Ex Ante Estimation of Payable Relief and Compensation Timing for Supplier Selection

1 Introduction

• CCA adds expected payable relief as a post-qualification supplier criterion, combining CPM’s bounded structural signal with concave bilateral capacity; cycle and path policies serve as independent validation environments.CCA evaluates whether a new supplier relation may enable gross obligations to be removed before residual cash settlement or external funding is required.Source: §1 · p. 2
• Across seven fully observed quarters, frozen log-CCA’s median Spearman correlation with future integrated relief was 0.638; persistent relations carried 93.5% of relief, and top-ranked relations captured 92.5% of buyer-specific best relief.Q4 2022 is interpreted as part of an unusually reciprocal and cycle-saturated period, not as a standalone success.Source: §1 · p. 3
• Across the two validation environments, 89–91% of attributed relief occurred within seven days and 94–96% within thirty days; exact waiting-time prediction was weaker.Log-CCA’s median correlations were 0.564 with integrated thirty-day relief and 0.566 with relief-days; its highest quartile had a 96.5% median incidence of positive thirty-day compensation, versus 57.6% in the lowest.Source: §1 · p. 3
• Median rank correlation rose from 0.526 weekly to 0.681 for the single complete annual origin, while relation persistence declined; the paper favors quarterly recalibration.Longer horizons reveal more eventual compensability but cover a smaller share of the future relational perimeter.Source: §1 · p. 3

2.1 The evolution of supplier-selection research

• Supplier models usually assess attributes dyadically, whereas CCA adds the supplier relation’s position in the wider payable network.Two commercially acceptable suppliers may occupy very different network positions.Source: §1 · p. 2, §2.1 · p. 4

2.2 Supply-network structure and network-aware operations

• Compensability is not centrality: maturity-compatible paths and cycles determine relief, making CCA a procurement signal before settlement of a given network.Cycle and path mechanisms reward different local structures.Source: §2.2 · p. 5, §2.4 · p. 6

2.3 Working capital and supply chain finance

• Unlike financing instruments that reallocate liquidity, compensation asks how much gross payable stock can be removed before residual funding.CCA offers an upstream input to working-capital analysis by estimating payable stock that may disappear before the remaining cash-to-cash requirement is financed.Source: §2.3 · p. 5

2.5 Circular economy, circular supply chains, and measurement

• Financial circularity concerns liquidity in obligations reduced or compressed under maturity and governance constraints, distinct from material circularity and literal graph cycles.The literature gap spans ex-ante supplier selection, network clearing, and temporal transport; a competitive capability also depends on data, governance, and organizational routines.Source: §2.5 · p. 7, §2.6 · p. 7, §2.7 · p. 7

3.1 Prospective validity

• A pre-period score should be positively associated with relief generated by subsequently issued invoices.The hypothesis covers CPM and concavely capacity-adjusted CCA variants frozen before the target period.Source: §3.1 · pp. 8–9

3.2 Repeated quarterly validity

• Log-CCA is hypothesized to remain positively associated with relief across every quarter of 2022 and 2023, subject to available follow-up.Repeating the design tests whether the relationship survives changes in participation, invoice concentration, maturities, and reciprocal structure.Source: §3.2 · p. 9

3.3 Capacity transformation

• Log-CCA is hypothesized to provide a more stable balance of rank correlation and magnitude alignment than raw CCA.Concave transformations are intended to retain capacity’s activation role while limiting the leverage of very large suppliers.Source: §3.3 · p. 9

3.4 Supplier-selection benefit

• Within each buyer’s feasible alternatives, the highest-log-CCA relation is hypothesized to outperform the mean candidate and capture substantial buyer-specific best relief.The decision test concerns buyer-conditioned choice, not only a global relation ranking.Source: §3.4 · p. 9

3.5 Timely compensation opportunity

• Log-CCA is hypothesized to associate positively with thirty-day relief and relief-days, but less strongly with exact waiting time among compensated relations.The motivation links earlier relief to shorter duration of outstanding gross obligations while recognizing execution-order variation.Source: §3.5 · p. 9

3.6 Horizon dependence

• Across weekly to annual horizons, predictive signal and relational coverage are expected to change on different margins.Short windows contain fewer events; longer windows average noise but allow more new relations to appear after the score is frozen.Source: §3.6 · p. 9

3.7 Calibration and drift

• The calibration hypothesis expects positive out-of-period value from models trained on completed prior quarters, alongside enough variation to justify recurrent recalibration and drift monitoring.The proposed approach preserves the transparent score while recalibrating its monetary and temporal mapping.Source: §3.7 · pp. 9–10

3.8 Strategic proposition

• CCA may support a competitive liquidity capability when proprietary network visibility, reliable maturity and residual data, governed participation, and procurement–treasury routines come together.The empirical hypotheses concern prediction, not causal firm performance.Source: §3.8 · p. 10

4.1 Decision setting and unit of analysis

• The contemplated decision is a new payable to a qualified supplier, with the target being expected gross-payable reduction at that network entry point, not generic supplier attractiveness.Source: §4.1 · p. 10

4.2 Effective payable-mass reduction

• Effective relief restores generated instructions rather than counting all replaced obligations as removed; integrated opportunity adds separate policy outcomes, not a jointly executable total.Source: §4.2 · pp. 10–11

4.3 Compensation timing and relief-days

• Timing evaluation tracks issue-to-event delay, maturity lead, timely relief, and relief-days, but admissible events do not guarantee creditor cash receipt.Capping maturity lead at one year changes aggregate relief-days by 0.37% in the path environment and 0.20% in the cycle environment.Source: §4.3 · p. 11

4.4 Expected relief and mechanism decomposition

• Expected relief separates operation probability from conditional relief multiple, distinguishing relations with equal expected values but different operational risks.CPM is a bounded structural representation of expected relief that preserves its ranking while compressing extreme multiples.Source: §4.4 · p. 11, §4.6 · p. 12

4.5 Cycle-restricted and path-enabled validation environments

• Cycle-restricted and path-enabled policies test different structures—reciprocal closure and accessible two-edge paths—and serve as independent validation environments, not competing technologies.Source: §4.5 · p. 12

4.7 Capacity adjustment and CCA

• CCA is a capacity-adjusted prioritization feature, not a euro-denominated estimate; log-CCA preserves structural-capacity complementarity while limiting domination by extreme volume.The worked example reports a capacity ratio of 20, raw CCA of 1,186.8, and log-CCA of 180.7.Source: §4.7 · p. 13, §4.9 · p. 13

4.8 Production-economic interpretation

• A financing scenario translates expected relief into avoided funding exposure, but it is sensitivity analysis—not an observed causal saving—and costs must be deducted before claiming net benefit.Source: §4.8 · p. 13

5.1 Research architecture; 5.2 Source archive and analytical population; 5.7 Frozen-origin score construction

• Scores are frozen from trailing nine-month histories before target windows, and six prespecified variants are tested across quarters, multiple horizons, and sequential calibration.The design includes eight quarter origins covering 2022–2023, with additional weekly, monthly, semester, and annual windows.Source: §5.1 · p. 14, §5.7 · pp. 15–16

5.3 Common-day capacity and effective relief

• Executable capacity uses atomic invoices simultaneously active on a common day, while effective relief measures post-instruction payable-mass reduction.Aggregate graphs discover candidate relations, but atomic records determine executable amounts and prevent false overlap across invoices.Source: §5.2 · p. 14, §5.3 · p. 14

5.4 Rolling physical state and the two-month annual bridge

• Continuous policy ledgers carry January–February bridge invoices into the next cohort; consumed fragments are not restored, and PMR is attributed by source issue cohort.This separates physical execution from cohort reporting while preserving additivity across issue cohorts.Source: §5.4 · pp. 14–15

5.5 Independent outcome environments; 5.6 Timing outcomes and shorter-term compensation

• Cycle-restricted and path-enabled policies run on separate residual ledgers; integrated labels combine their attributed outcomes for validation, not as executable settlement totals.Timing outcomes include short-window relief shares, issue-to-event delay, days remaining to maturity, relief-days, and conditional delay among positive-relief relations.Source: §5.5 · p. 15, §5.6 · p. 15

5.8 Forecast windows, follow-up, and outcome attribution; 5.9 Quarter, month, semester, year, and week designs

• Disjoint target windows use a two-month outcome bridge, while preselected weekly samples avoid overlapping windows; Q4 2023 lacks its planned complete bridge.The design also sets quarter, month, semester, and annual origins; Q4 2023 has 39 rather than 60 follow-up days.Source: §5.8 · p. 16, §5.9 · p. 16

5.10 Evaluation metrics

• Evaluation combines rank and magnitude correlations with buyer-specific capture and selection metrics; quarter-level uncertainty uses buyer-cluster bootstrap resampling.Bootstrap intervals are stability diagnostics for the observed network, not IID population confidence intervals.Source: §5.10 · pp. 16–17

5.11 Sequential calibration

• A sequential hurdle model trains only on completed earlier quarters to test whether recalibration improves magnitude prediction and buyer-specific selection.The transparent score remains the underlying construct rather than being replaced by the calibrated model.Source: §5.11 · p. 17

5.12 Audit and reconciliation

• Independent replay audits verify invoice activity, fragment and PMR identities, nonnegative residuals, and annual-state reconciliation across bridge boundaries.The reported streams have no duplicate introductions, overconsumption, negative residuals, or temporal violations.Source: §5.12 · pp. 17–18

6.1 Quarter-ahead association across Q1–Q4 2022 and 2023

• Log-CCA’s median Spearman correlation with integrated relief is 0.638 across seven complete quarters, with all quarter tests positive and buyer-cluster bootstrap ranges above zero.The complete-quarter correlation range is 0.592–0.663; Q4 2023 is right-censored and excluded from the complete-only median.Source: Table 4 · p. 18, §6.1 · pp. 18–19

6.2 Timely compensation and reduction of outstanding duration

• Across complete quarters, 89.4% of path-attributed and 90.8% of cycle-attributed relief occurs within seven days; Log-CCA also predicts thirty-day relief, but exact conditional delay is weaker.Log-CCA correlates 0.564 with integrated thirty-day relief and 0.566 with relief-days; its highest quartile has 96.5% median positive thirty-day relief versus 57.6% in the lowest.Source: Table 5 · p. 19, §6.2 · pp. 19–20, Table 6 · p. 20

6.3 Formula variants and the role of capacity

• Log-CCA has the highest complete-quarter median Spearman correlation among tested variants at 0.638, while CPM’s top decile captures 91.4% of total integrated relief versus 64.5% for log-CCA.Log-CCA is presented as a stable operational compromise, not a universal replacement for CPM’s structural signal.Source: §6.3 · p. 21, Figure 4 · p. 21

6.4 Independent path and cycle outcome checks

• Log-CCA correlations are positive under both independent outcome environments, with complete-quarter path correlations of 0.511–0.563 and cycle correlations of 0.472–0.578.The two channels are complementary construct-validity checks, not competing technologies.Source: §6.4 · p. 22, Table 8 · p. 22

6.5 Persistent relations carry most future relief; 6.6 Buyer-specific supplier prioritization

• Persistent relations carry a median 93.5% of integrated relief; selecting the highest-log-CCA relation captures 92.5% of buyer-specific best outcomes across complete quarters.Persistent relations comprise 61.1–80.2% of target relations, and selection produces a median 348.4% uplift over mean candidates.Source: §6.5 · p. 22, Table 9 · p. 22, §6.6 · p. 23

6.7 Horizon comparison from week to year

• Median Spearman correlation rises from 0.526 weekly to 0.681 annually, while relation persistence falls from 88.9% to 50.3% and relief coverage declines more slowly.The sole complete annual origin is 2022, so the horizon pattern supports a qualitative smoothing–coverage trade-off rather than precise annual superiority.Source: §6.7 · pp. 23–24, Table 11 · p. 23, Figure 5 · p. 24

6.8 Month-to-month evidence; 6.9 Pre-specified week-to-week samples; 6.10 Semester and annual windows

• Monthly correlation has a 0.615 median; weekly samples have a 0.526 median, while semester correlations are 0.640, 0.672, and 0.626 for H1 2022, H2 2022, and H1 2023.Monthly monitoring can track drift between quarterly recalibrations; weekly results are better treated as alerts, and the single complete annual origin does not establish annual superiority.Source: §6.8 · pp. 24–25, §6.9 · p. 25, §6.10 · pp. 25–26

6.11 Sequential temporal calibration; 6.12 Overall assessment of hypotheses

• Sequential full-control plus log-CCA retains positive performance in every test quarter, and the authors recommend a stable score with periodic calibration and monitoring.Its Spearman correlations range from 0.738 to 0.811, while calibration quality still varies over time.Source: §6.11 · p. 26, Table 12 · p. 26, §6.12 · p. 27

7.1 Prospective validity and temporal transport

• Frozen information retains positive but varying predictive value for later relief, supporting periodic recalibration rather than a timeless mapping.The authors describe the construct as stable enough to recur, but not invariant across quarters.Source: §7.1 · p. 27

7.2 Theoretical contribution to supplier selection

• CCA extends supplier selection beyond dyadic attributes by treating a qualified supplier relation as a maturity-aware network entry point.CPM captures structural compensability, while capacity complements it; Log-CCA is the better-balanced operational predictor and buyer-conditioned selector.Source: §7.2 · p. 27

7.3 Relief amount and compensation timing

• Log-CCA predicts thirty-day relief amount and the combined amount-duration outcome more strongly than exact delay conditional on an event.The discussion recommends presenting probability or expected amount for a defined horizon, not a promised compensation date.Source: §7.3 · pp. 27–28

7.4 Two compensation environments, one measurement question

• The cycle-restricted and path-enabled environments provide independent validation channels, not competing technologies or jointly executable settlement totals.Their integrated label combines opportunities generated on separate residual ledgers for predictive coverage.Source: §7.4 · p. 28

7.5 Forecast horizon and decision cadence

• Quarterly windows balance repeated validation, relief coverage, timing information, and procurement relevance; quarterly recalibration is the recommended default.Monthly monitoring and weekly exception diagnostics complement that cadence, while faster or slower updating may suit different categories.Source: §7.5 · p. 28

7.6 The 2022 structural context

• Q4 2022 falls within an unusually reciprocal, cycle-saturated period, so it should not be treated as uniquely favorable or representative.The full Q1–Q4 sequences in both years are the appropriate evidence.Source: §7.6 · pp. 28–29

7.7 Production-economic and supply-chain-finance implications

• CCA adds an endogenous-relief stage before external financing, but payable-mass reduction is not itself liquidity or proof of lower capital costs.Net funding benefit depends on acceptance, legal discharge, fees, payment acceleration, exposure, cash balances, and external-finance conditions.Source: §7.7 · p. 29

7.8 Competitive advantage and organizational capability; 7.9 Managerial implementation architecture

• CCA’s potential organizational advantage lies in the data and governance capabilities around the transparent formula, not the formula alone.The proposed implementation layers data verification, structural scoring, completed-period calibration, and governance; dashboards should retain horizon and calibration context.Source: §7.8 · p. 29, §7.9 · p. 29

8.1 Scientific impact: from static centrality to dated economic opportunity

• CCA shifts network analysis from static prominence toward whether a contemplated relation connects a buyer to active, maturity-constrained obligations with capacity for measurable relief.The framework treats timing-weighted relief as an economic outcome while distinguishing prediction from causal welfare.Source: §8.1 · pp. 29–30

8.2 Methodological transfer to other stateful systems

• The frozen-origin approach separates score-time information, operational state, future cohort, and evaluation horizon, while distinguishing rank, magnitude, decision, and timing validation.More complex timing models are proposed for comparison against transparent CPM and Log-CCA, not as automatic replacements.Source: §8.2 · p. 30

8.3 Procurement, treasury, and supplier-portfolio applications

• In qualified supplier sets, procurement and treasury could use CCA to assess relief opportunity, while portfolio analysis could test financially discretionary order allocation under operational constraints.These are decision-support uses, not automatic instructions, and require risk limits and separation of claim transformation from cash receipt.Source: §8.3 · pp. 30–31

8.4 Circular supply chains and industrial symbiosis

• Financial circularity is distinct from material circularity, so CCA is a financial complement rather than a universal circularity index.The discussion proposes studying whether industrial symbiosis also creates compensable financial structure, without assuming that liquidity causes environmental outcomes.Source: §8.4 · p. 31

8.5 Platform ecosystems, agentic coordination, and privacy-preserving clearing

• Platforms could use CCA to prioritize participation and governed opportunities, but agentic or privacy-preserving deployment still requires verification, consent, legal finality, and governance.The paper identifies sensitive network visibility and recommends evaluating disclosure, communication cost, accepted relief, finality, and fairness.Source: §8.5 · pp. 31–32

8.6 Public-sector, SME, cooperative, and community applications; 8.7 Resilience, early warning, and macro-network applications

• Applications to public and cooperative networks remain prospective, with SME safeguards needed because capacity-adjusted scoring may favor established high-volume firms.The discussion also calls for measuring whether compensability reduces distress or instead rearranges exposures or creates concentration risks; national representativeness is not established.Source: §8.6 · p. 32, §8.7 · p. 32

8.8 Societal safeguards and responsible deployment

• Responsible deployment requires fairness constraints, exposure limits, competition safeguards, and protected data governance; a high score is not authority to alter a claim.The authors call for evaluating accepted relief and treating refusals, disputes, reversals, and failed payments as outcomes.Source: §8.8 · p. 33

8.9 Application map and future research program

• The research agenda calls for broader out-of-time and jurisdictional evidence, direct observation of payment stages, causal procurement interventions, and assessment of topology changes.CCA is framed as a transparent predictive feature within a governed system, not an autonomous objective overriding other constraints.Source: §8.9 · pp. 33–34

• The evidence comes from one institutional archive with changing coverage, dependent observations, and right-censored later windows.Buyer-cluster bootstrap intervals are stability diagnostics, not population confidence intervals.Source: §9 · p. 34
• The two deterministic outcome environments establish structurally feasible relief under specified policies, not universal acceptance, legal finality, or a feasible joint policy.Timing measures track compensability or claim transformation, not necessarily cash receipt or days-sales-outstanding reduction.Source: §9 · p. 34
• Relief-days cap maturity lead at 365 days, while the horizon comparison has unequal numbers of complete origins and limited annual observations.The paper also reports path-stream discrepancies from non-unique local ordering and calls for canonical tie-breaking and replay specifications.Source: §9 · p. 34
• Historical invoice capacity omits committed future volume, supplier willingness, and category substitutability; observed buyer choice sets are not randomized alternatives.The study therefore does not establish causal benefit from following CCA recommendations, and new or low-volume suppliers face cold-start constraints.Source: §9 · p. 34
• Payable-mass reduction and relief-days are not equivalent to cash, interest savings, profitability, resilience, or welfare; their conversion depends on downstream conditions.The authors call for field studies and further complete years, jurisdictions, payment-finality data, supplier-choice experiments, and distributional audits.Source: §9 · pp. 34–35

10 Conclusion

• CCA treats supplier placement as a network-financial consequence, using expected relief as its monetary estimand and concave capacity transformations to temper leverage in heavy-tailed invoice volumes.CPM is the bounded, size-neutral structural representation; Log-CCA adds a commercial activation layer, but neither is an invariant euro forecast without calibration.Source: §10 · p. 35
• Across seven fully observed quarters, Log-CCA's median Spearman correlation with future integrated relief is 0.638; persistent relations carry 93.5% of relief, and the top-scoring relation captures 92.5% of buyer-specific best relief.The buyer-choice result shows prioritization value within buyers' own alternatives, while quarter-to-quarter results are not invariant.Source: §10 · p. 35
• Across the two validation environments, 89–91% of attributed relief occurs within seven days and 94–96% within thirty days; Log-CCA correlates 0.564 with thirty-day relief and 0.566 with relief-days.The highest quartile has a 96.5% median incidence of positive thirty-day compensation, versus 57.6% in the lowest quartile.Source: §10 · pp. 35–36
• Predictive association is positive from week to year, while quarterly estimates offer the strongest operating balance and support quarterly recalibration, monthly monitoring, and weekly diagnostics.The annual result is strategically informative but rests on one fully observed origin.Source: §10 · p. 36
• Cycle-restricted and path-enabled compensation serve as independent tests of CCA under different local structures, not as competing technologies or a jointly executable settlement total.Their integrated label broadens validation coverage but is not a jointly executable total.Source: §10 · p. 36
• CCA adds a network-aware decision stage before external finance, and financial circularity complements rather than substitutes for material circularity or environmental performance.Combining environmental and financial indicators to identify resource-efficient and financially sustainable configurations remains a possibility to be tested.Source: §10 · p. 36
• Deployment could favor established high-volume firms, increase concentration, or expose sensitive topology, so the paper calls for safeguards including fairness constraints, privacy-preserving access, consent, and oversight.The passage also identifies qualification rules, cold-start treatment, legal finality, and transparent fees.Source: §10 · p. 36
• The study establishes predictive validity and prioritization value, not causal financial or social impact; claims about cash arrival, financing cost, or days-sales-outstanding require operational data.The proposed next step is a prospective field intervention with qualified alternatives, followed by repeated studies across jurisdictions and sectors.Source: §10 · pp. 36–37

Data and code availability

• The pseudonymized database and a repository containing source code, preparation scripts, outcome engines, analyses, figures, tests, and verification workflows are available, while raw identifiable records and reversible identity mappings are not distributed.The database is identified as Esteva de la Rosa, Peplluis (2026), Mendeley Data, Version 1, doi: 10.17632/28rbmvwsm9.1.Source: Data and code availability · p. 37

Declaration of generative AI and AI-assisted technologies

• The authors used an AI-assisted language and coding system for editing, code review, artifact generation, and consistency checks, and reviewed the outputs while retaining responsibility for the work.Source: Declaration of generative AI and… · p. 37

A Complete quarterly formula comparison

• Table 14 compares formula variants against future integrated relief by quarter, with columns labeled Quarter, Score, Spearman, Log-Pearson, and Top-decile capture.Source: Table 14 · p. 37, A Complete quarterly formula comparison · p. 38

B Monthly detail

• Table 15 presents month-ahead Log-CCA results under continuous-state outcome attribution.The caption identifies the table’s scope but does not provide its outcome values.Source: Table 15 · p. 39

C Pre-specified weekly samples

• Table 16 covers two pre-specified weekly samples per quarter.The supplied passage identifies the sample design but provides no interpretable results.Source: Table 16 · p. 39

D Detailed compensation-timing results

• The timing results distinguish zero-inclusive relief outcomes from conditional waiting-time ordering, and median patterns reinforce that incidence is easier to predict than exact delay.Table 17’s third target is conditional on positive eventual relief; Table 18 summarizes the incidence-versus-delay pattern.Source: D Detailed compensation-timing results · p. 40, Table 17 · p. 40, Table 18 · p. 41
• Log-CCA is strongest for thirty-day relief, while CPM is marginally strongest for relief-days; Log-CCA provides the most balanced operational specification.Figure 9 compares median complete-quarter correlations across formula variants.Source: Figure 9 · p. 41

E Annual reconciliation with the companion algorithm study

• Cycle reproduction is exact to displayed precision, while path differences reach at most 0.371 percentage points; bridge and non-reuse identities are exact in both streams.Annual bridge-adjusted PMR reconciliation is the scope identified for Table 19.Source: E Annual reconciliation with the… · pp. 41–42, Table 19 · p. 41

F Reconciliation with the superseded restarted-window analysis

• All complete overlapping quarters change by less than 0.020 in Spearman correlation after correction, but buyer-level allocation is more sensitive to early consumption.The bridge-correct estimates supersede restarted results; the buyer set can also change slightly when positive-relief candidate relations change.Source: F Reconciliation with the superseded… · p. 42, Table 20 · p. 42, Table 21 · p. 42

G Deterministic bridge-correct algorithm

• The bridge-correct algorithm retains residual invoices between yearly phases and filters an immutable contribution log by source issue and execution dates to prevent bridge reuse.It asserts that each invoice UID is introduced once and consumption does not exceed face value.Source: G Deterministic bridge-correct algorithm · p. 43

H Reproduction workflow

• Public reproduction verifies aggregate outputs and synthetic accounting tests, but full source-level replay requires authorized access to the pseudonymized atomic ledger and operation contributions.Source: H Reproduction workflow · p. 43