docs/research/2026-11-05-estate-rule-sim/REPORT.md

@@ -1,6 +1,6 @@
 # Estate-rule sim: report (2026-11-05)
 
-Question: does the unified estate rule (estate votes decide the estate's vote) dampen populism? Spec: `SPEC.md` (written first, four revisions, each before the results it affects). Numbers: `results.md` (235 cells, 40 replicates x 500 motions each, paired draws). Rerun: `python3 -I run.py` (about 11 minutes on 8 jobs; `--quick` for a smoke; `python3 -I test_estatesim.py` for the 52 tests). Output is byte-identical across reruns and across `--jobs` values.
+Question: does the unified estate rule (estate votes decide the estate's vote) dampen populism? Spec: `SPEC.md` (written first, four revisions, each before the results it affects). Numbers: `results.md` (235 cells, 40 replicates x 500 motions each, paired draws). Rerun: `python3 -I run.py` (about 11 minutes on 8 jobs; `--quick` for a smoke; `python3 -I test_estatesim.py` for the 54 tests). Output is byte-identical across reruns and across `--jobs` values.
 
 ## Answer
 
@@ -41,13 +41,13 @@ Limits specific to this result: copying is triggered only when the holder is ove
 
 ## Purchased stake (E6, SPEC section 5c)
 
-Static weight analysis, not a motion simulation: it measures weight share, not PS or MT. Weight w = 1 + log_b(amount/unit), 0 below unit, per-estate b and unit (defaults b = 10, unit = 10 EUR, my choices, in SPEC 5c). The harness had no contribution mechanism, so contribution hours are a new per-agent input with their own per-estate conversion (defaults b = 10, unit = 10 hours); they add to the euro weight and matter to no buyer result below.
+Static weight analysis, not a motion simulation: it measures weight share, not PS or MT. Weight w = 1 + log_b(amount/unit), 0 at amount <= unit/b, per-estate b and unit (defaults b = 10, unit = 10 EUR, my choices, in SPEC 5c). The harness had no contribution mechanism, so contribution hours are a new per-agent input with their own per-estate conversion (defaults b = 10, unit = 10 hours); they add to the euro weight and matter to no buyer result below.
 
 **The working hypothesis, that logarithmic weight bounds buyout power, is only half true here, and the true half is not the log's doing.**
 
-- **Within the estate the log does not bound a million-euro buyer.** Against the harness's 4-patron roll (Pareto(1.16) donations from 10 EUR, 40 seeds) the buyer holds 0.524 +/- 0.008 of Patrons weight and alone decides the Patrons estate (share above one half) in 85% of seeds. The log shrinks the buyer from 100% (linear weight) to about half; it does not take it below a majority of a 4-person estate. This is the harness's own cell (roll 4, unit 10 EUR, b = 10), not a typical one. Swept over unit {1, 10, 100} EUR and roll {4, 40, 400} (40 seeds each, table in results.md) the buyer's mean share of Patrons weight runs from 0.007 to 0.953, and the buyer alone decides the estate in 0 to 100% of seeds depending on the cell (0.85 at the headline cell, 0.65 at roll 40 with unit 100, 1.00 at roll 4 with unit 100, 0.00 in the other six). The roll size, Pareto scale and unit are placeholders; the interval, not the point, is the finding. The weight is per identity, so all of this assumes one identity per buyer (next bullet).
+- **Within the estate the log does not bound a million-euro buyer.** Against the harness's 4-patron roll (Pareto(1.16) donations from 10 EUR, 40 seeds) the buyer holds 0.524 +/- 0.008 of Patrons weight and alone decides the Patrons estate (share above one half) in 85% of seeds. The log shrinks the buyer from 100% (linear weight) to about half; it does not take it below a majority of a 4-person estate. This is the harness's own cell (roll 4, unit 10 EUR, b = 10), not a typical one. Swept over unit {1, 10, 100} EUR and roll {4, 40, 400} (40 seeds each, table in results.md) the buyer's mean share of Patrons weight runs from 0.007 to 0.777, and the buyer alone decides the estate in 0 to 100% of seeds depending on the cell (0.85 at the headline cell, 1.00 at roll 4 with unit 100, 0.00 in the other seven). The roll size, Pareto scale and unit are placeholders; the interval, not the point, is the finding. The weight is per identity, so all of this assumes one identity per buyer (next bullet).
 - **At council level the bound comes from the estate weights.** With all four estates live the buyer's council share is 0.131 (equal weights) or 0.052 (minds-heavy), below the Patrons weight W_Patrons by construction; the half-influence cap never binds in 6,480 cell-seeds. Linear weight would give 0.25 and 0.10: the log halves the buyer's share, the estate structure sets its ceiling.
-- **The half-influence cap binds only when other estates are silent.** Fraction of (cell, seed) in which council share x >= .5 over 162 cells (b x unit x roll x amount x weights) x 40 seeds: all four live 0.000; Patrons + Minds live 0.044 (all of it the degenerate case where no other patron clears the unit, so there is nothing to cut against: unenforceable); Patrons alone live 0.222 (0.148 of cells bind in every seed, 0.089 of cell-seeds unenforceable). It binds more at small rolls (Patrons alone: 0.669 at roll 4 and b = 2 down to 0.000 at roll 400) and with a smaller log base. The Patrons-alone scenario is the renormalization case of prior section 10 (drop non-voting estates); how likely it is in practice is not a sim output.
+- **The half-influence cap binds only when other estates are silent.** Fraction of (cell, seed) in which council share x >= .5 over 162 cells (b x unit x roll x amount x weights) x 40 seeds: all four live 0.000; Patrons + Minds live 0.008 (all of it the degenerate case where no other patron clears the unit, so there is nothing to cut against: unenforceable); Patrons alone live 0.165 (0.099 of cells bind in every seed, 0.017 of cell-seeds unenforceable). It binds more at small rolls (Patrons alone: 0.669 at roll 4 and b = 2 down to 0.000 at roll 400) and with a smaller log base. The Patrons-alone scenario is the renormalization case of prior section 10 (drop non-voting estates); how likely it is in practice is not a sim output.
 - **Splitting wins, by orders of magnitude.** The same 1,000,000 EUR over k identities multiplies weight by 1.9 (k = 2), 8.3 (k = 10), 66.7 (k = 100), 500 (k = 1000), and 16,667 at k = amount/unit = 100,000 (each fake identity buying exactly the unit). The multiplier is (amount/unit) / (1 + log_b(amount/unit)); for b = 10, unit = 10 it is 250 at 10,000 EUR, 2,000 at 100,000 EUR. With k = 10 fake identities the buyer's Patrons-alone share is 0.901, with k = 2 it is 0.676. This refutes the log as a purchase bound unless identities are scarce.
 - **The half-influence cap is per identity and splitting evades it.** In the Patrons-alone case the single identity trips the cap in 85% of seeds; at k = 2 no identity does (each holds 0.34) while the joint share is 0.676, in every seed. A cap on a person's influence needs an identity oracle the harness does not have.
 - **SPEC names no sybil defence** (the charter's frozen roll, A6, bounds joins after notice, not pre-notice buying of identities), so none is implemented as policy. Three candidates are quantified in results.md and none is chosen: a per-person weight cap does not help (it caps the honest single purchase and the fakes are each below it; 100,000x at cap 1); a raised unit floor reduces the multiplier (250 at 1,000 EUR, 5 at 100,000 EUR, 1.0 only at 1,000,000 EUR, where no purchase under the buyer's amount buys any weight), so it neutralises splitting only by pricing out everyone smaller; a per-identity cost neutralises only at about half the budget (bisection values 49.3%, 49.8%, 49.95% of 10,000, 100,000, 1,000,000 EUR; the threshold is c = amount/2, where a second identity is left with nothing to buy), so it would also tax the honest buyer's single identity at that rate. The choice between pricing identities, verifying people or bounding total weight per verified person is a design fork left for the operator. Nothing here rules it.

docs/research/2026-11-05-estate-rule-sim/SPEC.md

@@ -95,7 +95,7 @@ Serves `heimdall-body:follow_up:chat-s1946-1946`.
 
 Serves the purchased-stake brief (operator relayed: Patron vote power is logarithmic in donation, prior section 4; operator influence strictly below half, ruling `operator-influence-below-half`, prior section 10). Not a motion simulation: a static weight analysis, so it measures weight share and decisiveness, not PS or MT.
 
-**Weight.** A purchase of `amount` EUR weighs w = 1 + log_b(amount/unit): 1 at amount = unit, 0 below unit (below the unit buys no weight, never negative). Each estate has its own conversion, set through `Config.overrides` entries `(estate, key, value)` with keys `euro_b`, `euro_unit`, `hours_b`, `hours_unit` (defaults in `STAKE_BASE`). Only Patrons (euros) and Members (hours) carry stake; Minds are counted once and Users are one-each, so both weigh 1.
+**Weight.** A purchase of `amount` EUR weighs w = 1 + log_b(amount/unit): 1 at amount = unit, continuous below it, 0 at amount <= unit/b (never negative). Each estate has its own conversion, set through `Config.overrides` entries `(estate, key, value)` with keys `euro_b`, `euro_unit`, `hours_b`, `hours_unit` (defaults in `STAKE_BASE`). Only Patrons (euros) and Members (hours) carry stake; Minds are counted once and Users are one-each, so both weigh 1.
 
 **Defaults chosen (assumptions, not rulings; the brief gave none).** Patrons and Members alike: euro b = 10, unit = 10 EUR; hours b = 10, unit = 10 hours. b = 10 reads as "each tenfold purchase adds one vote of weight", the simplest reading of the operator's "logarithmic"; 10 EUR is the smallest ordinary Patron donation in the prior ladder (prior section 4: 10, 50, 200, 5000); 10 hours is roughly a working day or so of contribution. The sweep varies b over {2, 10, 100} and unit over {1, 10, 100} EUR; hours are not swept because no buyer outcome depends on them (see below).
 

docs/research/2026-11-05-estate-rule-sim/results.md

@@ -793,7 +793,7 @@ PS by category threshold:
 
 ## E6 purchased stake: logarithmic weight, splitting, and the half-influence cap (SPEC section 5c)
 
-Static weight analysis (no motions are simulated, so no PS or MT): a buyer joins the Patrons estate with one purchase; the 4-patron roll of the harness (and 40, 400) holds Pareto(1.16) donations from 10 EUR, 40 seeds each. Weight w = 1 + log_b(amount/unit), 0 below unit; defaults b = 10, unit = 10 EUR. Share s is the buyer's share of Patrons weight; x is its share of council weight (estate weight W x s over the live estates' weights); the cap binds iff x >= .5.
+Static weight analysis (no motions are simulated, so no PS or MT): a buyer joins the Patrons estate with one purchase; the 4-patron roll of the harness (and 40, 400) holds Pareto(1.16) donations from 10 EUR, 40 seeds each. Weight w = 1 + log_b(amount/unit), 0 at amount <= unit/b; defaults b = 10, unit = 10 EUR. Share s is the buyer's share of Patrons weight; x is its share of council weight (estate weight W x s over the live estates' weights); the cap binds iff x >= .5.
 
 **Million-euro buyer, defaults, Patrons roll 4 (mean over seeds, 95% interval); linear = weight proportional to amount, the counterfactual the log is meant to beat**
 
@@ -812,24 +812,24 @@ Static weight analysis (no motions are simulated, so no PS or MT): a buyer joins
 |---|---|---|---|
 | 1 | 0.425 ±0.005 (0.00) | 0.069 ±0.000 (0.00) | 0.007 ±0.000 (0.00) |
 | 10 | 0.524 ±0.008 (0.85) | 0.098 ±0.001 (0.00) | 0.011 ±0.000 (0.00) |
-| 100 | 0.953 ±0.028 (1.00) | 0.579 ±0.040 (0.65) | 0.118 ±0.004 (0.00) |
+| 100 | 0.777 ±0.023 (1.00) | 0.251 ±0.008 (0.00) | 0.032 ±0.000 (0.00) |
 
-Interval over the swept cells: s from 0.007 to 0.953. The 0.524 headline is the harness's own cell (roll 4, unit 10), not a typical one: the buyer's majority of the estate depends on how few other patrons there are.
+Interval over the swept cells: s from 0.007 to 0.777. The 0.524 headline is the harness's own cell (roll 4, unit 10), not a typical one: the buyer's majority of the estate depends on how few other patrons there are.
 
 **Cap-binding rate over the sweep (b, unit, roll, amount, weights x live set; every cell run on every seed)**
 
 | live estates | cells | cells x seeds | binding (cell, seed) | cells binding in every seed | cells never binding | binding but unenforceable |
 |---|---|---|---|---|---|---|
 | all four estates | 162 | 6480 | 0.000 | 0.000 | 1.000 | 0.000 |
-| Patrons + Minds | 162 | 6480 | 0.044 | 0.000 | 0.889 | 0.044 |
-| Patrons alone | 162 | 6480 | 0.222 | 0.148 | 0.704 | 0.089 |
+| Patrons + Minds | 162 | 6480 | 0.008 | 0.000 | 0.981 | 0.008 |
+| Patrons alone | 162 | 6480 | 0.165 | 0.099 | 0.790 | 0.017 |
 
 Binding rate in the Patrons-alone scenario by Patrons roll and by log base (fraction of cells x seeds):
 
 | roll | b=2 | b=10 | b=100 |
 |---|---|---|---|
-| 4 | 0.669 | 0.447 | 0.333 |
-| 40 | 0.286 | 0.169 | 0.094 |
+| 4 | 0.669 | 0.447 | 0.114 |
+| 40 | 0.250 | 0.000 | 0.000 |
 | 400 | 0.000 | 0.000 | 0.000 |
 
 **Splitting: the same total split over k identities (defaults, one honest identity = k 1). Multiplier = total weight of the split / weight of the single purchase**
@@ -877,7 +877,7 @@ Best multiplier at 1,000,000 EUR by log base and unit (b rows, unit columns):
 
 | hours | 5 | 10 | 100 | 1000 | 10000 |
 |---|---|---|---|---|---|
-| weight | 0.00 | 1.00 | 2.00 | 3.00 | 4.00 |
+| weight | 0.70 | 1.00 | 2.00 | 3.00 | 4.00 |
 
 ## Claim tally over all cells (SPEC section 8)
 

docs/research/2026-11-05-estate-rule-sim/run.py

@@ -228,7 +228,7 @@ def stake_section(quick):
     L = ["## E6 purchased stake: logarithmic weight, splitting, and the half-influence cap (SPEC section 5c)", "",
          "Static weight analysis (no motions are simulated, so no PS or MT): a buyer joins the Patrons estate with one purchase; "
          f"the {E.ROLL['Patrons']}-patron roll of the harness (and 40, 400) holds Pareto({E.PARETO_ALPHA}) donations from {E.PARETO_XM:.0f} EUR, "
-         f"{seeds} seeds each. Weight w = 1 + log_b(amount/unit), 0 below unit; defaults b = {E.STAKE_BASE['Patrons']['euro_b']:.0f}, "
+         f"{seeds} seeds each. Weight w = 1 + log_b(amount/unit), 0 at amount <= unit/b; defaults b = {E.STAKE_BASE['Patrons']['euro_b']:.0f}, "
          f"unit = {E.STAKE_BASE['Patrons']['euro_unit']:.0f} EUR. Share s is the buyer's share of Patrons weight; x is its share of council weight "
          "(estate weight W x s over the live estates' weights); the cap binds iff x >= .5.", ""]
     ladders = {(n, s): E.stake_ladder(n, s) for n in rolls for s in range(seeds)}
@@ -306,7 +306,7 @@ def stake_section(quick):
         w1 = E.log_weight(a, b0, u0)
         bt, bk = E.best_split(a, b0, u0)
         L.append(f"| {a:g} | {w1:.2f} | " + " | ".join(
-            f"{E.split_weight(a, k, b0, u0)[0] / w1:.1f}" if a / k >= u0 else "0 (below unit)" for k in (2, 10, 100, 1000)) +
+            f"{E.split_weight(a, k, b0, u0)[0] / w1:.1f}" for k in (2, 10, 100, 1000)) +
             f" | {bk} | {bt / w1:.0f} |")
     L += ["", "Best multiplier at 1,000,000 EUR by log base and unit (b rows, unit columns):", "",
           "| b | " + " | ".join(f"unit={u:g}" for u in units) + " |", "|---|" + "---|" * len(units)]