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Table Table 1 Growth that compounds

The growth-loop evidence ledger

Do not call an arrow a loop until the next eligible unit, cost, and outcome window are visible.

Loop elementEvidence fieldSynthetic exampleNext-entry ruleFailure mode
Entry eventEligible unit, entry date, and inclusion rule100 active paying users at period startActive means paid and used under the declared periodTrial and paid units are mixed
Participant actionNamed action and actor32 users send a direct invitationInvitation is recorded once per recipientButton clicks are treated as transfers
TransferRecipient identity and delivery event20 invitations reach new recipientsRecipient is outside the starting populationExisting users are counted as new units
Received valueAcceptance or first-value event12 recipients accept the invitationAcceptance rule is timestampedDelivered message is called value
Next eligibilityEvent that admits the next distinct unit8 recipients pay and activateRecipient is deduplicated and qualifies within 30 daysEligibility has no time boundary
Reward or costIncentive, channel, and costEUR 160 in rewards and delivery costCost is assigned to the loop periodReward is called free
OutcomeContribution, retention, or later value30-day outcome remains unresolvedOutcome window closes before interpretationLoop conversion is called payback

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Reference & Evidence

Source: Author's synthetic loop ledger grounded in Biyalogorsky, Gerstner, and Libai (2001), Morgan and Hunt (1994), Kumar et al. (2010), and Villanueva et al. (2008). Counts, costs, and outcomes are illustrative, not campaign data or benchmarks.

Each line is a claim from the register this journal publishes against, resolved from the register at build time.

  • B Biyalogorsky et al. model customer referral management through referral incentives and show that reward design depends on the economic and behavioural conditions of the model: "We investigate when referral rewards should be offered to motivate referrals and derive the optimal combination of reward and price that will lead to the most profitable referrals" Biyalogorsky et al. (2001), full-text extract held · BGL01-C1
  • B Their analysis allows referral rewards to be profitable under some conditions while leaving risks such as free riding or reward misallocation visible: "rewards can sometimes be given to customers who would have recommended anyway, causing a waste of company resources" Biyalogorsky et al. (2001), full-text extract held · BGL01-C2
  • B The referral-reward result is a bounded model and does not establish a universal referral rate, loop coefficient, or reward percentage: "These results are consistent with the fact that referral rewards are not offered in all markets" Biyalogorsky et al. (2001), full-text extract held · BGL01-C3
  • B Morgan and Hunt identify commitment and trust as key mediating variables in successful relationship marketing in their tested relationship-marketing model: "successful relationship marketing requires relationship commitment and trust" and "model relationship commitment and trust as key mediating variables" Morgan and Hunt (1994), full-text extract held · MH94-C1
  • B The commitment-trust mechanism is a relationship condition, not proof that every customer referral or growth loop will compound: "using data from automobile tire retailers" and "compare their model with a rival that does not allow relationship commitment and trust to function as mediating variables" Morgan and Hunt (1994), full-text extract held · MH94-C2
  • B Kumar et al. distinguish customer engagement value beyond transactions through customer lifetime, referral, influencer, and knowledge components: "We propose four components of a customer’s engagement value (CEV) with a firm. The first component is customer lifetime value (the customer’s purchase behavior), the second is customer referral value (as it relates to incentivized referral of new customers), the third is customer influencer value" and "the fourth is customer knowledge value (the value added to the firm by feedback from the customer)" Kumar et al. (2010), full-text extract held · KAV10-C1
  • B Their framework warns that a transaction-only view can undervalue or overvalue customers when non-transactional contributions are relevant: "assessing the value of customers based solely upon their transactions with a firm may not be sufficient" and "valuing this engagement correctly is crucial in avoiding undervaluation and overvaluation of customers" Kumar et al. (2010), full-text extract held · KAV10-C2
  • B Customer engagement value is a valuation framework and not a measured universal growth-loop multiplier: "future research propositions regarding relationships between the four components of CEV are proposed" Kumar et al. (2010), full-text extract held · KAV10-C3
  • B Villanueva et al. compare marketing-induced and word-of-mouth acquisition and describe differences in acquisition speed, cost, and customer-equity development in a bounded setting: "Companies can acquire customers through costly but fast-acting marketing investments or through slower but cheaper word-of-mouth processes" Villanueva et al. (2008), full-text extract held · VYH08-C1
  • B Their web-hosting evidence reports a different short-term and long-term value path for marketing-induced and word-of-mouth customers; the setting and time horizon remain part of the result: "customers add more short" and "customers add nearly twice as much long" Villanueva et al. (2008), full-text extract held · VYH08-C2
  • B The acquisition comparison does not supply a universal channel ratio or prove that a referral loop compounds in another business: "An application to a Web hosting company reveals" Villanueva et al. (2008), full-text extract held · VYH08-C3
  • B A growth loop is a declared sequence from an entry event through participant action, transfer, receipt, and eligibility for the next iteration Author framework · G11LOOP-OWN-C1
  • B A loop entry event must create or expose a new eligible unit under a named population rule; activity alone is not loop transfer Author data framework · G11LOOP-OWN-C2
  • B A referral event, referral rate, referral value, and loop conversion are different objects and need different denominators Author metric taxonomy · G11LOOP-OWN-C3
  • B Paid acquisition, referral, influencer, knowledge, and retention contributions should remain separate before a team calls them one loop Author valuation framework · G11LOOP-OWN-C4
  • B A reward is both an incentive and a cost; the presence of a reward does not prove profitable or self-sustaining growth Author negative boundary · G11LOOP-OWN-C5
  • B Loop conversion can be calculated only after the eligible entrant population, next-entry event, time window, and exclusions are declared Author measurement framework · G11LOOP-OWN-C6
  • B The growth-loop ledger is synthetic and illustrative; it contains no customer, referral, campaign, or company data Author synthetic object · G11LOOP-OWN-C7
  • B A loop diagram can describe a mechanism, while causal growth or payback requires a separate comparison design and outcome window Author causal boundary · G11LOOP-OWN-C8

Grades: A, verified against the printed page of the primary source · B, primary source, text layer only · C, authoritative secondary · D, reported.

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