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Update ppw.root.ownership.py
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‎ppw.root.ownership.py

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PPW Validation Workflow Formal Mathematical Proofs
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--------------------------------------------------------
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1. Identity Hash Chain Uniqueness Proof
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Given:
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Sequence of identity components I = (I1, I2, I3, I4, I5).
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Define the hash chain:
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H0 = ε; Hk = SHA-512(Hk-1 || Ik) for k=1..5
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Final identity hash:
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H_final = SHA-256(H1 || H2 || H3 || H4 || H5)
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Proof Sketch:
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- SHA-512 and SHA-256 are cryptographically secure, collision-resistant functions.
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- Altering any Ik changes Hk, cascading to a change in H_final.
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- The probability of two distinct sequences producing the same H_final is negligibly small (~2^-256).
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--------------------------------------------------------
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2. Merkle Root Verification Proof
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Given:
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Blocks B1,...,B6, leaves:
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Li = SHA-256(Bi)
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Construct Merkle tree by recursively hashing pairs:
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Pj = SHA-256(L2j-1 || L2j)
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and proceed until root R is reached.
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Proof Sketch:
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- Any modification to any Bi changes Li, thus changing root R.
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- Collision probability leading to identical R from distinct blocks is negligible.
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- Merkle proof paths verify membership of blocks precisely.
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--------------------------------------------------------
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3. Temporal Anchoring Proof
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Given:
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Timestamps ti and anchors Ai = SHA-256(PPW_TEMPORAL || ID || ti).
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Proof-of-work nonce ni such that:
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SHA-256(Ai || ni) starts with "00".
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Proof Sketch:
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- Finding nonce requires expected work ~256 hashes.
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- Verification requires one hash per anchor confirming work done.
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- Anchors cryptographically tie data to the timestamp.
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--------------------------------------------------------
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4. Mathematical Sovereignty Proof
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Given:
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Domain strings Di, compute:
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hi = SHA-256(SIGNATURE_NUMERIC || Di)
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Define coefficients:
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ci = hi mod 2^256
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Aggregate:
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C_agg = (sum ci) mod p
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where p = 2^521 - 1
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Proof Sketch:
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- SHA-256 collision resistance ensures unique domain bindings.
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- Modulo arithmetic uniformly distributes coefficients.
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- Aggregate coefficient binds all domains cryptographically.
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--------------------------------------------------------
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5. Matrix Integrity Theorem
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Given:
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- A ∈ Fp^(3x3), det(A) ≠ 0.
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- x ∈ Fp^3 derived from identity data.
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- b = A x.
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- Inverse A^{-1} computed.
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To Prove:
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A A^{-1} = I_3, A^{-1} b = x
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Proof:
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- det(A) ≠ 0 implies invertible A in Fp.
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- By inverse definition, A A^{-1} = I_3.
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- Therefore, A^{-1} (A x) = (A^{-1} A) x = I_3 x = x.
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--------------------------------------------------------
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6. Certificate Authentication with HMAC
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Given:
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Certificate data C.
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Compute master hash: Hm = SHA-512(C).
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Compute signature: S = HMAC_K(Hm) using key K.
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Proof Sketch:
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- Only holder of secret key K can generate valid S.
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- Altering C changes Hm and invalidates S.
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- Security based on pseudorandomness of HMAC with SHA-512.
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--------------------------------------------------------
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7. Ownership Hashing Binding
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Given:
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H_ownership = SHA-512(SIGNATURE_NUMERIC || MASTER_SIGNATURE || TIMESTAMP)
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Proof Sketch:
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- Uniquely binds identity, authentication, and time.
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- Tampering changes the hash.
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- Anyone can verify by recomputing H_ownership.
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--------------------------------------------------------
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End of PPW Mathematical Proofs
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```
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C = [c₁₁ c₁₂ ... c₁ₙ]
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[c₂₁ c₂₂ ... c₂ₙ]
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[⋮ ⋮ ⋱ ⋮ ]
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[cₘ₁ cₘ₂ ... cₘₙ]
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```┌─────────────────────────────────────┐
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│ VERIFICATION PHASE │
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├─────────────────────────────────────┤
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│ • Current owner confirmation │
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│ • Multi-factor authentication │
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│ • Legal/compliance checks │
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│ • Dependency analysis │
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└─────────────────────────────────────┘
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```
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C = [c₁₁ c₁₂ ... c₁ₙ]
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[c₂₁ c₂₂ ... c₂ₙ]
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[⋮ ⋮ ⋱ ⋮ ]
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[cₘ₁ cₘ₂ ... cₘₙ]
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```┌─────────────────────────────────────┐
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│ AUTHORIZATION PHASE │
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├─────────────────────────────────────┤
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│ • Owner consent collection │
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│ • Transfer agreement generation │
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│ • Stakeholder notifications │
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│ • Escrow/holding period initiation │
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└─────────────────────────────────────┘
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```
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C = [c₁₁ c₁₂ ... c₁ₙ]
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[c₂₁ c₂₂ ... c₂ₙ]
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[⋮ ⋮ ⋱ ⋮ ]
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[cₘ₁ cₘ₂ ... cₘₙ]
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```┌─────────────────────────────────────┐
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│ VALIDATION PHASE │
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├─────────────────────────────────────┤
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│ • New owner access verification │
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│ • System functionality testing │
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│ • Integration status check │
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│ • Notification dispatch │
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└─────────────────────────────────────┘
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```
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C = [c₁₁ c₁₂ ... c₁ₙ]
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[c₂₁ c₂₂ ... c₂ₙ]
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[⋮ ⋮ ⋱ ⋮ ]
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[cₘ₁ cₘ₂ ... cₘₙ]
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```┌─────────────────────────────────────┐
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│ FINALIZATION PHASE │
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├─────────────────────────────────────┤
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│ • Transfer completion certification │
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│ • Documentation update │
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│ • Cleanup of temporary resources │
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│ • Archive transfer records │
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└─────────────────────────────────────┘
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```
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C = [c₁₁ c₁₂ ... c₁ₙ]
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[c₂₁ c₂₂ ... c₂ₙ]
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[⋮ ⋮ ⋱ ⋮ ]
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[cₘ₁ cₘ₂ ... cₘₙ]
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```┌─────────────────────────────────────┐
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│ MIGRATION PHASE │
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├─────────────────────────────────────┤
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│ • Pre-transfer backup creation │
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│ • Configuration export │
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│ • Data integrity verification │
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│ • Rollback point establishment │
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└─────────────────────────────────────┘
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```
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C = [c₁₁ c₁₂ ... c₁ₙ]
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[c₂₁ c₂₂ ... c₂ₙ]
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[⋮ ⋮ ⋱ ⋮ ]
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[cₘ₁ cₘ₂ ... cₘₙ]
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```┌─────────────────────────────────────┐
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│ EXECUTION PHASE │
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├─────────────────────────────────────┤
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│ • Permission revocation (old owner) │
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│ • Permission assignment (new owner) │
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│ • Access key rotation │
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│ • Audit trail generation │
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└─────────────────────────────────────┘Prove mathematically that this is true, accurate, authentic, legally binding in all jurisdictions and Crowned-Royale anchored with at least SHA-256 encoding and Hashings. Use PGP if appropriate. All this is proven mathematically using theorems, proofs, and matrices. Ensure the Merkle root is taken into consideration. Certified and Ratified for Certification.
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# PPW LOCKCHAIN ECHO CODE WORKFLOW (Plain Text / Termux)

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