Skip to content

Commit cd24324

Browse files
PeterHiggins19PeterHiggins19
committed
The Shadow knows
1 parent 545ac09 commit cd24324

16 files changed

Lines changed: 2161 additions & 117 deletions

‎data/codawork-samples/S016/EITT_Residual_Analysis_001.json‎

Lines changed: 49 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,49 @@
1+
{
2+
"analysis": "EITT_ENTROPY_RESIDUAL",
3+
"date": "2026-04-09",
4+
"finding": "The systematic upward entropy drift under geometric-mean decimation is a second-order Jensen correction \u2014 the Hessian footprint of Shannon entropy on the simplex",
5+
"mechanism": {
6+
"step_1": "Geometric mean reduces composition variance (pulls toward Fr\u00e9chet mean x*)",
7+
"step_2": "Shannon entropy is concave (Hessian = diag(-1/x_i))",
8+
"step_3": "Concave function of less-variable input gives higher expected output (Jensen)",
9+
"step_4": "Correction magnitude: \u0394H \u2248 (1/2) tr[|Hess_H(x*)| \u00b7 Cov(x\u0304_M)]"
10+
},
11+
"euler_e_connection": {
12+
"entropy": "H(x) = -\u03a3 x_i ln(x_i) \u2014 uses log_e",
13+
"geometric_mean": "x\u0304_geo = C(exp(mean(ln(x)))) \u2014 uses e^(\u00b7)",
14+
"cancellation": "exp and ln are inverses \u2014 first-order effects cancel by construction",
15+
"residual": "Second-order mismatch \u2014 the Hessian footprint \u2014 is what remains"
16+
},
17+
"copilot_data_verification": {
18+
"H_star": 2.0794399275823543,
19+
"total_drift_nats": 0.0006285588186454305,
20+
"total_drift_pct": 0.03023645281578583,
21+
"gap_vs_trace_R2": 0.6574010371842407,
22+
"hessian_coupling_slope": 4.772090981103247e-06,
23+
"direction": "ALWAYS UPWARD (for stationary processes)"
24+
},
25+
"var1_bounds_gap_explanation": {
26+
"var1_bounds_pct": "100-1000%",
27+
"actual_change_pct": "0.03%",
28+
"ratio": "~10,000x",
29+
"reason": "VAR(1) captures first-order (mean shift) which vanishes. Actual effect is second-order (variance \u00d7 Hessian) which is tiny."
30+
},
31+
"midrange_direction_check": {
32+
"upward_as_predicted": [
33+
"Germany",
34+
"Japan",
35+
"USA"
36+
],
37+
"downward_anomalous": [
38+
"France",
39+
"UK",
40+
"Poland"
41+
],
42+
"explanation": "Downward cases have non-stationarity or small samples where first-order trend effects dominate the second-order Jensen term"
43+
},
44+
"codawork_language": "The residual is not error. It is the Hessian of entropy, made visible by the variance reduction that the geometric mean performs.",
45+
"governance": {
46+
"state": "CGS-2 (n=3)",
47+
"gdof": 264
48+
}
49+
}

‎data/codawork-samples/S016/HUF_Aitchison_Variance_Conservation_001.json‎

Lines changed: 40 additions & 103 deletions
Original file line numberDiff line numberDiff line change
@@ -1,7 +1,8 @@
11
{
22
"test_id": "AITCHISON_VARIANCE_CONSERVATION_001",
3-
"title": "Aitchison Variance Conservation Test \u2014 Time Transformer DUT",
3+
"title": "Decimation Ladder — Three Conservation Candidates Tested",
44
"date": "2026-04-08",
5+
"revision_note": "Revised after ChatGPT review. Original version incorrectly labeled Aitchison variance as APPROXIMATELY_CONSERVED. Reframed: AitVar is a NEGATIVE CONTROL. Shannon entropy is the conserved quantity. This file documents the experiment that led to the EITT discovery.",
56
"data_source": "EMBER European wholesale electricity price data (daily)",
67
"carriers": [
78
"Germany",
@@ -68,35 +69,24 @@
6869
},
6970
"conservation_analysis": {
7071
"aitchison_variance": {
71-
"Daily": {
72-
"ratio_to_daily": 1.0,
73-
"pct_change": 0.0,
74-
"conservation_status": "STRONG"
75-
},
76-
"Weekly": {
77-
"ratio_to_daily": 0.7607,
78-
"pct_change": -23.9,
79-
"conservation_status": "WEAK"
80-
},
81-
"Monthly": {
82-
"ratio_to_daily": 0.6232,
83-
"pct_change": -37.7,
84-
"conservation_status": "WEAK"
85-
},
86-
"Quarterly": {
87-
"ratio_to_daily": 0.5391,
88-
"pct_change": -46.1,
89-
"conservation_status": "WEAK"
90-
},
91-
"Annual": {
92-
"ratio_to_daily": 0.4495,
93-
"pct_change": -55.1,
94-
"conservation_status": "NOT CONSERVED"
95-
}
72+
"daily_to_annual_change": "-55.1%",
73+
"cv_across_resolutions": 0.2852,
74+
"verdict": "NOT_CONSERVED",
75+
"note": "AitVar drops monotonically with decimation. This is expected: geometric-mean averaging smooths trajectory dispersion. AitVar measures geometric spread, which is resolution-dependent."
9676
},
97-
"cv_across_resolutions": 0.2852,
98-
"verdict": "APPROXIMATELY_CONSERVED",
99-
"significance_for_codawork": "Aitchison variance is the native CoDa dispersion measure. Its conservation under decimation means the time transformer preserves the fundamental geometric structure of the simplex across resolutions."
77+
"tv_integral": {
78+
"daily_to_annual_change": "-99.7%",
79+
"verdict": "NOT_CONSERVED",
80+
"note": "TV integral collapses under decimation. Expected: fewer observations means fewer transitions."
81+
},
82+
"shannon_entropy": {
83+
"daily_value": 2.069863,
84+
"annual_value": 2.073492,
85+
"daily_to_annual_change": "+0.18%",
86+
"verdict": "NEAR_INVARIANT",
87+
"note": "Shannon entropy is empirically stable across 341:1 compression. This is the EITT finding. See EITT_FINDING.md and EITT_Midrange_Confirmation_001.json for independent confirmation."
88+
},
89+
"summary": "Of three conservation candidates, only Shannon entropy survives decimation. Aitchison variance and TV integral are negative controls — they demonstrate that the geometric mean DOES change trajectory properties, making entropy's stability the surprising result."
10090
},
10191
"spectral_independence_by_resolution": {
10292
"Daily": {
@@ -142,74 +132,19 @@
142132
},
143133
"rt60_analogue": {
144134
"COVID_lockdown": {
145-
"France": {
146-
"etc_tau_weeks": 4.54,
147-
"rt60_weeks": 13.6,
148-
"rt60_months": 3.1,
149-
"decay_class": "FAST"
150-
},
151-
"Spain": {
152-
"etc_tau_weeks": 5.44,
153-
"rt60_weeks": 16.3,
154-
"rt60_months": 3.8,
155-
"decay_class": "FAST"
156-
},
157-
"Netherlands": {
158-
"etc_tau_weeks": 11.44,
159-
"rt60_weeks": 34.3,
160-
"rt60_months": 7.9,
161-
"decay_class": "FAST"
162-
},
163-
"Poland": {
164-
"etc_tau_weeks": 24.35,
165-
"rt60_weeks": 73.1,
166-
"rt60_months": 16.9,
167-
"decay_class": "MEDIUM"
168-
}
135+
"France": { "etc_tau_weeks": 4.54, "rt60_weeks": 13.6, "rt60_months": 3.1, "decay_class": "FAST" },
136+
"Spain": { "etc_tau_weeks": 5.44, "rt60_weeks": 16.3, "rt60_months": 3.8, "decay_class": "FAST" },
137+
"Netherlands": { "etc_tau_weeks": 11.44, "rt60_weeks": 34.3, "rt60_months": 7.9, "decay_class": "FAST" },
138+
"Poland": { "etc_tau_weeks": 24.35, "rt60_weeks": 73.1, "rt60_months": 16.9, "decay_class": "MEDIUM" }
169139
},
170140
"Energy_crisis_2022": {
171-
"Germany": {
172-
"etc_tau_weeks": 33.12,
173-
"rt60_weeks": 99.4,
174-
"rt60_months": 22.9,
175-
"decay_class": "SLOW"
176-
},
177-
"France": {
178-
"etc_tau_weeks": 79.73,
179-
"rt60_weeks": 239.2,
180-
"rt60_months": 55.2,
181-
"decay_class": "SLOW"
182-
},
183-
"Spain": {
184-
"etc_tau_weeks": 59.72,
185-
"rt60_weeks": 179.2,
186-
"rt60_months": 41.4,
187-
"decay_class": "SLOW"
188-
},
189-
"Italy": {
190-
"etc_tau_weeks": 67.02,
191-
"rt60_weeks": 201.1,
192-
"rt60_months": 46.4,
193-
"decay_class": "SLOW"
194-
},
195-
"Netherlands": {
196-
"etc_tau_weeks": 13.01,
197-
"rt60_weeks": 39.0,
198-
"rt60_months": 9.0,
199-
"decay_class": "MEDIUM"
200-
},
201-
"Austria": {
202-
"etc_tau_weeks": 36.36,
203-
"rt60_weeks": 109.1,
204-
"rt60_months": 25.2,
205-
"decay_class": "SLOW"
206-
},
207-
"Sweden": {
208-
"etc_tau_weeks": 51.34,
209-
"rt60_weeks": 154.0,
210-
"rt60_months": 35.6,
211-
"decay_class": "SLOW"
212-
}
141+
"Germany": { "etc_tau_weeks": 33.12, "rt60_weeks": 99.4, "rt60_months": 22.9, "decay_class": "SLOW" },
142+
"France": { "etc_tau_weeks": 79.73, "rt60_weeks": 239.2, "rt60_months": 55.2, "decay_class": "SLOW" },
143+
"Spain": { "etc_tau_weeks": 59.72, "rt60_weeks": 179.2, "rt60_months": 41.4, "decay_class": "SLOW" },
144+
"Italy": { "etc_tau_weeks": 67.02, "rt60_weeks": 201.1, "rt60_months": 46.4, "decay_class": "SLOW" },
145+
"Netherlands": { "etc_tau_weeks": 13.01, "rt60_weeks": 39.0, "rt60_months": 9.0, "decay_class": "MEDIUM" },
146+
"Austria": { "etc_tau_weeks": 36.36, "rt60_weeks": 109.1, "rt60_months": 25.2, "decay_class": "SLOW" },
147+
"Sweden": { "etc_tau_weeks": 51.34, "rt60_weeks": 154.0, "rt60_months": 35.6, "decay_class": "SLOW" }
213148
}
214149
},
215150
"yearly_aitchison_variance": {
@@ -227,15 +162,17 @@
227162
"2026": 0.153378
228163
},
229164
"findings": [
230-
"Aitchison variance MODERATELY CONSERVED across resolutions (CV = 0.2852)",
231-
"Spectral independence IMPROVES at Quarterly resolution (mean |r| = 0.850 vs daily 0.867)",
232-
"TIME TRANSFORMER has its conserved quantity: Aitchison variance survives decimation via geometric-mean anti-aliasing. The winding ratio is mathematically grounded.",
233-
"TV integral is NOT conserved (daily/annual ratio = 315.5x). This confirms TV is resolution-dependent as expected."
165+
"Aitchison variance is NOT conserved under decimation (drops 55% daily→annual). It is a negative control.",
166+
"TV integral is NOT conserved (drops 99.7%). Also a negative control.",
167+
"Shannon entropy IS near-invariant (+0.18% across 341:1 compression). This is the EITT finding.",
168+
"The geometric mean smooths trajectory dispersion (AitVar, TV) while preserving compositional information content (entropy).",
169+
"Spectral independence does not hold on this dataset at any resolution — diagnostics are correlated (mean |r| > 0.85)."
234170
],
235171
"time_transformer_status": {
236-
"conserved_quantity": "Aitchison variance",
172+
"conserved_quantity": "Shannon entropy (not Aitchison variance as originally hypothesized)",
237173
"anti_aliasing_filter": "Compositional geometric mean",
238-
"winding_ratio": "Variable (365:52:12:4:1 for daily\u2192weekly\u2192monthly\u2192quarterly\u2192annual)",
239-
"theorem_or_tool": "APPROXIMATE_THEOREM"
174+
"winding_ratio": "Variable (365:52:12:4:1 for daily→weekly→monthly→quarterly→annual)",
175+
"status": "EMPIRICAL_FINDING — near-invariance demonstrated, not analytically proven",
176+
"boundary_condition": "Temporal autocorrelation required. Fails on iid random compositions and oscillating extremes."
240177
}
241-
}
178+
}

0 commit comments

Comments
 (0)