The Measuring Problem

01 / The blindspot is live

BPS is the industry KPI for Bitcoin treasury companies. Every BTCTC of meaningful size reports it. Every one of them carries senior claims the metric does not subtract. The contradiction is not theoretical and it is not limited to Strategy. The four examples below are this quarter, in four jurisdictions, in four different instrument categories, across four operators widely respected within the BTCTC space.

Strategy. Carries over 15 billion dollars of preferred stock across five series. Four of those series, STRF, STRC, STRD, and STRE, are perpetual and do not convert to common shares. STRC alone, at over 10 billion dollars, is larger than the other four series combined, and it carries no conversion at all. The fifth series, STRK, is convertible. For the four non-convertible series, the if-converted method has nothing to fold in. Fully diluted shares do not move when those series are issued, expanded through ATM activity, or modified, which means the bulk of a 15 billion dollar claim stack never touches the BPS denominator. The KPI footnote in every Strategy press release discloses, in writing, that BTC Yield “does not take into account debt and other liabilities and claims on company assets that would be senior to common equity.” The metric is reported anyway. Year-to-date BTC Yield through Q1 2026 is 9.4%. CEBE Yield over the same period is 1.7%. The gap is 7.7 percentage points. It is not a math error, it is the actual cost of putting the Bitcoin on the balance sheet that BPS cannot see.

The Smarter Web Company. Drew on a Bitcoin-backed credit facility from Coinbase Credit, took the borrowed dollars, bought Bitcoin with them, and reported a BTC Yield among the highest in the sector for the quarter. The facility is a senior claim. It is secured against the company’s existing Bitcoin. BPS does not subtract it. So the borrowed dollars became Bitcoin, the new Bitcoin lifted the per-share count, and the per-share count printed as a yield achievement with the loan that funded it nowhere in the number. The yield is real only if the reader ignores the claim that produced it. This is the cleanest version of the blindspot in the dataset, because the cause and effect are a single step apart: borrow, buy, report.

Metaplanet. Carries two distinct senior claim categories. A 247 million dollar USD credit facility, dollar-denominated. A MERCURY Class B preferred at 23.61 billion yen, roughly 148 million dollars, yen-denominated. The MERCURY preferred is structurally constrained to cash dividends only, because the Japanese Companies Act prohibits the share-payment election Strategy uses on STRK and STRD. Both claims sit between common shareholders and the 40,177 BTC the company holds. BPS does not subtract either. In Q4 2025, Metaplanet added 405 million dollars in new claims. BPS rose 11.9% on the strength of new Bitcoin acquisition. CEBE fell 4.5% because the senior claim grew faster than the asset. The same quarter produced two metrics pointing in opposite directions.

Capital B. Carries 1,060 BTC of senior claims denominated in Bitcoin itself, not in dollars or euros. The OCA convertibles do not compress in BTC terms when Bitcoin rises and do not expand when Bitcoin falls. The claim is 1,060 BTC at 50,000 dollar Bitcoin. The claim is 1,060 BTC at 150,000 dollar Bitcoin. Drag is static rather than continuous. BPS does not subtract the claim. The market has priced that structural insulation across 553 consecutive days in which Capital B has never closed below 1.0x net asset value. CEBE captures the static senior claim that the market is paying a premium to obtain.

Four companies, four jurisdictions, four instrument categories, one blindspot. Strategy’s senior claims are perpetual preferred with no conversion mechanism on the bulk of the stack. Smarter Web’s are a secured, Bitcoin-collateralized credit line. Metaplanet’s are split across a dollar-denominated facility and a yen-denominated preferred, compressing on different vectors at different rates. Capital B’s are denominated in Bitcoin itself, which means they do not compress at all. Different jurisdictions, different instruments, different mechanics, each one invisible to BPS in its own way.

This is not a Strategy story. BPS is the BTCTC reporting standard, used by treasuries that carry every kind of senior claim a corporate balance sheet can carry. The metric was designed to measure accumulation per share. It does not subtract what stands between the holder and the asset because subtraction was never in the formula. The blindspot is not an implementation flaw. It is what BPS is.

02 / The three metrics

BPS divides total Bitcoin by fully diluted shares. The if-converted method folds convertible debt into the share count whenever those converts are dilutive. Preferred stock, non-convertible debt, and cash do not enter the calculation. Strategy publishes the period-over-period change in BPS as its key non-GAAP performance indicator, calls it the centerpiece of value-creation reporting, and discloses in the same KPI footnote that the metric “does not take into account debt and other liabilities and claims on company assets that would be senior to common equity.” The company tells investors to measure it on BPS. The company tells investors BPS is incomplete. The metric is reported anyway, and other BTCTCs have adopted the same KPI under the same name. The reporting standard is industry-wide.

mNAV is the valuation metric, and it is the one the market actually watches. The trouble is that mNAV is several numbers wearing the same name. Basic mNAV divides plain market cap by the gross Bitcoin reserve. Diluted mNAV uses a fully diluted market cap. EV mNAV uses enterprise value: market capitalization plus debt plus preferred minus cash. The three do not agree. Strategy reported all three on the same day in late 2025 at 0.856, 0.954, and 1.105. One company, one balance sheet, one afternoon, three valuation multiples, one of them below parity and one above it. The word mNAV names a family of numbers that disagree, and the measuring problem is reproduced inside a single metric. Part 2 unpacks how this ambiguity produced Strategy’s 1.22 accretion threshold and why the number the market calls a breakeven is really the drag, renamed.

Amplification divides gross senior claims, debt plus preferred, by the Bitcoin reserve, and presents the result as the upside multiplier on common equity’s Bitcoin exposure. Cash is not netted. The denominator is Bitcoin only, even though the preferred prospectuses state in writing that the instruments are not Bitcoin-backed. The obligation stands against the entire corporate balance sheet. A Bitcoin-only denominator treats the reserve as the sole resource behind claims that in fact rank against everything the company owns, and that inflates the multiplier.

The same companies that disclaim Bitcoin backing in the prospectus also promote a BTC Rating: total Bitcoin value divided by senior claims, a coverage ratio that frames the Bitcoin as exactly the backing the prospectus says it is not. The legal document and the investor narrative contradict each other on the most basic question of what stands behind the preferred. The contradiction is structural. An unsecured preferred claim is paid in a liquidation from the whole net estate, after more senior obligations, alongside every general creditor. Pairing the Bitcoin reserve directly against the preferred describes a security interest the indenture does not grant. Where the claim runs the other way, as with Nakamoto’s Bitcoin-collateralized loan and its forced-liquidation trigger, the same gross accounting understates the danger, because the loan can seize Bitcoin and accelerate the loss to common equity while sitting in the denominator as a fixed number. Gross claims accounting fails in both directions. It overstates the Bitcoin’s role where the claim is unsecured and understates the danger where the claim is collateralized.

That uneven failure is worth naming. The toolkit does not mismeasure every company the same way. It under-credits the cleanest operators, because a structure carrying no senior claims is invisible to a metric that cannot see structure, and it conceals the most dangerous, because a forced-liquidation trigger reads as a flat number in a denominator. The best actors get no measurement benefit for being clean. The weakest get their real risk hidden. One broken toolkit, opposite disservices at opposite ends of the quality range.

Three metrics, each mathematically valid on its own terms. Each one missing the piece the others contain.

03 / The contradictions

Each metric treats each line item that sits between common shareholders and the Bitcoin reserve differently. The same balance sheet produces three different stories about what is owed and what is owned.

Read the table column by column and each metric is internally consistent. Read it row by row and preferred stock gets three treatments in the same earnings release. Non-convertible debt gets three. Cash gets three opposite ones. The one line where BPS does engage, convertible debt, gets asymmetric treatment: the if-converted method captures the dilution but not the claim. A convertible bond is simultaneously a debt instrument and a potential share. BPS sees the shares. It does not see the debt. Capital B’s OCAs are denominated in Bitcoin itself, which means even when the if-converted method folds them in, the claim does not compress with price. The same metric handles two structurally different convertibles as if they were the same instrument.

Each metric is internally coherent. The three metrics together are not a measurement system. They are a toolkit.

04 / Why the toolkit exists

The toolkit produces three different readings of the same quarter, and each one lands with a different audience.

When the company raises capital, BPS is the metric. New share issuance funds new Bitcoin purchases. BPS shows the Bitcoin going up. The dilution shows up in the share count. The proceeds show up as accumulation. Senior claims issued alongside or before the equity raise are invisible. Smarter Web reports a positive BTC Yield while drawing on the Coinbase facility because BPS does not see the loan. Metaplanet reported a BTC Yield gain in Q4 2025 even as 405 million dollars in new claims drove CEBE down in the same quarter. Strategy reports BTC Yield growth driven by preferred ATM activity because BPS does not see the preferred. The story BPS tells is that accumulation is happening. The story it does not tell is what the accumulation costs in senior claims. Strategy is direct that BPS sits at the top of the hierarchy: its own Q1 2026 slide states that Bitcoin per share accretion is the primary goal and mNAV is an input. The company published its own org chart for the toolkit.

When the company justifies the stock price, mNAV is the metric. A premium to net asset value proves the capital structure is being rewarded by the market. The trouble is that mNAV is several numbers, and the metric’s structure lets the senior claims sit on whichever side of the fraction produces the most favorable reading. The metric does the job of justifying the premium that funds the next ATM tranche.

When the company pitches leverage, Amplification is the metric. The senior claims that BPS ignored are now the engine. They amplify Bitcoin exposure. The wrapper fee that would price the leverage is not published alongside. The cash that would shrink the multiplier is not netted. The corporate-wide nature of the obligation, disclosed in every preferred prospectus, is replaced by a Bitcoin-only denominator that inflates the leverage further. The same instruments do triple duty: invisible in BPS, a numerator weight in mNAV, an asset in Amplification.

One balance sheet, one quarter, three metrics. The toolkit does not require anyone to choose the flattering number. It produces three numbers, and the flattering one is always among them.

This is the measuring problem. It is structural. Why it gets tolerated is a separate question, and it is the subject of Part 2.

05 / The resolution

The per-share metric whose math is internally consistent with the valuation metric exists. It is CEBE: Common Equity Bitcoin Exposure.

Net Senior Claims is convertible debt, non-convertible debt, and preferred stock, with cash netted. Basic shares because that is what common shareholders actually own. Convertible debt is already subtracted as a claim in the numerator, so folding those same instruments into the share count would price the dilution twice. Basic shares count what is issued, not what might be issued if a conversion trigger fires. The numerator answers one question: how much Bitcoin is left for common equity after the company settles what ranks ahead of it.

The foundation article uses a mortgage analogy that holds across every BTCTC. A house worth 500,000 dollars with a 300,000 dollar mortgage is not 500,000 dollars of equity. Nobody confuses the two. The Bitcoin in a BTCTC’s treasury is the house. The senior claims are the mortgage. CEBE is the equity. BPS counts the house and reports it as equity. CEBE measures what is actually yours.

CEBE has a valuation companion that uses the same subtraction. CEBE mNAV is market capitalization measured against the net reserve, the Bitcoin that belongs to common equity after senior claims, rather than against the gross reserve. Because the claims are subtracted out of the asset base rather than added into a numerator, CEBE and CEBE mNAV cannot contradict each other on any balance sheet line.

Convertibles get dual treatment because they are dual-natured instruments. They appear in CEBE’s claim numerator as fiat-denominated or BTC-denominated senior claims, depending on the issuer. They appear in FD BPS’s share denominator via if-converted when the converts are dilutive. FD BPS captures the dilution. CEBE captures the claim. Both effects are real. This is the part of FD BPS that works.

CEBE is the static per-share answer. The CEBE framework names three further measurements that close the rest of the math.

Drag is the percentage of Bitcoin pledged to senior claims, net of cash. It is the same balance-sheet ratio Amplification reframes as a multiplier. Drag uses net senior claims. Amplification uses gross claims with no cash netting. The same ratio, viewed from opposite sides: drag names the cost to common equity, Amplification names the upside of the leverage. Companies report the upside framing. The CEBE framework reports the cost framing with cash properly netted.

Wrapper Fee is the annualized flow cost of carrying the capital structure, expressed as a percentage of the Bitcoin reserve value. Preferred dividends, convertible interest, stock-based compensation, executive cash compensation, offsetting business income. It is the cost side of leverage that Amplification omits. A 1.5x amplification at a 0.5% wrapper fee is not the same trade as 1.5x at 1.7%.

Ownership Acceleration, a term coined by Adam B. Livingston and adopted with attribution, is the dynamic that makes drag compression a thesis rather than just a cost. Fiat-denominated senior claims are fixed in dollars. As Bitcoin appreciates, the same dollar claim shrinks in BTC terms. Sats that were pledged to senior claims transfer back to common equity at no incremental cost. Capital B’s BTC-denominated debt is the structural opposite: drag does not compress because the claim is denominated in the same unit as the asset.

The toolkit reports three metrics that contradict each other across every balance sheet line. The CEBE framework reports a system that closes the math at every dimension: CEBE for what common owns, drag for what fraction is pledged, wrapper fee for the price of the structure, CEBE mNAV for the valuation measured against the reserve common equity actually owns, ownership acceleration for the dynamic that runs the engine.

06 / The gap is already measured

The cumulative gap between FD BPS and CEBE on Strategy is documented across 58 verified weeks of 8-K filings. As of the April 20, 2026 snapshot at a 77,453 dollar reference price, the per-share divergence is 51,974 sats. That is forty dollars per share. Across Strategy’s 349.3 million basic shares outstanding, the aggregate is roughly 14.1 billion dollars of common-equity exposure that FD BPS does not register.

The same analysis identified the source of the divergence as binary. Cumulative gap expansion comes from preferred-issuance weeks. Non-event weeks compress the gap. Falsifiability claims for Q2 and Q3 2026 are on the record. The audit trail lives in CEBE Under the Hood.

This is one company in one capital structure. The same dynamic operates wherever a BTCTC carries senior claims that BPS does not subtract. The structural blindspot scales with the balance sheet it sits on. The Finish the Math series documents the same divergence in Smarter Web’s facility, in Metaplanet’s dual-currency claims, and in Capital B’s Bitcoin-denominated debt. Different structures, different magnitudes, same gap.

07 / The standard

One measuring system. The same math at every company, every quarter.

CEBE for what common shareholders own after the company settles what ranks ahead of them. Drag for what fraction of the Bitcoin sits ahead of you. Wrapper Fee for the annual price of carrying the structure. CEBE mNAV for how the market prices the ownership. Ownership Acceleration for the dynamic that makes the leverage work when Bitcoin appreciates.

BPS reports what is in the warehouse. Published mNAV reports a valuation that carries the senior claims in the numerator and comes in variants that disagree. Amplification reports an upside multiplier with the cost omitted. Three numbers, each telling a partial story. The CEBE framework completes the math the toolkit leaves open.

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