Chunked Pipeline Scheduling

Tools

`pipeline_schedule`

Given P items, N stages, and chunk size B, compute the chunked pipeline schedule. Returns total steps T = ceil(P/B) + (N-1), speedup vs sequential (P*N), the triangle ramp-up visualization, and per-st...

`wallington_rotation`

Given a multi-stage pipeline with per-stage service times, compute the optimal Wallington Rotation: chunk size B, rotation order, expected throughput, and the modeled speedup range (3.1x-267x from the...

`pipeline_triangle`

Visualize the pipeline triangle for given parameters. Returns ASCII art of the time x stage grid showing chunk flow, wavefront diagonal, and utilization percentage. From "Being Irreversible" Section 1...

`bottleneck_analysis`

Identify bottlenecks in a pipeline: stages where service time exceeds others, head-of-line blocking points, and suggested mitigations (chunking, reordering, parallelizing). From "Being Irreversible" S...

`compare_strategies`

Compare sequential vs pipelined vs chunked-pipelined execution for a workload. Returns step counts, speedups, utilization, and idle time for each strategy. From "Being Irreversible" Section 13, Layer ...

`pipeline_speedup_sandwich`

Compute the pipeline speedup sandwich: 1 ≤ speedup ≤ B×N. Returns sequential, pipelined, and fork/race/fold times with regime separation.

`thm_s7_whip`

Worthington Whip savings shape [LEDGER: THM-S7-WHIP]

`thm_s7_spec`

Speculative Tree positivity constraints [LEDGER: THM-S7-SPEC]

`thm_s7_turb`

Turbulent idle fraction stays bounded [LEDGER: THM-S7-TURB]

`thm_s7_occ`

Pipeline occupancy deficit is the complement of frontier fill and equals turbulent idle fraction in the canonical pipeline envelope [LEDGER: THM-S7-OCC]

`thm_s7_wallace`

Wallace metric (`wally`) on a bounded three-layer frontier is bounded, complementary to frontier fill, zero exactly at full envelope occupancy, and reduces to `2(k-1)/(3k)` on the symmetric diamond wi...

`thm_s7_mux_mono`

Turbulent multiplexing monotonicity: with fixed useful work and legal recovered overlap, multiplexing cannot increase the Wallace metric and strictly lowers it when overlap is actually recovered [LEDG...

`thm_s7_stagger`

Staged expansion dominates naive widening on the bounded diamond witness: with positive topology deficit and the same added frontier budget, filling underfilled shoulders first yields higher frontier ...

`thm_s7_warm_eff`

Warm-up efficiency: for homologous workloads with fixed useful work, recovered overlap is worth the added Buley cost exactly when the weighted Wallace reduction exceeds the Burden Scalar; equivalently...

`thm_s7_warm_dyn`

Dynamic warm-up cooling: under bounded entropy creep, reachable burden threshold, and cooling strength that can clear any reachable overlap, the dynamic warm-up controller keeps overlap bounded and ev...

`thm_s7_warm_ctrl`

Warm-up controller optimality: under one-hot topology mismatch, the score-minimizing controller chooses `expand` for underfilled topology below the redline, `constrain` for overprovisioned topology be...

`thm_s7_warm_ctrl_tie`

Exact redline ties are deterministic: at `BurdenScalar = Redline`, an underfilled topology chooses `expand` rather than `shed-load`, and an overprovisioned topology chooses `constrain` rather than `sh...

`thm_s7_whip_crossover`

Cross-shard correction crossover is finite and over-sharding becomes non-improving [LEDGER: THM-S7-WHIP-CROSSOVER]

`thm_staged_expansion`

Staged expansion frontier: the three-stage expansion area formula matches naive widening. Peak is preserved across stages. Wallace numerator measures wasted capacity in the expansion envelope [LEDGER:...

`thm_warmup_controller`

Warmup controller action scoring over expand/constrain/shedLoad: the controller selects the action with minimum score. Repair redline = deficitWeight + shedPenalty. Warmup worth = Wallace benefit exce...

`thm_multiplexing_capacity`

Multiplexing capacity = sequential minus recovered overlap. Wallace numerator is monotone under multiplexing. Wallace numerator drop equals overlap identity [LEDGER: THM-MULTIPLEXING-CAPACITY]

`thm_rotation_admissible`

The Wallington Rotation produces an admissible schedule for any fork/race/fold DAG: positive finite makespan, respects stage ordering. [LEDGER: THM-ROTATION-ADMISSIBLE]

`thm_rotation_makespan_bound`

The rotation makespan equals the critical path: numStages × maxStageTime. No admissible schedule can achieve lower makespan because stages are sequential dependencies. Bound is tight for balanced DAGs...

`thm_rotation_dominates_sequential`

For any DAG with β₁ > 0 (numPaths ≥ 2), the rotation strictly dominates the sequential schedule: rotationMakespan < sequentialMakespan. The speedup factor is exactly numPaths. [LEDGER: THM-ROTATION-DO...

`thm_rotation_pareto_schedule`

The rotation is Pareto-optimal in (makespan, resources): sequential uses fewer resources (1 vs numPaths) but has strictly higher makespan. No schedule simultaneously beats both dimensions. [LEDGER: TH...

`thm_rotation_deficit_correlation`

The rotation's speedup factor equals the topological deficit reduction plus one: speedup = β₁(rotation) - β₁(sequential) + 1 = numPaths. Larger deficit reduction → larger speedup, monotonically. [LEDG...