Chapter 69

Lucy density — synthetic organism

github.com/openfluke/welvet/lucy✅ BuildLPD

Why it exists

A new host (char LM, MNIST, a layer sprint) should not copy tide's goldilocks math. The question is always the same: can the net run and train at the same time in a small box, then how far that live-fit condenses without becoming a trap. That ruler belongs in the engine.

What it is

lucy.BuildLPD ranks Samples for consciousness (Acc / Throughput / Availability keep vs learner peaks) then Lucy density (Q × shrink vs Acc-champ RAM). Gold / near / keep / trap bands, consciousness radar, and memory-density radar are computed here. Tide dash and Lucy PDF only draw the board.

WHY
  Industry ships dead calculators: INT8 inference, no on-device train.
  Synthetic organism = serve while learning, then shrink without falling
  into chance-Acc "tiny & fast" traps.

PILLARS (consciousness)
  Acc    = argmax %          (did it learn?)
  Thru   = outputs / second  (can it act while live?)
  Avail  = InferMs / busy    (can you still talk to it while it trains?)
  Score  = T × Avail × Acc / 10_000     live-fit
  SoftAcc is serve-confidence — not a pillar.

DENSITY (memory intelligence)
  Acc champ = RAM reference (best learner, not the Score champ)
  Learner   = RelAcc ≥ 70% of Acc champ   (traps do not set Thru/Avail peaks)
  Q         = geomean(RelAcc, RelThru, RelAvail)
  shrink    = AccChampRAM / thisRAM   (capped ×32)
  LPD       = Q × shrink    if RelAcc ≥ 70% else 0

BANDS
  gold  all 3 pillars ≥80% and RAM ≤20% of Acc champ
  near  Acc + (Thru or Avail) ≥80% at ≤50% RAM
  trap  RAM ≤20% and Acc keep <70%     (binary looking dense)
  Score/MiB is the trap metric — do not use it for goldilocks.

RADARS (for PDF / dash — math here, drawing in tide)
  Consciousness  = (RelAcc, RelThru, RelAvail)
  Memory density = (RelAcc, RelThru, RelAvail) × shrink   traps at origin

Why we measure this

The goal is not a better chatbot and not a paper for a faculty board. It is a synthetic organism: a net that owns time — continuous serve, continuous train, no turn-based halt, no phone-home. Lucy Score asks the thermodynamic question tide was built for: does SGD that blocks inference die, and do proxy / Split / Sparse paths keep the live loop while still learning?

Hard Acc is whether it learned. Availability is whether it still breathes. Throughput is how many actions it took while both were happening. Multiply them and you get live-fit. SoftAcc is how confident the serve looked — useful, not the Acc term.

Memory density asks the second question: once you have a learner, how far can dtype / quant / cameral width condense that live-fit versus the Acc champ's RAM without collapsing to chance Acc. A binary cell that is 30× smaller and 4× faster with 12% Acc is a trap (LPD = 0). An int8 that keeps ≥70% of Acc-champ Acc at a fifth the RAM is goldilocks.

Formulas

What tide still owns

Tide is the race: serve+train pulses, permute matrix, dashboard, Lucy PDF (including drawing the two radars). tide/report.BuildLPD pretty-prints cell IDs then calls lucy.BuildLPD. A new thing that only needs the ruler:

import "github.com/openfluke/welvet/lucy"
board := lucy.BuildLPD(samples)
_ = board.Top[0].Consciousness()  // Acc, Thru, Avail keep
_ = board.Top[0].MemoryDensity()  // same × shrink; traps at 0

Classification hosts should train with TrainStackCE so the Acc pillar can leave chance; MSE on a one-hot stays uniform. That is a loss gap in layers/parallel, not a Lucy formula.

Pulse math: §66. Train modes: §67.

package main

import (
	"fmt"

	"github.com/openfluke/welvet/lucy"
)

func main() {
	board := lucy.BuildLPD([]lucy.Sample{
		{ID: "f32", Mode: "sgd", Acc: 90, Thru: 200, Avail: 40, Score: 100, RAMKiB: 1000},
		{ID: "int8", Mode: "sgd", Acc: 82, Thru: 180, Avail: 38, Score: 85, RAMKiB: 180},
		{ID: "bin", Mode: "sgd", Acc: 12, Thru: 400, Avail: 50, Score: 40, RAMKiB: 40},
	})
	top := board.Top[0]
	fmt.Printf("lead=%s band=%s LPD=%.2f trap=%s\n",
		top.ID, top.Band, top.LPD, board.Trap[0].ID)
}

lead=int8 band=gold LPD=5.11 trap=bin