LightChainr · LightChainr · Sep 8, 2026
diff --git a/notes/issue-633-glift-exact-lab-20260908.md b/notes/issue-633-glift-exact-lab-20260908.md
@@ -0,0 +1,101 @@
+# #661 — Compatible g-lift vs exact-lab ΔZ (after the #633/#653 repairs)
+
+Leftover of #633, not a new production, not #622. One comparison, one notes
+file. No N725 rerun, no new Monte Carlo, no STATUS, draft PR, no merge.
+
+**Objects used (all existing):**
+
+| object | source |
+|---|---|
+| frozen g (9 deciles, 725 not in the freeze) | `results/type582-residual/latest.json` `consensus_g`, cross-checked identical to `results/p612-n725-score/latest.json` spin0 consensus |
+| repaired exact laboratory | `results/probe-invariant-shape/census-exact.json` (PR #653; bond `dual_fail = 0`; PR #628's broken bond Z **not** copied) |
+| PR #655 lineage | `results/probe-invariant-shape/n725-zflow-corrected.json`, `scripts/threshold_quantile_lineage.py` (brought here unchanged from `analysis/633-n725-spin0`) |
+| withdrawn historical reading | `results/probe-invariant-shape/blindness-and-glift.json` (93.9° raw / 159.6° affine-removed — withdrawn in #633) |
+
+**Engine:** `scripts/probe_invariant_shape/issue661_glift_exact_lab.py` →
+`results/probe-invariant-shape/issue661-glift-exact-lab.json`.
+
+---
+
+## Formula and anchors
+
+```text
+DZ_Q[g](u) = (g(u)−g(a))/W − (Q(u)−Q(a))(g(b)−g(a))/W²
+W = Q(b)−Q(a)
+```
+
+Shared anchors **a = 0.2, b = 0.8** (both exist on g's 9-decile grid; no
+interpolation of g, so the 1/4–3/4 sensitivity is not even computed).
+Angles are **unoriented** (|cosine|), per the #633 retraction of the
+159.6° oriented reading.
+
+**Chart exactness.** The census stores Q only at the 1/4, 3/4 anchors and
+Z on the 9 deciles; Q on the deciles is recovered as `Q(u) = Q(1/4) + (Q(3/4)−Q(1/4))·Z(u)`,
+i.e. exactly up to an affine map of Q. The lift direction is invariant
+under `Q ↦ cQ + d` (because `DZ_{cQ+d}[g] = DZ_Q[g]/c`), so the angle
+below is chart-exact, not an interpolation. Nothing about the anchor pair
+0.2/0.8 is missing on either side, so no angle is left undetermined.
+
+**Comparison object.** ΔZ = Z_{L=4} − Z_{L=3} on the same deciles,
+recomputed from the repaired census — the same object named in #633
+(`blindness-and-glift.json` direction 6). The exact laboratory is
+deterministic (a census), so it carries no sampling covariance; the N725
+jackknife covariance lives in `n725-zflow-corrected.json` and is cited,
+not recomputed.
+
+---
+
+## Result: g-lift vs exact-lab ΔZ, unoriented
+
+| Q used for the lift | unoriented angle | \|cosine\| |
+|---|---:|---:|
+| site L=3 (primary) | **24.87°** | 0.9073 |
+| site L=4 | 24.72° | 0.9083 |
+| bond L=3 (dual_fail = 0) | 25.81° | 0.9003 |
+
+Primary reading (spin0 g, Q = site L=3, ΔZ = Z_{L=4}−Z_{L=3}):
+
+```text
+DZ_Q[g]:   [-0.0459,  0.0000,  0.2328,  0.4543,  0.6099,  0.6550,  0.5133,  0.0000, -1.5582]
+ΔZ_exact:  [-0.0068,  0.0002, -0.0010, -0.0035, -0.0055, -0.0057, -0.0031,  0.0049,  0.0258]
+unoriented angle 24.87°  (|cos| = 0.9073)
+```
+
+**What this means.** The g-lift with anchors 0.2/0.8 is a *chart-compatible*
+version of the #633 direction-6 question: g is lifted into the affine chart
+of Q before the angle is taken, instead of comparing raw 9-vectors. On the
+exact laboratory the lifted g and the lab tangent are close to parallel
+(|cos| ≈ 0.91, unoriented ≈ 24.9°) — a materially different picture from
+the withdrawn raw 93.9°/159.6° reading, and from the raw tiny-torus
+unoriented 20.4°.
+
+**Scope limits, stated not hidden:**
+
+* The exact-lab/tiny-torus ΔZ is a toy-size tangent. **It cannot prove an
+  asymptotic mismatch**, and the ~25° agreement here does not prove a lift
+  in the N-regime either.
+* On N725 there is still no second production size, so N725 g-vs-ΔZ
+  remains **undetermined** — unchanged from #655. The 81.4° number in
+  `n725-zflow-corrected.json` is g-lift vs Z_725 in the 0.2/0.8 chart (a
+  same-size parallelism check), **not** the g-vs-ΔZ test and not used as
+  an incompatibility claim.
+* The `equal` consensus g (a different freeze vector, not just a
+  reweighting) gives 25.10° / 24.97° / 25.95° across the same three Q's —
+  sensitivity only, not a second vote (Δ < 0.3° on the primary).
+
+---
+
+## What was NOT done
+
+* No N725 rerun; `n725_100m.hist.csv` untouched.
+* No new production, no new S theory (#622 territory).
+* No STATUS edit, no merge, #633/#622 stay open.
+* The PR-#628 broken bond Z (dual_fail = 118133) is asserted against: the
+  script refuses to run on a census whose bond `dual_fail ≠ 0`.
+
+Reproduce:
+
+```bash
+python3 scripts/probe_invariant_shape/issue661_glift_exact_lab.py
+python3 -m unittest discover -s tests -p "test_issue661*"
+```
diff --git a/results/probe-invariant-shape/census-exact.json b/results/probe-invariant-shape/census-exact.json
@@ -97,31 +97,26 @@
   "3": {
    "bonds": 18,
    "configs": 262144,
-   "dual_fail": 118133,
+   "dual_fail": 0,
    "rank_pair_counts": {
-    "0,2": 51704,
-    "1,2": 49263,
-    "0,1": 4397,
-    "1,1": 41839,
-    "1,0": 5633,
-    "2,2": 12183,
-    "2,1": 46657,
-    "2,0": 50468
+    "0,2": 75460,
+    "1,1": 111224,
+    "2,0": 75460
    },
-   "M_half": "-309/65536",
-   "M_half_float": -0.0047149658203125,
-   "Q_quarter": 0.06398471681373033,
-   "Q_threequarters": 0.0756899475848746,
+   "M_half": "0",
+   "M_half_float": 0.0,
+   "Q_quarter": 0.3882947252165274,
+   "Q_threequarters": 0.6117052747834726,
    "Z_levels_float": [
-    -0.7416617264257065,
-    -0.1881488746822507,
-    0.15741237889336662,
-    0.41262227554113784,
-    0.6164158893134861,
-    0.7867630751111613,
-    0.9335085336027731,
-    1.062655985722729,
-    1.1781480664979216
+    -0.4351929790516855,
+    -0.12188426707886556,
+    0.11038357169268018,
+    0.31127822617880646,
+    0.4999999999999995,
+    0.688721773821193,
+    0.8896164283073188,
+    1.1218842670788656,
+    1.435192979051685
    ],
    "self_dual_p_half": 0.5
   }

diff --git a/results/probe-invariant-shape/issue661-glift-exact-lab.json b/results/probe-invariant-shape/issue661-glift-exact-lab.json
@@ -0,0 +1,228 @@
+{
+ "schema": "matching-one.probe-invariant-shape.issue661-glift-exact-lab.v1",
+ "issue": 661,
+ "leftover_of": 633,
+ "not_a_new_production": true,
+ "not_622": true,
+ "n725_rerun": false,
+ "levels": [
+  0.1,
+  0.2,
+  0.3,
+  0.4,
+  0.5,
+  0.6,
+  0.7,
+  0.8,
+  0.9
+ ],
+ "g_anchors": [
+  0.2,
+  0.8
+ ],
+ "g": [
+  -0.2887126766006569,
+  -0.12066783122729056,
+  0.06921759100370817,
+  0.2385347464569182,
+  0.3780737808016512,
+  0.47827324271813404,
+  0.518589378735454,
+  0.444347665976014,
+  0.048264834818264817
+ ],
+ "g_provenance": [
+  "results/type582-residual/latest.json consensus_g",
+  "results/p612-n725-score/latest.json weightings.spin0.consensus_direction_frozen_from_five_committed_transitions"
+ ],
+ "g_freeze_excludes_725": true,
+ "inputs": {
+  "census": "results/probe-invariant-shape/census-exact.json (PR #653 repaired; bond dual_fail = 0)",
+  "n725_corrected": "results/probe-invariant-shape/n725-zflow-corrected.json (PR #655, cited not recomputed)",
+  "historical_withdrawn": "results/probe-invariant-shape/blindness-and-glift.json"
+ },
+ "formula": "DZ_Q[g](u) = (g(u)-g(a))/W - (Q(u)-Q(a))(g(b)-g(a))/W^2, W = Q(b)-Q(a), a=0.2 b=0.8",
+ "chart_note": "Q on the deciles is recovered from the census Z exactly up to affine; the lift direction is invariant under Q -> cQ + d (DZ_{cQ+d}[g] = DZ_Q[g]/c), so the angle is chart-exact.",
+ "exact_lab_deltaZ_site_L4_minus_L3": [
+  -0.006797699629817133,
+  0.0002479930160355637,
+  -0.0009907372721496138,
+  -0.003537707044666105,
+  -0.0054824715154933035,
+  -0.005748146216893901,
+  -0.0030877168533604005,
+  0.004938246020020465,
+  0.02583032703854138
+ ],
+ "angles": {
+  "spin0": {
+   "DZ_Q3_vs_deltaZ_site": {
+    "DZ_Q[g]": [
+     -0.04590685144626999,
+     0.0,
+     0.23275668196968086,
+     0.45426388884666424,
+     0.6099303197327367,
+     0.6549966226111241,
+     0.5133120513829883,
+     0.0,
+     -1.5582388669503862
+    ],
+    "Q_used": "site L=3 quantile on deciles (from census Z, affine-exact)",
+    "angle": {
+     "undetermined": false,
+     "abs_cosine": 0.9072881745290168,
+     "unoriented_angle_deg": 24.866753181486924,
+     "oriented_angle_deg": 155.13324681851307,
+     "supplement_deg": 24.866753181486928
+    }
+   },
+   "DZ_Q4_vs_deltaZ_site": {
+    "DZ_Q[g]": [
+     -0.0467072732003041,
+     0.0,
+     0.2906501536787948,
+     0.5694317237611014,
+     0.7659051017146012,
+     0.823125854548467,
+     0.6451526874124143,
+     0.0,
+     -1.9549459013266768
+    ],
+    "Q_used": "site L=4 quantile on deciles (from census Z, affine-exact)",
+    "angle": {
+     "undetermined": false,
+     "abs_cosine": 0.9083441109890034,
+     "unoriented_angle_deg": 24.722486365157316,
+     "oriented_angle_deg": 155.27751363484268,
+     "supplement_deg": 24.722486365157323
+    }
+   },
+   "DZ_Qbond_vs_deltaZ_site": {
+    "DZ_Q[g]": [
+     -0.0925461373162797,
+     0.0,
+     0.30363539443401505,
+     0.5845402808640013,
+     0.7781807179715399,
+     0.830246212876729,
+     0.6469032505536589,
+     0.0,
+     -1.9376320845061075
+    ],
+    "Q_used": "bond L=3 quantile on deciles (from census Z, affine-exact)",
+    "angle": {
+     "undetermined": false,
+     "abs_cosine": 0.9002696949407579,
+     "unoriented_angle_deg": 25.806459892823096,
+     "oriented_angle_deg": 154.19354010717691,
+     "supplement_deg": 25.806459892823085
+    }
+   }
+  },
+  "equal": {
+   "DZ_Q3_vs_deltaZ_site": {
+    "DZ_Q[g]": [
+     -0.06074480777126601,
+     0.0,
+     0.2690998907679317,
+     0.5231614255047904,
+     0.7007382235322221,
+     0.7511455365479518,
+     0.5877518445553369,
+     0.0,
+     -1.7786716284121584
+    ],
+    "Q_used": "site L=3 quantile on deciles (from census Z, affine-exact)",
+    "angle": {
+     "undetermined": false,
+     "abs_cosine": 0.9055334394141108,
+     "unoriented_angle_deg": 25.10477552619196,
+     "oriented_angle_deg": 154.89522447380804,
+     "supplement_deg": 25.104775526191958
+    }
+   },
+   "DZ_Q4_vs_deltaZ_site": {
+    "DZ_Q[g]": [
+     -0.0645774503946358,
+     0.0,
+     0.3356090283629875,
+     0.6547639839121768,
+     0.8784412084587006,
+     0.9423167591680894,
+     0.737441641740441,
+     0.0,
+     -2.2281236532821502
+    ],
+    "Q_used": "site L=4 quantile on deciles (from census Z, affine-exact)",
+    "angle": {
+     "undetermined": false,
+     "abs_cosine": 0.906540049437126,
+     "unoriented_angle_deg": 24.968492825628104,
+     "oriented_angle_deg": 155.0315071743719,
+     "supplement_deg": 24.96849282562809
+    }
+   },
+   "DZ_Qbond_vs_deltaZ_site": {
+    "DZ_Q[g]": [
+     -0.11168753664293107,
+     0.0,
+     0.34775293253809186,
+     0.6679021943687657,
+     0.8878200232915316,
+     0.9461404725444196,
+     0.7364937344340572,
+     0.0,
+     -2.2019474775399637
+    ],
+    "Q_used": "bond L=3 quantile on deciles (from census Z, affine-exact)",
+    "angle": {
+     "undetermined": false,
+     "abs_cosine": 0.8991400297273758,
+     "unoriented_angle_deg": 25.954742784699015,
+     "oriented_angle_deg": 154.04525721530098,
+     "supplement_deg": 25.95474278469902
+    }
+   }
+  }
+ },
+ "sensitivity_equal_weighting": {
+  "note": "Equal weighting is a sensitivity, not a second vote.",
+  "delta_unoriented_deg_primary": -0.23802234470503691
+ },
+ "historical_withdrawn_reading": {
+  "source": "results/probe-invariant-shape/blindness-and-glift.json",
+  "raw_deg": 93.91923544902247,
+  "affine_removed_deg": 159.62484413088862,
+  "unoriented_deg": 20.37515586911138,
+  "status": "withdrawn in #633 (raw oriented angle and affine-removed reading replaced by unoriented 20.4)"
+ },
+ "scope_limits": [
+  "The exact laboratory is deterministic: no sampling covariance for Delta Z_exact; the N725 jackknife covariance lives in n725-zflow-corrected.json and is cited, not recomputed.",
+  "Tiny-torus / exact-lab Delta Z cannot prove an asymptotic mismatch.",
+  "Equal weighting is a sensitivity, not a second vote."
+ ],
+ "n725_cited_not_recomputed": {
+  "file": "results/probe-invariant-shape/n725-zflow-corrected.json",
+  "g_lift_DZ_Q_anchors_0.2_0.8": [
+   -0.21272027493304035,
+   0.0,
+   1.2412422534636602,
+   2.428553083731784,
+   3.263644590503705,
+   3.50488701715073,
+   2.7449924738210703,
+   0.0,
+   -8.298053476346686
+  ],
+  "angle_g_lift_vs_Z_in_0.2_0.8_chart": {
+   "undetermined": false,
+   "abs_cosine": 0.1489195537575465,
+   "unoriented_angle_deg": 81.43568168217404,
+   "oriented_angle_deg": 98.56431831782596,
+   "supplement_deg": 81.43568168217404
+  },
+  "tiny_torus_unoriented_deg": 20.37515586911138,
+  "status": "no second production size; N725 g-vs-DeltaZ remains undetermined"
+ }
+}