| Period | Region | Operating profit | Embedded capital gain | Recorded profit | Gain in firm dividends | |
|---|---|---|---|---|---|---|
| 5 | 11 | Z1 | 266.2418 | -2.719059 | 263.5228 | -2.719059 |
| 6 | 11 | Z2 | 1145.8083 | 3.427059 | 1149.2354 | 3.427059 |
| 23 | 20 | Z1 | 251.1821 | -4.215972 | 246.9661 | -4.215972 |
| 24 | 20 | Z2 | 1170.5571 | 5.609147 | 1176.1663 | 5.609147 |
OPENFLEX: capital revaluation in the archived accounting matrices
Real-capital gains enter amortization and profits; household currency gains have a separate entry
Finding and correction
The archived two-area balance-sheet and transaction-flow-matrix code in old/5A_Tables (D5.2, 2024).R corroborates private real-capital valuation as aggregate capital times the investment deflator, k p_I. Revaluation is present in the model: the amortization allowance deducts real-capital price gains, which therefore enter corporate profits and their distribution. The transaction-flow matrix has a separate household currency-revaluation entry. A zero explicit revaluation cell in the firms’ capital column does not mean that real-capital gains are absent.
The earlier aggregate audit treated k p_I as an explicit assumption without a supplied historical balance-sheet source. That qualification can now be narrowed: the private aggregate valuation is corroborated by archived code. An industry asset inventory, independent capital resale prices and the government real-asset valuation remain unverified. The historical table is presentation code with rounding, a display offset and asymmetric entries; it is not a newly certified full accounting matrix for current OPENFLEX.
On the five previously saved early histories, the independent replacement valuation reconciles the capital-gain components of amortization, total profit, retained profit and firm dividends on 120 region-period observations. Maximum scaled residual is 2.55882e-15. No model equations or calibration changed.
What the historical matrices establish
The script was parsed, not sourced or executed. The receipt retains 212 cells from four balance-sheet and six transaction columns, with row labels, original formulas, formulas before rounding, assignment start lines and source hashes. It does not require period-75 historical simulation variables to be available. Its February 11, 2026 import commit is 07999df; the filename’s 2024 label does not independently establish authorship or execution date.
| Archived entry | Source location | What follows |
|---|---|---|
| Z1 firms’ capital stock: k p_I − 0.01 | Lines 63–65 | Aggregate valuation is present. The constant display offset does not affect changes in net worth. |
| Z2 firms’ capital stock: xr × k p_I | Lines 151–161 | The same private valuation is converted to the table’s Z1 currency. |
| Firms’ current account: −profit and −amortization | Z1 column beginning line 387 | Both are transferred out of the current account; amortization already contains revaluation. |
| Firms’ capital account: +amortization, investment and financing | Z1 column beginning line 423; Z2 beginning line 668 | The explicit revaluation row is zero in both columns; this does not undo the gain inside amortization. |
| Household revaluation | Z1 column beginning line 336; Z2 beginning line 580 | Currency gains are explicitly displayed separately from firm amortization. |
The historical presentation needs qualifications. Z1 retained profit is placed under the row labelled “Bank profit”; the corresponding Z2 capital column omits retained profit from both its individual cells and its total. Firms’ net-financial-wealth row is zero while the total calculates real assets minus loans and equity; a computed total is not a proof that it is zero. Historical household currency formulas use current holdings and different conversion expressions from the retained current engine. These formulas are traced for provenance, not adopted as correct current formulas. The archived government capital-stock cell is zero and does not corroborate the separate k_G p_IG audit valuation.
Where real revaluation enters current profits
Let R denote replacement expenditure independently reconstructed from the empirical K matrix, output and current firm buyer prices. Let Δp_I denote the change in the investment deflator. The retained launch engine uses
\[ AF_t = R_t-k_t\Delta p_{I,t}. \]
Define operating profit for this decomposition as value added in the profit equation (yn) minus wages, replacement expenditure and interest on previous loans. It excludes the embedded capital-price gain; it is an analytical category, not a replacement for the recorded profit variable. Then the source implies
\[ F_t = F_t^{operating}+k_t\Delta p_{I,t},\qquad F_t^{retained}=\omega F_t,\qquad DIV_t=(1-\omega)F_t. \]
These are checked against af, f_f, f_f_u and div_h1, rather than inferred from a zero explicit revaluation row. Replacement expenditure comes from the prior independently reconstructed capital ledger, whose parent and input-bundle hashes are checked. The present decomposition uses five histories, both regions and periods 9–20. The denominator for each scaled residual is the maximum of one, absolute recorded profit and replacement expenditure. The largest absolute capital-gain/current-value- added ratio across these observations is 0.00408479. That is a level ratio, not a causal amplification estimate.
Both regions have zero retention parameter in this parent. Consequently, the gain component enters firm dividends in full, even though retained profits are zero. Z1 records a capital-price loss and Z2 a gain in these control observations. Firm dividends are subsequently allocated to households using the engine’s shareholding/conversion matrix; the table above records issuer dividends, not each household’s final dividend income.
Current source locations are the retained launch model/code/MVP_model_2026.R: replacement expenditure at lines 250–275, amortization at 845–847, and settled profits, loans and dividends at 2185–2207. The archive model/old/MVP_model_aug14.R, lines 243–253, already has the same current-k price-gain subtraction, but prices depreciation at the previous investment deflator. The current engine prices replacement independently. These depreciation conventions must not be interchanged when deriving stock-flow bridges.
Relation to Zezza’s revaluation accounting
Nikiforos and Zezza’s 2017 survey, printed pages 12–13, explains that closing asset values include opening values, transactions and capital gains. Equation (4) separates current-price quantity changes from price changes on opening holdings; a revaluation matrix records the latter. This supports retaining gains and making their classification explicit. It does not by itself adjudicate this model’s amortization convention or the distribution of capital gains through corporate profits. Stock-flow Consistent Macroeconomic Models: A Survey, WP 891.
For private real assets the exact decomposition is
\[ \Delta(kp_I)=p_{I,t}\Delta k+k_{t-1}\Delta p_I. \]
Combining it with the current investment and financing equations yields
\[ \Delta NW_F=F_t^{retained}-\Delta k\Delta p_I, \quad NW_F=kp_I-L_F-E_F. \]
Here retained profit already includes its share of the gain. Adding a full holding gain to this unchanged bridge would count it twice. Separating transactions and revaluation for presentation requires a consistent reclassification of amortization, profits and financing. It must not be implemented by adding a gain to existing income. For comparison, the archived depreciation/financing convention implies ΔNW_F = retained profit − i_d Δp_I under the same valuation: its investment is i_d p_I and its depreciation allowance uses d_a p_{I,t-1}. This is an algebraic source comparison, not a new historical numerical run.
Consequence for the instability investigation
The completed one-period timing experiment changed current k to beginning k in the gain term while retaining revaluation. It removed the conditional net-worth cross term but left the tested quote response amplified. It therefore says little about the importance of the whole revaluation channel. It did not remove capital gains or test a propagated alternate trajectory.
The source now supplies a concrete hypothesis to examine on admissible real/financial histories: capital-price changes alter amortization and gain-inclusive dividends; household income and wealth affect portfolio demand; foreign-bill clearing then changes the exchange quote. This chain is sourced as a possible mechanism. Its signed contribution, feedback closure and necessity for instability are not yet established. The next causal calculation must retain the real/history coordinates needed by cash demand, income, lending and government debt. Independent wealth or quote surgery violates previously measured accounting constraints.
OPENFLEX remains excluded; Task 3 remains partial. No canonical change, stable candidate, complete transition spectrum or minimal causal loop is claimed. The historical valuation correction strengthens the accounting basis for the next calculation without closing an author convention choice.
Reproduction and evidence
Rscript R/dynamics/openflex_matrix_reconciliation.R \
--bundle-dir output/calibration/openflex_attack/leeds_diagnosis/pulses_full_01 \
--out-dir /tmp/openflex_matrix_reconciliation_fresh
python3 tools/calibration/openflex_freeze.pyUse a fresh empty output directory. The receipt and CSVs are retained in output/calibration/openflex_attack/leeds_diagnosis/matrix_reconciliation_01/: historical_matrix_cells.csv, capital_revaluation_source_map.csv, profit_revaluation_decomposition.csv, check_summary.csv and matrix_reconciliation_receipt.json. Parent, historical sources, retained engine, prior capital ledger and five bundle hashes are recorded. The canonical parent hash is 80dc540620c1ddd971c2c4a68fa3a95959140518445521ef9dba6789ae257471.
Read alongside 2026-10-03-openflex-real-capital.qmd, 2026-10-03-openflex-revaluation-probe.qmd and 2026-10-03-openflex-financial-coordinates.qmd in this report directory. This report supersedes only the earlier absence-of-historical-private- valuation-source qualification; the earlier numerical receipts remain intact.