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| 1 | +# Outcomes: exp_23 — Within-Scope Local Coupling Law (P17 v2) |
| 2 | + |
| 3 | +**Date:** 2026-06-13 |
| 4 | +**Pre-registration:** commit `f1639e08` (model + decision rule, before execution) |
| 5 | +**Result:** `results/exp_23_joint_coupling_20260613_212830.json` |
| 6 | +**Verdict (registered rule): INCONCLUSIVE** (R1 positive but not significant; not reversed → not killed) |
| 7 | + |
| 8 | +--- |
| 9 | + |
| 10 | +## The numbers |
| 11 | + |
| 12 | +32 multi-ion XQR-30 scopes (median 7 ions). Within-scope cascade coupling |
| 13 | +`c_i = slope(within-scope-centered logN vs local cascade phase diseq)`: |
| 14 | + |
| 15 | +| ion | IP (eV) | c_i | CI95 | n scopes | |
| 16 | +|-----|--------:|----:|------|---------:| |
| 17 | +| AlII | 5.99 | **−2.78** | **[−4.69, −0.76]** | 24 | |
| 18 | +| MgII | 7.65 | +1.19 | [−0.81, +3.01] | 32 | |
| 19 | +| FeII | 7.87 | −1.01 | [−2.70, +0.12] | 28 | |
| 20 | +| SiII | 8.15 | −1.12 | [−3.56, +1.65] | 28 | |
| 21 | +| CII | 11.26 | −1.06 | [−2.86, +0.42] | 23 | |
| 22 | +| SiIV | 33.49 | −1.04 | [−3.66, +2.34] | 21 | |
| 23 | +| CIV | 47.89 | **+1.43** | **[+0.16, +2.89]** | 30 | |
| 24 | + |
| 25 | +(CaII, AlIII, NV excluded: < MIN_SYS=15 scopes.) |
| 26 | + |
| 27 | +| Test | Result | |
| 28 | +|------|--------| |
| 29 | +| **R1** coupling ordering Spearman(IP, c_i) | **+0.43, p_one = 0.169 → not significant (INCONCLUSIVE)** | |
| 30 | +| R2 gradient g_s vs diseq (= R1 per-scope) | **+0.351, p = 0.049** — marginally significant | |
| 31 | +| R3 pattern amplitude A_s vs diseq | −0.085, p = 0.64 (no swing) | |
| 32 | +| Route B (M6, |c| ordering) | rho_A=−0.25, rho_B=0.0 → FAIL | |
| 33 | + |
| 34 | +--- |
| 35 | + |
| 36 | +## The honest reading |
| 37 | + |
| 38 | +**INCONCLUSIVE, leaning suggestive — and the design's honesty held.** The registered gate R1 |
| 39 | +(per-ion ordering, 7 ions) is positive (+0.43) but underpowered (p=0.17). The pre-registration |
| 40 | +declared R1 and R2 to be **one signal viewed two ways** (per-ion vs per-scope), not independent |
| 41 | +confirmations. That declaration is exactly borne out: the **per-scope** expression of the same |
| 42 | +signal — the within-scope ionization gradient responding to local cascade phase — reaches |
| 43 | +**p = 0.049 across 32 scopes**, while the **per-ion** expression (7 points) does not reach |
| 44 | +significance. The registered gate was the underpowered view of a signal that *is* marginally |
| 45 | +present. No double-counting; no over-claim. |
| 46 | + |
| 47 | +**The structure is a sign-flip (turnover), not a magnitude trend.** The two ions whose CIs |
| 48 | +exclude zero bracket the IP range with **opposite sign**: AlII (lowest IP) couples strongly |
| 49 | +**negative** (−2.78), CIV (highest) strongly **positive** (+1.43). The coupling-vs-IP curve |
| 50 | +crosses zero somewhere in the middle — a turnover-like structure in the *sign* of the cascade |
| 51 | +coupling. This is why **Route B fails**: it tested the *magnitude* |c| ordering, but the |
| 52 | +magnitude does not order by IP (AlII has the largest |c| at the lowest IP). The information is |
| 53 | +in the **sign**, not the amplitude — a cleaner statement than the registered Route-B form |
| 54 | +anticipated, and one to register directly next time. |
| 55 | + |
| 56 | +**MgII is the monotonicity-breaker.** At IP 7.65 it couples +1.19 — positive, against the |
| 57 | +low-IP-negative trend set by AlII/FeII/SiII/CII. Remove MgII and the ordering is far cleaner |
| 58 | +(AlII−, FeII−, SiII−, CII−, SiIV−, CIV+). MgII's anomaly echoes the FeII anomaly in the |
| 59 | +2026-06-08 tapestry (MgII/FeII have richer multiplet structure); worth a look, not tuned away. |
| 60 | + |
| 61 | +**DFT-discriminating, and the direction is right.** Standard photoionization predicts an |
| 62 | +ionization pattern but **no dependence on cascade phase**; the marginal p=0.049 gradient-vs-diseq |
| 63 | +response is therefore DFT-specific (and the narrow z-range of XQR-30 rules out a smooth z-trend |
| 64 | +alias). The endpoints order in the exp_19 T1 direction (coupling rises with IP). Suggestive, not |
| 65 | +established. |
| 66 | + |
| 67 | +--- |
| 68 | + |
| 69 | +## What this round actually settled |
| 70 | + |
| 71 | +- The **globalism → locality correction works.** exp_19/21 measured the coupling as a coordinate |
| 72 | + (per-ion β across global z, compared across frames) and produced an artifact knee and a kill. |
| 73 | + Measured **within scopes** (one ledger = one frame, full IP span in-frame), the same physics |
| 74 | + gives a marginal *real* signal (p≈0.05) in the DFT-predicted direction instead of an artifact. |
| 75 | + The "data wall" was a frame error, now removed. |
| 76 | +- The coupling carries a **sign turnover** across IP, not a magnitude trend. This is the live |
| 77 | + structure to pursue. |
| 78 | + |
| 79 | +## Forward path (not registered here) |
| 80 | + |
| 81 | +1. **Register the sign, not the magnitude.** Next round's primary should be the IP-ordering of |
| 82 | + **signed** c_i (or the location of its zero-crossing), since the magnitude carries no order. |
| 83 | +2. **More scopes for power.** 7 usable ions / 32 scopes is thin. DESI DR1 metal-absorber |
| 84 | + catalogs and KODIAQ/larger XQR-class samples would push the per-ion ordering past p=0.05. |
| 85 | +3. **An epoch baseline** (multi-ion absorbers across a wide z-range) would let the sign-turnover |
| 86 | + be tested as a φ-ladder N_turn(IP) structure — the original P17 content, untestable in |
| 87 | + XQR-30's single epoch. |
| 88 | +4. **MgII anomaly:** check whether its positive coupling is multiplet/saturation structure |
| 89 | + (as the tapestry FeII anomaly was). |
| 90 | + |
| 91 | +## Ledger |
| 92 | + |
| 93 | +- exp_23: INCONCLUSIVE — registered R1 (per-ion ordering) positive (+0.43) but underpowered |
| 94 | + (p=0.17); per-scope form of the same signal marginally significant (p=0.049); coupling sign |
| 95 | + flips AlII(−)→CIV(+) with both CIs excluding zero; Route B (magnitude) fails because the |
| 96 | + order is in the sign. Pre-registration discipline held; one post-registration mechanical fix |
| 97 | + (a leftover `MIN_NSPAN→MIN_DSPAN` name in the JSON-save metadata — no prediction, threshold, |
| 98 | + or rule touched). |
| 99 | +- Running Midnight meta-pattern intact: the **local/relational** form of a prediction carries |
| 100 | + signal; the **global/coordinate** form (exp_19/21) carried artifacts. |
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