# PHASE-GRID-R1 — FINDINGS

**Pre-registration `8dec109` (sha256 `e7908507…`), Amendment 1 (sha256 `cb6ef7d2…`, C3 inputs
pinned). Run `backtest/out/phase_grid_r1_20260814T101905Z/`. All seven controls PASS.**

**INTERNAL EVIDENCE. No sentence here is a public claim; §4 is assembled from earned ladder rungs
only, and this document records which rungs were earned.**

## Controls (§10)

| Control | Result |
|---|---|
| C1 engine pin | PASS — `37d21b14…`, trf_v2 MATCH, series_loader MATCH |
| C2 linearity | PASS — arm `0.1088438514` vs closed form `0.1088438514` |
| C3 SCEN-DCA regression (inputs pinned to `c9c8e57`) | **PASS — 430/430 windows, worst delta `0.00e+00`** |
| C4 fee invariance | PASS — worst delta across legs `1.11e-15`, the pre-registered prediction |
| C5 dominance | PASS — smallest `coins_p - coins_arm` margin `+0.00015577` |
| C6 week counts | PASS, per phase |
| C7 phase table | PASS — recomputes to the frozen §3 table exactly |

## Phase table — `phases.csv` (`f2d07c1b…`)

| # | Kind | From | To | Wk | Move |
|---|---|---|---|---|---|
| P1 | partial expansion | 2016-05-02 | 2017-12-11 | 84 | +4031.9% |
| P2 | decline | 2017-12-11 | 2018-12-10 | 52 | −83.2% |
| P3 | expansion | 2018-12-10 | 2021-11-08 | 152 | +1951.9% |
| P4 | decline | 2021-11-08 | 2022-11-14 | 53 | −75.2% |
| P5 | expansion | 2022-11-14 | 2025-09-29 | 150 | +659.1% |
| P6 | decline (UNGRADED) | 2025-09-29 | 2026-06-22 | 38 | −51.8% |

## Primary result — full-phase deployment, headline leg 0.25%

Source `phase_results.csv` (`dd7b676f…`) and `phase_grid_raw.json` (`528c699d…`). Ratios are
identical at 0.10% and 0.50% (C4).

| # | contribution c/a | band | verdict | contribution c/p | band | verdict | deployer c vs a | deployer c vs p | weeks deployed |
|---|---|---|---|---|---|---|---|---|---|
| P1 | **0.325767** | 2.589% | no parity | **0.306986** | 2.503% | no parity | 1.710279 | 1.611678 | **28/84** |
| P2 | **1.063998** | 2.156% | no parity (above) | **0.477854** | 8.852% | boundary-sensitive | 1.063998 | 0.477854 | **47/52** |
| P3 | **0.965491** | 0.131% | no parity | **0.772565** | 0.576% | no parity | 1.133241 | 0.906795 | 139/152 |
| P4 | **1.005253** | 0.553% | **PARITY** (vs flat DCA) | **0.585274** | 7.627% | boundary-sensitive | 1.005253 | 0.585274 | **53/53** |
| P5 | **0.958761** | 0.149% | no parity | **0.898329** | 0.324% | no parity | 1.073240 | 1.005593 | 149/150 |
| P6 | 1.000888 | 0.256% | UNGRADED (§3) | 0.754597 | 4.015% | UNGRADED (§3) | 1.000888 | 0.754597 | 38/38 |

**"No parity" means DISTINGUISHABLE FROM PARITY at that phase's own boundary-sensitivity band. It
carries no direction.** P2 and P6 are distinguishable **above** 1.0; `PARITY-CLASS` limb 1 bars any
claim built on that, and this document does not make one.

**Ceilings, printed as emitted:** contribution frame — *PARITY-CLASS limb 1: PA may not claim more
coins than flat DCA*. Deployer frame — *conditional on DEPLOY-CLOSURE, NOT satisfied: no public
claim available*.

## Secondary — rolling W=52, `rolling_windows_phase.csv` (`ebf53604…`)

| # | Windows | Win % | Median |
|---|---|---|---|
| P1 | 33 | 0.0 | 0.2795 |
| P3 | 101 | 27.7 | 0.9903 |
| P4 | 2 | 100.0 | 1.0040 |
| P5 | 99 | 13.1 | 0.9598 |

*Rolling windows overlap; win rates are not independent trials, and no significance test is implied
or offered.* **Never substitutable for the primary.**

**DISCLOSED: P4 appears here and §7's parenthetical listed only P1/P3/P5.** The frozen RULE is
"phases holding >= 2 windows"; P4 holds exactly 2 and the code applied the rule. The parenthetical
was an incomplete enumeration, not a different rule. Recorded rather than silently included.

## The ladder, graded rung by rung (§9)

| # | Verdict | Basis |
|---|---|---|
| L1 | **STRUCK** as pre-registered | replaced by the emitted phase table's own dates |
| L2 | **EARNED** | all three arms present, all controls pass |
| L3 | **EARNED** by construction | arm (p)'s frozen definition |
| L4 | **NOT EARNED** | parity required against BOTH benchmarks in EVERY graded phase. Earned in one phase against one benchmark (P4 vs flat DCA). Against perfect foresight: nowhere |
| L5 | **NOT EARNED** | P3 c/a `0.965491`, band `0.131%` |
| L6 | **NOT EARNED** | requires 100% of weeks in P2 AND P4. **P4 is 53/53. P2 is 47/52 — five skipped weeks** |
| L7 | **NOT EARNED** | P5 c/a `0.958761`, band `0.149%` |
| L8 | **STRUCK** as pre-registered | replaced by pre-reg commit + artifact path + sha256 |
| L9a | **EARNED** by construction | a true statement about what a backtest is |
| L9b | **STRUCK** | unearnable by any backtest; PA has no behavioural data |
| L10 | **EARNED** | rests on L2+L3, and was pre-registered to survive L4's failure |
| L11 | **first half STRUCK, second half NOT EARNED** | second half rests on L6 |

**Earned: L2, L3, L9a, L10. Struck as pre-registered: L1, L8, L9b, L11a. Not earned: L4, L5, L6,
L7, L11b.**

## The §13 reading that obtained: (iii)

**No graded phase earned parity against both benchmarks.** §4 reports the measured per-phase figures
(ruling D). **L10 stands** — the no-alpha sentence was pre-registered to survive exactly this
outcome and does. **L6 does not stand**: its condition was mechanical and it failed on a count.

## What the numbers show, stated once and without decoration

**The ladder's behaviour is phase-shaped, and the shape is structural rather than incidental.** It
withholds in expensive zones, so in an expansion that ends at a top it acquires fewer coins
(P1 `0.326`, P3 `0.965`, P5 `0.959`) and in a decline it acquires slightly more (P2 `1.064`,
P4 `1.005`, P6 `1.001`). **A rule that buys less when the composite reads expensive cannot match a
rule that always buys, over a window that ends expensive** — that is arithmetic, not a defect, and
the whitepaper's grid implied parity in every phase.

**P1 is the extreme case and it is the honest one to look at:** across 84 weeks the ladder spent
**16.0 of 84 units** and ended holding **68.0** in cash, acquiring **32.6%** of flat DCA's coins.
The same phase's deployer frame is **1.710** — it bought far cheaper with the money it actually
spent. **Both figures are true, they point in opposite directions, and the deployer frame carries no
public claim today.**

**The five skipped weeks in P2 are the finding with the most consequence**, because they fall in the
first weeks after the December-2017 peak, when the composite still read Distribution and the
multiplier was 0.0. The bear-continuation sentence describes a rule that keeps buying through the
decline; **the rule as ruled does not buy at the start of a decline that begins from a top**.
P4 (53/53) and P6 (38/38) show it does buy through a decline once the composite has left
Distribution — which is a different sentence from the one on the ladder.