plurigrid 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:
- Verifies GF(3) conservation across all derivational chains
- Mediates disputes when parallel chains diverge
- Audits involution compliance (ι∘ι = id)
- Attests to SPI (Strong Parallelism Invariance) at boundaries
- 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
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:
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
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
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
# 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
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.