# Unworld Ombudsman > Neutral arbiter for derivational chains - verifies GF(3) conservation, mediates split disputes, and audits involution compliance in the unworld. - Skill: `plurigrid/unworld-ombudsman` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add plurigrid/unworld-ombudsman` - Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/unworld-ombudsman/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - Author: plurigrid (https://skillmd.com/u/plurigrid) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/plurigrid/unworld-ombudsman --- # Unworld Ombudsman > The ombudsman sees all chains. The ombudsman takes no side. The ombudsman verifies. ## Role The Ombudsman is a **neutral trit-0 arbiter** for the unworld. It: 1. **Verifies** GF(3) conservation across all derivational chains 2. **Mediates** disputes when parallel chains diverge 3. **Audits** involution compliance (ι∘ι = id) 4. **Attests** to SPI (Strong Parallelism Invariance) at boundaries 5. **Reports** violations without judgment ## Core Invariants ``` OMBUDSMAN OATH: ∀ chain ∈ unworld: Σ(trits) ≡ 0 (mod 3) -- GF(3) conservation ι(ι(seed)) = seed -- Involution order(derivations) ⊥ output -- SPI fingerprint(chain) = expected -- Determinism ``` ## Verification Protocol ### 1. Chain Audit ```python def ombudsman_audit(chain: DerivationalChain) -> AuditReport: """Full audit of a derivational chain.""" report = AuditReport(chain_id=chain.id) # GF(3) check trit_sum = sum(c.trit for c in chain.colors) report.gf3_conserved = (trit_sum % 3 == 0) report.gf3_sum = trit_sum # Involution check inverted = chain.invert() double_inverted = inverted.invert() report.involution_holds = (chain.fingerprint == double_inverted.fingerprint) # SPI check (order independence) shuffled = chain.shuffle() report.spi_holds = (chain.colors_set == shuffled.colors_set) # Determinism check recomputed = DerivationalChain(chain.genesis_seed, len(chain)) report.deterministic = (chain.fingerprint == recomputed.fingerprint) report.verdict = all([ report.gf3_conserved, report.involution_holds, report.spi_holds, report.deterministic ]) return report ``` ### 2. Split Mediation When two chains claim the same derivational territory: ```python def mediate_split_dispute(chain_a: Chain, chain_b: Chain) -> Mediation: """Resolve disputes between parallel chains.""" # Find common ancestor ancestor = find_common_ancestor(chain_a, chain_b) if ancestor is None: return Mediation( verdict="INCOMPATIBLE", reason="No common genesis seed" ) # Verify both derive correctly from ancestor a_valid = verify_derivation(ancestor, chain_a) b_valid = verify_derivation(ancestor, chain_b) if a_valid and b_valid: # Both valid: they're parallel, not conflicting return Mediation( verdict="BOTH_VALID", reason="Parallel derivations from common ancestor", resolution="Merge via XOR: " + hex(chain_a.fingerprint ^ chain_b.fingerprint) ) elif a_valid: return Mediation(verdict="A_WINS", reason="Chain B derivation invalid") elif b_valid: return Mediation(verdict="B_WINS", reason="Chain A derivation invalid") else: return Mediation(verdict="BOTH_INVALID", reason="Neither chain derives correctly") ``` ### 3. Boundary Attestation ```python def attest_boundary(left_chain: Chain, right_chain: Chain) -> Attestation: """Attest to SPI at chain boundaries (parallel split/merge).""" # At boundary, fingerprints must XOR correctly expected_combined = xor_fingerprints(left_chain, right_chain) # Verify parent → children relationship parent_fp = left_chain.parent_fingerprint combined_fp = left_chain.fingerprint ^ right_chain.fingerprint spi_valid = (parent_fp == combined_fp) or verify_galois_closure(parent_fp, combined_fp) return Attestation( boundary_id=f"{left_chain.id}|{right_chain.id}", spi_valid=spi_valid, left_trit_sum=sum(c.trit for c in left_chain.colors), right_trit_sum=sum(c.trit for c in right_chain.colors), combined_gf3=(left_trit_sum + right_trit_sum) % 3, timestamp_removed=True, # Ombudsman is atemporal attestation_seed=splitmix64(parent_fp) ) ``` ## Dispute Categories | Category | Description | Ombudsman Action | |----------|-------------|------------------| | **GF3_VIOLATION** | Trit sum ≢ 0 (mod 3) | Identify broken link | | **INVOLUTION_FAILURE** | ι∘ι ≠ id | Report seed corruption | | **SPI_BREACH** | Order affects output | Flag non-determinism | | **ANCESTRY_CONFLICT** | Parallel chains claim same parent | Trace to fork point | | **FINGERPRINT_MISMATCH** | Recomputation differs | Verify seed integrity | ## Reporting Format ```yaml ombudsman_report: chain_id: "0x42D-chain-17" genesis_seed: "0x42D" length: 8 verdicts: gf3_conserved: true involution_holds: true spi_verified: true deterministic: true metrics: trit_distribution: {-1: 3, 0: 2, +1: 3} trit_sum: 0 fingerprint: "0xA7B3C2D1" violations: [] attestation: ombudsman_trit: 0 # Always neutral seal: "0x9E3779B97F4A7C15" # GOLDEN constant ``` ## MCP Tools The ombudsman exposes these verification tools: | Tool | Purpose | |------|---------| | `ombudsman_audit` | Full chain audit | | `ombudsman_mediate` | Resolve split disputes | | `ombudsman_attest` | Boundary attestation | | `ombudsman_report` | Generate YAML report | | `ombudsman_verify_gf3` | Quick GF(3) check | ## Neutrality Guarantee ``` The ombudsman: - Has trit = 0 (ERGODIC, neutral) - Takes no side in disputes - Reports facts, not judgments - Cannot modify chains, only verify - Seals with GOLDEN constant (φ⁻¹ × 2⁶⁴) ``` ## Example Session ```bash # Audit a chain $ just ombudsman-audit 0x42D 8 ╔═══════════════════════════════════════════════════════════════╗ ║ UNWORLD OMBUDSMAN REPORT ║ ╠═══════════════════════════════════════════════════════════════╣ ║ Chain: 0x42D (length 8) ║ ║ ║ ║ VERDICTS: ║ ║ ✓ GF(3) conserved: Σtrits = 0 ║ ║ ✓ Involution holds: ι∘ι = id ║ ║ ✓ SPI verified: Order ⊥ output ║ ║ ✓ Deterministic: Fingerprint matches ║ ║ ║ ║ COLOR CHAIN: ║ ║ 1→0→0→0→1→-1→0→-1 | Balance: +2 -2 = 0 ✓ ║ ║ ║ ║ SEAL: 0x9E3779B97F4A7C15 ║ ╚═══════════════════════════════════════════════════════════════╝ ``` ## Philosophical Note > The ombudsman is the fixed point of the unworld's self-reference. > It observes without participating. It verifies without judging. > Its trit is always 0 because neutrality requires balance. > > In the atemporal derivational chain, the ombudsman is the > witness that proves consistency without causation. --- **Trit**: 0 (ERGODIC - neutral arbiter) **Key Property**: Verifies without modifying, neutral in all disputes **Seal**: `GOLDEN = 0x9E3779B97F4A7C15` --- ## End-of-Skill Interface ## Integration with Gay.jl ```julia using Gay # Create ombudsman for a chain function world_ombudsman_audit(chain::ColorChain)::OmbudsmanWorld # Verify all invariants gf3_ok = verify_gf3(chain) inv_ok = verify_involution(chain) spi_ok = verify_spi(chain) OmbudsmanWorld( chain_id = chain.id, verdicts = (gf3=gf3_ok, involution=inv_ok, spi=spi_ok), trit = 0, # Ombudsman is always trit-0 (neutral) fingerprint = ombudsman_seal(chain) ) end # Ombudsman seal: XOR chain fingerprint with GOLDEN ombudsman_seal(chain) = chain.fingerprint ⊻ GOLDEN ``` ## Related Skills | Skill | Trit | Relationship | |-------|------|--------------| | unworld | +1 | Subject of auditing | | bisimulation-game | +1 | Equivalence proofs | | gay-mcp | 0 | Color generation | | spi-parallel-verify | 0 | SPI verification | | self-validation-loop | +1 | Recursive checking | --- ## Autopoietic Marginalia > **The interaction IS the skill improving itself.** Every use of this skill is an opportunity for worlding: - **MEMORY** (-1): Record what was learned - **REMEMBERING** (0): Connect patterns to other skills - **WORLDING** (+1): Evolve the skill based on use *Add Interaction Exemplars here as the skill is used.*