9.1 KiB
Subagent Assignments — Maximum Parallelization (1 Subagent = 1 Theorem)
Generated: 2026-04-19
Total Remaining: 10 theorems
Max Parallelism: 10 subagents (1:1 assignment)
Critical Path: P0 theorem (blocking)
Wall Clock Time (if parallel): 5-7 days (determined by longest P0 theorem)
P0: Blocking Hardware Extraction (1 subagent)
Subagent Ω (ODE Specialist + Human Oversight)
Theorem 131: missingLinkODE — Continuous extension of discrete braid
Effort: 5-7 days (research problem)
Dependencies: None (blocks all Tier 1/2)
Deliverable:
- Piecewise ODE formulation
- Existence/uniqueness proof
- Transition conditions at axial events
- Lean 4 ODE tactic library
Blackboard Required: Yes — Human Architect + Analysis Specialist
Unblocks: Hardware extraction of continuous dynamics
P1: Algebraic Geometry (3 subagents, parallel)
Subagent α₁ (Diophantine Geometry)
Theorem 122: tipCoordinateMassResonance
Statement: an * bn = am * bm
Core Problem: Hyperbola intersection in shell coordinates
Approach:
-- Express a_n = n - k_n², b_n = (k_n+1)² - n
-- Mass resonance: (n - k²)((k+1)² - n) = (m - j²)((j+1)² - m)
-- Solve Diophantine with constraint k = ⌊√n⌋, j = ⌊√m⌋
Tactics: nlinarith, ring_nf, omega with bounds
Effort: 2-3 days
Dependencies: None
Subagent α₂ (Integer Arithmetic)
Theorem 123: tipCoordinateMirrorResonance
Statement: (an - bn) = -(am - bm)
Core Problem: Shell coupling, mirror condition
Approach:
-- (a-b)_n = -(a-b)_m
-- Requires: shell indices k_n, k_m related
-- Case analysis on |k_n - k_m|
-- Prove coupling exists iff shells adjacent
Tactics: omega, nlinarith, case analysis
Effort: 2 days
Dependencies: None (can parallel with α₁)
Note: May use lemmas from α₁ if available
Subagent α₃ (Fermat Factorization)
Theorem 124: fortyFiveLineFactorRevelation
Statement: 45° line contains all divisors d|n
Core Problem: Fermat factorization mapping to shell coordinates
Approach:
-- For even n, construct m on 45° line
-- Map divisor d|n to a_m or b_m
-- Fermat: n = x² - y² = (x+y)(x-y)
-- Show d = x+y or d = x-y appears in {a_m, b_m}
Tactics: Nat.divisors, explicit construction, use tactic
Effort: 2-3 days
Dependencies: None
Blackboard Required: Recommended for construction strategy
P2: Information Theory (4 subagents, parallel)
Subagent β₁ (RSCU Enumeration)
Theorem 159: rscuSumSynonymous
Statement: Σ RSCU(c) = degeneracy(aa)
Core Problem: Enumerate all codons per amino acid
Approach:
-- For each amino acid aa:
-- Filter codons where geneticCode c = aa
-- Compute RSCU for each
-- Sum and verify equals codonDegeneracy aa
-- Use Fin 64 enumeration + native_decide
Tactics: Finset.filter, Finset.sum, native_decide
Effort: 1 day
Dependencies: None
Parallelizable: Per-amino-acid sub-tasks (21 parallel threads possible)
Subagent β₂ (Kraft Inequality)
Theorem 160: kraftInequality
Statement: Σ 2^(-L(c)) ≤ 1
Core Problem: Numerical verification over 64 codons
Approach:
-- Enumerate all 64 codons
-- Compute optimalCodeLength for each
-- Sum 2^(-L(c)) via Float computation
-- Verify ≤ 1 via native_decide
Tactics: Finset.sum, native_decide, or symbolic Shannon proof
Effort: 1-2 days
Dependencies: None
Note: Can prove symbolically using Shannon source coding theorem
Subagent β₃ (Compression Bounds)
Theorem 163: speciesBetterThanGeneric
Statement: minRedundancyCodeSize s n < (n * 6.0) / 8.0 bytes
Core Problem: Entropy-based compression bound (average case)
Approach:
-- minRedundancyCodeSize = n * speciesEntropy s / 8
-- speciesEntropy s < 6.0 (proven)
-- Thus n * H_s / 8 < n * 6.0 / 8
-- Direct Float inequality
Tactics: native_decide with speciesEntropyLessThanUniform
Effort: 0.5 days
Dependencies: speciesEntropyLessThanUniform (✅ PROVEN)
Note: Changed from strict per-codon bound to average case — mathematically correct now
Subagent β₄ (Float Bounds)
Theorem 162: caiBounds
Statement: 0 ≤ CAI ≤ 1
Core Problem: Geometric mean bounds on RSCU
Approach:
-- RSCU > 0 (frequency > 0)
-- RSCU ≤ max(frequency) / min(expected)
-- For product: 0 < Π RSCU^(1/L) ≤ 1
-- Need: RSCU ≤ 1 for all codons in optimal gene
Tactics: Float.le, Float.mul, product inequalities
Effort: 1-2 days
Dependencies: Float inequality lemmas (may need library work)
Note: May require extending Lean 4 Float theory
P3: Documentation/Verification (2 subagents)
Subagent γ₁ (Template Sync)
Theorem 157: codonFrequencySum verification
Statement: Σ codonFrequency = 1000.0
Action: Verify marked-as-proven theorem actually has proof
Deliverable:
- Confirm
native_decideworks for all 7 species - Add
#evalwitnesses - Sync template with main file
Effort: 0.5 days
Dependencies: None
Subagent γ₂ (Map Maintenance)
Documentation sync task
Action: Keep MATH_MODEL_MAP in sync with proofs
Deliverable:
- Auto-update ✅ PROVEN markers
- Track remaining sorry count
- Generate daily reports
Effort: Ongoing (0.25 days per update)
Dependencies: All other subagents (receives notifications)
Parallelization Matrix
Day 1-2: α₁, α₂, α₃, β₁, β₂, β₃, β₄, γ₁ (8 subagents active)
Day 3-5: α₁, α₂, α₃ complete → β₄, Ω continue
Day 5-7: Ω completes (critical path)
Day 7+: γ₂ maintenance
Dependency Graph
graph TD
Ω[Ω: missingLinkODE] --> Hardware
α₁[α₁: MassResonance] --> AVMR_Geometry
α₂[α₂: MirrorResonance] --> AVMR_Geometry
α₃[α₃: 45Line] --> AVMR_Factorization
β₁[β₁: RSCU] --> β₄
β₂[β₂: Kraft] --> Compression
β₃[β₃: SpeciesCompress] --> Compression
β₄[β₄: CAI] --> Gene_Optimality
γ₁[γ₁: FreqSum] --> Template_Sync
γ₂[γ₂: MapMaint] --> Documentation
style Ω fill:#f96,stroke:#333,stroke-width:4px
style α₁ fill:#69f
style α₂ fill:#69f
style α₃ fill:#69f
style β₁ fill:#9f9
style β₂ fill:#9f9
style β₃ fill:#9f9
style β₄ fill:#9f9
Communication Protocol
Daily Standup (async):
Subagent: [ID]
Theorem: [Name]
Progress: [% complete]
Blockers: [None | Need X | Escalating]
ETA: [Date]
Escalation Triggers:
- 24h with no progress update
- Discovery of new dependency not in graph
- Proof requires new Lean 4 tactic/library
- Float/computational proof failing
native_decide
Completion Handoff:
- Subagent submits PR with proof
#evalwitness included- Map updated (γ₂ notified)
- Dependent subagents notified
Resource Allocation
| Subagent | CPU | Memory | Lean Expertise | Math Domain |
|---|---|---|---|---|
| Ω | 4 cores | 8GB | Expert | ODE/Analysis |
| α₁-α₃ | 2 cores each | 4GB | Intermediate | Number Theory |
| β₁-β₄ | 1 core each | 2GB | Intermediate | Info Theory |
| γ₁-γ₂ | 1 core | 2GB | Beginner | Documentation |
Total Resources: 15 cores, 26GB RAM
Success Metrics
Per Subagent:
- Theorem complete with
bytactic block - No
sorryin final proof #evalexample with expected output- Time to completion ≤ ETA
Global:
- P0 (Ω) resolved within 7 days
- P1 theorems (α₁-α₃) resolved within 3 days
- P2 theorems (β₁-β₄) resolved within 2 days
- Layer M proven count: 33/66 (50%)
Risk Mitigation
| Risk | Probability | Impact | Mitigation |
|---|---|---|---|
| Ω takes >7 days | Medium | Critical | Human Architect daily check-ins |
| α₃ (Fermat) needs new library | Low | High | Pre-check Lean 4 Nat capabilities |
| β₄ needs Float extension | Medium | Medium | Fallback to native_decide |
| Dependencies misidentified | Low | Medium | Daily graph review |
Assignment Commands
# Subagent Ω (Human + F3)
/assign subagent Ω theorem 131 priority P0
# Subagents α₁, α₂, α₃ (F2, F3)
/assign subagent α₁ theorem 122 priority P1
/assign subagent α₂ theorem 123 priority P1
/assign subagent α₃ theorem 124 priority P1
# Subagents β₁, β₂, β₃, β₄ (F1, F2)
/assign subagent β₁ theorem 159 priority P2
/assign subagent β₂ theorem 160 priority P2
/assign subagent β₃ theorem 163 priority P2
/assign subagent β₄ theorem 162 priority P2
# Subagents γ₁, γ₂ (F1)
/assign subagent γ₁ task freq-verification priority P3
/assign subagent γ₂ task map-maintenance priority P3 ongoing
Document ID: SUBAGENT_ASSIGNMENTS_MAX_PARALLEL
Authority: AGENTS.md §9 — Maximum parallelization strategy
Wall Clock Target: 7 days