assembly-economics/models/GADM-0.3.md

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# Generative Assembly Dynamics Model — GADM-0.3

**Status:** complete for ASSEMBLY-WP-0005, exploratory. Power channels
(§ 2, T03), wealth separated from power (§ 3, T04), attention recalibration
and organism grid (§ 4, T05), life-cycle cohorts (§ 5, T06). Open items are
in § 6 and ASSEMBLY-WP-0006.

GADM-0.3 builds on GADM-0.2 (`GADM-0.2.md`). Everything not described here is
unchanged; the implementation reuses `gadm02.py`. Time unit: one year.

---

## 1. Why channels

GADM-0.2's sensitivity analysis showed that the membrane-control and
lineage-diffusion levers dominate outcomes. A single P stock cannot show
*which* channel drives domination, or whether channels behave differently.
`GADM-0.3-Candidates.md` § 2.2 proposed splitting P into channel sub-stocks.

---

## 2. Power channels (T03)

### 2.1 Channels

| Code | Channel | Driver d_k | Counter C_k |
|---|---|---|---|
| `Pm` | market | p₁ V_sel (1 − B): private returns of success | B + N: broad claims and entry |
| `Pi` | infrastructure | p_i K (1 − std): capacity under closed standards | X · std + 0.1: interoperable commons |
| `Pd` | discovery / attention | p₂ disc (0.5 + 0.5 K_Ω) | (1 − disc) Q + 0.1: plural discovery |
| `Pmem` | membrane | p₃ K_Ω (1 − m) | m + 0.1: user/community control |
| `Plin` | lineage | p₄ K_Ω (1 − L) | L + 0.1: lineage diffusion |
| `Ppol` | political / institutional | p_pol · P_econ · (1 − B) | Q S: checks |

`P_econ` aggregates the five economic channels. The political channel
converts economic control into political influence.

### 2.2 Dynamics

\[
\dot P_k = (d_k + r_k P_k^2)(1-P_k) - c_k C_k P_k
\]

The superlinear term \(r_k P_k^2\) represents increasing returns to control.
It allows thresholds: with drivers held fixed, a channel can have a low and a
high stable equilibrium separated by an unstable one.

For the lineage channel, self-reinforcement grows with learning with use
(loop R7): \(r_{lin} = r(1 + lw \cdot K_\Omega Q)\).

### 2.3 Aggregation

\[
P = 1 - \prod_k (1-P_k)^{1/6}
\]

One fully dominant channel gives P = 1, and equal channels give P equal to
that common value.

*Rejected alternative:* the plain product \(1-\prod_k(1-P_k)\) compounds
moderate channels (six channels at 0.5 give P = 0.98) and drove P to 1 in
almost every scenario.

### 2.4 Calibration

- Initial channels: market 0.50, infrastructure 0.45, discovery 0.50,
  membrane 0.05, lineage 0.05, political 0.50 (total P ≈ 0.37; GADM-0.2:
  0.40). Membrane and lineage start low because organism capability starts at
  0.05.
- r_k = 0.3 for all channels (0.4 for discovery). This is a uniform
  assumption, not an estimate.
- The counter coefficients c_k are computed by `calibrate()` so that every
  channel starts in equilibrium in the baseline.

**A calibration pitfall, found and guarded against.** The first calibration
put the market, membrane and lineage channels exactly on their *unstable*
root, so small drift decided which way each went. A channel's starting
equilibrium is stable when \(P_0 \ge 0.5\) or \(r < d/(P_0^2(1-2P_0))\). The
initial values above satisfy this, and a unit test now checks that every
calibrated channel starts at a stable equilibrium.

### 2.5 Scenario results

Final values at t = 100 years:

| Scenario | VFAC (0.2 → 0.3) | P (0.2 → 0.3) | market | infra | discovery | membrane | lineage | political |
|---|---|---|---|---|---|---|---|---|
| Baseline | 0.461 → 0.345 | 0.52 → 0.79 | 0.80 | 0.74 | 0.69 | 0.79 | 0.84 | 0.83 |
| Automated capitalism | 0.317 → 0.248 | 0.73 → 0.89 | 0.90 | 0.78 | 0.81 | 0.91 | 0.93 | 0.92 |
| Dividend abundance | 0.445 → 0.338 | 0.54 → 0.79 | 0.76 | 0.76 | 0.70 | 0.80 | 0.86 | 0.82 |
| Universal venture access | 0.487 → 0.371 | 0.52 → 0.78 | 0.79 | 0.74 | 0.69 | 0.79 | 0.84 | 0.80 |
| Commons-rich | 0.544 → 0.466 | 0.48 → 0.70 | 0.73 | **0.05** | 0.61 | 0.79 | 0.86 | 0.75 |
| Attention oligopoly | 0.372 → 0.296 | 0.69 → 0.86 | 0.81 | 0.76 | **0.91** | 0.91 | 0.83 | 0.87 |
| Generative regime | 0.650 → **0.692** | 0.31 → **0.14** | 0.39 | 0.05 | 0.08 | 0.09 | 0.14 | 0.04 |
| — concentrated lineages | 0.530 → 0.452 | 0.50 → 0.70 | 0.68 | 0.08 | 0.08 | **0.86** | **0.95** | 0.60 |
| — attention extraction | 0.575 → 0.599 | 0.41 → 0.32 | 0.27 | 0.06 | **0.80** | 0.08 | 0.12 | 0.11 |

### 2.6 Readings

These are model behaviour under assumed structure, not claims about
economies.

1. **Domination polarizes.** With channels and increasing returns, every
   non-generative regime ends with P between 0.70 and 0.89 (GADM-0.2:
   0.48–0.73), while the generative regime falls to 0.14. The VFAC spread
   widens accordingly. This sharpening comes directly from the assumed
   self-reinforcement r.
2. **Each regime defeats only the channels it targets.** The commons-rich
   regime removes infrastructure control (0.74 → 0.05) but leaves the other
   five channels high. Dividends move none of them. Only the generative
   regime, which acts on several levers at once, keeps all channels low.
3. **Organism channels spill into politics.** In the concentrated-lineages
   variant, membrane and lineage control (0.86, 0.95) raise political control
   to 0.60, even though market, infrastructure and discovery channels stay
   low.
4. **Single-channel domination is visible, not hidden.** In the
   attention-extraction variant, discovery control reaches 0.80 while total P
   is only 0.32. The channel view shows a concentration that the aggregate
   understates. Report channels, not just P.

### 2.7 Hypotheses P1 and P2

Full tables: `simulations/gadm02/results/power_channels.md`.

**P1: channels become self-sustaining above a threshold. Mostly not
supported over 100 years.** Sweeping each channel's initial value, the final
value is the same for most channels, whatever the start: drifting drivers
dominate. There are two exceptions:

- **Lineage, generative regime: hysteresis.** If lineage control starts
  above about 0.25–0.30, it locks in at 0.68, despite high lineage diffusion
  (L = 0.8). Below that, it stays at about 0.15.
- **Market, baseline:** only a market that starts near zero stays low (0.22).
  Any start above 0.15 ends at about 0.8.

**P2: membrane/lineage control plus learning with use forms a
natural-monopoly regime unless L exceeds a critical value. Supported.** The
critical L (final lineage control below 0.5) rises with learning
amplification `lw`:

| lw | Baseline | Generative regime |
|---|---|---|
| 0 | 0.50 | 0.60 |
| 2 (default) | 0.60 | 0.80 |
| 4 | 0.70 | 0.85 |

### 2.8 Implications for the research program

- **Timing matters (WS-12, transition dynamics).** The lineage hysteresis
  means that lineage governance has to come *before* concentration. A
  generative regime introduced after lineages concentrate does not undo it in
  this model.
- **Stronger organism learning raises the governance bar.** The more
  organisms learn from use, the more lineage diffusion is needed (P2). This
  ties WS-13 (organism lens) to WS-07 (power).
- **Report channels, not just P** (reading 4). Added to the metrics catalog
  as a requirement for the domination bundle.

### 2.9 Limitations

- r_k is uniform and assumed. The channel counters include ad-hoc floors
  (+0.1) so that no counter vanishes entirely.
- The baseline market channel starts in its high basin (start 0.50, threshold
  about 0.42). The initial split across channels is a modeling choice.
- Thresholds were computed with other stocks moving. Frozen-state roots
  (`channel_roots()`) differ from long-run behaviour.
- Python pitfall seen during development: a stale bytecode cache can mask
  quick same-size edits. Use `python3 -B` after rapid edits.

---

## 3. Wealth separated from power (T04)

### 3.1 Wealth stock

\[
\dot W = a_w (1-B)\,Y^*\,(1-W) - (d_w + t_w\,wtax)\,W
\]

W is wealth concentration: it accumulates from privately captured returns
(the part of output not reaching the broad population, 1 − B) and dissipates
through `d_w` (inheritance splitting, failure, competition) and a wealth tax
`wtax` ∈ [0, 1]. Initial W = 0.5.

### 3.2 Conversion into power

Wealth converts into the **market** and **political** channels only:

\[
d_m \mathrel{+}= \kappa W,\qquad d_{pol} \mathrel{+}= \kappa W,\qquad
\kappa = k_w (1 - Q S)
\]

Epistemic capacity and cohesion (checks) reduce conversion. Membrane,
lineage, infrastructure and discovery control do not depend on wealth: they
come from organism ownership, capacity and discovery structure. This is the
"wealth is not power" separation that GADM-0.1 § 13 asks for.

W is not a VFAC factor. Inequality of wealth matters in this model only
through what it converts into.

Setting `wealth_on = 0` (helper `gadm03.t03_params()`) reproduces the T03
model exactly. This was verified: `power_channels.py` output is identical
before and after T04.

### 3.3 Hypothesis P3: supported

*P3: wealth taxation alone does not bound P when the membrane channel
dominates.* Full tables: `simulations/gadm02/results/wealth.md`.

| Setting | W (wtax 0 → 1) | market | political | membrane | P |
|---|---|---|---|---|---|
| Membrane/lineage-dominated | 0.37 → 0.12 | 0.62 → 0.44 | 0.54 → 0.38 | 0.86 → 0.86 | 0.68 → 0.64 |
| Baseline | 0.37 → 0.12 | 0.77 → 0.75 | 0.80 → 0.79 | 0.79 → 0.79 | 0.78 → 0.77 |
| Automated capitalism | 0.51 → 0.19 | 0.89 → 0.88 | 0.91 → 0.90 | 0.91 → 0.91 | 0.88 → 0.88 |

Robustness to the conversion strength (calibration recomputed for each
value):

| k_w | Setting | P at wtax 0 → 1 | market at wtax 0 → 1 |
|---|---|---|---|
| 0.04 (default) | baseline | 0.78 → 0.77 | 0.77 → 0.75 |
| 0.20 | baseline | 0.75 → 0.71 | 0.68 → 0.45 |
| 0.04 (default) | membrane/lineage-dominated | 0.68 → 0.64 | 0.62 → 0.44 |
| 0.20 | membrane/lineage-dominated | 0.66 → 0.61 | 0.51 → 0.21 |

### 3.4 Readings

1. **P3 holds and is robust.** A full wealth tax lowers total domination by
   only 0.01–0.05 across settings and conversion strengths, because
   membrane and lineage control do not run on wealth. Bounding organism-era
   domination needs organism-specific levers (membrane control `m`, lineage
   diffusion `L`), consistent with the GADM-0.2 sensitivity results.
2. **Wealth taxation does reduce the channels it reaches,** but how much
   depends on the conversion strength. At the default `k_w`, channels already
   locked in their high state (baseline, automated capitalism) barely
   respond. At five times the conversion, the tax pulls the market channel
   down substantially even at baseline. The earlier statement "taxing wealth
   cannot unlock entrenched channels" therefore depends on `k_w` and is not
   claimed.
3. **Adding wealth changes the scenario results only slightly** (P −0.00 to
   −0.03 against the T03 stage). Part of this is a calibration effect: the
   counters were calibrated at W = 0.5, while W settles at about 0.25, so the
   wealth driver weakens over time. The within-model tax sweep is not
   affected by this.

### 3.5 Limitations

- W is not initialised at its own equilibrium (see reading 3).
- `k_w` is assumed; reading 2 shows a qualitative dependence on it.
- Wealth does not buy discovery or infrastructure control in this model,
  although it plausibly could (through acquisitions). This is a deliberate
  simplification to make P3 testable, and it biases the result toward P3.

---

## 4. Attention recalibration and the organism grid (T05)

### 4.1 Attention extraction against time-use evidence

GADM-0.2 flagged attention dynamics as too weak: under its `aext` = 0.12,
baseline attention headroom A *rose* from 0.50 to 0.65.

Evidence used as the calibration anchor:

- **American Time Use Survey 2023:** about 5.2 hours of leisure per day, of
  which TV takes about 2.7 hours, over half (BLS).
- **Social media:** roughly 2 h 20 min to 2 h 25 min per day for the average
  internet user worldwide (DataReportal/GWI, Statista).

Together these suggest that engagement-funded media already claim around half
of discretionary time. Target: baseline A ≈ 0.45–0.5 (current state),
falling to about 0.3 under an extraction regime.

Solving the A equilibrium for these targets gives **`aext` = 0.275**:

| Scenario | A (GADM-0.2 aext) | A (recalibrated) |
|---|---|---|
| Baseline | 0.69 | 0.49 |
| Attention oligopoly | 0.57 | 0.37 |
| Generative regime | 0.77 | 0.60 |
| Generative, attention extraction | 0.44 | 0.26 |

VFAC falls by 0.015–0.04 across scenarios. P and the scenario ordering are
unchanged. This is an order-of-magnitude anchor, not an estimate: the
mapping from hours of engagement media to "unclaimed attention" is itself an
assumption (see the Goodhart note in `metrics/MetricsCatalog.md`, A).

The T03 and T04 stages remain reproducible (`t03_params()`,
`t04_params()`), verified by identical output.

### 4.2 The 2 × 2 × 2 organism grid

Axes (from `InformationOrganismsInGADM.md` § 5): **lineage ownership**
(concentrated: L = lin_open = 0.1 / diffuse: 0.8), **membrane control**
(operator: m = 0.2 / user-community: 0.8), **attention regime** (extraction:
x_att = 0.9 / protected: 0.2). Each grid is run on the baseline and the
generative background. Full tables:
`simulations/gadm02/results/organism_grid.md`.

Factorial effects (average change from the first to the second level):

| Effect | VFAC, baseline bg. | VFAC, generative bg. | P, baseline bg. | P, generative bg. |
|---|---|---|---|---|
| lineage diffuse | **+0.130** | **+0.127** | −0.242 | −0.340 |
| membrane user-controlled | +0.090 | +0.089 | −0.175 | −0.216 |
| attention protected | +0.046 | +0.060 | −0.009 | +0.002 |
| lineage × membrane | +0.040 | −0.005 | −0.093 | −0.032 |
| other interactions | ≤ 0.011 | ≤ 0.006 | ≤ 0.006 | ≤ 0.005 |

Consistency check: the (diffuse, user, protected) corner on the generative
background reproduces the generative regime exactly (VFAC 0.672).

### 4.3 Readings

1. **Lineage ownership is the strongest organism lever,** ahead of membrane
   control, on both backgrounds. This agrees with the GADM-0.2 Sobol
   results only partly: there, `m` ranked above `L`. In the channel model,
   lineage concentration feeds a self-reinforcing channel with learning with
   use (P2), which strengthens its effect.
2. **Lineage and membrane governance are complements where governance is
   otherwise weak.** On the baseline background, doing both is worth +0.04
   VFAC beyond the sum of the parts. On the generative background, the
   interaction vanishes.
3. **Attention protection improves VFAC but not power.** It acts through
   attention headroom A, not through domination. In this model the attention
   regime and discovery concentration are separate levers. The
   attention-oligopoly scenario sets both.
4. **Better organism governance increases attention pressure unless attention
   is protected.** Under extraction, A is lowest in the best-governed corner
   (0.29 versus 0.36 at baseline), because better-governed organisms grow
   larger, and extraction scales with K_Ω. Organism governance and attention
   protection have to go together.
5. **Organism governance alone does not reach the generative regime.** On the
   baseline background, the best organism corner (VFAC 0.560) closes about 70 %
   of the gap to the full generative regime (0.672). The discovery channel
   stays at about 0.6, because it depends on discovery concentration, which
   is not an organism lever.

---

## 5. Life-cycle cohorts (T06)

Implemented in `simulations/gadm02/gadm03c.py` on top of the full GADM-0.3.

### 5.1 Structure

| Cohort | Ages | Carries | Notes |
|---|---|---|---|
| children `ch` | 0–19 | H | education, adult attention as care input, seniors' mentoring |
| working age `w` | 20–64 | H, A | GADM-0.2 learning; deskilling; mentoring inflow T_g; main care provider |
| seniors `s` | 65–79 | H, A | half learning rate, 1.5× depreciation; provides a share of care |
| very old `d` | 80+ | H | 3× depreciation; main care need |

Population counts follow births (`birth` × N_w) and ageing rates of 1/20,
1/45 and 1/15 per year, with deaths of the very old at 1/8 per year. At
`birth` = 1/45 (replacement), the age structure is stationary at about
23 / 51 / 17 / 9 %. A unit test checks this.

Aggregates passed to the rest of the model: H is population-weighted over all
cohorts; A is weighted over working age and seniors. G remains a single
aggregate.

Care need = 0.5 × share of children + 1.0 × share of very old. Its attention
cost is split between working age and seniors (`care_sen`), and reduced by
participation claims: relief = 1 − 3 × cp.

### 5.2 Effect on the scenarios

With cohorts, the baseline VFAC is 0.323 (0.334 without cohorts) and the
generative regime 0.656 (0.672). Capability and attention are a little lower,
because of senior depreciation and care load. The scenario ordering is
unchanged.

### 5.3 Hypotheses L1–L3

Full tables: `simulations/gadm02/results/life_cycle.md`.

**L1: strong intergenerational transfer lets an ageing society keep H.
Supported.**

| Demography | T_g = 0 | T_g = 0.05 | T_g = 0.15 |
|---|---|---|---|
| stable (ΔH over 100 years) | −0.043 | −0.032 | −0.011 |
| ageing, births at 75 % of replacement | −0.053 | −0.040 | −0.018 |

An ageing society with strong mentoring loses less capability than a stable
society without it. A first formulation of T_g, which transferred only
max(0, H_s − H_w), was inert because senior capability decays below
working-age capability. It was replaced by an inflow proportional to senior
capability and working-age headroom.

**L2: without recognized care participation, A falls fastest in the
working-age cohort. Conditionally supported.** Attention is lowest in
whichever cohort carries the higher care load *per person*:

- with seniors providing 10 % of care, working-age A is lowest (0.40 vs. 0.44);
- with 30 %, senior A is lowest (0.40 vs. 0.42), because there are fewer
  seniors to share it.

Care relief through participation claims (cp = 0.15) raises working-age
attention by 0.034–0.042 in every setting. So the post-work participation
channel directly protects the attention of carers.

**L3: education reaches working-age capability with a 15–20 year lag. Not
supported in this model.** Raising education intensity by 50 % raises
children's capability by +0.067, but working-age capability only by +0.010,
with half of the effect reached after about 9 years. The cause is structural:
working-age capability relaxes to its own conditions within roughly 8 years
(adult learning and depreciation rates). That washes out the cohort inflow,
so H has almost no memory of childhood. Human-capital research generally
finds persistent effects of early education, so this points to a missing
mechanism, not an empirical result. The fix belongs in GADM-0.4: split H
into a durable, education-formed component and a current component.

### 5.4 Further observations

- **Ageing is slow in this demography.** At 75 % of replacement fertility,
  the share of seniors and very old rises only from 0.26 to 0.29 in 100 years,
  and total care need barely changes (fewer children offset more very old at
  the chosen weights).
- **Aggregate H declines at baseline even with stationary demography**
  (−0.043), because of senior and very-old depreciation, which the
  single-population model did not have.

---

## 6. Open items (handed to ASSEMBLY-WP-0006)

- Split H into durable and current components (L3). *Done in GADM-0.4* (`GADM-0.4.md` § 1): L3 now supported.
- Agency G per cohort.
- Initialise W and the cohort attention stocks at their own equilibria (§ 3.4
  reading 3, § 5.3 L2 note).
- Estimates instead of assumptions for the channel self-reinforcement r_k, the
  wealth conversion k_w, and organism depreciation `dO` (the top driver in the
  GADM-0.2 Sobol analysis).
- Global sensitivity analysis on GADM-0.3 (the Sobol run so far covers
  GADM-0.2).

## Reproduce

```bash
python3 -B -m unittest discover -s simulations/gadm02
cd simulations/gadm02 && python3 -B power_channels.py   # T03 stage (wealth off)
cd simulations/gadm02 && python3 -B wealth.py           # T04: P3 and scenarios
cd simulations/gadm02 && python3 -B organism_grid.py    # T05: 2 × 2 × 2 organism grid
cd simulations/gadm02 && python3 -B life_cycle.py       # T06: cohorts, L1–L3
```