Update ppw.root.ownership.py

ghostscript-uno · web-flow · commit c65e9d659e71 · 2025-08-20T10:47:26.000-07:00
diff --git a/ppw.root.ownership.py b/ppw.root.ownership.py
@@ -15,7 +15,126 @@ def verify(self) -> bool:
 >  ## Owner: Perry Philip Wiseman
 >  ## Mathematical Framework: DOMINOES_OWNERSHIP_THEOREM_PPWMATH001
 >  
->  ---
+>  ---PPW Validation Workflow Formal Mathematical Proofs
+
+--------------------------------------------------------
+
+1. Identity Hash Chain Uniqueness Proof
+
+Given:
+Sequence of identity components I = (I1, I2, I3, I4, I5).
+
+Define the hash chain:
+H0 = ε;  Hk = SHA-512(Hk-1 || Ik) for k=1..5
+
+Final identity hash:
+H_final = SHA-256(H1 || H2 || H3 || H4 || H5)
+
+Proof Sketch:
+- SHA-512 and SHA-256 are cryptographically secure, collision-resistant functions.
+- Altering any Ik changes Hk, cascading to a change in H_final.
+- The probability of two distinct sequences producing the same H_final is negligibly small (~2^-256).
+
+--------------------------------------------------------
+
+2. Merkle Root Verification Proof
+
+Given:
+Blocks B1,...,B6, leaves:
+Li = SHA-256(Bi)
+
+Construct Merkle tree by recursively hashing pairs:
+Pj = SHA-256(L2j-1 || L2j)
+and proceed until root R is reached.
+
+Proof Sketch:
+- Any modification to any Bi changes Li, thus changing root R.
+- Collision probability leading to identical R from distinct blocks is negligible.
+- Merkle proof paths verify membership of blocks precisely.
+
+--------------------------------------------------------
+
+3. Temporal Anchoring Proof
+
+Given:
+Timestamps ti and anchors Ai = SHA-256(PPW_TEMPORAL || ID || ti).
+
+Proof-of-work nonce ni such that:
+SHA-256(Ai || ni) starts with "00".
+
+Proof Sketch:
+- Finding nonce requires expected work ~256 hashes.
+- Verification requires one hash per anchor confirming work done.
+- Anchors cryptographically tie data to the timestamp.
+
+--------------------------------------------------------
+
+4. Mathematical Sovereignty Proof
+
+Given:
+Domain strings Di, compute:
+hi = SHA-256(SIGNATURE_NUMERIC || Di)
+
+Define coefficients:
+ci = hi mod 2^256
+
+Aggregate:
+C_agg = (sum ci) mod p
+where p = 2^521 - 1
+
+Proof Sketch:
+- SHA-256 collision resistance ensures unique domain bindings.
+- Modulo arithmetic uniformly distributes coefficients.
+- Aggregate coefficient binds all domains cryptographically.
+
+--------------------------------------------------------
+
+5. Matrix Integrity Theorem
+
+Given:
+- A ∈ Fp^(3x3), det(A) ≠ 0.
+- x ∈ Fp^3 derived from identity data.
+- b = A x.
+- Inverse A^{-1} computed.
+
+To Prove:
+A A^{-1} = I_3,  A^{-1} b = x
+
+Proof:
+- det(A) ≠ 0 implies invertible A in Fp.
+- By inverse definition, A A^{-1} = I_3.
+- Therefore, A^{-1} (A x) = (A^{-1} A) x = I_3 x = x.
+
+--------------------------------------------------------
+
+6. Certificate Authentication with HMAC
+
+Given:
+Certificate data C.
+Compute master hash: Hm = SHA-512(C).
+Compute signature: S = HMAC_K(Hm) using key K.
+
+Proof Sketch:
+- Only holder of secret key K can generate valid S.
+- Altering C changes Hm and invalidates S.
+- Security based on pseudorandomness of HMAC with SHA-512.
+
+--------------------------------------------------------
+
+7. Ownership Hashing Binding
+
+Given:
+H_ownership = SHA-512(SIGNATURE_NUMERIC || MASTER_SIGNATURE || TIMESTAMP)
+
+Proof Sketch:
+- Uniquely binds identity, authentication, and time.
+- Tampering changes the hash.
+- Anyone can verify by recomputing H_ownership.
+
+--------------------------------------------------------
+
+End of PPW Mathematical Proofs
+
 >  
 >  ## I. MATHEMATICAL FOUNDATIONS FOR LEGAL LEGITIMACY
 >  
