plurigrid MDM Cobordism Skill: Auth Manifolds as State Transitions
Status: ✅ Production Ready Trit: 0 (ERGODIC - transport/derivation) Color: #26D826 (Green) Principle: Auth is cobordism W: ∂₀ → ∂₁, not event sequence Frame: No demos, only derivation
Overview
MDM Cobordism models authentication and device management as cobordisms — manifolds with boundaries representing auth state transitions. Following the unworld philosophy:
- Credentials don't "exist" — they derive
- There is no "authentication event" — only state derivation
- Keys don't "expire" — their chain position becomes unreachable
GF(3) Triads
Forms valid triads with MINUS (-1) and PLUS (+1) skills:
sheaf-cohomology (-1) ⊗ mdm-cobordism (0) ⊗ gay-mcp (+1) = 0 ✓ [Credential Derivation]
temporal-coalgebra (-1) ⊗ mdm-cobordism (0) ⊗ oapply-colimit (+1) = 0 ✓ [State Observation]
three-match (-1) ⊗ mdm-cobordism (0) ⊗ koopman-generator (+1) = 0 ✓ [Pattern Learning]
Auth Cobordisms
| Cobordism | Source → Target | Trit | Role |
|---|---|---|---|
| W₁ generate_key | Unauth → HasKey | +1 | Generator |
| W₂ request_scep | HasKey → HasCert | 0 | Coordinator |
| W₃ validate_cert | HasCert → HasToken | -1 | Validator |
| W₄ check_in_mdm | HasToken → Enrolled | +1 | Generator |
| W₅ verify_enroll | Enrolled → Enrolled | -1 | Validator |
GF(3) Conservation: +1 + 0 + (-1) + (+1) + (-1) = 0 ✓
Boundary Types
# Auth manifold boundaries
Unauthenticated # ∂₀: No identity
HasKey # Device has private key
HasCertificate # Device has CA-signed cert
HasToken # Device has session token
Enrolled # Device enrolled in MDM
Supervised # Device under full management
Keychain Integration
macOS Keychain operations with GF(3) tracking:
# Store (+1) → Retrieve (0) → Validate (-1) = 0 ✓
Keychain.store_then_verify(service, account, secret)
| Operation | Trit | Description |
|---|---|---|
store |
+1 | Create credential |
retrieve |
0 | Transport credential |
delete |
-1 | Remove credential |
Commands
# Run MDM cobordism demo
python src/mdm_mcp_server.py
# Keychain operations (macOS)
security add-generic-password -s "mdm-token" -a "$USER" -w
security find-generic-password -s "mdm-token" -a "$USER" -w
security delete-generic-password -s "mdm-token" -a "$USER"
# Verify GF(3) for auth flow
just mdm-gf3-check
API
from mdm_mcp_server import (
W1_GENERATE_KEY, W2_REQUEST_CERT, W3_VALIDATE_CERT,
W4_CHECK_IN, W5_VERIFY, Unauthenticated, verify_gf3
)
# Execute enrollment chain
state = Unauthenticated(device_serial="C02XG1PDJHD4")
state = W1_GENERATE_KEY(state)
state = W2_REQUEST_CERT(state)
state = W3_VALIDATE_CERT(state)
state = W4_CHECK_IN(state)
state = W5_VERIFY(state)
# Verify GF(3)
trits = [W1.trit, W2.trit, W3.trit, W4.trit, W5.trit]
assert verify_gf3(trits) # True
Apple MDM Protocol
SCEP Enrollment
<dict>
<key>PayloadType</key>
<string>com.apple.security.scep</string>
<key>URL</key>
<string>https://scep.example.com/scep</string>
<key>KeySize</key>
<integer>2048</integer>
</dict>
DEP/ABM Supervision
Device activates → DEP lookup → MDM URL → Enroll → Supervised
Supervision is an irreversible cobordism in normal flow.
Philosophy
No Demos
There are no demonstrations. MDM enrollment is not a "process that runs" but a derivation chain that is.
Demo: "Watch me enroll this device" → temporal, performative
Derivation: "Enrollment derives from serial" → atemporal, structural
Untological Credentials
Credentials don't "exist" with properties. They derive from chain positions:
# Ontological (what IS this key?)
key.is_valid? # property of thing
# Untological (what DERIVES this key?)
key = derive(device_serial, enrollment_time)
key.chain_position # position in derivation
Cobordism Composition
Auth flows compose like cobordisms:
W = W₅ ∘ W₄ ∘ W₃ ∘ W₂ ∘ W₁ : Unauthenticated → Enrolled
The composite W is itself a cobordism with GF(3) = 0.
Security Best Practices
- Never store secrets in env vars — use Keychain
- Use SCEP for certificate enrollment — not PKCS#12 import
- Verify GF(3) for all auth flows — ensures completeness
- Supervision = irreversible — plan accordingly
MCP Tools
mdm_enroll_device // Initiate enrollment (trit: +1)
keychain_store // Store credential (trit: +1)
keychain_retrieve // Retrieve credential (trit: 0)
keychain_delete // Delete credential (trit: -1)
auth_cobordism_check // Verify GF(3) (trit: -1)
Files
src/mdm_mcp_server.py— Cobordism state machinearchitecture/MDM_AUTH_COBORDISM.md— Architecture docs
Skill Name: mdm-cobordism Type: Device Management / Auth State Machine Trit: 0 (ERGODIC) Color: #26D826 (Green) GF(3): Conserved by construction Demos: None (νο δῆμος) Ontology: Replaced with untology