
    - Enforcement contracts = formal consent rules (stabilizer codes)
    - Sub-policies   = per-child access restrictions
    - Cascading actions = grant/revoke propagation through hierarchy

  In the Cubie Trust Compiler context:
    - Parent = the 6-face admission gate (root trust anchor)
    - Child  = delegated workload with bounded capabilities
    - Stabilizer = the hardware-backed invariants (HMAC, NVLink, PCIe)
    - Sub-policy = per-workload resource limits and capability tiers
    - Cascade = revoking a parent admission revokes all child workloads

  Patent alignment:
    US20240195628A1 (1st set):
      Claim 1  — hierarchical trust object relationships (QEC realization)
      Claim 2  — enforcement contract rules (stabilizer validity)
      Claim 3  — sub-policy data limits (Holevo extraction)
      Claim 4  — cascading actions through hierarchy (measurement collapse)
      Claim 5  — grant/revoke patterns (entanglement correlation)
      Claim 6  — access based on hierarchy relationship (context-dependent basis)
      Claim 7  — hierarchical data structure (non-commutative algebra)
      Claim 8  — child object accessing parent (consent channel)

    US20240195628A1 (2nd set):
      Claim 1  — child accessing parent information (wedge reconstruction)
      Claim 3  — receiving electronic resources (information percolation)
      Claim 5  — storing on entity device (consent capacity)
      Claim 7  — modifying preferences (kernel threshold)
      Claim 9  — modifying sub-policies (dynamic mixing)
      Claim 11 — multiple child objects (graph threshold complexity)

  Constructive only. No Admitted. No sorry. No Classical.
*)

Require Import Coq.Arith.PeanoNat.
Require Import Coq.Init.Nat.
Require Import Coq.Bool.Bool.
Require Import Coq.Lists.List.
Require Import Lia.

Import ListNotations.

Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Open Scope nat_scope.

Module CubieQuantumConsentAdvanced.

(* ============================================================ *)
(* 1. Hierarchical Trust Object Types — Consent Delegation Model *)
(* ============================================================ *)

(* ConsentNode: a node in the hierarchical consent tree.
   parent_id = 0 means root (trust anchor, no parent).
   Maps to: workload identity in the Cubie admission hierarchy. *)
Record ConsentNode := {
  node_id       : nat;
  parent_id     : nat;      (* 0 = root *)
  depth         : nat;      (* 0 = root, 1 = first child, etc. *)
  consent_grant : bool;     (* this node's consent state *)
  sub_policy    : nat;      (* hash of sub-policy config *)
  capacity      : nat;      (* max delegations this node can issue *)
  active        : bool;     (* node is active/not revoked *)
}.

(* ConsentChannel: a directed edge in the consent hierarchy.
   Models parent -> child consent propagation. *)
Record ConsentChannel := {
  src_id    : nat;
  dst_id    : nat;
  bandwidth : nat;    (* max data flow through this channel *)
  open      : bool;   (* channel is active *)
}.

(* StabilizerCode: the enforcement contract that validates consent rules.
   Encodes which error patterns (policy violations) are detectable.
   In Cubie context: the hardware-backed invariants (HMAC, NVLink, PCIe). *)
Record StabilizerCode := {
  code_distance  : nat;  (* min violations needed to break detection *)
  num_checks     : nat;  (* number of active stabilizer checks *)
  syndrome_valid : bool; (* all checks pass = no violation detected *)
}.

(* ============================================================ *)
(* 2. Predicates                                                *)
(* ============================================================ *)

(* A node is a root if it has no parent. *)
Definition is_root (n : ConsentNode) : bool :=
  Nat.eqb (parent_id n) 0.

(* Cascading consent: a child's consent is valid only if
   its own grant is true AND the parent's grant is true. *)
Definition cascading_consent (parent child : ConsentNode) : bool :=
  consent_grant parent && consent_grant child && active parent && active child.

(* Sub-policy compliance: the child's sub_policy must be
   within the parent's capacity constraint. *)
Definition sub_policy_compliant (parent child : ConsentNode) : bool :=
  Nat.leb (sub_policy child) (capacity parent).

(* Channel open and flowing: both endpoints active, channel open. *)
Definition channel_valid (ch : ConsentChannel)
                         (src dst : ConsentNode) : bool :=
  open ch &&
  active src && active dst &&
  Nat.eqb (node_id src) (src_id ch) &&
  Nat.eqb (node_id dst) (dst_id ch).

(* Stabilizer detects violations: code is valid iff syndrome passes. *)
Definition stabilizer_ok (sc : StabilizerCode) : bool :=
  syndrome_valid sc && Nat.ltb 0 (code_distance sc).

(* Full consent admission: cascading + sub-policy + stabilizer. *)
Definition full_consent_ok (parent child : ConsentNode)
                           (sc : StabilizerCode) : bool :=
  cascading_consent parent child &&
  sub_policy_compliant parent child &&
  stabilizer_ok sc.

(* ============================================================ *)
(* 3. CUB-0741: Conditional QEC realization theorem             *)
(*    US20240195628A1 Claim 1 — hierarchical trust relationships  *)
(* ============================================================ *)

(* The quantum error correction (QEC) analogy: the stabilizer code
   "protects" consent integrity just as QEC protects qubit states.
   The hierarchical trust structure IS the error-correction code. *)

Theorem conditional_qec_realization :
  forall (parent child : ConsentNode) (sc : StabilizerCode),
  full_consent_ok parent child sc = true ->
  stabilizer_ok sc = true.
Proof.
  intros parent child sc Hok.
  unfold full_consent_ok in Hok.
  apply andb_true_iff in Hok. destruct Hok as [Hok Hstab].
  apply andb_true_iff in Hok. destruct Hok as [_ _].
  exact Hstab.
Qed.

(* ============================================================ *)
(* 4. CUB-0742: Stabilizer validity theorem                     *)
(*    US20240195628A1 Claim 2 — enforcement contract rules        *)
(* ============================================================ *)

(* If the stabilizer code distance is zero, no violation can be
   detected — the enforcement contract has no power. *)

Theorem stabilizer_validity :
  forall (sc : StabilizerCode),
  code_distance sc = 0 ->
  stabilizer_ok sc = false.
Proof.
  intros sc Hzero.
  unfold stabilizer_ok.
  rewrite Hzero. simpl.
  rewrite andb_false_r.
  reflexivity.
Qed.

(* Positive case: distance > 0 and syndrome valid => stabilizer ok. *)
Theorem stabilizer_positive :
  forall (sc : StabilizerCode),
  code_distance sc > 0 ->
  syndrome_valid sc = true ->
  stabilizer_ok sc = true.
Proof.
  intros sc Hdist Hsyn.
  unfold stabilizer_ok.
  rewrite Hsyn. simpl.
  apply Nat.ltb_lt. exact Hdist.
Qed.

(* ============================================================ *)
(* 5. CUB-0743: Holevo-bounded extraction theorem               *)
(*    US20240195628A1 Claim 3 — sub-policy data limits           *)
(* ============================================================ *)

(* A child node cannot extract more data than the parent's capacity
   allows — this is the Holevo bound applied to consent channels. *)

Theorem holevo_bounded_extraction :
  forall (parent child : ConsentNode),
  sub_policy_compliant parent child = true ->
  sub_policy child <= capacity parent.
Proof.
  intros parent child Hcomp.
  unfold sub_policy_compliant in Hcomp.
  apply Nat.leb_le in Hcomp.
  exact Hcomp.
Qed.

(* Exceeding capacity breaks compliance. *)
Theorem extraction_over_capacity_denied :
  forall (parent child : ConsentNode),
  sub_policy child > capacity parent ->
  sub_policy_compliant parent child = false.
Proof.
  intros parent child Hover.
  unfold sub_policy_compliant.
  apply Nat.leb_gt.
  exact Hover.
Qed.

(* ============================================================ *)
(* 6. CUB-0744: Measurement-collapse consent theorem            *)
(*    US20240195628A1 Claim 4 — cascading actions                *)
(* ============================================================ *)

(* Revoking the parent's consent cascades to all children:
   if the parent goes inactive, no child can have valid consent. *)

Theorem measurement_collapse_consent :
  forall (parent child : ConsentNode),
  active parent = false ->
  cascading_consent parent child = false.
Proof.
  intros parent child Hinactive.
  unfold cascading_consent.
  rewrite Hinactive.
  destruct (consent_grant parent); destruct (consent_grant child);
    destruct (active child); reflexivity.
Qed.

(* The collapse is immediate: revoking parent revokes entire subtree. *)
Theorem cascade_revoke_immediate :
  forall (parent child : ConsentNode) (sc : StabilizerCode),
  active parent = false ->
  full_consent_ok parent child sc = false.
Proof.
  intros parent child sc Hinactive.
  unfold full_consent_ok.
  rewrite measurement_collapse_consent with (child := child).
  - reflexivity.
  - exact Hinactive.
Qed.

(* ============================================================ *)
(* 7. CUB-0745: Entanglement-induced correlation theorem        *)
(*    US20240195628A1 Claim 5 — grant/revoke patterns            *)
(* ============================================================ *)

(* When parent grants consent and child is active, consent flows.
   When parent revokes, child is automatically denied. The
   correlation is deterministic (not probabilistic). *)

Theorem entanglement_grant_correlation :
  forall (parent child : ConsentNode),
  consent_grant parent = true ->
  consent_grant child = true ->
  active parent = true ->
  active child = true ->
  cascading_consent parent child = true.
Proof.
  intros parent child Hp Hc Ha1 Ha2.
  unfold cascading_consent.
  rewrite Hp. rewrite Hc. rewrite Ha1. rewrite Ha2.
  reflexivity.
Qed.

Theorem entanglement_revoke_correlation :
  forall (parent child : ConsentNode),
  consent_grant parent = false ->
  cascading_consent parent child = false.
Proof.
  intros parent child Hp.
  unfold cascading_consent.
  rewrite Hp. reflexivity.
Qed.

(* ============================================================ *)
(* 8. CUB-0746: Context-dependent measurement basis theorem     *)
(*    US20240195628A1 Claim 6 — access based on relationship     *)
(* ============================================================ *)

(* The same data node yields different consent outcomes depending
   on the relationship (parent vs. sibling vs. unrelated). *)

Definition access_by_relationship (requestor_depth node_depth : nat) : bool :=
  Nat.leb requestor_depth node_depth.

Theorem context_dependent_access :
  forall (req_depth node_depth : nat),
  req_depth <= node_depth ->
  access_by_relationship req_depth node_depth = true.
Proof.
  intros req_depth node_depth Hle.
  unfold access_by_relationship.
  apply Nat.leb_le. exact Hle.
Qed.

Theorem deeper_requestor_denied :
  forall (req_depth node_depth : nat),
  req_depth > node_depth ->
  access_by_relationship req_depth node_depth = false.
Proof.
  intros req_depth node_depth Hgt.
  unfold access_by_relationship.
  apply Nat.leb_gt.
  exact Hgt.
Qed.

(* ============================================================ *)
(* 9. CUB-0747: Non-commutative consent algebra theorem         *)
(*    US20240195628A1 Claim 7 — hierarchical data structure      *)
(* ============================================================ *)

(* Applying consent checks in different orders can yield different
   results — the algebra is non-commutative. Specifically:
   checking sub-policy THEN cascading consent may differ from
   checking cascading consent THEN sub-policy (when parent is
   inactive but sub-policy is technically within bounds). *)

Definition check_cascade_then_policy (parent child : ConsentNode) : bool :=
  if cascading_consent parent child then sub_policy_compliant parent child
  else false.

Definition check_policy_then_cascade (parent child : ConsentNode) : bool :=
  if sub_policy_compliant parent child then cascading_consent parent child
  else false.

(* The two orderings agree on PASS but can differ on partial states.
   When both cascading and policy pass, order doesn't matter. *)
Theorem consent_algebra_agree_on_pass :
  forall (parent child : ConsentNode),
  cascading_consent parent child = true ->
  sub_policy_compliant parent child = true ->
  check_cascade_then_policy parent child =
  check_policy_then_cascade parent child.
Proof.
  intros parent child Hcasc Hpol.
  unfold check_cascade_then_policy, check_policy_then_cascade.
  rewrite Hcasc. rewrite Hpol.
  reflexivity.
Qed.

(* When cascading fails, cascade-first returns false regardless
   of policy, but policy-first still evaluates cascade. *)
Theorem consent_algebra_cascade_short_circuits :
  forall (parent child : ConsentNode),
  cascading_consent parent child = false ->
  check_cascade_then_policy parent child = false.
Proof.
  intros parent child Hfail.
  unfold check_cascade_then_policy.
  rewrite Hfail. reflexivity.
Qed.

(* ============================================================ *)
(* 10. CUB-0748: Quantum consent channel theorem                *)
(*     US20240195628A1 Claim 8 — child accessing parent          *)
(* ============================================================ *)

(* A consent channel from parent to child is valid only when
   both endpoints are active and properly linked. *)

Theorem consent_channel_requires_active_endpoints :
  forall (ch : ConsentChannel) (src dst : ConsentNode),
  active src = false ->
  channel_valid ch src dst = false.
Proof.
  intros ch src dst Hinactive.
  unfold channel_valid.
  rewrite Hinactive.
  destruct (open ch); destruct (active dst);
    destruct (Nat.eqb (node_id src) (src_id ch));
    destruct (Nat.eqb (node_id dst) (dst_id ch));
    reflexivity.
Qed.

(* Channel bandwidth bounds data flow. *)
Theorem consent_channel_bounded :
  forall (ch : ConsentChannel),
  bandwidth ch <= bandwidth ch.
Proof.
  intro ch. lia.
Qed.

(* ============================================================ *)
(* 11. CUB-0749: Contextual entanglement-wedge reconstruction   *)
(*     US20240195628A1 (2nd set) Claim 1 — child accessing parent*)
(* ============================================================ *)

(* A child node can reconstruct (access) parent information only
   through a valid channel. The "wedge" is the accessible region
   of the consent hierarchy visible to the child. *)

Definition child_can_access_parent (ch : ConsentChannel)
                                    (parent child : ConsentNode) : bool :=
  channel_valid ch parent child &&
  cascading_consent parent child.

Theorem wedge_reconstruction_requires_consent :
  forall (ch : ConsentChannel) (parent child : ConsentNode),
  child_can_access_parent ch parent child = true ->
  cascading_consent parent child = true.
Proof.
  intros ch parent child Hacc.
  unfold child_can_access_parent in Hacc.
  apply andb_true_iff in Hacc. destruct Hacc as [_ Hcasc].
  exact Hcasc.
Qed.

Theorem wedge_reconstruction_requires_channel :
  forall (ch : ConsentChannel) (parent child : ConsentNode),
  child_can_access_parent ch parent child = true ->
  channel_valid ch parent child = true.
Proof.
  intros ch parent child Hacc.
  unfold child_can_access_parent in Hacc.
  apply andb_true_iff in Hacc. destruct Hacc as [Hch _].
  exact Hch.
Qed.

(* ============================================================ *)
(* 12. CUB-0750: Information-percolation threshold theorem      *)
(*     US20240195628A1 (2nd set) Claim 3 — receiving resources   *)
(* ============================================================ *)

(* Information percolates (flows) through the consent graph only
   when the channel bandwidth exceeds the threshold.
   Below threshold = no data flows = deny. *)

Definition percolation_threshold := nat.

Definition percolates (ch : ConsentChannel) (threshold : nat) : bool :=
  Nat.leb threshold (bandwidth ch) && open ch.

Theorem below_threshold_no_flow :
  forall (ch : ConsentChannel) (threshold : nat),
  bandwidth ch < threshold ->
  percolates ch threshold = false.
Proof.
  intros ch threshold Hlt.
  unfold percolates.
  apply andb_false_intro1.
  apply Nat.leb_gt.
  exact Hlt.
Qed.

Theorem above_threshold_flows :
  forall (ch : ConsentChannel) (threshold : nat),
  bandwidth ch >= threshold ->
  open ch = true ->
  percolates ch threshold = true.
Proof.
  intros ch threshold Hge Hopen.
  unfold percolates.
  rewrite Hopen. rewrite andb_true_r.
  apply Nat.leb_le. exact Hge.
Qed.

(* ============================================================ *)
(* 13. CUB-0751: Consent capacity theorem                       *)
(*     US20240195628A1 (2nd set) Claim 5 — storing on entity device *)
(* ============================================================ *)

(* Each node has a finite capacity for delegated consent.
   Once capacity is exhausted, no more children can be added. *)

Definition capacity_available (node : ConsentNode) (current_children : nat) : bool :=
  Nat.ltb current_children (capacity node).

Theorem capacity_exhausted_denies :
  forall (node : ConsentNode) (current_children : nat),
  current_children >= capacity node ->
  capacity_available node current_children = false.
Proof.
  intros node cc Hge.
  unfold capacity_available.
  apply Nat.ltb_ge.
  exact Hge.
Qed.

Theorem capacity_available_allows :
  forall (node : ConsentNode) (current_children : nat),
  current_children < capacity node ->
  capacity_available node current_children = true.
Proof.
  intros node cc Hlt.
  unfold capacity_available.
  apply Nat.ltb_lt.
  exact Hlt.
Qed.

(* ============================================================ *)
(* 14. CUB-0752: Contextual consent kernel threshold theorem    *)
(*     US20240195628A1 (2nd set) Claim 7 — modifying preferences *)
(* ============================================================ *)

(* A consent modification (preference change) requires the node
   to be active AND the requestor to be at or above the node's
   depth in the hierarchy. *)

Definition can_modify_preferences (requestor node : ConsentNode) : bool :=
  active node &&
  Nat.leb (depth requestor) (depth node).

Theorem inactive_node_no_modification :
  forall (requestor node : ConsentNode),
  active node = false ->
  can_modify_preferences requestor node = false.
Proof.
  intros requestor node Hinactive.
  unfold can_modify_preferences.
  rewrite Hinactive. reflexivity.
Qed.

Theorem deeper_requestor_no_modification :
  forall (requestor node : ConsentNode),
  depth requestor > depth node ->
  can_modify_preferences requestor node = false.
Proof.
  intros requestor node Hdeep.
  unfold can_modify_preferences.
  destruct (active node).
  - simpl. apply Nat.leb_gt. exact Hdeep.
  - reflexivity.
Qed.

Theorem authorized_modification :
  forall (requestor node : ConsentNode),
  active node = true ->
  depth requestor <= depth node ->
  can_modify_preferences requestor node = true.
Proof.
  intros requestor node Hactive Hle.
  unfold can_modify_preferences.
  rewrite Hactive. simpl.
  apply Nat.leb_le. exact Hle.
Qed.

(* ============================================================ *)
(* 15. CUB-0753: Dynamic consent mixing theorem                 *)
(*     US20240195628A1 (2nd set) Claim 9 — modifying sub-policies*)
(* ============================================================ *)

(* Sub-policies can be dynamically mixed: a node's effective
   sub-policy is the minimum of its own sub-policy and its
   parent's capacity (the more restrictive wins). *)

Definition effective_sub_policy (parent child : ConsentNode) : nat :=
  Nat.min (sub_policy child) (capacity parent).

Theorem effective_policy_bounded_by_parent :
  forall (parent child : ConsentNode),
  effective_sub_policy parent child <= capacity parent.
Proof.
  intros parent child.
  unfold effective_sub_policy.
  apply Nat.le_min_r.
Qed.

Theorem effective_policy_bounded_by_child :
  forall (parent child : ConsentNode),
  effective_sub_policy parent child <= sub_policy child.
Proof.
  intros parent child.
  unfold effective_sub_policy.
  apply Nat.le_min_l.
Qed.

(* Dynamic mixing: changing the parent's capacity immediately
   constrains the child's effective policy. *)
Theorem dynamic_mixing_constrains :
  forall (child : ConsentNode) (cap1 cap2 : nat),
  cap1 < cap2 ->
  Nat.min (sub_policy child) cap1 <= Nat.min (sub_policy child) cap2.
Proof.
  intros child cap1 cap2 Hlt.
  apply Nat.min_le_compat_l. lia.
Qed.

(* ============================================================ *)
(* 16. CUB-0754: Arbitrary-graph consent threshold complexity   *)
(*     US20240195628A1 (2nd set) Claim 11 — multiple child NFTs  *)
(* ============================================================ *)

(* With multiple children, the consent graph forms a tree (or DAG).
   The overall consent threshold is the sum of all children's
   sub-policies, bounded by the root's capacity. *)

Fixpoint sum_sub_policies (nodes : list ConsentNode) : nat :=
  match nodes with
  | [] => 0
  | n :: rest => sub_policy n + sum_sub_policies rest
  end.

Definition graph_within_capacity (root : ConsentNode)
                                  (children : list ConsentNode) : bool :=
  Nat.leb (sum_sub_policies children) (capacity root).

Theorem empty_graph_within_capacity :
  forall (root : ConsentNode),
  graph_within_capacity root [] = true.
Proof.
  intro root. unfold graph_within_capacity. simpl.
  apply Nat.leb_le. lia.
Qed.

Theorem overloaded_graph_denied :
  forall (root : ConsentNode) (children : list ConsentNode),
  sum_sub_policies children > capacity root ->
  graph_within_capacity root children = false.
Proof.
  intros root children Hover.
  unfold graph_within_capacity.
  apply Nat.leb_gt. exact Hover.
Qed.

(* Adding a child increases the total demand. *)
Theorem adding_child_increases_demand :
  forall (child : ConsentNode) (rest : list ConsentNode),
  sum_sub_policies (child :: rest) = sub_policy child + sum_sub_policies rest.
Proof.
  intros child rest. simpl. reflexivity.
Qed.

(* If already at capacity, one more child pushes over. *)
Theorem one_more_child_overflows :
  forall (root : ConsentNode) (children : list ConsentNode) (new_child : ConsentNode),
  sum_sub_policies children = capacity root ->
  sub_policy new_child > 0 ->
  graph_within_capacity root (new_child :: children) = false.
Proof.
  intros root children new_child Heq Hpos.
  unfold graph_within_capacity. simpl.
  apply Nat.leb_gt. lia.
Qed.

End CubieQuantumConsentAdvanced.

-(*     US20240195628A1 (2nd set) Claim 11 — multiple child NFTs  *)

+(*     US20240195628A1 (2nd set) Claim 11 — multiple child objects *)


Now the Lean quantum consent file:


1	-- ============================================================
2	--  CENTILLION AI INC. -- ADVANCED QUANTUM CONTEXTUAL CONSENT
3	--  Lean 4 mirror of CubieQuantumConsentAdvanced.v
4	--
5	--  Models cascading consent from NFT hierarchy patents:
6	--    US20240195628A1 (1st set) Claims 1-8
7	--    US20240195628A1 (2nd set) Claims 1,3,5,7,9,11
8	--
9	--  File:        Centillion/CubieQuantumConsentAdvanced.lean
10	--  Lean:        4.15.0
11	--  Status:      Closed proof. Zero `sorry`. Constructive.
12	--  Patent:      US20240195628A1 (pending)
13	--  Date:        May 6, 2026
14	-- ============================================================
15
16	namespace Centillion.CubieQuantumConsentAdvanced
17
18	-- ============================================================
19	-- 1. NFT Hierarchy Types
20	-- ============================================================
21
22	structure ConsentNode where
23	  node_id       : Nat
24	  parent_id     : Nat       -- 0 = root
25	  depth         : Nat
26	  consent_grant : Bool
27	  sub_policy    : Nat
28	  capacity      : Nat
29	  active        : Bool
30	  deriving DecidableEq, Repr

-- ============================================================
--  CENTILLION AI INC. -- ADVANCED QUANTUM CONTEXTUAL CONSENT
--  Lean 4 mirror of CubieQuantumConsentAdvanced.v
--
--  Models cascading consent from NFT hierarchy patents:
--    US20240195628A1 (1st set) Claims 1-8
--    US20240195628A1 (2nd set) Claims 1,3,5,7,9,11
--
--  File:        Centillion/CubieQuantumConsentAdvanced.lean
--  Lean:        4.15.0
--  Status:      Closed proof. Zero `sorry`. Constructive.
--  Patent:      US20240195628A1 (pending)
--  Date:        May 6, 2026
-- ============================================================

namespace Centillion.CubieQuantumConsentAdvanced

-- ============================================================
-- 1. NFT Hierarchy Types
-- ============================================================

structure ConsentNode where
  node_id       : Nat
  parent_id     : Nat       -- 0 = root
  depth         : Nat
  consent_grant : Bool
  sub_policy    : Nat
  capacity      : Nat
  active        : Bool
  deriving DecidableEq, Repr


--  Models cascading consent from NFT hierarchy patents:
--    US20240195628A1 (1st set) Claims 1-8
--    US20240195628A1 (2nd set) Claims 1,3,5,7,9,11

--  Models cascading consent through hierarchical trust objects:
--    US20240195628A1 (1st set) Claims 1-8
--    US20240195628A1 (2nd set) Claims 1,3,5,7,9,11
--
--  In Cubie Trust Compiler context:
--    Parent = 6-face admission gate (root trust anchor)
--    Child  = delegated workload with bounded capabilities
--    Stabilizer = hardware-backed invariants (HMAC, NVLink, PCIe)
--    Sub-policy = per-workload resource limits and capability tiers


The file C:\Users\NickV\cubie-verification\lean\CubieQuantumConsentAdvanced.lean has been updated successfully.

--  Models cascading consent through hierarchical trust objects:
--    US20240195628A1 (1st set) Claims 1-8
--    US20240195628A1 (2nd set) Claims 1,3,5,7,9,11
--
--  In Cubie Trust Compiler context:
--    Parent = 6-face admission gate (root trust anchor)
--    Child  = delegated workload with bounded capabilities
--    Stabilizer = hardware-backed invariants (HMAC, NVLink, PCIe)
--    Sub-policy = per-workload resource limits and capability tiers

-- ============================================================
--  CENTILLION AI INC. -- ADVANCED QUANTUM CONTEXTUAL CONSENT
--  Lean 4 mirror of CubieQuantumConsentAdvanced.v
--
--  Models cascading consent from NFT hierarchy patents:
--    US20240195628A1 (1st set) Claims 1-8
--    US20240195628A1 (2nd set) Claims 1,3,5,7,9,11
--
--  File:        Centillion/CubieQuantumConsentAdvanced.lean
--  Lean:        4.15.0
--  Status:      Closed proof. Zero `sorry`. Constructive.
--  Patent:      US20240195628A1 (pending)
--  Date:        May 6, 2026
-- ============================================================

namespace Centillion.CubieQuantumConsentAdvanced

-- ============================================================
-- 1. NFT Hierarchy Types
-- ============================================================

structure ConsentNode where
  node_id       : Nat
  parent_id     : Nat       -- 0 = root
  depth         : Nat
  consent_grant : Bool
  sub_policy    : Nat
  capacity      : Nat
  active        : Bool
  deriving DecidableEq, Repr

structure ConsentChannel where
  src_id    : Nat
  dst_id    : Nat
  bandwidth : Nat
  open      : Bool
  deriving DecidableEq, Repr

structure StabilizerCode where
  code_distance  : Nat
  num_checks     : Nat
  syndrome_valid : Bool
  deriving DecidableEq, Repr

-- ============================================================
-- 2. Predicates
-- ============================================================

def is_root (n : ConsentNode) : Bool := n.parent_id == 0

def cascading_consent (parent child : ConsentNode) : Bool :=
  parent.consent_grant && child.consent_grant && parent.active && child.active

def sub_policy_compliant (parent child : ConsentNode) : Bool :=
  child.sub_policy <= parent.capacity

def channel_valid (ch : ConsentChannel) (src dst : ConsentNode) : Bool :=
  ch.open && src.active && dst.active &&
  (src.node_id == ch.src_id) && (dst.node_id == ch.dst_id)

def stabilizer_ok (sc : StabilizerCode) : Bool :=
  sc.syndrome_valid && (0 < sc.code_distance)

def full_consent_ok (parent child : ConsentNode) (sc : StabilizerCode) : Bool :=
  cascading_consent parent child &&
  sub_policy_compliant parent child &&
  stabilizer_ok sc

-- ============================================================
-- 3. CUB-0741: Conditional QEC realization
-- ============================================================

theorem conditional_qec_realization (parent child : ConsentNode) (sc : StabilizerCode)
    (h : full_consent_ok parent child sc = true) :
    stabilizer_ok sc = true := by
  simp [full_consent_ok] at h
  exact h.2.2

-- ============================================================
-- 4. CUB-0742: Stabilizer validity
-- ============================================================

theorem stabilizer_validity (sc : StabilizerCode)
    (h : sc.code_distance = 0) :
    stabilizer_ok sc = false := by
  simp [stabilizer_ok, h]

theorem stabilizer_positive (sc : StabilizerCode)
    (hdist : sc.code_distance > 0) (hsyn : sc.syndrome_valid = true) :
    stabilizer_ok sc = true := by
  simp [stabilizer_ok, hdist, hsyn]

-- ============================================================
-- 5. CUB-0743: Holevo-bounded extraction
-- ============================================================

theorem holevo_bounded_extraction (parent child : ConsentNode)
    (h : sub_policy_compliant parent child = true) :
    child.sub_policy ≤ parent.capacity := by
  simp [sub_policy_compliant] at h
  exact h

theorem extraction_over_capacity_denied (parent child : ConsentNode)
    (h : child.sub_policy > parent.capacity) :
    sub_policy_compliant parent child = false := by
  simp [sub_policy_compliant]
  omega

-- ============================================================
-- 6. CUB-0744: Measurement-collapse consent
-- ============================================================

theorem measurement_collapse_consent (parent child : ConsentNode)
    (h : parent.active = false) :
    cascading_consent parent child = false := by
  simp [cascading_consent, h]

theorem cascade_revoke_immediate (parent child : ConsentNode) (sc : StabilizerCode)
    (h : parent.active = false) :
    full_consent_ok parent child sc = false := by
  simp [full_consent_ok, cascading_consent, h]

-- ============================================================
-- 7. CUB-0745: Entanglement-induced correlation
-- ============================================================

theorem entanglement_grant_correlation (parent child : ConsentNode)
    (hp : parent.consent_grant = true) (hc : child.consent_grant = true)
    (ha1 : parent.active = true) (ha2 : child.active = true) :
    cascading_consent parent child = true := by
  simp [cascading_consent, hp, hc, ha1, ha2]

theorem entanglement_revoke_correlation (parent child : ConsentNode)
    (h : parent.consent_grant = false) :
    cascading_consent parent child = false := by
  simp [cascading_consent, h]

-- ============================================================
-- 8. CUB-0746: Context-dependent measurement basis
-- ============================================================

def access_by_relationship (requestor_depth node_depth : Nat) : Bool :=
  requestor_depth <= node_depth

theorem context_dependent_access (req_depth node_depth : Nat)
    (h : req_depth ≤ node_depth) :
    access_by_relationship req_depth node_depth = true := by
  simp [access_by_relationship, h]

theorem deeper_requestor_denied (req_depth node_depth : Nat)
    (h : req_depth > node_depth) :
    access_by_relationship req_depth node_depth = false := by
  simp [access_by_relationship]
  omega

-- ============================================================
-- 9. CUB-0747: Non-commutative consent algebra
-- ============================================================

def check_cascade_then_policy (parent child : ConsentNode) : Bool :=
  if cascading_consent parent child then sub_policy_compliant parent child
  else false

def check_policy_then_cascade (parent child : ConsentNode) : Bool :=
  if sub_policy_compliant parent child then cascading_consent parent child
  else false

theorem consent_algebra_agree_on_pass (parent child : ConsentNode)
    (hcasc : cascading_consent parent child = true)
    (hpol : sub_policy_compliant parent child = true) :
    check_cascade_then_policy parent child =
    check_policy_then_cascade parent child := by
  simp [check_cascade_then_policy, check_policy_then_cascade, hcasc, hpol]

theorem consent_algebra_cascade_short_circuits (parent child : ConsentNode)
    (h : cascading_consent parent child = false) :
    check_cascade_then_policy parent child = false := by
  simp [check_cascade_then_policy, h]

-- ============================================================
-- 10. CUB-0748: Quantum consent channel
-- ============================================================

theorem consent_channel_requires_active_endpoints (ch : ConsentChannel)
    (src dst : ConsentNode) (h : src.active = false) :
    channel_valid ch src dst = false := by
  simp [channel_valid, h]

-- ============================================================
-- 11. CUB-0749: Contextual entanglement-wedge reconstruction
-- ============================================================

def child_can_access_parent (ch : ConsentChannel)
    (parent child : ConsentNode) : Bool :=
  channel_valid ch parent child && cascading_consent parent child

theorem wedge_reconstruction_requires_consent (ch : ConsentChannel)
    (parent child : ConsentNode)
    (h : child_can_access_parent ch parent child = true) :
    cascading_consent parent child = true := by
  simp [child_can_access_parent] at h
  exact h.2

theorem wedge_reconstruction_requires_channel (ch : ConsentChannel)
    (parent child : ConsentNode)
    (h : child_can_access_parent ch parent child = true) :
    channel_valid ch parent child = true := by
  simp [child_can_access_parent] at h
  exact h.1

-- ============================================================
-- 12. CUB-0750: Information-percolation threshold
-- ============================================================

def percolates (ch : ConsentChannel) (threshold : Nat) : Bool :=
  (threshold <= ch.bandwidth) && ch.open

theorem below_threshold_no_flow (ch : ConsentChannel) (threshold : Nat)
    (h : ch.bandwidth < threshold) :
    percolates ch threshold = false := by
  simp [percolates]
  omega

theorem above_threshold_flows (ch : ConsentChannel) (threshold : Nat)
    (hge : ch.bandwidth ≥ threshold) (hopen : ch.open = true) :
    percolates ch threshold = true := by
  simp [percolates, hopen]
  omega

-- ============================================================
-- 13. CUB-0751: Consent capacity
-- ============================================================

def capacity_available (node : ConsentNode) (current_children : Nat) : Bool :=
  current_children < node.capacity

theorem capacity_exhausted_denies (node : ConsentNode) (cc : Nat)
    (h : cc ≥ node.capacity) :
    capacity_available node cc = false := by
  simp [capacity_available]
  omega

theorem capacity_available_allows (node : ConsentNode) (cc : Nat)
    (h : cc < node.capacity) :
    capacity_available node cc = true := by
  simp [capacity_available, h]

-- ============================================================
-- 14. CUB-0752: Contextual consent kernel threshold
-- ============================================================

def can_modify_preferences (requestor node : ConsentNode) : Bool :=
  node.active && (requestor.depth <= node.depth)

theorem inactive_node_no_modification (requestor node : ConsentNode)
    (h : node.active = false) :
    can_modify_preferences requestor node = false := by
  simp [can_modify_preferences, h]

theorem deeper_requestor_no_modification (requestor node : ConsentNode)
    (h : requestor.depth > node.depth) :
    can_modify_preferences requestor node = false := by
  simp [can_modify_preferences]
  omega

theorem authorized_modification (requestor node : ConsentNode)
    (hactive : node.active = true) (hle : requestor.depth ≤ node.depth) :
    can_modify_preferences requestor node = true := by
  simp [can_modify_preferences, hactive]
  omega

-- ============================================================
-- 15. CUB-0753: Dynamic consent mixing
-- ============================================================

def effective_sub_policy (parent child : ConsentNode) : Nat :=
  min child.sub_policy parent.capacity

theorem effective_policy_bounded_by_parent (parent child : ConsentNode) :
    effective_sub_policy parent child ≤ parent.capacity := by
  simp [effective_sub_policy]
  exact Nat.min_le_right _ _

theorem effective_policy_bounded_by_child (parent child : ConsentNode) :
    effective_sub_policy parent child ≤ child.sub_policy := by
  simp [effective_sub_policy]
  exact Nat.min_le_left _ _

theorem dynamic_mixing_constrains (child : ConsentNode) (cap1 cap2 : Nat)
    (h : cap1 < cap2) :
    min child.sub_policy cap1 ≤ min child.sub_policy cap2 := by
  apply Nat.min_le_min_left
  omega

-- ============================================================
-- 16. CUB-0754: Arbitrary-graph consent threshold complexity
-- ============================================================

def sum_sub_policies : List ConsentNode → Nat
  | [] => 0
  | n :: rest => n.sub_policy + sum_sub_policies rest

def graph_within_capacity (root : ConsentNode) (children : List ConsentNode) : Bool :=
  sum_sub_policies children ≤ root.capacity

theorem empty_graph_within_capacity (root : ConsentNode) :
    graph_within_capacity root [] = true := by
  simp [graph_within_capacity, sum_sub_policies]

theorem overloaded_graph_denied (root : ConsentNode) (children : List ConsentNode)
    (h : sum_sub_policies children > root.capacity) :
    graph_within_capacity root children = false := by
  simp [graph_within_capacity]
  omega

theorem adding_child_increases_demand (child : ConsentNode) (rest : List ConsentNode) :
    sum_sub_policies (child :: rest) = child.sub_policy + sum_sub_policies rest := by
  simp [sum_sub_policies]

theorem one_more_child_overflows (root : ConsentNode) (children : List ConsentNode)
    (new_child : ConsentNode) (heq : sum_sub_policies children = root.capacity)
    (hpos : new_child.sub_policy > 0) :
    graph_within_capacity root (new_child :: children) = false := by
  simp [graph_within_capacity, sum_sub_policies, heq]
  omega

end Centillion.CubieQuantumConsentAdvanced

---  Models cascading consent from NFT hierarchy patents:

+--  Models cascading consent through hierarchical trust objects:

+--    Parent = 6-face admission gate (root trust anchor)

+--    Child  = delegated workload with bounded capabilities

+--    Stabilizer = hardware-backed invariants (HMAC, NVLink, PCIe)

+--    Sub-policy = per-workload resource limits and capability tiers


-- ============================================================
--  CENTILLION AI INC. -- ADVANCED QUANTUM CONTEXTUAL CONSENT
--  Lean 4 mirror of CubieQuantumConsentAdvanced.v
--
--  Models cascading consent through hierarchical trust objects:
--    US20240195628A1 (1st set) Claims 1-8
--    US20240195628A1 (2nd set) Claims 1,3,5,7,9,11
--
--  In Cubie Trust Compiler context:
--    Parent = 6-face admission gate (root trust anchor)
--    Child  = delegated workload with bounded capabilities
--    Stabilizer = hardware-backed invariants (HMAC, NVLink, PCIe)
--    Sub-policy = per-workload resource limits and capability tiers
--
--  File:        Centillion/CubieQuantumConsentAdvanced.lean
--  Lean:        4.15.0
--  Status:      Closed proof. Zero `sorry`. Constructive.
--  Patent:      US20240195628A1 (pending)
--  Date:        May 6, 2026
-- ============================================================

namespace Centillion.CubieQuantumConsentAdvanced

-- ============================================================
-- 1. NFT Hierarchy Types
-- ============================================================

structure ConsentNode where
  node_id       : Nat
  parent_id     : Nat       -- 0 = root
  depth         : Nat
  consent_grant : Bool
  sub_policy    : Nat
  capacity      : Nat
  active        : Bool
  deriving DecidableEq, Repr

structure ConsentChannel where
  src_id    : Nat
  dst_id    : Nat
  bandwidth : Nat
  open      : Bool
  deriving DecidableEq, Repr

structure StabilizerCode where
  code_distance  : Nat
  num_checks     : Nat
  syndrome_valid : Bool
  deriving DecidableEq, Repr

-- ============================================================
-- 2. Predicates
-- ============================================================

def is_root (n : ConsentNode) : Bool := n.parent_id == 0

def cascading_consent (parent child : ConsentNode) : Bool :=
  parent.consent_grant && child.consent_grant && parent.active && child.active

def sub_policy_compliant (parent child : ConsentNode) : Bool :=
  child.sub_policy <= parent.capacity

def channel_valid (ch : ConsentChannel) (src dst : ConsentNode) : Bool :=
  ch.open && src.active && dst.active &&
  (src.node_id == ch.src_id) && (dst.node_id == ch.dst_id)

def stabilizer_ok (sc : StabilizerCode) : Bool :=
  sc.syndrome_valid && (0 < sc.code_distance)

def full_consent_ok (parent child : ConsentNode) (sc : StabilizerCode) : Bool :=
  cascading_consent parent child &&
  sub_policy_compliant parent child &&
  stabilizer_ok sc

-- ============================================================
-- 3. CUB-0741: Conditional QEC realization
-- ============================================================

theorem conditional_qec_realization (parent child : ConsentNode) (sc : StabilizerCode)
    (h : full_consent_ok parent child sc = true) :
    stabilizer_ok sc = true := by
  simp [full_consent_ok] at h
  exact h.2.2

-- ============================================================
-- 4. CUB-0742: Stabilizer validity
-- ============================================================

theorem stabilizer_validity (sc : StabilizerCode)
    (h : sc.code_distance = 0) :
    stabilizer_ok sc = false := by
  simp [stabilizer_ok, h]

theorem stabilizer_positive (sc : StabilizerCode)
    (hdist : sc.code_distance > 0) (hsyn : sc.syndrome_valid = true) :
    stabilizer_ok sc = true := by
  simp [stabilizer_ok, hdist, hsyn]

-- ============================================================
-- 5. CUB-0743: Holevo-bounded extraction
-- ============================================================

theorem holevo_bounded_extraction (parent child : ConsentNode)
    (h : sub_policy_compliant parent child = true) :
    child.sub_policy ≤ parent.capacity := by
  simp [sub_policy_compliant] at h
  exact h

theorem extraction_over_capacity_denied (parent child : ConsentNode)
    (h : child.sub_policy > parent.capacity) :
    sub_policy_compliant parent child = false := by
  simp [sub_policy_compliant]
  omega

-- ============================================================
-- 6. CUB-0744: Measurement-collapse consent
-- ============================================================

theorem measurement_collapse_consent (parent child : ConsentNode)
    (h : parent.active = false) :
    cascading_consent parent child = false := by
  simp [cascading_consent, h]

theorem cascade_revoke_immediate (parent child : ConsentNode) (sc : StabilizerCode)
    (h : parent.active = false) :
    full_consent_ok parent child sc = false := by
  simp [full_consent_ok, cascading_consent, h]

-- ============================================================
-- 7. CUB-0745: Entanglement-induced correlation
-- ============================================================

theorem entanglement_grant_correlation (parent child : ConsentNode)
    (hp : parent.consent_grant = true) (hc : child.consent_grant = true)
    (ha1 : parent.active = true) (ha2 : child.active = true) :
    cascading_consent parent child = true := by
  simp [cascading_consent, hp, hc, ha1, ha2]

theorem entanglement_revoke_correlation (parent child : ConsentNode)
    (h : parent.consent_grant = false) :
    cascading_consent parent child = false := by
  simp [cascading_consent, h]

-- ============================================================
-- 8. CUB-0746: Context-dependent measurement basis
-- ============================================================

def access_by_relationship (requestor_depth node_depth : Nat) : Bool :=
  requestor_depth <= node_depth

theorem context_dependent_access (req_depth node_depth : Nat)
    (h : req_depth ≤ node_depth) :
    access_by_relationship req_depth node_depth = true := by
  simp [access_by_relationship, h]

theorem deeper_requestor_denied (req_depth node_depth : Nat)
    (h : req_depth > node_depth) :
    access_by_relationship req_depth node_depth = false := by
  simp [access_by_relationship]
  omega

-- ============================================================
-- 9. CUB-0747: Non-commutative consent algebra
-- ============================================================

def check_cascade_then_policy (parent child : ConsentNode) : Bool :=
  if cascading_consent parent child then sub_policy_compliant parent child
  else false

def check_policy_then_cascade (parent child : ConsentNode) : Bool :=
  if sub_policy_compliant parent child then cascading_consent parent child
  else false

theorem consent_algebra_agree_on_pass (parent child : ConsentNode)
    (hcasc : cascading_consent parent child = true)
    (hpol : sub_policy_compliant parent child = true) :
    check_cascade_then_policy parent child =
    check_policy_then_cascade parent child := by
  simp [check_cascade_then_policy, check_policy_then_cascade, hcasc, hpol]

theorem consent_algebra_cascade_short_circuits (parent child : ConsentNode)
    (h : cascading_consent parent child = false) :
    check_cascade_then_policy parent child = false := by
  simp [check_cascade_then_policy, h]

-- ============================================================
-- 10. CUB-0748: Quantum consent channel
-- ============================================================

theorem consent_channel_requires_active_endpoints (ch : ConsentChannel)
    (src dst : ConsentNode) (h : src.active = false) :
    channel_valid ch src dst = false := by
  simp [channel_valid, h]

-- ============================================================
-- 11. CUB-0749: Contextual entanglement-wedge reconstruction
-- ============================================================

def child_can_access_parent (ch : ConsentChannel)
    (parent child : ConsentNode) : Bool :=
  channel_valid ch parent child && cascading_consent parent child

theorem wedge_reconstruction_requires_consent (ch : ConsentChannel)
    (parent child : ConsentNode)
    (h : child_can_access_parent ch parent child = true) :
    cascading_consent parent child = true := by
  simp [child_can_access_parent] at h
  exact h.2

theorem wedge_reconstruction_requires_channel (ch : ConsentChannel)
    (parent child : ConsentNode)
    (h : child_can_access_parent ch parent child = true) :
    channel_valid ch parent child = true := by
  simp [child_can_access_parent] at h
  exact h.1

-- ============================================================
-- 12. CUB-0750: Information-percolation threshold
-- ============================================================

def percolates (ch : ConsentChannel) (threshold : Nat) : Bool :=
  (threshold <= ch.bandwidth) && ch.open

theorem below_threshold_no_flow (ch : ConsentChannel) (threshold : Nat)
    (h : ch.bandwidth < threshold) :
    percolates ch threshold = false := by
  simp [percolates]
  omega

theorem above_threshold_flows (ch : ConsentChannel) (threshold : Nat)
    (hge : ch.bandwidth ≥ threshold) (hopen : ch.open = true) :
    percolates ch threshold = true := by
  simp [percolates, hopen]
  omega

-- ============================================================
-- 13. CUB-0751: Consent capacity
-- ============================================================

def capacity_available (node : ConsentNode) (current_children : Nat) : Bool :=
  current_children < node.capacity

theorem capacity_exhausted_denies (node : ConsentNode) (cc : Nat)
    (h : cc ≥ node.capacity) :
    capacity_available node cc = false := by
  simp [capacity_available]
  omega

theorem capacity_available_allows (node : ConsentNode) (cc : Nat)
    (h : cc < node.capacity) :
    capacity_available node cc = true := by
  simp [capacity_available, h]

-- ============================================================
-- 14. CUB-0752: Contextual consent kernel threshold
-- ============================================================

def can_modify_preferences (requestor node : ConsentNode) : Bool :=
  node.active && (requestor.depth <= node.depth)

theorem inactive_node_no_modification (requestor node : ConsentNode)
    (h : node.active = false) :
    can_modify_preferences requestor node = false := by
  simp [can_modify_preferences, h]

theorem deeper_requestor_no_modification (requestor node : ConsentNode)
    (h : requestor.depth > node.depth) :
    can_modify_preferences requestor node = false := by
  simp [can_modify_preferences]
  omega

theorem authorized_modification (requestor node : ConsentNode)
    (hactive : node.active = true) (hle : requestor.depth ≤ node.depth) :
    can_modify_preferences requestor node = true := by
  simp [can_modify_preferences, hactive]
  omega

-- ============================================================
-- 15. CUB-0753: Dynamic consent mixing
-- ============================================================

def effective_sub_policy (parent child : ConsentNode) : Nat :=
  min child.sub_policy parent.capacity

theorem effective_policy_bounded_by_parent (parent child : ConsentNode) :
    effective_sub_policy parent child ≤ parent.capacity := by
  simp [effective_sub_policy]
  exact Nat.min_le_right _ _

theorem effective_policy_bounded_by_child (parent child : ConsentNode) :
    effective_sub_policy parent child ≤ child.sub_policy := by
  simp [effective_sub_policy]
  exact Nat.min_le_left _ _

theorem dynamic_mixing_constrains (child : ConsentNode) (cap1 cap2 : Nat)
    (h : cap1 < cap2) :
    min child.sub_policy cap1 ≤ min child.sub_policy cap2 := by
  apply Nat.min_le_min_left
  omega

-- ============================================================
-- 16. CUB-0754: Arbitrary-graph consent threshold complexity
-- ============================================================

def sum_sub_policies : List ConsentNode → Nat
  | [] => 0
  | n :: rest => n.sub_policy + sum_sub_policies rest

def graph_within_capacity (root : ConsentNode) (children : List ConsentNode) : Bool :=
  sum_sub_policies children ≤ root.capacity

theorem empty_graph_within_capacity (root : ConsentNode) :
    graph_within_capacity root [] = true := by
  simp [graph_within_capacity, sum_sub_policies]

theorem overloaded_graph_denied (root : ConsentNode) (children : List ConsentNode)
    (h : sum_sub_policies children > root.capacity) :
    graph_within_capacity root children = false := by
  simp [graph_within_capacity]
  omega

theorem adding_child_increases_demand (child : ConsentNode) (rest : List ConsentNode) :
    sum_sub_policies (child :: rest) = child.sub_policy + sum_sub_policies rest := by
  simp [sum_sub_policies]

theorem one_more_child_overflows (root : ConsentNode) (children : List ConsentNode)
    (new_child : ConsentNode) (heq : sum_sub_policies children = root.capacity)
    (hpos : new_child.sub_policy > 0) :
    graph_within_capacity root (new_child :: children) = false := by
  simp [graph_within_capacity, sum_sub_policies, heq]
  omega

end Centillion.CubieQuantumConsentAdvanced


Now update the Verus consent hierarchy spec:


1	// cubie_consent_hierarchy_spec.rs — Verus spec for NFT hierarchical consent
2	//
3	// Corresponds to: US20240195628A1 Claims 1-8 (1st set) + Claims 1,3,5,7,9,11 (2nd set)
4	// Models cascading consent through parent/child NFT hierarchy.
5	//
6	// Design constraints:
7	//   - ConsentNode has parent_id, depth, consent_grant, sub_policy, capacity
8	//   - Cascading consent: child valid only if parent active + granted
9	//   - Sub-policy bounded by parent capacity (Holevo bound analogy)
10	//   - Stabilizer code = smart contract enforcement
11	//   - Capacity limits number of child delegations
12	//   - Graph threshold: total sub-policies bounded by root capacity
13
14	#![allow(unused_imports)]
15	use vstd::prelude::*;

// cubie_consent_hierarchy_spec.rs — Verus spec for NFT hierarchical consent
//
// Corresponds to: US20240195628A1 Claims 1-8 (1st set) + Claims 1,3,5,7,9,11 (2nd set)
// Models cascading consent through parent/child NFT hierarchy.
//
// Design constraints:
//   - ConsentNode has parent_id, depth, consent_grant, sub_policy, capacity
//   - Cascading consent: child valid only if parent active + granted
//   - Sub-policy bounded by parent capacity (Holevo bound analogy)
//   - Stabilizer code = smart contract enforcement
//   - Capacity limits number of child delegations
//   - Graph threshold: total sub-policies bounded by root capacity

#![allow(unused_imports)]
use vstd::prelude::*;


// cubie_consent_hierarchy_spec.rs — Verus spec for NFT hierarchical consent
//
// Corresponds to: US20240195628A1 Claims 1-8 (1st set) + Claims 1,3,5,7,9,11 (2nd set)
// Models cascading consent through parent/child NFT hierarchy.
//
// Design constraints:
//   - ConsentNode has parent_id, depth, consent_grant, sub_policy, capacity
//   - Cascading consent: child valid only if parent active + granted
//   - Sub-policy bounded by parent capacity (Holevo bound analogy)
//   - Stabilizer code = smart contract enforcement
//   - Capacity limits number of child delegations
//   - Graph threshold: total sub-policies bounded by root capacity

// cubie_consent_hierarchy_spec.rs — Verus spec for hierarchical consent delegation
//
// Corresponds to: US20240195628A1 Claims 1-8 (1st set) + Claims 1,3,5,7,9,11 (2nd set)
// Models cascading consent through parent/child hierarchical trust objects.
//
// In the Cubie Trust Compiler context:
//   - Parent = 6-face admission gate (root trust anchor)
//   - Child  = delegated workload with bounded capabilities
//   - Stabilizer = hardware-backed invariants (HMAC, NVLink, PCIe)
//   - Sub-policy = per-workload resource limits and capability tiers
//
// Design constraints:
//   - ConsentNode has parent_id, depth, consent_grant, sub_policy, capacity
//   - Cascading consent: child valid only if parent active + granted
//   - Sub-policy bounded by parent capacity (Holevo bound analogy)
//   - Stabilizer code = enforcement contract validation
//   - Capacity limits number of child delegations
//   - Graph threshold: total sub-policies bounded by root capacity


The file C:\Users\NickV\cubie-verification\verus\cubie_consent_hierarchy_spec.rs has been updated successfully.

// cubie_consent_hierarchy_spec.rs — Verus spec for hierarchical consent delegation
//
// Corresponds to: US20240195628A1 Claims 1-8 (1st set) + Claims 1,3,5,7,9,11 (2nd set)
// Models cascading consent through parent/child hierarchical trust objects.
//
// In the Cubie Trust Compiler context:
//   - Parent = 6-face admission gate (root trust anchor)
//   - Child  = delegated workload with bounded capabilities
//   - Stabilizer = hardware-backed invariants (HMAC, NVLink, PCIe)
//   - Sub-policy = per-workload resource limits and capability tiers
//
// Design constraints:
//   - ConsentNode has parent_id, depth, consent_grant, sub_policy, capacity
//   - Cascading consent: child valid only if parent active + granted
//   - Sub-policy bounded by parent capacity (Holevo bound analogy)
//   - Stabilizer code = enforcement contract validation
//   - Capacity limits number of child delegations
//   - Graph threshold: total sub-policies bounded by root capacity

// cubie_consent_hierarchy_spec.rs — Verus spec for NFT hierarchical consent
//
// Corresponds to: US20240195628A1 Claims 1-8 (1st set) + Claims 1,3,5,7,9,11 (2nd set)
// Models cascading consent through parent/child NFT hierarchy.
//
// Design constraints:
//   - ConsentNode has parent_id, depth, consent_grant, sub_policy, capacity
//   - Cascading consent: child valid only if parent active + granted
//   - Sub-policy bounded by parent capacity (Holevo bound analogy)
//   - Stabilizer code = smart contract enforcement
//   - Capacity limits number of child delegations
//   - Graph threshold: total sub-policies bounded by root capacity

#![allow(unused_imports)]
use vstd::prelude::*;

verus! {

// ---------------------------------------------------------------------------
// Constants
// ---------------------------------------------------------------------------

/// Maximum depth in the consent hierarchy (matches delegation MAX_DELEGATION_DEPTH).
pub const MAX_CONSENT_DEPTH: u8 = 8u8;

// ---------------------------------------------------------------------------
// Structs
// ---------------------------------------------------------------------------

/// A node in the NFT consent hierarchy.
pub struct ConsentNode {
    pub node_id:       u64,
    pub parent_id:     u64,   // 0 = root
    pub depth:         u8,
    pub consent_grant: bool,
    pub sub_policy:    u64,
    pub capacity:      u64,
    pub active:        bool,
}

/// A consent channel between parent and child nodes.
pub struct ConsentChannel {
    pub src_id:    u64,
    pub dst_id:    u64,
    pub bandwidth: u64,
    pub ch_open:   bool,
}

/// Stabilizer code: the "smart contract" enforcing consent invariants.
pub struct StabilizerCode {
    pub code_distance:  u64,
    pub num_checks:     u64,
    pub syndrome_valid: bool,
}

// ---------------------------------------------------------------------------
// Spec functions
// ---------------------------------------------------------------------------

/// Cascading consent: parent must be active+granted, child must be active+granted.
pub open spec fn cascading_consent(parent: &ConsentNode, child: &ConsentNode) -> bool {
    parent.consent_grant && child.consent_grant && parent.active && child.active
}

/// Sub-policy bounded by parent capacity.
pub open spec fn sub_policy_compliant(parent: &ConsentNode, child: &ConsentNode) -> bool {
    child.sub_policy <= parent.capacity
}

/// Stabilizer (smart contract) is valid: syndrome passes and distance > 0.
pub open spec fn stabilizer_ok(sc: &StabilizerCode) -> bool {
    sc.syndrome_valid && sc.code_distance > 0
}

/// Full consent admission: cascading + sub-policy + stabilizer.
pub open spec fn full_consent_ok(parent: &ConsentNode, child: &ConsentNode, sc: &StabilizerCode) -> bool {
    cascading_consent(parent, child) && sub_policy_compliant(parent, child) && stabilizer_ok(sc)
}

/// Channel validity: both endpoints active, IDs match, channel open.
pub open spec fn channel_valid(ch: &ConsentChannel, src: &ConsentNode, dst: &ConsentNode) -> bool {
    ch.ch_open && src.active && dst.active &&
    src.node_id == ch.src_id && dst.node_id == ch.dst_id
}

/// Access by hierarchy depth: requestor must be at or above target depth.
pub open spec fn access_by_relationship(requestor_depth: u8, node_depth: u8) -> bool {
    requestor_depth <= node_depth
}

/// Child can access parent through a valid channel with cascading consent.
pub open spec fn child_can_access_parent(ch: &ConsentChannel, parent: &ConsentNode, child: &ConsentNode) -> bool {
    channel_valid(ch, parent, child) && cascading_consent(parent, child)
}

/// Percolation: data flows only when bandwidth >= threshold and channel open.
pub open spec fn percolates(ch: &ConsentChannel, threshold: u64) -> bool {
    threshold <= ch.bandwidth && ch.ch_open
}

/// Capacity available: current children count < node's capacity.
pub open spec fn capacity_available(node: &ConsentNode, current_children: u64) -> bool {
    current_children < node.capacity
}

/// Preference modification: node active and requestor at/above node depth.
pub open spec fn can_modify_preferences(requestor: &ConsentNode, node: &ConsentNode) -> bool {
    node.active && requestor.depth <= node.depth
}

/// Effective sub-policy: min of child's sub-policy and parent's capacity.
pub open spec fn effective_sub_policy(parent: &ConsentNode, child: &ConsentNode) -> u64 {
    if child.sub_policy <= parent.capacity { child.sub_policy } else { parent.capacity }
}

// ---------------------------------------------------------------------------
// Invariant proofs — CUB-0741 through CUB-0754
// ---------------------------------------------------------------------------

/// CUB-0741: Full consent implies stabilizer is valid.
proof fn conditional_qec_realization(parent: &ConsentNode, child: &ConsentNode, sc: &StabilizerCode)
    requires full_consent_ok(parent, child, sc)
    ensures  stabilizer_ok(sc)
{
    // full_consent_ok = cascading && sub_policy && stabilizer_ok
}

/// CUB-0742: Zero code distance => stabilizer invalid.
proof fn stabilizer_validity(sc: &StabilizerCode)
    requires sc.code_distance == 0
    ensures  !stabilizer_ok(sc)
{
    // stabilizer_ok requires code_distance > 0
}

/// CUB-0743: Sub-policy compliant implies child ≤ parent capacity.
proof fn holevo_bounded_extraction(parent: &ConsentNode, child: &ConsentNode)
    requires sub_policy_compliant(parent, child)
    ensures  child.sub_policy <= parent.capacity
{
}

/// CUB-0744: Parent inactive => cascading consent fails.
proof fn measurement_collapse_consent(parent: &ConsentNode, child: &ConsentNode)
    requires !parent.active
    ensures  !cascading_consent(parent, child)
{
}

/// CUB-0744b: Parent inactive => full consent fails.
proof fn cascade_revoke_immediate(parent: &ConsentNode, child: &ConsentNode, sc: &StabilizerCode)
    requires !parent.active
    ensures  !full_consent_ok(parent, child, sc)
{
}

/// CUB-0745: All conditions true => cascading consent holds.
proof fn entanglement_grant_correlation(parent: &ConsentNode, child: &ConsentNode)
    requires parent.consent_grant && child.consent_grant && parent.active && child.active
    ensures  cascading_consent(parent, child)
{
}

/// CUB-0745b: Parent consent revoked => cascading fails.
proof fn entanglement_revoke_correlation(parent: &ConsentNode, child: &ConsentNode)
    requires !parent.consent_grant
    ensures  !cascading_consent(parent, child)
{
}

/// CUB-0746: Requestor at/above target depth => access granted.
proof fn context_dependent_access(req_depth: u8, node_depth: u8)
    requires req_depth <= node_depth
    ensures  access_by_relationship(req_depth, node_depth)
{
}

/// CUB-0746b: Deeper requestor => access denied.
proof fn deeper_requestor_denied(req_depth: u8, node_depth: u8)
    requires req_depth > node_depth
    ensures  !access_by_relationship(req_depth, node_depth)
{
}

/// CUB-0748: Inactive source => channel invalid.
proof fn consent_channel_requires_active_endpoints(ch: &ConsentChannel, src: &ConsentNode, dst: &ConsentNode)
    requires !src.active
    ensures  !channel_valid(ch, src, dst)
{
}

/// CUB-0749: Child access requires cascading consent.
proof fn wedge_reconstruction_requires_consent(ch: &ConsentChannel, parent: &ConsentNode, child: &ConsentNode)
    requires child_can_access_parent(ch, parent, child)
    ensures  cascading_consent(parent, child)
{
}

/// CUB-0750: Below threshold => no data flow.
proof fn below_threshold_no_flow(ch: &ConsentChannel, threshold: u64)
    requires ch.bandwidth < threshold
    ensures  !percolates(ch, threshold)
{
}

/// CUB-0751: Capacity exhausted => deny new children.
proof fn capacity_exhausted_denies(node: &ConsentNode, current_children: u64)
    requires current_children >= node.capacity
    ensures  !capacity_available(node, current_children)
{
}

/// CUB-0752: Inactive node => no preference modification.
proof fn inactive_node_no_modification(requestor: &ConsentNode, node: &ConsentNode)
    requires !node.active
    ensures  !can_modify_preferences(requestor, node)
{
}

/// CUB-0753: Effective sub-policy bounded by parent capacity.
proof fn effective_policy_bounded_by_parent(parent: &ConsentNode, child: &ConsentNode)
    ensures effective_sub_policy(parent, child) <= parent.capacity
{
}

/// CUB-0753b: Effective sub-policy bounded by child sub-policy.
proof fn effective_policy_bounded_by_child(parent: &ConsentNode, child: &ConsentNode)
    ensures effective_sub_policy(parent, child) <= child.sub_policy
{
}

// ---------------------------------------------------------------------------
// Exec functions — runtime entry points
// ---------------------------------------------------------------------------

/// EXEC: cascading consent gate.
pub fn exec_cascading_consent(parent: &ConsentNode, child: &ConsentNode) -> (result: bool)
    ensures result == cascading_consent(parent, child)
{
    parent.consent_grant && child.consent_grant && parent.active && child.active
}

/// EXEC: full consent admission gate.
pub fn exec_full_consent_ok(parent: &ConsentNode, child: &ConsentNode, sc: &StabilizerCode) -> (result: bool)
    ensures result == full_consent_ok(parent, child, sc)
{
    parent.consent_grant && child.consent_grant && parent.active && child.active
    && child.sub_policy <= parent.capacity
    && sc.syndrome_valid && sc.code_distance > 0
}

/// EXEC: capacity check.
pub fn exec_capacity_available(node: &ConsentNode, current_children: u64) -> (result: bool)
    ensures result == capacity_available(node, current_children)
{
    current_children < node.capacity
}

/// EXEC: percolation check.
pub fn exec_percolates(ch: &ConsentChannel, threshold: u64) -> (result: bool)
    ensures result == percolates(ch, threshold)
{
    threshold <= ch.bandwidth && ch.ch_open
}

/// EXEC: preference modification check.
pub fn exec_can_modify_preferences(requestor: &ConsentNode, node: &ConsentNode) -> (result: bool)
    ensures result == can_modify_preferences(requestor, node)
{
    node.active && requestor.depth <= node.depth
}

} // verus!

-// cubie_consent_hierarchy_spec.rs — Verus spec for NFT hierarchical consent

+// cubie_consent_hierarchy_spec.rs — Verus spec for hierarchical consent delegation

-// Models cascading consent through parent/child NFT hierarchy.

+// Models cascading consent through parent/child hierarchical trust objects.

+// In the Cubie Trust Compiler context:

+//   - Parent = 6-face admission gate (root trust anchor)

+//   - Child  = delegated workload with bounded capabilities

+//   - Stabilizer = hardware-backed invariants (HMAC, NVLink, PCIe)

+//   - Sub-policy = per-workload resource limits and capability tiers

-//   - Stabilizer code = smart contract enforcement

+//   - Stabilizer code = enforcement contract validation


/// A node in the NFT consent hierarchy.

/// A node in the hierarchical consent tree (trust object).