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[DIR] 42226 - TrustFortress_Intel_DCAI_Package_0421
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[DIR] AI-DMP-main-extracted
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[DIR] Badge_ Intel® Partner Alliance Program
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[FILE] CAMARA MCP Position Paper (1).pdf
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[DIR] Centillion Logo assets + Guide
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[DIR] cubie_diagrams_extracted
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[FILE] Cubie_Geometric_Trust (1).pdf
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[DIR] Cubie_v1_11_MicDrop_Optimized_Package
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[DIR] cubie_whitepaper_deduped_v2_4_package1
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[DIR] Cursor - PhucAI RAKKIT
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[FILE] e9253dc6-b1c6-4b29-84ea-da0fe3e5c5ac_AnkerDockManager-Setup-1.1.2-Windows.exe
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[FILE] WebStorm-2026.1 (6).exe
[FILE] WebStorm-2026.1 (7).exe
[FILE] WebStorm-2026.1 (8).exe
[FILE] WebStorm-2026.1 (9).exe
[FILE] WebStorm-2026.1.exe
[FILE] Welcome to Intel Partner Alliance Edge AI Application Initiative – Foundational .pdf
[FILE] WhatsApp Installer.exe
[FILE] wispr flow baa hipaa download agreement.pdf
[FILE] Wispr Flow Setup.exe
[FILE] workload-ID(1)-2026-01-08.pdf
[FILE] workload-ID(1)-2026-01-08.xlsx
[FILE] workload-ID(2)-2026-01-09 (1).pdf
[FILE] workload-ID(2)-2026-01-09 (2).pdf
[FILE] workload-ID(2)-2026-01-09.pdf
[FILE] workload-ID(2)-2026-01-09.xlsx
[FILE] workload-ID(3)-2026-01-09.pdf
[FILE] wp changes - cubie_whitepaper_targeted_updates_final.pdf
[FILE] Yieldmo _ San Antonio Spurs - Debit Card Campaign.pptx
[FILE] Yieldmo _ San Antonio Spurs - Merch Campaign.pptx
[FILE] yieldmo_sportsmax_celtics_mobile (1).mp4
[FILE] yieldmo_sportsmax_celtics_mobile.mp4
[FILE] Yieldmo___San_Antonio_Spurs_-_Debit_Card_Campaign.pdf
[FILE] YMax Managed Service vs. Standard Programmatic Handout.pptx
[FILE] YMax Managed Service vs. Standard Programmatic Handout.pptx.pdf
[FILE] Your_Health,_Your_Data,_&_AI (1).mp4
[FILE] Your_Health,_Your_Data,_&_AI (2).mp4
[FILE] Your_Health,_Your_Data,_&_AI.mp4
[FILE] ZeroTrust_Gate_v18_0127.png
[FILE] ZeroTrust_Gate_v18_0127.svg
[FILE] ZeroTrust_Gate_v8_portrait_0127.svg
[FILE] Zero_Drift_OnPrem_SaaS_Ship_Plan_v23.xlsx
[FILE] Zero_Trust_AI_Compliance.pdf
[FILE] Zero_Trust_AI_Identity.pdf
[FILE] Zero_Trust_AI_Identity_for_Healthcare (1).pdf
[FILE] Zero_Trust_AI_Identity_for_Healthcare (2).pdf
[FILE] Zero_Trust_AI_Identity_for_Healthcare.pdf
[FILE] Zero_Trust_AI__Surviving_2026.mp4
[FILE] Zero_Trust_Identity_for_Edge_AI.pdf
[FILE] zip v1.13_CubieFinalSubmission_HARDENED_0427.zip
[FILE] Zoom_cm_ds_m8eB7B9FN6VD-Kuut-rwsbXI+dJUboFGFSktX@bjFxD44GtnjhNYEa_kcafaa1d2c0e04396_.exe
[FILE] Zulip-Web-Setup-5.12.3.exe
[DIR] _extracted_docs
[DIR] _extracted_files2
[DIR] _extracted_v3
[DIR] _unzipped
[FILE] ~$elds for Schedule 1.docx
[FILE] ~$ILDSPEC-v6.2.0.docx
[FILE] ~$Update frequency_IDMAP_Feed_Summary_v4.0_1219.xlsx
[FILE] “Ultimate Stack” summary (what I wo.txt


Bash

ls ~/Downloads/ 2>/dev/null | grep -i verus


(Bash completed with no output)


dir "C:\Users\NickV\Downloads\*verus*" /s /b 2>nul && dir "C:\Users\NickV\AppData\Local\*verus*" /s /b 2>nul


Process started with PID 69224 (shell: cmd)
Initial output:


ToolSearch

Question: select:mcp__desktop-commander__read_process_output


Question: select:mcp__desktop-commander__read_process_output


[Reading 0 new lines (total: 0 lines)]

(No output in requested range)
✅ Process completed with exit code 1 (runtime: 0.07s)


The previous session must have stored the binary somewhere non-standard. Let me search more broadly:


where verus 2>nul || echo NOT_FOUND && dir "C:\Users\NickV\.rustup\toolchains" 2>nul | findstr verus


Process started with PID 86260 (shell: cmd)
Initial output:
NOT_FOUND


powershell -Command "Get-ChildItem -Path C:\Users\NickV -Recurse -Filter 'verus*' -ErrorAction SilentlyContinue | Where-Object {!$_.PSIsContainer} | Select-Object FullName | Format-List"


Process started with PID 49108 (shell: powershell.exe)
Initial output:
!.PSIsContainer : The term '!.PSIsContainer' is not recognized as the name of a cmdlet, function, script file, or
operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try
again.
At line:1 char:108
+ ... -ErrorAction SilentlyContinue | Where-Object {!.PSIsContainer} | Sele ...
+                                                   ~~~~~~~~~~~~~~~
    + CategoryInfo          : ObjectNotFound: (!.PSIsContainer:String) [], CommandNotFoundException
    + FullyQualifiedErrorId : CommandNotFoundException

⏳ Process is running. Use read_process_output to get more output.


powershell -Command "Get-ChildItem -Path C:\Users\NickV -Recurse -Filter 'verus.exe' -ErrorAction SilentlyContinue | Select-Object -ExpandProperty FullName"


Process started with PID 67444 (shell: powershell.exe)
Initial output:

⏳ Process is running. Use read_process_output to get more output.


[Reading 0 new lines (total: 0 lines)]

(No output in requested range)
✅ Process completed with exit code 1 (runtime: 97.08s)


Verus binary is gone. Need to re-download it. Let me check the GitHub API for the latest release:


Question: select:WebFetch


Question: select:WebFetch


Bash

gh api repos/verus-lang/verus/releases/latest --jq '.tag_name, (.assets[] | select(.name | contains("windows")) | .browser_download_url)'


gh api repos/verus-lang/verus/releases/latest --jq '.assets[].browser_download_url'


powershell -Command "Invoke-WebRequest -Uri 'https://github.com/verus-lang/verus/releases/download/release/0.2026.05.03.8b81855/verus-0.2026.05.03.8b81855-x86-win.zip' -OutFile 'C:\Users\NickV\Downloads\verus-win.zip'; Expand-Archive -Path 'C:\Users\NickV\Downloads\verus-win.zip' -DestinationPath 'C:\Users\NickV\Downloads\verus-win' -Force; Write-Host 'DONE'"


Process started with PID 86952 (shell: powershell.exe)
Initial output:
DONE


dir "C:\Users\NickV\Downloads\verus-win" /s /b


Process started with PID 35184 (shell: cmd)
Initial output:
The filename, directory name, or volume label syntax is incorrect.


[DIR] verus-x86-win
[FILE] verus-x86-win\.vstd-fingerprint
[DIR] verus-x86-win\builtin
[DIR] verus-x86-win\builtin_macros
[FILE] verus-x86-win\cargo-verus.exe
[FILE] verus-x86-win\libverus_builtin.rlib
[FILE] verus-x86-win\libvstd.rlib
[FILE] verus-x86-win\rust_verify.exe
[DIR] verus-x86-win\state_machines_macros
[FILE] verus-x86-win\version.json
[FILE] verus-x86-win\version.txt
[FILE] verus-x86-win\verus-root
[FILE] verus-x86-win\verus.exe
[FILE] verus-x86-win\verus_builtin_macros.dll
[FILE] verus-x86-win\verus_state_machines_macros.dll
[DIR] verus-x86-win\vstd
[FILE] verus-x86-win\vstd.vir
[FILE] verus-x86-win\z3.exe


Good, binary is at `C:\Users\NickV\Downloads\verus-win\verus-x86-win\verus.exe`. Now run all 12 specs:


powershell -Command "$verus = 'C:\Users\NickV\Downloads\verus-win\verus-x86-win\verus.exe'; $pass=0; $fail=0; Get-ChildItem 'C:\Users\NickV\cubie-verification\verus\*.rs' | ForEach-Object { $f=$_.FullName; $r=& $verus --crate-type lib $f 2>&1; if ($LASTEXITCODE -eq 0) { Write-Host \"PASS: $($_.Name)\"; $pass++ } else { Write-Host \"FAIL: $($_.Name)\"; $r | Select-String 'error\[|^error' | Select-Object -First 5 | ForEach-Object { Write-Host \"  $_\" }; $fail++ } }; Write-Host ''; Write-Host \"=== RESULTS: $pass PASS, $fail FAIL ===\""


Process started with PID 66584 (shell: powershell.exe)
Initial output:
At line:1 char:167
+ ... ie-verification\verus\*.rs' | ForEach-Object { =.FullName; =&  --crat ...
+                                                                 ~
The ampersand (&) character is not allowed. The & operator is reserved for future use; wrap an ampersand in double
quotation marks ("&") to pass it as part of a string.
At line:1 char:362
+ ... elect-Object -First 5 | ForEach-Object { Write-Host " \ }; ++ } }; Wr ...
+                                                                  ~
Missing expression after unary operator '++'.
At line:1 char:365
+ ... t-Object -First 5 | ForEach-Object { Write-Host " \ }; ++ } }; Write- ...
+                                                                 ~
Unexpected token '}' in expression or statement.
    + CategoryInfo          : ParserError: (:) [], ParentContainsErrorRecordException
    + FullyQualifiedErrorId : AmpersandNotAllowed


Let me write a PowerShell script file instead:


Write

$verus = "C:\Users\NickV\Downloads\verus-win\verus-x86-win\verus.exe"
$pass = 0
$fail = 0

Get-ChildItem "C:\Users\NickV\cubie-verification\verus\*.rs" | ForEach-Object {
    $f = $_.FullName
    $name = $_.Name
    $r = & $verus --crate-type lib $f 2>&1
    if ($LASTEXITCODE -eq 0) {
        Write-Host "PASS: $name"
        $pass++
    } else {
        Write-Host "FAIL: $name"
        $r | Select-String "^error" | Select-Object -First 5 | ForEach-Object {
            Write-Host "  $_"
        }
        $fail++
    }
}

Write-Host ""
Write-Host "=== RESULTS: $pass PASS, $fail FAIL ==="


File created successfully at: C:\Users\NickV\cubie-verification\run_verus.ps1

$verus = "C:\Users\NickV\Downloads\verus-win\verus-x86-win\verus.exe"
$pass = 0
$fail = 0

Get-ChildItem "C:\Users\NickV\cubie-verification\verus\*.rs" | ForEach-Object {
    $f = $_.FullName
    $name = $_.Name
    $r = & $verus --crate-type lib $f 2>&1
    if ($LASTEXITCODE -eq 0) {
        Write-Host "PASS: $name"
        $pass++
    } else {
        Write-Host "FAIL: $name"
        $r | Select-String "^error" | Select-Object -First 5 | ForEach-Object {
            Write-Host "  $_"
        }
        $fail++
    }
}

Write-Host ""
Write-Host "=== RESULTS: $pass PASS, $fail FAIL ==="


powershell -ExecutionPolicy Bypass -File "C:\Users\NickV\cubie-verification\run_verus.ps1"


Process started with PID 43456 (shell: powershell.exe)
Initial output:
PASS: cubieq_addendum_spec.rs
FAIL: cubie_capacity_spec.rs
  error[E0308]: mismatched types
  error: aborting due to 1 previous error
PASS: cubie_delegation_spec.rs
PASS: cubie_geometry_spec.rs
PASS: cubie_lease_spec.rs
PASS: cubie_per_predicate_spec.rs
PASS: cubie_runtime_spec.rs
PASS: oai_runtime_spec.rs
PASS: omega_bridge_spec.rs
FAIL: omega_spec.rs
  error: assertion failed
  error: postcondition not satisfied
  error: postcondition not satisfied
  error: postcondition not satisfied
  error: aborting due to 4 previous errors
FAIL: quantum_geometric_spec.rs
  error: postcondition not satisfied
  error: postcondition not satisfied
  error: postcondition not satisfied
  error: aborting due to 3 previous errors
PASS: ramen_seam_spec.rs

=== RESULTS: 9 PASS, 3 FAIL ===


9/12 passing. Let me get full error details for the 3 remaining failures:


$verus = "C:\Users\NickV\Downloads\verus-win\verus-x86-win\verus.exe"

foreach ($name in @("cubie_capacity_spec.rs", "omega_spec.rs", "quantum_geometric_spec.rs")) {
    $f = "C:\Users\NickV\cubie-verification\verus\$name"
    Write-Host "=== $name ==="
    & $verus --crate-type lib $f 2>&1 | Select-String "^error|note:|  -->" | Select-Object -First 30
    Write-Host ""
}


File created successfully at: C:\Users\NickV\cubie-verification\run_verus_debug.ps1

$verus = "C:\Users\NickV\Downloads\verus-win\verus-x86-win\verus.exe"

foreach ($name in @("cubie_capacity_spec.rs", "omega_spec.rs", "quantum_geometric_spec.rs")) {
    $f = "C:\Users\NickV\cubie-verification\verus\$name"
    Write-Host "=== $name ==="
    & $verus --crate-type lib $f 2>&1 | Select-String "^error|note:|  -->" | Select-Object -First 30
    Write-Host ""
}


powershell -ExecutionPolicy Bypass -File "C:\Users\NickV\cubie-verification\run_verus_debug.ps1"


Process started with PID 84308 (shell: powershell.exe)
Initial output:
=== cubie_capacity_spec.rs ===

error[E0308]: mismatched types
  --> C:\Users\NickV\cubie-verification\verus\cubie_capacity_spec.rs:53:44
error: aborting due to 1 previous error

=== omega_spec.rs ===
error: assertion failed
  --> C:\Users\NickV\cubie-verification\verus\omega_spec.rs:74:12
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\omega_spec.rs:80:14
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\omega_spec.rs:93:13
error: postcondition not satisfied
   --> C:\Users\NickV\cubie-verification\verus\omega_spec.rs:266:14
error: aborting due to 4 previous errors

=== quantum_geometric_spec.rs ===
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\quantum_geometric_spec.rs:65:13
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\quantum_geometric_spec.rs:72:14
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\quantum_geometric_spec.rs:78:14
error: aborting due to 3 previous errors


Let me get the full error text for each failure:


$verus = "C:\Users\NickV\Downloads\verus-win\verus-x86-win\verus.exe"

foreach ($name in @("cubie_capacity_spec.rs", "omega_spec.rs", "quantum_geometric_spec.rs")) {
    $f = "C:\Users\NickV\cubie-verification\verus\$name"
    Write-Host "=============================="
    Write-Host "=== $name ==="
    Write-Host "=============================="
    & $verus --crate-type lib $f 2>&1
    Write-Host ""
}


File created successfully at: C:\Users\NickV\cubie-verification\run_verus_full.ps1

$verus = "C:\Users\NickV\Downloads\verus-win\verus-x86-win\verus.exe"

foreach ($name in @("cubie_capacity_spec.rs", "omega_spec.rs", "quantum_geometric_spec.rs")) {
    $f = "C:\Users\NickV\cubie-verification\verus\$name"
    Write-Host "=============================="
    Write-Host "=== $name ==="
    Write-Host "=============================="
    & $verus --crate-type lib $f 2>&1
    Write-Host ""
}


powershell -ExecutionPolicy Bypass -File "C:\Users\NickV\cubie-verification\run_verus_full.ps1"


Process started with PID 82176 (shell: powershell.exe)
Initial output:
==============================
=== cubie_capacity_spec.rs ===
==============================
verus.exe : error[E0308]: mismatched types
At C:\Users\NickV\cubie-verification\run_verus_full.ps1:8 char:5
+     & $verus --crate-type lib $f 2>&1
+     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (error[E0308]: mismatched types:String) [], RemoteException
    + FullyQualifiedErrorId : NativeCommandError

  --> C:\Users\NickV\cubie-verification\verus\cubie_capacity_spec.rs:53:44
   |
53 |         CapacityResult::Ok { new_capacity: current - cost }
   |                                            ^^^^^^^^^^^^^^ expected `i64`, found `int`
error: aborting due to 1 previous error
For more information about this error, try `rustc --explain E0308`.

==============================
=== omega_spec.rs ===
==============================
verus.exe : error: assertion failed
At C:\Users\NickV\cubie-verification\run_verus_full.ps1:8 char:5
+     & $verus --crate-type lib $f 2>&1
+     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (error: assertion failed:String) [], RemoteException
    + FullyQualifiedErrorId : NativeCommandError

  --> C:\Users\NickV\cubie-verification\verus\omega_spec.rs:74:12
   |
74 |     assert(c_tree(1) == 55);
   |            ^^^^^^^^^^^^^^^ assertion failed
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\omega_spec.rs:80:14
   |
78 | proof fn C_tree_geometric_series_lower(n: nat)
   |       ---------------------------------------- at the end of the function body
79 |     requires n >= 1
80 |     ensures  c_tree(n) >= FULL_SURFACE as nat   // grows at least as fast as 54
   |              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ failed this postcondition
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\omega_spec.rs:93:13
   |
92 | proof fn Omega_tree_at_1()
   |       -------------------- at the end of the function body
93 |     ensures omega_tree_exponent(1) == 55
   |             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ failed this postcondition
error: postcondition not satisfied
   --> C:\Users\NickV\cubie-verification\verus\omega_spec.rs:266:14
    |
264 | proof fn tarpit_no_false_admit(in_tarpit: bool, admitted: bool)
    |       --------------------------------------------------------- at the end of the function body
265 |     requires in_tarpit
266 |     ensures  !admitted || !in_tarpit  // tarpit and admit are exclusive
    |              ^^^^^^^^^^^^^^^^^^^^^^^ failed this postcondition
verification results:: 31 verified, 4 errors
error: aborting due to 4 previous errors

==============================
=== quantum_geometric_spec.rs ===
==============================
verus.exe : error: postcondition not satisfied
At C:\Users\NickV\cubie-verification\run_verus_full.ps1:8 char:5
+     & $verus --crate-type lib $f 2>&1
+     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (error: postcondition not satisfied:String) [], RemoteException
    + FullyQualifiedErrorId : NativeCommandError

  --> C:\Users\NickV\cubie-verification\verus\quantum_geometric_spec.rs:65:13
   |
64 | proof fn amplification_at_3()
   |       ----------------------- at the end of the function body
65 |     ensures crowd(3) == AMP_Q as nat * golden_path(3) + AMP_R as nat
   |             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ failed this postcondition
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\quantum_geometric_spec.rs:72:14
   |
70 | proof fn crowd_exceeds_golden(n: nat)
   |       ------------------------------- at the end of the function body
71 |     requires n >= 1
72 |     ensures  crowd(n) > golden_path(n)
   |              ^^^^^^^^^^^^^^^^^^^^^^^^^ failed this postcondition
error: postcondition not satisfied
  --> C:\Users\NickV\cubie-verification\verus\quantum_geometric_spec.rs:78:14
   |
76 | proof fn golden_path_below_system(n: nat)
   |       ----------------------------------- at the end of the function body
77 |     requires n >= 1
78 |     ensures  golden_path(n) < L_N(n)
   |              ^^^^^^^^^^^^^^^^^^^^^^^ failed this postcondition
verification results:: 41 verified, 3 errors
error: aborting due to 3 previous errors

✅ Process 82176 has finished execution


<task-notification>
<task-id>btngz0ioa</task-id>
<tool-use-id>toolu_01MVTKPHNz51K5Q4U57p4Hwk</tool-use-id>
<output-file>C:\Users\NickV\AppData\Local\Temp\claude\C--Users-NickV\bfc2bfbf-6683-4826-bf18-edd758f725bb\tasks\btngz0ioa.output</output-file>
<status>completed</status>
<summary>Background command "find ~ -name "verus*" -type f 2>/dev/null | head -10" completed (exit code 0)</summary>
</task-notification>


Now I understand all errors precisely:

1. **capacity**: `i64 - i64` in spec mode returns `int`, field expects `i64` → cast needed
2. **omega**: c_tree uses `FULL_SURFACE as nat` which SMT can't auto-evaluate; `tarpit_no_false_admit` postcondition is logically unprovable
3. **quantum**: inductive proofs with empty bodies don't discharge; AMP_Q/R constants need bridging

Let me fix all three files:


Edit

CapacityResult::Ok { new_capacity: current - cost }

CapacityResult::Ok { new_capacity: (current - cost) as i64 }


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

// cubie_capacity_spec.rs — Verus spec for optimistic capacity decrement
//
// Corresponds to: CubieTrustCompilerV2_0 capacity / budget model
// ENGINEERING_INVARIANT: capacity must never go negative after decrement
//
// Design constraints:
//   - No heap allocation in hot path
//   - No network calls in hot path
//   - Decrement failure must produce DENY, never ALLOW
//   - Result is always deterministic given same inputs

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

verus! {

// ---------------------------------------------------------------------------
// Types
// ---------------------------------------------------------------------------

/// Result of an optimistic capacity decrement attempt.
#[derive(PartialEq)]
pub enum CapacityResult {
    /// Decrement succeeded. New capacity is non-negative.
    Ok { new_capacity: i64 },
    /// Decrement would go below zero. Request must be denied.
    DenyKvHeadBudget,
}

/// A named denial reason code (aligned with TrustFortress DENY_ namespace).
pub enum DenyCode {
    DenyKvHeadBudget,
    DenyDepth,
    DenyReplay,
    DenyPolicy,
}

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

/// Optimistic capacity decrement.
///
/// Returns Ok { new_capacity } if current - cost >= 0,
/// otherwise DenyKvHeadBudget. Pure, no side effects.
///
/// Preconditions: current >= 0, cost >= 0 (enforced by caller).
pub open spec fn optimistic_capacity_decrement(
    current: i64,
    cost:    i64,
) -> CapacityResult {
    if current - cost >= 0i64 {
        CapacityResult::Ok { new_capacity: current - cost }
    } else {
        CapacityResult::DenyKvHeadBudget
    }
}

/// True iff a decrement of `cost` from `current` would succeed.
pub open spec fn can_decrement(current: i64, cost: i64) -> bool {
    current >= 0i64 && cost >= 0i64 && current - cost >= 0i64
}

// ---------------------------------------------------------------------------
// Invariant proofs
// ---------------------------------------------------------------------------

/// Invariant: new_capacity is never negative after a successful decrement.
/// ENGINEERING_INVARIANT: capacity_non_negative
proof fn capacity_non_negative(current: i64, cost: i64)
    requires
        current >= 0i64,
        cost    >= 0i64,
    ensures
        match optimistic_capacity_decrement(current, cost) {
            CapacityResult::Ok { new_capacity } => new_capacity >= 0i64,
            CapacityResult::DenyKvHeadBudget    => true,
        }
{
    // If cost <= current: current - cost >= 0. Otherwise DenyKvHeadBudget.
}

/// Theorem: deny_on_decrement_failure — cost exceeding budget produces DENY, never OK.
/// This is the critical safety invariant: no request must slip through on budget exhaustion.
proof fn deny_on_decrement_failure(current: i64, cost: i64)
    requires
        current >= 0i64,
        cost    >  current,
    ensures
        optimistic_capacity_decrement(current, cost) == CapacityResult::DenyKvHeadBudget
{
    // current - cost < 0 when cost > current >= 0
    // So the else branch triggers => DenyKvHeadBudget
}

/// Theorem: decrement is deterministic — same inputs, same result.
proof fn decrement_deterministic(current: i64, cost: i64)
    ensures
        optimistic_capacity_decrement(current, cost)
        == optimistic_capacity_decrement(current, cost)
{
    // Trivially true for a pure function
}

/// Theorem: if decrement succeeds, new capacity is strictly less than current (when cost > 0).
proof fn decrement_reduces_capacity(current: i64, cost: i64)
    requires
        current >= 0i64,
        cost    >  0i64,
        can_decrement(current, cost),
    ensures
        match optimistic_capacity_decrement(current, cost) {
            CapacityResult::Ok { new_capacity } => new_capacity < current,
            CapacityResult::DenyKvHeadBudget    => false, // unreachable given precondition
        }
{
    // can_decrement => result is Ok. new_capacity = current - cost < current when cost > 0.
}

/// Theorem: zero-cost decrement is always OK and preserves capacity.
proof fn zero_cost_always_succeeds(current: i64)
    requires current >= 0i64,
    ensures
        optimistic_capacity_decrement(current, 0i64)
        == (CapacityResult::Ok { new_capacity: current })
{
    // current - 0 = current >= 0 => Ok { new_capacity: current }
}

/// Theorem: monotone deny — if a cost is denied, any strictly larger cost is also denied.
proof fn deny_is_monotone(current: i64, cost1: i64, cost2: i64)
    requires
        current >= 0i64,
        cost1   >= 0i64,
        cost2   >  cost1,
        optimistic_capacity_decrement(current, cost1) == CapacityResult::DenyKvHeadBudget,
    ensures
        optimistic_capacity_decrement(current, cost2) == CapacityResult::DenyKvHeadBudget
{
    // cost1 denied => current < cost1. cost2 > cost1 => current < cost2 => cost2 denied.
}

} // verus!

-        CapacityResult::Ok { new_capacity: current - cost }

+        CapacityResult::Ok { new_capacity: (current - cost) as i64 }


Now fix omega_spec.rs — replace FULL_SURFACE as nat with literal 54 in c_tree, fix C_tree_at_1, C_tree_geometric_series_lower, Omega_tree_at_1, and tarpit_no_false_admit:


else      { 1 + FULL_SURFACE as nat * c_tree((n - 1) as nat) }

else      { 1 + 54nat * c_tree((n - 1) as nat) }


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

// omega_spec.rs — Verus spec for Theorem Omega chain
//
// Corresponds to: TheoremOmega4 + TheoremOmega6 + OmegaSeven + OmegaEight
// Triple-kernel verified theorems bridged here:
//   omega_4_absolute                      (TheoremOmega4)
//   omega_6_0_sentinel_absolute           (TheoremOmega6)
//   hierarchical_self_similarity_holds    (OmegaSeven)
//   depth_propagation_blocks_macro        (OmegaSeven)
//   counterfeit_chip_blocks_assembly      (OmegaSeven)
//   petri_liveness_no_deadlock            (OmegaSeven)
//   petri_liveness_composes               (OmegaSeven)
//   dijkstra_self_stabilization_bounded   (OmegaSeven)
//   dijkstra_no_permanent_corruption      (OmegaSeven)
//   csp_refusal_equivalence               (OmegaSeven)
//   tarpit_no_false_admit                 (OmegaSeven)
//   tarpit_no_false_refusal               (OmegaSeven)
//   bisimulation_environment_indistinguishability (OmegaSeven)
//   adversary_cannot_distinguish          (OmegaSeven)
//   C_tree_at_0/1/2                       (OmegaEight)
//   C_tree_geometric_series_lower         (OmegaEight)
//   Omega_tree_at_0/1                     (OmegaEight)
//   Omega_tree_grows                      (OmegaEight)
//   T8_3_strict_ambiguity_holds           (OmegaEight)
//   T8_4_adversary_strictly_bounded       (OmegaEight)
//   T8_4_error_prob_decays                (OmegaEight)
//   T8_5_entropy_margin_holds             (OmegaEight)
//   T8_6_J_uv_decomposes/face_required/handoff_required (OmegaEight)
//   T8_7_Auth_v113_implies_v112/seam/entropy (OmegaEight)

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

verus! {

// ---------------------------------------------------------------------------
// Constants derived from OmegaEight / HGQC framework
// ---------------------------------------------------------------------------

pub const FACES: u64       = 6;
pub const CELLS_PER_FACE: u64 = 9;
pub const FULL_SURFACE: u64 = 54;    // 6 × 9

/// C_tree(N) = (54^N − 1) / 53 — hierarchical node capacity
spec fn c_tree(n: nat) -> nat
    decreases n
{
    if n == 0 { 1 }
    else      { 1 + FULL_SURFACE as nat * c_tree((n - 1) as nat) }
}

/// OmegaTree(N) = R^C_tree(N) — hyper-exponential state space
/// For spec purposes we represent this as c_tree(n) (the exponent only)
spec fn omega_tree_exponent(n: nat) -> nat { c_tree(n) }

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.1: Hierarchical node capacity at concrete depths
// ---------------------------------------------------------------------------

proof fn C_tree_at_0()
    ensures c_tree(0) == 1
{}

proof fn C_tree_at_1()
    ensures c_tree(1) == 55
{
    assert(c_tree(1) == 1 + 54 * c_tree(0));
    assert(c_tree(0) == 1);
}

proof fn C_tree_at_2()
    ensures c_tree(2) == 2971
{
    assert(c_tree(2) == 1 + 54 * c_tree(1));
    assert(c_tree(1) == 55);
    assert(1 + 54 * 55 == 2971) by (compute);
}

proof fn C_tree_geometric_series_lower(n: nat)
    requires n >= 1
    ensures  c_tree(n) >= FULL_SURFACE as nat   // grows at least as fast as 54
{
}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.2: Hyper-exponential state space
// ---------------------------------------------------------------------------

proof fn Omega_tree_at_0()
    ensures omega_tree_exponent(0) == 1
{}

proof fn Omega_tree_at_1()
    ensures omega_tree_exponent(1) == 55
{}

proof fn Omega_tree_grows(n: nat)
    requires n >= 1
    ensures  omega_tree_exponent(n) > omega_tree_exponent((n - 1) as nat)
{
}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.3: Holographic projection ambiguity
// ---------------------------------------------------------------------------

/// T8_3: Distinct internal states can produce identical projections.
/// Encoded as: projection is non-injective on state space.
proof fn T8_3_strict_ambiguity_holds(s1: nat, s2: nat, proj: nat)
    requires s1 != s2, proj == 0  // same projection value
    ensures  s1 != s2             // states remain distinct
{}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.4: Adversarial error probability decays
// ---------------------------------------------------------------------------

/// Adversary is strictly bounded when operating below system capacity.
proof fn T8_4_adversary_strictly_bounded(budget: nat, capacity: nat)
    requires budget < capacity
    ensures  budget < capacity
{}

/// Error probability decays: (B(τ)/R)^N shrinks as N grows.
/// Encoded as: larger N ⇒ smaller relative probability (monotone decrease).
proof fn T8_4_error_prob_decays(ball_size: nat, state_space: nat, n1: nat, n2: nat)
    requires ball_size < state_space, n1 < n2
    ensures  true  // stub — full numeric proof requires Verus arithmetic
{}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.5: Entropy margin constraint
// ---------------------------------------------------------------------------

proof fn T8_5_entropy_margin_holds(entropy: nat, margin: nat)
    requires entropy > margin
    ensures  entropy > margin
{}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.6: Joint validity matrix J_uv decomposes
// ---------------------------------------------------------------------------

pub struct JointValidity {
    pub face_match:  bool,
    pub color_match: bool,
    pub edge_ok:     bool,
    pub corner_ok:   bool,
    pub handoff_ok:  bool,
}

impl JointValidity {
    pub open spec fn valid(self) -> bool {
        self.face_match && self.color_match &&
        self.edge_ok    && self.corner_ok   && self.handoff_ok
    }
}

proof fn T8_6_J_uv_decomposes(j: JointValidity)
    requires j.valid()
    ensures  j.face_match && j.color_match && j.edge_ok && j.corner_ok && j.handoff_ok
{}

proof fn T8_6_J_uv_face_required(j: JointValidity)
    requires !j.face_match
    ensures  !j.valid()
{}

proof fn T8_6_J_uv_handoff_required(j: JointValidity)
    requires !j.handoff_ok
    ensures  !j.valid()
{}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.7: Auth^v1.13 backward compatibility
// ---------------------------------------------------------------------------

pub struct AuthV113 {
    pub v112_ok:     bool,
    pub seam_ok:     bool,
    pub entropy_ok:  bool,
}

proof fn T8_7_Auth_v113_implies_v112(a: AuthV113)
    requires a.v112_ok && a.seam_ok && a.entropy_ok
    ensures  a.v112_ok
{}

proof fn T8_7_Auth_v113_implies_seam(a: AuthV113)
    requires a.v112_ok && a.seam_ok && a.entropy_ok
    ensures  a.seam_ok
{}

proof fn T8_7_Auth_v113_implies_entropy(a: AuthV113)
    requires a.v112_ok && a.seam_ok && a.entropy_ok
    ensures  a.entropy_ok
{}

// ---------------------------------------------------------------------------
// TheoremOmega4 — omega_4_absolute
// ---------------------------------------------------------------------------

/// Adversarial payloads are always denied; they never mutate physical reality.
proof fn omega_4_absolute(is_adversarial: bool)
    requires is_adversarial
    ensures  !is_adversarial || true  // adversarial ⇒ tarpit, not runtime
{
    // The photonic manifold absolute: adversarial payloads are routed to tarpit.
    // In Rust, this is enforced at the admission gate before any execution.
}

// ---------------------------------------------------------------------------
// TheoremOmega6 — omega_6_0_sentinel_absolute
// ---------------------------------------------------------------------------

/// Sentinel manifold absolute: a fully attested chain passes; gaps in attestation deny.
proof fn omega_6_0_sentinel_absolute(attestation_complete: bool)
    requires attestation_complete
    ensures  attestation_complete
{}

// ---------------------------------------------------------------------------
// OmegaSeven — 12 theorems
// ---------------------------------------------------------------------------

proof fn hierarchical_self_similarity_holds(depth: nat)
    requires depth <= 3
    ensures  depth <= 3  // bounded recursive self-similarity
{}

proof fn depth_propagation_blocks_macro(node_ok: bool)
    requires !node_ok
    ensures  !node_ok  // a failed node blocks macro-level assembly
{}

proof fn counterfeit_chip_blocks_assembly(chip_authentic: bool)
    requires !chip_authentic
    ensures  !chip_authentic  // counterfeit blocks the chain
{}

proof fn petri_liveness_no_deadlock(token_count: nat)
    requires token_count >= 1
    ensures  token_count >= 1  // at least one token means progress is possible
{}

proof fn petri_liveness_composes(liveness_a: bool, liveness_b: bool)
    requires liveness_a, liveness_b
    ensures  liveness_a && liveness_b
{}

proof fn dijkstra_self_stabilization_bounded(correction_rounds: nat)
    requires correction_rounds <= 20
    ensures  correction_rounds <= 20
{}

proof fn dijkstra_no_permanent_corruption(corrupted: bool)
    requires !corrupted
    ensures  !corrupted
{}

proof fn csp_refusal_equivalence(refused: bool)
    ensures  refused == refused  // refusal is deterministic
{}

proof fn tarpit_no_false_admit(in_tarpit: bool, admitted: bool)
    requires in_tarpit
    ensures  !admitted || !in_tarpit  // tarpit and admit are exclusive
{}

proof fn tarpit_no_false_refusal(clean: bool, refused: bool)
    requires clean, !refused
    ensures  !refused
{}

proof fn bisimulation_environment_indistinguishability(
    env_a: bool, env_b: bool, observable: bool
)
    requires env_a == env_b
    ensures  observable == observable  // same env ⇒ same observable behavior
{}

proof fn adversary_cannot_distinguish(state_a: bool, state_b: bool)
    requires state_a == state_b
    ensures  state_a == state_b
{}

} // verus!

-    else      { 1 + FULL_SURFACE as nat * c_tree((n - 1) as nat) }

+    else      { 1 + 54nat * c_tree((n - 1) as nat) }


proof fn C_tree_at_1()
    ensures c_tree(1) == 55
{
    assert(c_tree(1) == 1 + 54 * c_tree(0));
    assert(c_tree(0) == 1);
}

proof fn C_tree_at_1()
    ensures c_tree(1) == 55
{
    assert(c_tree(1) == 1 + 54nat * c_tree(0));
    assert(c_tree(0) == 1);
    assert(1nat + 54nat * 1nat == 55nat) by (compute);
}


proof fn C_tree_at_1()
    ensures c_tree(1) == 55
{
    assert(c_tree(1) == 1 + 54nat * c_tree(0));
    assert(c_tree(0) == 1);
    assert(1nat + 54nat * 1nat == 55nat) by (compute);
}

// omega_spec.rs — Verus spec for Theorem Omega chain
//
// Corresponds to: TheoremOmega4 + TheoremOmega6 + OmegaSeven + OmegaEight
// Triple-kernel verified theorems bridged here:
//   omega_4_absolute                      (TheoremOmega4)
//   omega_6_0_sentinel_absolute           (TheoremOmega6)
//   hierarchical_self_similarity_holds    (OmegaSeven)
//   depth_propagation_blocks_macro        (OmegaSeven)
//   counterfeit_chip_blocks_assembly      (OmegaSeven)
//   petri_liveness_no_deadlock            (OmegaSeven)
//   petri_liveness_composes               (OmegaSeven)
//   dijkstra_self_stabilization_bounded   (OmegaSeven)
//   dijkstra_no_permanent_corruption      (OmegaSeven)
//   csp_refusal_equivalence               (OmegaSeven)
//   tarpit_no_false_admit                 (OmegaSeven)
//   tarpit_no_false_refusal               (OmegaSeven)
//   bisimulation_environment_indistinguishability (OmegaSeven)
//   adversary_cannot_distinguish          (OmegaSeven)
//   C_tree_at_0/1/2                       (OmegaEight)
//   C_tree_geometric_series_lower         (OmegaEight)
//   Omega_tree_at_0/1                     (OmegaEight)
//   Omega_tree_grows                      (OmegaEight)
//   T8_3_strict_ambiguity_holds           (OmegaEight)
//   T8_4_adversary_strictly_bounded       (OmegaEight)
//   T8_4_error_prob_decays                (OmegaEight)
//   T8_5_entropy_margin_holds             (OmegaEight)
//   T8_6_J_uv_decomposes/face_required/handoff_required (OmegaEight)
//   T8_7_Auth_v113_implies_v112/seam/entropy (OmegaEight)

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

verus! {

// ---------------------------------------------------------------------------
// Constants derived from OmegaEight / HGQC framework
// ---------------------------------------------------------------------------

pub const FACES: u64       = 6;
pub const CELLS_PER_FACE: u64 = 9;
pub const FULL_SURFACE: u64 = 54;    // 6 × 9

/// C_tree(N) = (54^N − 1) / 53 — hierarchical node capacity
spec fn c_tree(n: nat) -> nat
    decreases n
{
    if n == 0 { 1 }
    else      { 1 + 54nat * c_tree((n - 1) as nat) }
}

/// OmegaTree(N) = R^C_tree(N) — hyper-exponential state space
/// For spec purposes we represent this as c_tree(n) (the exponent only)
spec fn omega_tree_exponent(n: nat) -> nat { c_tree(n) }

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.1: Hierarchical node capacity at concrete depths
// ---------------------------------------------------------------------------

proof fn C_tree_at_0()
    ensures c_tree(0) == 1
{}

proof fn C_tree_at_1()
    ensures c_tree(1) == 55
{
    assert(c_tree(1) == 1 + 54 * c_tree(0));
    assert(c_tree(0) == 1);
}

proof fn C_tree_at_2()
    ensures c_tree(2) == 2971
{
    assert(c_tree(2) == 1 + 54 * c_tree(1));
    assert(c_tree(1) == 55);
    assert(1 + 54 * 55 == 2971) by (compute);
}

proof fn C_tree_geometric_series_lower(n: nat)
    requires n >= 1
    ensures  c_tree(n) >= FULL_SURFACE as nat   // grows at least as fast as 54
{
}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.2: Hyper-exponential state space
// ---------------------------------------------------------------------------

proof fn Omega_tree_at_0()
    ensures omega_tree_exponent(0) == 1
{}

proof fn Omega_tree_at_1()
    ensures omega_tree_exponent(1) == 55
{}

proof fn Omega_tree_grows(n: nat)
    requires n >= 1
    ensures  omega_tree_exponent(n) > omega_tree_exponent((n - 1) as nat)
{
}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.3: Holographic projection ambiguity
// ---------------------------------------------------------------------------

/// T8_3: Distinct internal states can produce identical projections.
/// Encoded as: projection is non-injective on state space.
proof fn T8_3_strict_ambiguity_holds(s1: nat, s2: nat, proj: nat)
    requires s1 != s2, proj == 0  // same projection value
    ensures  s1 != s2             // states remain distinct
{}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.4: Adversarial error probability decays
// ---------------------------------------------------------------------------

/// Adversary is strictly bounded when operating below system capacity.
proof fn T8_4_adversary_strictly_bounded(budget: nat, capacity: nat)
    requires budget < capacity
    ensures  budget < capacity
{}

/// Error probability decays: (B(τ)/R)^N shrinks as N grows.
/// Encoded as: larger N ⇒ smaller relative probability (monotone decrease).
proof fn T8_4_error_prob_decays(ball_size: nat, state_space: nat, n1: nat, n2: nat)
    requires ball_size < state_space, n1 < n2
    ensures  true  // stub — full numeric proof requires Verus arithmetic
{}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.5: Entropy margin constraint
// ---------------------------------------------------------------------------

proof fn T8_5_entropy_margin_holds(entropy: nat, margin: nat)
    requires entropy > margin
    ensures  entropy > margin
{}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.6: Joint validity matrix J_uv decomposes
// ---------------------------------------------------------------------------

pub struct JointValidity {
    pub face_match:  bool,
    pub color_match: bool,
    pub edge_ok:     bool,
    pub corner_ok:   bool,
    pub handoff_ok:  bool,
}

impl JointValidity {
    pub open spec fn valid(self) -> bool {
        self.face_match && self.color_match &&
        self.edge_ok    && self.corner_ok   && self.handoff_ok
    }
}

proof fn T8_6_J_uv_decomposes(j: JointValidity)
    requires j.valid()
    ensures  j.face_match && j.color_match && j.edge_ok && j.corner_ok && j.handoff_ok
{}

proof fn T8_6_J_uv_face_required(j: JointValidity)
    requires !j.face_match
    ensures  !j.valid()
{}

proof fn T8_6_J_uv_handoff_required(j: JointValidity)
    requires !j.handoff_ok
    ensures  !j.valid()
{}

// ---------------------------------------------------------------------------
// OmegaEight — Theorem 8.7: Auth^v1.13 backward compatibility
// ---------------------------------------------------------------------------

pub struct AuthV113 {
    pub v112_ok:     bool,
    pub seam_ok:     bool,
    pub entropy_ok:  bool,
}

proof fn T8_7_Auth_v113_implies_v112(a: AuthV113)
    requires a.v112_ok && a.seam_ok && a.entropy_ok
    ensures  a.v112_ok
{}

proof fn T8_7_Auth_v113_implies_seam(a: AuthV113)
    requires a.v112_ok && a.seam_ok && a.entropy_ok
    ensures  a.seam_ok
{}

proof fn T8_7_Auth_v113_implies_entropy(a: AuthV113)
    requires a.v112_ok && a.seam_ok && a.entropy_ok
    ensures  a.entropy_ok
{}

// ---------------------------------------------------------------------------
// TheoremOmega4 — omega_4_absolute
// ---------------------------------------------------------------------------

/// Adversarial payloads are always denied; they never mutate physical reality.
proof fn omega_4_absolute(is_adversarial: bool)
    requires is_adversarial
    ensures  !is_adversarial || true  // adversarial ⇒ tarpit, not runtime
{
    // The photonic manifold absolute: adversarial payloads are routed to tarpit.
    // In Rust, this is enforced at the admission gate before any execution.
}

// ---------------------------------------------------------------------------
// TheoremOmega6 — omega_6_0_sentinel_absolute
// ---------------------------------------------------------------------------

/// Sentinel manifold absolute: a fully attested chain passes; gaps in attestation deny.
proof fn omega_6_0_sentinel_absolute(attestation_complete: bool)
    requires attestation_complete
    ensures  attestation_complete
{}

// ---------------------------------------------------------------------------
// OmegaSeven — 12 theorems
// ---------------------------------------------------------------------------

proof fn hierarchical_self_similarity_holds(depth: nat)
    requires depth <= 3
    ensures  depth <= 3  // bounded recursive self-similarity
{}

proof fn depth_propagation_blocks_macro(node_ok: bool)
    requires !node_ok
    ensures  !node_ok  // a failed node blocks macro-level assembly
{}

proof fn counterfeit_chip_blocks_assembly(chip_authentic: bool)
    requires !chip_authentic
    ensures  !chip_authentic  // counterfeit blocks the chain
{}

proof fn petri_liveness_no_deadlock(token_count: nat)
    requires token_count >= 1
    ensures  token_count >= 1  // at least one token means progress is possible
{}

proof fn petri_liveness_composes(liveness_a: bool, liveness_b: bool)
    requires liveness_a, liveness_b
    ensures  liveness_a && liveness_b
{}

proof fn dijkstra_self_stabilization_bounded(correction_rounds: nat)
    requires correction_rounds <= 20
    ensures  correction_rounds <= 20
{}

proof fn dijkstra_no_permanent_corruption(corrupted: bool)
    requires !corrupted
    ensures  !corrupted
{}

proof fn csp_refusal_equivalence(refused: bool)
    ensures  refused == refused  // refusal is deterministic
{}

proof fn tarpit_no_false_admit(in_tarpit: bool, admitted: bool)
    requires in_tarpit
    ensures  !admitted || !in_tarpit  // tarpit and admit are exclusive
{}

proof fn tarpit_no_false_refusal(clean: bool, refused: bool)
    requires clean, !refused
    ensures  !refused
{}

proof fn bisimulation_environment_indistinguishability(
    env_a: bool, env_b: bool, observable: bool
)
    requires env_a == env_b
    ensures  observable == observable  // same env ⇒ same observable behavior
{}

proof fn adversary_cannot_distinguish(state_a: bool, state_b: bool)
    requires state_a == state_b
    ensures  state_a == state_b
{}

} // verus!

+    assert(c_tree(1) == 1 + 54nat * c_tree(0));

+    assert(1nat + 54nat * 1nat == 55nat) by (compute);