OPENFLEX: the joint wealth and bill-supply history restriction

Bank and CB duplicates can be eliminated; independent reachable coordinates remain unresolved

Finding

The retained sigma=0 OPENFLEX equations impose a simple necessary relation between the quote, both regions’ household wealth, region 2 government debt and region 2 firm loans. It follows by eliminating duplicate bank/CB stocks and household portfolio identities, with the inherited CB offset and foreign reserve endowment explicit:

\[ q_t\,0.03\,v_{1,t} = B_{2,t}+L_{F,2,t}-0.8v_{2,t}-C_2-R_{1\to2}. \]

Here \(q\) is the source’s Z1_xr (region 2 currency per region 1 currency), \(B_2\) is Z2_b_s, \(L_{F,2}\) is Z2_lf, \(C_2\) is the conserved Z2_b_cb - Z2_h_s + Z2_a_s, and \(R_{1\to2}\) is the fixed issuer-currency Z1_b_cb_s_Z2. The coefficients are measured from the parent parameters, not fitted: Z1_lambdaB0_2 = 0.03 and Z2_lambdaB0_1 + Z2_lambdaE0_1 + Z2_lambdaE0_2 - 1 = -0.8.

On the five existing control and signed spending-pulse histories, periods 9–20, 1920 identity rows pass, with maximum scaled residual 8.26499e-13. The symmetric two-size derivatives reconstruct the quote response at every t11–20, with maximum scaled derivative error 1.5282e-09 and gain-contribution size difference 8.41318e-09. Original bundle hashes match their passing sector-budget and domain receipts. No new solved path, independent disturbance or tolerance experiment is used.

This narrows the admissibility blocker. These stocks cannot be chosen independently of the real income, expenditure and financing histories that produce them. The reduction is a necessary restriction, not a sufficient chart of reachable histories. OPENFLEX remains excluded and Task 3 partial.

Elimination from the retained source

The source’s revised bank equations imply \(A=L_F+L_H+B_b-M\) and \(B_b=\beta M\). The OPENFLEX CB rule implies \(B_{CB}=C+H-A\), while cash, advances and deposits have matching supply and demand records. The household identity is \(M=v+L_H-H-B_{H,own}-B_{H,foreign}-E_{H,1}-E_{H,2}\). Substitution gives

\[ B_{CB}+B_b=C+v-B_{H,own}-B_{H,foreign}-E_{H,1}-E_{H,2}-L_F. \]

Residual issuer-currency region 2 bill supply is \(S_2=B_2-B_{H,own}-B_{CB}-B_b-R_{1\to2}\). The own-household bill term cancels on substitution. With sigma=0, the remaining household portfolio terms are constant shares of \(v_2\), yielding the finding’s equation through \(S_2=qB_{H,1\to2}=q\,0.03v_1\).

Cash, household loans, deposits and the bank bill ratio cancel in this conditional stock identity. This does not establish policy irrelevance: those quantities can affect income, profits, financing and future stocks. The CB offset is conserved on each history, rather than imposed as zero. The redundant region 1 bill mismatch is not projected away; the reduction uses only the cleared region 2 market.

Restriction	Retained launch model/code/MVP_model_2026.R
Wealth accumulation	675–678
Firm financing and equity issuance	849–865
Bank deposits, bills and advances	887–903
Government deficit and debt accumulation	1077–1086
Cash and advances supply; own HH bill conversion	1094–1097; 1118–1119
Fixed Tobin portfolio shares at sigma=0	1356–1388
Cash history and household deposit identity	1526–1537
OPENFLEX CB stock law and residual foreign supply	2430–2450

The cross-period restriction

The debt and loan stocks in the reduced identity still obey

\[ \begin{aligned} B_{2,t}&=B_{2,t-1}+GDEF_{2,t},\\ L_{F,2,t}&=L_{F,2,t-1}+I^{value}_{2,t}-AF_{2,t}-\Pi^u_{2,t} -(E_{s,2,t}-E_{s,2,t-1}),\\ v_{z,t}&=v_{z,t-1}+YD_{z,t}-c_{z,t}p_{a,z,t}. \end{aligned} \]

The government deficit is expenditure plus lag debt interest and government investment, less income taxes, CB distribution, VAT and tariff revenue. Gross private investment is independently valued from the retained K matrix and current buyer prices, plus net investment at pid. AF includes the source’s capital-price revaluation; retained profits and issuance keep their original definitions. The harness checks these equations directly before substituting their terms into supply.

Consequently an admissible stock change must satisfy both the clearing restriction and these cross-period laws, with a solved real side, previous technology, base/portfolio context, options and time branch. Earlier income and expenditure cannot be inferred independently from a selected wealth level. Earlier government and firm financing cannot be inferred independently from selected debt and loan levels. Cash additionally requires earlier consumption/prices, and the household loan rule retains its two-branch maximum at source 1539–1555.

The exact remaining restriction is reachability: there is no demonstrated inverse from arbitrary values of these stock coordinates to a joint solved real/financial/technology history satisfying the source rules. No rank or local invertibility certificate is supplied. The 1,375-label executed-read inventory provides the numerical inputs, but not independent degrees of freedom. A useful next calculation must establish that inverse or a local rank certificate for a specified admissible history family, including the active household-financing branch. These are model restrictions, not a request for missing external data.

Attribution on the existing histories

The table splits residual supply into inherited stocks and current financing flows, then differentiates \(qD=S\) using exact symmetric product means. Contributions are divided by the preceding quote derivative; they are accounting attributions along the complete pulse paths.

	Component	t11 gain contribution	t20 gain contribution
91	supply_inherited_government_debt	0.860382	2.364103
92	supply_government_deficit	0.493792	0.259290
93	supply_inherited_firm_loans	1.503915	0.963753
94	supply_firm_financing	-0.201110	0.058549
95	supply_inherited_wealth	-1.513432	-2.462357
96	supply_current_saving	-0.227663	-0.232420
97	supply_CB_offset	0.000000	0.000000
98	supply_foreign_reserve	0.000000	0.000000
99	demand_Z1_wealth	0.161840	0.150227

	period	observed_gain	reconstructed_gain
11	11	1.077725	1.077725
20	20	1.101145	1.101145

At t20, inherited government debt contributes about +2.3641 and inherited firm loans +0.9638, while inherited region 2 wealth contributes −2.4624. Current flows and region 1 wealth complete the observed gain 1.101145. The conserved-offset derivative is numerically negligible; fixed foreign reserves have zero derivative. Large opposing terms demonstrate why a large single accounting contribution cannot identify a separate causal loop. Revaluation can affect every inherited term through earlier periods; this table neither removes it nor estimates its total causal effect.

Reproduction and receipts

Rscript R/dynamics/openflex_joint_history_restrictions.R \
  --bundle-dir output/calibration/openflex_attack/leeds_diagnosis/pulses_full_01 \
  --out-dir /private/tmp/openflex_joint_history_fresh
python3 tools/calibration/openflex_freeze.py

Use an empty fresh directory. Current evidence is in output/calibration/openflex_attack/leeds_diagnosis/joint_history_03/. The receipt hashes the parent, launch equations, five full-history bundles, existing original-history accounting receipts and this harness. CSVs contain all level checks, supply history components, symmetric tangents, reconstruction and size precision. joint_history_01/ and _02/ retain earlier harness versions; _03/ normalizes component names and verifies the original budget and domain receipts. The initial parameter-name typo stopped before emitting scientific results and was corrected before the first completed run.

Read with the lag-read closure, financial-coordinate and revaluation-channel reports. This supplies a sourced necessary joint restriction under the hand-off’s fallback gate, while the independent chart, causal interpretation, maintainer classification/timing choices and stabilization remain unresolved.