These checks reproduce specified accounting and cost calculations within Recognition Economics. Physical morality governs the actual relations among people. Applying these results requires identifying those relations and quantities. Computed non-worsening does not establish authored consent. Selected quadratic costs and exact reciprocal J costs retain their distinct meanings.
86 of 86 checks passed in the recorded run. Each row names the paper number or theorem it reproduces. Planted positive: the triangle bystander charged 1/18. Planted negatives: the specified small-debt kinked example leaves the bystander untouched; a bridge at rest leaves the rewrite unchanged. Degenerate inputs fail. The checks distinguish two networks that have the same who-owes-whom table.
| result | check | expected | got | source |
|---|---|---|---|---|
| pass | triangle, quadratic cost: u* = (2/3, -1/3, -1/3) | (0.6667, -0.3333, -0.3333) | [0.6667, -0.3333, -0.3333] | framework thm:bystander, 'The numbers' |
| pass | triangle, quadratic cost: party 2 charged 1/18 (planted positive) | 0.055556 | 0.055556 | framework thm:bystander |
| pass | triangle: party 2 reached (both open lines drawn in) | ['r12', 'r20'] | ['r12', 'r20'] | thm:bystander |
| pass | triangle: circulation at the booked position is nonzero | nonzero | -0.57735 | thm:cutspace (c) |
| pass | triangle, J on amounts (4,1,1): u* = -0.174 | -0.174 | -0.174 | framework thm:bystander numbers |
| pass | triangle, J on amounts: party 2 charge J(0.826) = 0.018 | 0.018 | 0.018 | framework thm:bystander numbers |
| pass | triangle, J on amounts: stationarity 3 = (4+u)^-2 + 2(1+u)^-2 | 3.0 | 3.0 | framework thm:bystander numbers |
| pass | triangle, log reading: e^{c*} = sqrt(3/8) | 0.612372 | 0.612372 | framework thm:bystander numbers |
| pass | triangle, log reading: party 2 charge J(sqrt(3/8)) = 0.123 | 0.123 | 0.123 | framework thm:bystander numbers |
| pass | triangle, kinked cost 3|u|+u^2: rewrite does not move (planted negative) | u* = u0, party 2 not reached | {'moved': [], 'reached': []} | framework rem:kink |
| pass | bridge at rest (pendant relationship) leaves the rewrite unchanged | [0.666667, -0.333333, -0.333333] | [0.666667, -0.333333, -0.333333] | thm:cutspace; Bridge |
| pass | planted pair: same who-owes-whom table | True | True | Projection (blindness) |
| pass | planted pair: different reach (A reaches nobody new, B reaches party 2) | {'A': [], 'B': ['0', '1', '2']} | {'A': [], 'B': ['0', '1', '2']} | Projection (blindness) |
| pass | engine reports the table blind on the triangle books | True | True | Projection |
| pass | gap conserved by 50 random cross postings | 0.2 | 0.2 | PremiseLedger gap conservation |
| pass | buffer identity on random balanced books: free total = -net for every party | True | True | Genesis.freeTotal_eq_neg_ownNet |
| pass | unmatched relationship reported not reachable by legal moves | True | True | gap conservation |
| pass | dispute interval is the two figures, width the gap | [1.628732, 1.828732, 'width 0.2'] | [1.628732, 1.828732, 'width 0.2'] | two figures |
| pass | fully designated chart is closed and every party frozen | {'closed': True, 'frozen': ['0', '1', '2']} | {'closed': True, 'frozen': ['0', '1', '2']} | ClosedChart.closed_frozen |
| pass | cross posting through designated accounts is refused | refused | refused | LegalStep.crossPost freeness |
| pass | fully closed chart with nonzero nets is not consistent (nets vanish on a closed chart) | False | False | ClosedChart nets zero |
| pass | cash-closed chart (free accounts for goods only) is consistent | True | True | D-econ-cash-closed |
| pass | issuer detected | Z | ['Z'] | ClosedChart.Issuer |
| pass | payment is six entries | 6 | 6 | ClosedChart.payment |
| pass | payment keeps consistency | True | True | ClosedChart payment_consistent |
| pass | issuer with no free account has net zero before and after | [0.0, 0.0] | [0.0, 0.0] | CashClosed.issuer_net_zero |
| pass | claim extinguished by the payment | 0.0 | 0.0 | ClosedChart.payment |
| pass | gaps sum to zero on the closed network | 0.0 | 0.0 | ClosedChart gaps sum |
| pass | interest: accrual and cash payment move the same nets (creditor +y, debtor -y, others 0) | {'0': 0.3, '1': -0.3, '2': 0.0, 'Z': 0.0} | {'accrual': {'0': 0.3, '1': -0.3, '2': 0.0, 'Z': 0.0}, 'cash': {'0': 0.3, '1': -0.3, '2': 0.0, 'Z': 0.0}} | CashClosed.interest_net_transfer_forced |
| pass | interest: the two bookings are different books | True | True | CashClosed.interest_bookings_differ |
| pass | degenerate input fails: empty chart | EngineError | EngineError | meter contract |
| pass | degenerate input fails: chart with no relationships: nothing to rewrite | EngineError | EngineError | meter contract |
| pass | degenerate input fails: empty ledger extract | EngineError | EngineError | meter contract |
| pass | ledger extract: the disagreement on INV-2002 is a gap of 50 with interval [450, 500] | {'gap': 50.0, 'interval': [450.0, 500.0]} | {'gap': 50.0, 'interval': [450.0, 500.0]} | two figures; gap conservation |
| pass | ledger extract: INV-3003 is an open line the table drops | ['INV-3003'] | ['INV-3003'] | Projection |
| pass | ledger extract: buffer identity holds for every entity | True | True | Genesis.freeTotal_eq_neg_ownNet |
| pass | ledger extract: several rows per document sum to the record (1000 - 200 = 800 both sides, matched) | {'creditor': 800.0, 'debtor': 800.0, 'matched': True} | {'creditor': 800.0, 'debtor': 800.0, 'matched': True} | SCHEMA format A |
| pass | ledger extract refuses: second currency | EngineError | EngineError | SCHEMA format A |
| pass | ledger extract refuses: parties disagree between rows of one document | EngineError | EngineError | SCHEMA format A |
| pass | ledger extract refuses: amount not a number | EngineError | EngineError | SCHEMA format A |
| pass | coalition: v({0,1,2}) = 1/12 | 0.083333 | 0.083333 | framework thm:firm |
| pass | coalition: every pair has value -1/36 | [-0.027778, -0.027778, -0.027778] | [-0.027778, -0.027778, -0.027778] | framework thm:firm |
| pass | coalition: every singleton 0 | [0, 0, 0] | [0.0, 0.0, 0.0] | framework thm:firm |
| pass | coalition: books' allocation (2/9, 2/9, -1/36), sum 5/12 | [0.222222, 0.222222, -0.027778] | [0.222222, 0.222222, -0.027778] | framework thm:firm |
| pass | coalition: books' allocation is outside the core (sum 5/12 not 1/12; party 2 below 0) | outside | outside | framework thm:firm |
| pass | coalition: an equal split of 1/12 is in the core (planted positive) | inside | inside | framework thm:firm |
| pass | K4: 39 of 64 kept-sets admissible | 39 | 39 | Pruning K4.T_optimal / nadm_* |
| pass | K4: efficient network is the tree {01, 03, 23} with total 1519/900 | {0, 2, 5}, 1519/900 | {0, 2, 5}, 1519/900 | K4.efficient_tree |
| pass | K4: efficient tree has beta 0 | 0 | 0 | K4.beta_tree |
| pass | K4: four-cycle carrier (-3/4, -5/4, 1/4, -3/4) on (01, 03, 12, 23) | (-3/4, -5/4, 1/4, -3/4) | ('-3/4', '-5/4', '1/4', '-3/4') | K4 cycle carrier |
| pass | K4: four-cycle burdens (4261/7200, 1303/5600, 877/3360, 893/1440) | (4261/7200, 1303/5600, 877/3360, 893/1440) | ('4261/7200', '1303/5600', '877/3360', '893/1440') | K4 burden table |
| pass | K4: four-cycle total 21491/12600, cutting 12 lowers the total by 1/56 | 21491/12600, 1/56 | 21491/12600, 1/56 | K4 burden table |
| pass | K4: cutting 12 takes party 1 from 1303/5600 to 51/200 and party 2 from 877/3360 to 17/60 (both rise) | (51/200, 17/60) | (51/200, 17/60) | K4 burden table (classical paper) |
| pass | K4: four-cycle is pairwise stable with beta 1 (private > efficient cycle content) | stable, beta 1 | stable, beta 1 | universal_private_le_efficient_false_quad |
| pass | K4: efficient tree is not pairwise stable | False | False | K4 (computed) |
| pass | K4: exactly five pairwise-stable networks: the four-cycle and four forests | [[0, 1, 5], [0, 2, 3, 5], [0, 4, 5], [1, 2, 4], [2, 3]] | [[0, 1, 5], [0, 2, 3, 5], [0, 4, 5], [1, 2, 4], [2, 3]] | K4.stable_22 + computed |
| pass | K4: pruning from the complete graph, 1 cuts 13 then 2 cuts 02, stops at the four-cycle (beta 1) | four-cycle, no further cut | {0, 2, 3, 5}, cuts left 0 | K4.prune_selects_by_history |
| pass | K4: pruning 2 cuts 23, 1 cuts 12, 1 cuts 01, stops at the forest {02, 03, 13} (beta 0) | {1, 2, 4}, beta 0, no further cut | {1, 2, 4}, beta 0, cuts left 0 | K4.prune_selects_by_history |
| pass | P5: five admissible networks (four spanning trees and the whole graph) | 5 | 5 | P5.nadm_* |
| pass | P5: the only pairwise-stable network is the whole graph, beta 1 | [{0,1,2,3,4}], beta 1 | [{0, 1, 2, 3, 4}], beta [1] | stable_forest_exists_false_quad |
| pass | P5: the tree {03, 12, 13, 24} is an admissible forest (beta 0) and not stable | admissible, beta 0, not stable | admissible, beta 0, not stable | P5.adm_30, beta_30, not_stable_30 |
| pass | unit triangle, m=1/20 < 1/12: efficient network is the cycle (beta 1), private prunes to {01} | efficient {0,1,2}; stable {0} | efficient {0, 1, 2}; stable [{0}] | Pruning triangle_* (planted) |
| pass | four-party pair: same exposures matrix (a single 1 at (0,1)) and positions (1,-1,0,0) | True | True | paper 'The pair' |
| pass | four-party pair A (two two-cycles): rewrite (1/2, -1/2, 0, 0) | [0.5, -0.5, 0.0, 0.0] | [0.5, -0.5, 0.0, 0.0] | paper 'The pair' |
| pass | four-party pair B (four-cycle): rewrite (3/4, -1/4, -1/4, -1/4) | [0.75, -0.25, -0.25, -0.25] | [0.75, -0.25, -0.25, -0.25] | paper 'The pair' |
| pass | four-party pair: party 2's half-share charge 0 in A, 1/32 in B; non-worsened in A, increased in B | [0.0, 0.03125] | [0.0, 0.03125] | paper 'The pair'; thm:classicalblind |
| pass | SNA consolidation with sectors {0,1},{2,3}: the zero table in both systems | zero table, both | {'A': {('S1', 'S2'): 0.0, ('S2', 'S1'): 0.0}, 'B': {('S1', 'S2'): 0.0, ('S2', 'S1'): 0.0}} | thm:sna-consolidation |
| pass | consolidation worth: allocation sum = freed carrying cost - maintenance = 5/12; exceeds v(N)=1/12 by the rewrite cost 1/3 | [0.416667, 0.083333, 0.333333] | [0.416667, 0.083333, 0.333333] | thm:freed; thm:firm |
| pass | corridor charge: J(e^v) = cosh v - 1 (half at each end) | 0.255169006 | 0.255169006 | paper rent theorem; corridor_charge_exact |
| pass | partition similarity: p^a + (1-p)^a equals 1 at a=1 and decreases | f(1)=1, decreasing | [1.384383, 1.0, 0.749979, 0.58, 0.37] | prop:geom / PartitionProcess |
| pass | certificate on pair A: no allocated cost rises, no bystander reached (the antiparallel line 1->0 is drawn in by the debt's own parties) | {'cost_increased_parties': [], 'bystanders': [], 'drawn_in': ['10']} | {'cost_increased_parties': [], 'bystanders': [], 'drawn_in': ['10']} | thm:dictionary b; 'The pair' |
| pass | certificate on pair B: bystanders 2 and 3 incur higher cost; full incident change for 2 is 2/32 | {'cost_increased_parties': ['2', '3'], 'bystanders': ['2', '3'], 'incident_change_2': 0.0625} | {'cost_increased_parties': ['2', '3'], 'bystanders': ['2', '3'], 'incident_change_2': 0.0625} | thm:dictionary a,b; 'The pair' |
| pass | certificate: parties 0 and 1 incur lower allocated cost in B | True | True | thm:dictionary b |
| pass | certificate under a kinked objective (gross-notional style): flagged kinked, nobody reached | {'kinked': True, 'reached': []} | {'kinked': True, 'reached': []} | rem:kink |
| pass | certificate, triangle log reading: full incident cost change for party 2 is 2 J(sqrt(3/8)) | 0.245366 | 0.245366 | thm:dictionary a |
| pass | certificate refuses a proposal that changes positions (not a rewrite) | refused | refused | def rewrite (positions fixed) |
| pass | one-sided record: entity-balanced, not matched, gap on 01 is 1 | {'balanced': True, 'matched': False, 'gap01': 1.0} | {'balanced': True, 'matched': False, 'gap01': 1.0} | TwoRecords.bal₁_entityBalanced / excess_bal₁_zero |
| pass | debtor view of the one-sided record is the zero network; debtor view of matched books is the books | {'debtor_view_coords': [0.0, 0.0, 0.0, 0.0], 'matched_fixed': True} | {'debtor_view_coords': [-0.0, 0.0, 0.0, 0.0], 'matched_fixed': True} | TwoRecords.projDebtor_bal₁ / projDebtor_eq_proj_iff |
| pass | two records, two cost comparisons: creditors' books increase party 2's charge by 1/32; debtors' books increase nobody's charge | {'creditor_cost_increased': ['2', '3'], 'debtor_cost_increased': [], 'charge2_creditor': 0.03125, 'charge2_debtor': 0.0, 'disagree': ['2', '3']} | {'creditor_cost_increased': ['2', '3'], 'debtor_cost_increased': [], 'charge2_creditor': 0.03125, 'charge2_debtor': 0.0, 'disagree': ['2', '3']} | TwoRecords.verdicts_differ / creditor_charge_two / debtor_pareto |
| pass | two records on matched books: cost comparisons agree (planted negative) | {'matched': True, 'cost_comparisons_agree': True} | {'matched': True, 'cost_comparisons_agree': True} | TwoRecords.verdict_agree_of_matched |
| pass | after a cross-posting on the one-sided record the gap is still 1 and the readings still differ | {'gap01': 1.0, 'readings_differ': True} | {'gap01': 1.0, 'readings_differ': True} | TwoRecords.no_legal_reconciliation |
| pass | certificate on the identity rewrite: no allocated cost changes, nothing moved (planted negative) | {'moved': [], 'cost_increased_parties': []} | {'moved': [], 'cost_increased_parties': []} | thm:dictionary b |
| pass | dispute sheet: one sheet, two figures 1.0 and 0.8, gap 0.2, interval [0.8, 1.0] | {'n': 1, 'interval': [0.8, 1.0], 'gap': 0.2} | {'n': 1, 'interval': [0.8, 1.0], 'gap': 0.2} | two figures |
| pass | dispute sheet: matched books yield no sheet (planted negative) | 0 | 0 | two figures |
| pass | open-line register on pair B: zero consolidated table; three open lines recorded, one intra-sector | {'table_zero': True, 'n_open': 3, 'intra': 1} | {'table_zero': True, 'n_open': 3, 'intra': 1} | thm:sna-consolidation |
| pass | bystander charge varies with the debt (meter not constant): amt^2/18 | [0.013889, 0.055556, 0.222222, 0.888889] | [0.013889, 0.055556, 0.222222, 0.888889] | meter contract |