assembly-economics/models/CrossBorder.md

Cross-border coupling in GADM

Status: v0.1 (2026-10-13), ASSEMBLY-WP-0011-T01 (channel inventory) and T02 (coupling design). Implementation: T03.

1. Why

The calibrated model (models/Calibration.md v0.4) puts domination at or above the floor in every jurisdiction (US 0.68, EU 0.72, AR 0.75), and the largest contributions are measured. Three firms take 88 % of frontier-model spend, one search engine has 85–94 %, and two mobile operating systems divide the market. Outside the US, all of these operators are foreign. A closed model reads them as domestic, so the EU, already at rights-first levers, cannot lower its domination (BR-007). The coupled model must say whether, and through which channel, levers can act on operators set abroad.

2. Channel inventory (T01)

Foreign share f = share of the channel held by operators headquartered in another jurisdiction, as seen from the host.

#	Channel	Model quantities	Evidence (2026)	f for EU / AR (US)	Indicator	Priority
C1	Discovery and membrane operators	Pd, Pmem; disc, m	Google 85–94 % search share; iOS + Android ≈ 100 % of mobile OS (StatCounter, Sept 2026)	≈ 1.0 / ≈ 1.0 (0)	StatCounter shares × operator home	1
C2	Lineage import	Plin; L, lin_open	top-3 US developers 88 % of enterprise model spend (Menlo, Dec 2025); open-weight lineages from US, China and EU (Mistral)	≈ 0.9 / ≈ 1.0 (≈ 0.1)	P4 + origin of open-weight downloads (Hugging Face)	1
C3	Compute and infrastructure	Pi; std	Amazon, Microsoft, Google 63 % of world cloud (Synergy Q2 2026); EU providers a small share of their home market	≈ 0.75 (prior) / ≈ 0.9 (0)	P1 by region	2
C4	Investment and capital	aO inflow, K_Ω	US information-processing investment $1.92 trn SAAR (L5, 2026 Q2); frontier capex concentrated in the US	adoption follows the frontier set abroad	L5 per jurisdiction; FDI in data centres	2
C5	Regulatory spillover ("Brussels effect")	foreign part of Pd, Pmem, expl	DMA obligations (choice screens, interoperability) and AI Act transparency (since Aug 2026) bind global operators	host rules act on operators abroad	L7 and operator compliance changes	2
C6	Trade in organism output	demand dem, Y*	digital services exports	—	WDI ICT services exports	3
C7	Talent and founders	H, F	AI talent migration (AI Index)	—	AI talent flows	3
C8	Sentiment and media	Σ	sentiment trends move together across countries (Pew, Ipsos)	—	L6 across jurisdictions	3

Minimal set for T03: C1, C2, C3 (where domination comes from) and C5 (the only lever a host has on foreign operators), plus C4 for adoption. C6–C8 come later, when a reading depends on them.

3. Coupling structure (T02)

3.1 Split channels

For each host j and channel c ∈ {Pd, Pmem, Plin, Pi}, the channel level is a mix:

P_c^j = (1 − f_c^j) · D_c^j + f_c^j · O_c^{h(c)}

• D_c^j is the domestic part. Its dynamics are the current GADM channel equation under the host's own levers.

• O_c^h is the operator part. It is the channel level of the operators' home jurisdiction h (for C1–C3 today: the US), under the home's levers, and modified by the host's market-access rules (C5):

  dO_c^{h→j} = (home channel dynamics)
               − a_c^j · O_c^{h→j}        (host access rule, e.g. DMA)
  

  a_c^j ≥ 0 is the host's market-access lever. One host's rule lowers only its own operator part, unless the operator applies it globally. That is the spillover share σ_c: a fraction σ_c of every host's rule also acts in the home market and in all other hosts.

• The foreign share f_c^j is a parameter set from data (§ 2). In later versions it can become a state that moves with relative quality and access rules.

3.2 Lineage import (C2)

The host's effective lineage levers are the import-weighted mix:

L_eff^j        = (1 − f_lin^j) · L^j        + f_lin^j · L^h
lin_open_eff^j = (1 − f_lin^j) · lin_open^j + f_lin^j · lin_open^h

A rights-first host with open domestic lineages, which uses mostly imported closed lineages, therefore has low effective openness. That is the mechanism BR-007 suspects.

3.3 Adoption and frontier (C4)

Organism learning in the host draws on the frontier, not only on its own stock:

learning term:  ell · max(K_Ω^j, κ · K_Ω^frontier) · dem · Q

with access κ ∈ [0, 1] (κ = 0 recovers the closed model). The frontier is the largest K_Ω among the coupled jurisdictions.

3.4 Numerical scheme

Synchronous step: at each time step, all jurisdictions compute their derivatives from the previous state of all others, then all update together. The step size stays at dt = 0.1 years.

3.5 Required properties (tests for T03)

1. Uncoupled = closed. With all f = 0, κ = 0 and a = 0, each jurisdiction reproduces gadm04.simulate exactly.
2. Symmetry. Identical jurisdictions coupled symmetrically stay identical to each other and to one uncoupled jurisdiction.
3. Operator consistency. With f = 1 and a = 0, a host's channel equals the home channel.
4. Lever reach. A host rule a_c^j > 0 lowers the host's channel and leaves the home channel unchanged when σ = 0.

3.6 Two scenario modes

• Global: all jurisdictions (US, EU, AR, and a J4 reference bloc) are simulated together with this coupling.
• Local in context: one host is simulated in full. The operator parts O_c^h(t) and the frontier K_Ω^frontier(t) are given paths (T04 context scenarios), taken from a global run or set by hand.

The comparison between the two modes (T05) shows when the context approximation fails.

3.7 Calibration hook

Hosts start from results/calibrated_starts.json. Split the measured channel level into parts so that P_c^j stays at its calibrated value at t 0: D_c^j(0) = O_c^h(0) = P_c^j(0). The coupling then changes the dynamics, not the measured starting point.

4. First results: the BR-007 test (T05, first part)

simulations/gadm02/world.py implements § 3 (tests test_world.py: closed equivalence, symmetry, operator tracking, lever reach, spillover, frontier access). cross_border.py runs US (operators' home), EU and AR (hosts) from Calibration v0.4 (results/cross_border.md). Foreign shares are from § 2; frontier access κ = 0.8 is a prior.

Lever (coupled model)	EU P at t 100	US	AR
current levers	0.82 (floor broken)	0.82	0.83
DMA as observed (a fitted ≈ 0, at most 0.006 per year)	0.82	0.82	0.83
strong access rule, a = 0.15 per year on foreign Pd and Pmem	0.68	0.82	0.83
strong access rule, applied globally by operators (σ 0.5)	0.68	0.75	0.76
US moves to rights-first (J1) levers	0.63	0.60	0.66
US J1 + strong EU access rule	0.42	0.60	0.66

Calibrating the access rule. The DMA has applied since March 2024. Google's share fell 6.5 points in Germany, 3.0 in France and 3.1 in the US (no DMA), comparing March 2023–February 2024 with October 2025–September 2026 (StatCounter). The EU-specific excess is about −1.7 points (0 to −3.4). The coupled model without any rule already produces −2.6 points, because the EU's operator part converges toward the operator's home level. So the observed decline is consistent with no measurable DMA effect on search concentration, and the data allow at most a ≈ 0.006 per year. That is about 1/25 of the strong rule.

Readings

1. BR-007 is explained. The EU's domination channels are run by foreign operators, so its own rights levers act only on the small domestic part. This is not visible in a closed model, which attributes the channels to the host.
2. Two levers reach foreign-run channels: a host access rule on foreign operators, and the home's own levers. The home's levers are the strongest single lever for every jurisdiction. A US move to rights-first levers brings all three under the floor (US 0.60, EU 0.63, AR 0.66).
3. The access rule works only far above its observed strength. As practised so far (2024–2026), it has no measurable effect on search concentration. A rule about 25 times stronger would bring the EU under the floor. This is a quantitative statement about enforcement, not about the law's text.
4. Spillover helps others. If operators apply the host's rule worldwide (σ 0.5), US and AR domination fall too (0.82 → 0.75, 0.83 → 0.76).
5. Lineage concentration (Plin ≈ 0.9) is reachable only through the home. No host rule in this setup acts on imported lineages. An access rule for lineages (interoperability, model portability) is the open design question, and the most direct link to break-register entry BR-003.

Caveats: the foreign shares and κ are first estimates. The access rule is a removal rate on the operator part, not a model of how regulation works. The legitimacy loop is off.

5. Context scenarios and hypothesis re-test (T04, T05)

world.py supports local runs in a context: context(rows) makes a jurisdiction follow given rows instead of being simulated (test: a local run against a context taken from a global run reproduces that run to nine decimals). world_scenarios.py (results/world_scenarios.md) runs four contexts globally (US, EU, AR and a J4 reference bloc) with the legitimacy loop off and on. Calibration v0.5 (Argentina's E measured too, 40 of 40 targets in range).

Context	Definition
X1 US-led concentrated frontier	current levers
X2 open-lineage world	US moves to rights-first (J1) levers
X3 accelerating frontier	US and J4 with self-enhancement (B4-like)
X4 fragmented blocs	hosts' frontier access 0.2, foreign shares halved

Output is compared relative to each jurisdiction's own start. Model output levels are normalized and not comparable across jurisdictions.

5.1 "Europe lags" (H1)

	loop off	loop on
EU adoption below US and AR at t 10	yes, in all four contexts	no, in all four contexts
EU − US relative output, years 0–25	−0.03 to −0.24 (largest when the frontier accelerates)	−0.04 to +0.08
EU − US VFAC at t 100	+0.03 to +0.05, except open-lineage world −0.02	+0.01 to +0.02, except open-lineage world −0.02

After the BR-009 fix (sentiment anchored at measured levels), the verdicts stay the same. With the loop on, EU and US adoption at t 10 are now equal in X1 and X4 (0.27 / 0.26–0.27), and in X2 and X3 the US leads (0.44). The relative-output differences with the loop on become −0.09 to +0.05.

Reading: Europe lags in adoption only if sentiment does not matter. With the measured sentiment levels (US Σ 0.29, EU 0.54) and the legitimacy loop, US adoption brakes and the EU no longer lags. Lagging costs output early, most in an accelerating-frontier world, but the EU ends with higher VFAC than the US unless the US itself moves to rights-first levers.

5.2 "Argentina may thrive" (H2)

Not supported in any context or loop setting. Relative to its start, Argentina grows less than the EU (−0.02 to −0.07 over years 0–25) and ends with lower VFAC (−0.04 to −0.06). It starts with the highest domination (0.75), all of it run from abroad (f = 1), under deregulated levers. That leaves no domestic lever on domination, and its frontier access does not compensate. Argentina gains most from the open-lineage world (X2), that is, from US policy, not from its own.

5.3 When the context approximation fails

For host outcomes, the local run in a context equals the global run (max |ΔP| < 0.001), including with a strong EU access rule and spillover. Hosts do not feed back on the home in the current coupling: spillover changes the home's path, and the host already applies its own rule. Global runs are therefore needed for the home's outcomes, for spillover effects on third jurisdictions, and for frontier leadership changes. Local runs suffice for a single host's questions.

5.4 Limitations

• Foreign shares f are fixed. In reality they would move with access rules and domestic alternatives.
• Frontier access κ = 0.8 is a prior.
• The J4 bloc is uncalibrated. It reuses the US start with J4 levers.
• Trade, talent and sentiment contagion (C6–C8) are not modeled.
• No host rule reaches imported lineages (BR-008).

These are handed to ASSEMBLY-WP-0016.

6. Host rules on imported lineages and on cloud (WP-0016-T01, T03)

world.make(..., port=...) adds a lineage portability rule. A share port of imported-lineage use can move to domestic or open lineages, which lowers the effective lineage import share in the channel mix and in the effective lineage openness. Lineage access rules use the existing access mechanism on Plin. Cloud switching (the Data Act's switching rules) is an access rule on Pi. cross_border.py, EU at t 100 (counterfactual strengths, legitimacy loop off):

EU host rule	EU Plin t100	EU P t100	Δ P vs. current
none (current)	0.91	0.82	—
lineage access rule a 0.15 on Plin	0.19	0.73	−0.09
lineage portability 0.5	0.92	0.82	+0.00
lineage access 0.15 + portability 0.5	0.56	0.76	−0.06
cloud switching a 0.15 on Pi	0.91	0.77	−0.06
all host rules (Pd, Pmem, Plin, Pi at 0.15; portability 0.5)	0.57	0.35	−0.47

Readings:

1. A host can reach imported-lineage concentration without the home's cooperation, through an access rule on foreign lineage operators. BR-008's "only through the home" was a limit of the earlier setup, not of the mechanism.
2. Portability alone does nothing in the current model. This is an artifact. The calibration hook starts the domestic part of each channel at the measured level (0.88), so the market that portability moves users to is assumed to be as concentrated as the imported one. Testing portability needs the concentration of the domestic and open-lineage market (indicator CB3: open-weight downloads by developer). Evidence so far does not show portability gains: the open-weight share of enterprise use fell to about 13 % in 2025 (Menlo Ventures).
3. Together, host rules can bring the EU far below the floor (0.35), but only at strengths about 25 times the observed DMA effect. All observed host rules so far are consistent with zero effect.

Frontier access κ (T03). Early EU growth barely depends on κ up to 0.8 (one-year adoption ratio 1.453 at κ 0, 1.470 at 0.8, observed 1.48). κ 1.0 overshoots (1.52). κ is therefore not identified by today's data, and the prior 0.8 does not double-count the calibrated adoption speed. κ matters only when the frontier pulls far ahead (context X3).

7. Export channel and "Argentina may thrive" (WP-0016-T04)

gadm02 parameter xport (default 0) adds foreign demand for organism-enabled output: dem += xport · K_Ω. Argentina's knowledge-based services exports were USD 9.6 bn in 2025 (INDEC, +8.1 %), about 1.5 % of GDP. The sector's goal is USD 30 bn (about 4.5 %). exports.py sets Argentina's export demand to a share of its domestic demand at the calibrated start (results/exports.md).

Context, loop	Export share	AR Ȳ 0–25 / 0–100	EU Ȳ 0–25 / 0–100	AR − EU VFAC
X1, off	none	0.99 / 0.81	1.01 / 0.85	−0.041
X1, off	1.5 % (today, upper bound)	1.00 / 0.82	1.01 / 0.85	−0.042
X1, off	4.5 % (sector goal)	1.03 / 0.85	1.01 / 0.85	−0.045
X1, off	10 % (export hub)	1.07 / 0.90	1.02 / 0.85	−0.052
X1, on	10 %	0.93 / 0.71	0.95 / 0.76	−0.040
X2, off	10 %	1.14 / 1.00	1.09 / 1.01	−0.071

Ȳ is relative to each jurisdiction's own start.

Readings:

1. H2a, output: Argentina can out-grow the EU through exports, but only well above today's level. At the sector goal (4.5 % of GDP), early output growth passes the EU's. As an export hub (10 %), long-run growth does too. Today's knowledge-services exports, even counted fully as organism-enabled, do not change the result. With the legitimacy loop on, Argentina stays behind in every case.
2. H2b, VFAC: no. More exports lower Argentina's VFAC relative to the EU (−0.041 → −0.052 in X1, −0.055 → −0.071 in X2). The extra organism capacity brings more displacement and attention extraction, while domination stays at 0.83, all of it run from abroad.
3. "Thriving" therefore splits. A J2 jurisdiction can become richer through AI-enabled exports, but not better off on the program's measure, as long as its domination channels are foreign-run and its levers deregulated. Checkpoint indicators that would show the path: knowledge-services exports (INDEC, quarterly), and L3 adoption for Argentina.

Caveats: export demand scales only with Argentina's own K_Ω (no price or competition effects, no partner demand). Adding it at t 0 shifts the calibrated rest point slightly; this is negligible at 1.5 % and noticeable at 10 %.

8. Endogenous foreign shares and the split calibration hook (WP-0016-T02)

Endogenous shares. world.make(..., endo=...) lets each foreign share f relax (speed λ) toward

f* = f0 · (1 + γ · Δ frontier lead) · (1 − δ · Δ(X · N))

that is, toward more foreign use when the home's frontier lead grows and less when domestic alternatives (commons X, diversity N) grow. At the start f* = f0, so the measured shares are a rest point. Priors: λ = 0.1 per year, γ = δ = 1.

Split calibration hook. The first hook set the domestic and operator parts of each channel to the same measured level. That made every share-shifting lever (portability, endogenous shares) ineffective by construction: moving users between equally concentrated segments changes nothing. With d0 = {channel: domestic-segment concentration}, the domestic part starts at d0 with its own counter coefficients, so it is at rest there. The operator part is solved so that the total keeps its measured level. EU priors: search 0.5 (Ecosia, Qwant: 1–2 % share, one or two firms), cloud 0.3 (EU providers, about 15 %, several firms), lineages 0.5 (Mistral, open-weight models). Mobile OS has no EU segment.

EU lever (coupled, t 100)	EU P	Δ vs. current
endogenous shares, current levers	0.818	−0.003
commons push (IX × 3), fixed shares	0.807	−0.014
split hook + commons push + endogenous shares	0.793	−0.027
split hook + lineage portability 0.5	0.802	−0.019
(for comparison) strong access rule on Pd, Pmem	0.683	−0.138
(for comparison) US moves to J1 levers	0.635	−0.186

Readings:

1. Share-shifting levers work once the domestic segment is measured separately. Portability and commons-driven substitution lower EU domination, but by a fifth to a tenth of what access rules or the home's levers achieve.
2. The measured foreign shares are close to rest under current levers (−0.003 over 100 years): nothing in today's dynamics shifts users toward domestic alternatives by itself.
3. The domestic-segment levels d0 are priors. They need indicator CB3 (open-weight downloads by developer) and the domestic-provider shares in CB1 and CB4.

Calibration note: runs without d0 keep the original hook, so all earlier results are unchanged.