# std79-doe LaTeX report: the fleet conservation invariant K

**Read `report/std79_doe_report.pdf`** — this supersedes `../analysis-20260912/`
(the first, markdown-only pass) as the primary deliverable for this dataset.
That first pass was correctly flagged as inadequate: it never captured K
(the fleet-wide execution-heat conservation invariant) at all, and presented
results as a plain markdown page rather than in this project's established
LaTeX report style (see `experiments/bare_metal/analysis/report/` for the
precedent this follows — same document class, packages, colour palette,
light/dark figure pairs, abstract-first structure with headline numbers).

## What changed to make this possible

`src/starkernel/doe_log.c`'s per-heartbeat-tick CSV gained two new columns
(`fleet_k_q48`, `fleet_conserved` — see the file's own header comment for
the full 20-column schema), requiring a kernel rebuild and a fresh DoE
campaign rerun on all three architectures
(`../results-20260912-with-k/*-doe-raw.log` + `*-heartbeat.csv`).

## Pipeline (same shape as `../analysis-20260912/`, extended for K)

1. `correlate_doe.py <raw_log> <out_csv>` — per architecture, against
   `../results-20260912-with-k/{amd64,aarch64,riscv64}-doe-raw.log` →
   `{amd64,aarch64,riscv64}-correlated.csv` (committed, not scratch).
2. `combine.py <in1.csv> [in2.csv ...] <out.csv>` → `combined.csv` (775 rows).
   Decodes `fleet_k_q48` to a plain float and **derives** `fleet_conserved`
   from `fleet_k_q48` directly (using the same epsilon
   `vm_physics_conserved()` uses, `capsule_vm_physics.c`) rather than
   trusting the raw `fleet_conserved` field — that field is
   `doe_log_tick_row()`'s very last printed column, with nothing after it
   in the row to bound a regex match against, so a resumed trial digit can
   merge into it with zero separator on the wire (confirmed live: raw
   values like `19223372036854775807` where `0`/`1` was expected). See the
   script's own comment for the full explanation.
3. `analysis.R` (run from this directory) — computes the K result
   (trivial: one distinct value, `sd = 0`, reported directly rather than
   via a formal test — see the report's own \S5.1 for why), per-cell
   architecture × identity summaries, and two-way ANOVA for 12 secondary
   metrics; writes `charts/*.svg` (light+dark pairs, matching
   `experiments/bare_metal/analysis/analyse_bare_metal.R`'s theme
   convention) and `tables/*.csv`.
4. SVGs converted to PDF for LaTeX via `rsvg-convert` into `report/figures/`.
5. `report/std79_doe_report.tex`, hand-authored following
   `experiments/bare_metal/analysis/report/bare_metal_doe_report.tex`'s
   structure and conventions; compiled with `pdflatex` (three passes for
   cross-references/TOC).

## Headline result

$K = 1.0000000000$ (raw Q48.16 `65536`) on **every one of 775
heartbeat-tick observations**, `sd(K) = 0`, `fleet_conserved = 1` on 100% of
rows, across all three architectures, nine identities, and three
replicates. Zero deviation. See the report for the full discussion,
including why this is also a free regression check on the two Stadium
subsystem fixes (FABRIC-3.md §XVI–XVII) that landed the same week.

## Known limitation

Same interleaving-correlation caveat as `../analysis-20260912/`: 1 of 27
`run_id` markers was unrecoverable on 2 of 3 architectures this run
(aarch64/riscv64: `run_id` 1 folded into `run_id` 0). `fleet_k_q48` itself
is entirely unaffected by this — it's read directly at each tick regardless
of trial attribution, so the K result does not depend on trial labeling
being correct at all. See report §2.3/§6.4 for the full explanation.