# Statement Map

| Mathematical content | Lean declaration | File | Status |
| --- | --- | --- | --- |
| Accelerated Collatz map | `Erdos1135.Terras.accelerated` | `Erdos1135/Terras/Core/Defs.lean` | Defined locally |
| Orbit reachability | `Erdos1135.KrasikovLagarias.Reaches` | `Erdos1135/KrasikovLagarias/PredecessorCount.lean` | Defined |
| Natural-cutoff count | `Erdos1135.KrasikovLagarias.predecessorCount` | `Erdos1135/KrasikovLagarias/PredecessorCount.lean` | Defined |
| Real-cutoff count | `Erdos1135.KrasikovLagarias.predecessorCountReal` | `Erdos1135/KrasikovLagarias/Envelope.lean` | Defined |
| Exact level-18 LP validity | `Erdos1135.KrasikovLagarias.k18Gamma901EncodedCertificate_valid` | `Erdos1135/KrasikovLagarias/Generated/K18Gamma901.lean` | Native checked |
| Adaptive-potential validity | `Erdos1135.KrasikovLagarias.k18AdaptiveForcedPotentialCertificate_valid` | `Erdos1135/KrasikovLagarias/Generated/K18AdaptiveForcedPotential.lean` | Native checked |
| Level-18 envelope growth | `Erdos1135.KrasikovLagarias.K18CriticalChoice.phiValues18_exponential_lower_bound` | `Erdos1135/KrasikovLagarias/K18CriticalChoice.lean` | Proved |
| Positive-constant `x^0.901` bound | `Erdos1135.KrasikovLagarias.K18PredecessorAllTargets.eventually_const_mul_rpow_901_1000_le_predecessorCountReal` | `Erdos1135/KrasikovLagarias/K18PredecessorAllTargets.lean` | Proved, comparator target |
| Unit-coefficient `x^0.90` bound | `Erdos1135.KrasikovLagarias.K18PredecessorAllTargets.eventually_rpow_9_10_le_predecessorCountReal` | `Erdos1135/KrasikovLagarias/K18PredecessorAllTargets.lean` | Proved, comparator target |
| Natural-cutoff `x^0.90` form | `Erdos1135.KrasikovLagarias.K18PredecessorAllTargets.eventually_natCast_rpow_9_10_le_predecessorCount` | `Erdos1135/KrasikovLagarias/K18PredecessorAllTargets.lean` | Proved, comparator target |
| Public real-cutoff wrapper | `CollatzPredecessor090.predecessor_count_lower_bound_090` | `CollatzPredecessor090.lean` | Proved |
| Public natural-cutoff wrapper | `CollatzPredecessor090.predecessor_count_lower_bound_090_nat` | `CollatzPredecessor090.lean` | Proved |
| Public strong-exponent wrapper | `CollatzPredecessor090.predecessor_count_lower_bound_0901` | `CollatzPredecessor090.lean` | Proved |

## Exact Scope

The assumptions are `0 < a` and `a % 3 != 0`. The count includes positive
sources no larger than the floor of the cutoff. Reachability permits zero
steps, so the target counts itself once the cutoff is large enough.

All three conclusions are eventual statements at `Filter.atTop`. No explicit
numerical cutoff is claimed.