Bitcoin Runs on a Clock: Why Every Price Indicator Dies and the Halving Clock Doesn't

May combine two claims.

Event studies of the halvings find positive but delayed price responses, with predictive power that several authors describe as weakening.

“Event studies of the halvings (e.g., Meynkhard, 2019; subsequent work reviewed in MDPI's JRFM) find positive but delayed price responses, with predictive power that several authors describe as weakening.”

• cites Meynkhard, 2019 sourcePartly supported

  The Methods and Conclusion (page numbers unavailable) report that prices remained near prior levels for four periods after both halvings studied, with a reaction after about five months, and conclude that halving increased market value. The paper does not report that halving’s predictive power was weakening; the citing sentence appears to associate that part with subsequent work, which cannot be assessed from this source. (LLM, conf=0.86)

  Experimental — accuracy not yet measured

May combine two claims.

Re-expressing the clock in block height recovers partial bottom structure the calendar null misses, though the cycle-shape and volatility overlays do not improve.

“it also recovers partial bottom structure the calendar null misses, though the cycle-shape and volatility overlays do not improve.”

May combine two claims.

Money-supply growth and the yield curve exhibit the same era-dependent sign instability as the price indicators; in a joint HAC regression only cycle phase survives.

“Money-supply growth and the yield curve exhibit the same era-dependent sign instability as the price indicators; in a joint HAC regression only cycle phase survives;”

May combine two claims.

Re-expressing the clock in block height rather than calendar days holds the tops' null at zero of 10,000 and widens its separation from look-alike clocks, because the halving is an exact 210,000-block period rather than a drifting four-year one.

“Re-expressing the clock in its native protocol unit, block height rather than calendar days, holds the tops' null at zero of 10,000 and widens its separation from look-alike clocks, because the halving is an exact 210,000-block period rather than a drifting four-year one;”

May combine two claims.

We provide the first per-epoch stability test of the M2-price relationship, and find it to be a one-era artifact.

“We provide, to our knowledge, the first perepoch stability test of this relationship, and find it to be a one-era artifact (Section 5.6).”

May combine two claims.

The power law's risk-adjusted timing edge over buy-and-hold improves monotonically across all four cycles, turning positive in the current one.

“and whose risk-adjusted timing edge over buy-and-hold improves monotonically across all four cycles, turning positive in the current one (a single-window holdout, suggestive rather than decisive).”

May combine two claims.

Using rank information coefficients with autocorrelation-robust inference, short-horizon price indicators decay to statistical noise across epochs (RSI-14's 30-day IC falls from +0.28 to -0.02), and several invert sign.

“Using rank information coefficients with autocorrelation-robust inference (Newey-West and circular block bootstrap), we show that shorthorizon price indicators decay to statistical noise across epochs (RSI-14's 30-day IC falls from +0.28 to -0.02), that several invert sign,”

May combine two claims.

The cycle's amplitude response is weakening, consistent with the maturation literature, but its timing regularity strengthened; the 2025 top was the most punctual yet.

“Our results cut against both views in a specific way: the cycle's amplitude response is indeed weakening, consistent with the maturation literature, but its timing regularity strengthened.The 2025 top was the most punctual yet.”

May combine two claims.

The per-cycle maxima of the five major top-calling oscillators decline monotonically across all four epochs while their per-cycle minima end the era higher than they began.

“First, the per-cycle maxima of the five major top-calling oscillators decline monotonically across all four epochs while their per-cycle minima end the era higher than they began, so any threshold calibrated on past cycles must eventually stop firing.”

May combine two claims.

In the 2024-26 episode, liquidity kept expanding while Bitcoin topped on schedule and entered a bear market.

“in the 2024-26 episode, liquidity kept expanding while Bitcoin topped on schedule and entered a bear market.”

May combine two claims.

The October 2025 top arrived 534 days after the April 2024 halving, against 525 days in 2017 and 546 days in 2021.

“Yet the top itself arrived almost exactly where Bitcoin's previous two mature cycles would have put it: 534 days after the April 2024 halving, against 525 days in 2017 and 546 days in 2021.”

May combine two claims.

The Pi Cycle Top indicator marked the December 2013 top to within one day, the December 2017 top to the day, and the April 2021 peak to within one day.

“The Pi Cycle Top indicator marked the December 2013 top to within one day, the December 2017 top to the day, and the April 2021 peak to within one day.”

May combine two claims.

MVRV above 3.7 and the Mayer Multiple above 2.4 flagged every major top from 2013 through early 2021 within a month; the Puell Multiple above 4.0 flagged every top through 2017.

“MVRV above 3.7 and the Mayer Multiple above 2.4 flagged every major top from 2013 through early 2021 within a month; the Puell Multiple above 4.0 flagged every top through 2017.”

May combine two claims.

The power law's long-horizon relationship replicates on an independent price source and on Ethereum with a different exponent.

“whose long-horizon relationship replicates on an independent price source and on Ethereum with a different exponent,”

May combine two claims.

Bitcoin's time structure remains fixed: the three mature-cycle tops occurred 525, 546, and 534 days after their respective halvings, and the three completed bear-market bottoms 406, 364, and 366 days after their tops.

“Third, Bitcoin's time structure remains fixed: the three mature-cycle tops occurred 525, 546, and 534 days after their respective halvings, and the three completed bear-market bottoms 406, 364, and 366 days after their tops.”

May combine two claims.

Under the deterministic construction, no synthetic path in 10,000 block-bootstrapped Bitcoin histories reproduces the observed ≤21-day halving-phase top cluster; under the conservative construction, 0.10-0.25% do.

“under the deterministic construction, no synthetic path in 10,000 (2,000 per block length, five block lengths) reproduces the observed ≤21-day halving-phase cluster; under the conservative construction, 0.10-0.25%do.”

• AssumptionThe authors state this as an assumption: Circular block-bootstrap of Bitcoin's own daily log returns preserves volatility clustering and drawdown geometry.

May combine two claims.

Every widely followed Bitcoin cycle indicator (Pi Cycle Top, MVRV, Mayer Multiple, Puell Multiple, 200-week moving average) called the market's tops and bottoms with striking precision for a decade, then degraded in a common sequence: precise, then early, then silent.

“Every widely followed Bitcoin cycle indicator (the Pi Cycle Top, MVRV, the Mayer Multiple, the Puell Multiple, the 200-week moving average) called the market's tops and bottoms with striking precision for a decade, then degraded in a common sequence: precise, then early, then silent.”

May combine two claims.

Candidate macro drivers (M2 growth, the yield curve) exhibit the same era-dependent sign instability as the price indicators and are eliminated in a joint horse race.

“Candidate macro drivers (M2 growth, the yield curve) exhibit the same era-dependent sign instability as the price indicators and are eliminated in a joint horse race;”

May combine two claims.

The first cycle's top (371 days) is the documented exception, consistent with every other warmup effect in the study.

“The first cycle's top (371 days) is the documented exception, consistent with every other warmup effect in the study (Section 5.4).”

May combine two claims.

In the wider descriptive battery, the only other constructions that hold direction at the 180-day horizon are themselves slow and trend-anchored (price relative to the 200-week average; the Puell Multiple) or pure time (phase); every fast oscillator flips.

“In the wider descriptive battery, the only other constructions that hold direction at this horizon are themselves slow and trend-anchored (price relative to the 200-week average; the Puell Multiple) or pure time (phase); every fast oscillator flips.”

May combine two claims.

Measured backward from the next halving, the same three bottoms cluster in a 29-day window that this null reproduces in only 1.5% of paths, against 39% for the after-top anchor under identical machinery; the bottoms appear pinned to the upcoming halving more tightly than to anything behind them.

“Measured backward from the next halving, however, the same three bottoms cluster in a 29-day window that this null reproduces in only 1.5% of paths, against 39% for the after-top anchor under identical machinery; the bottoms appear pinned to the upcoming halving more tightly than to anything behind them”

• AssumptionThe authors state this as an assumption: Circular block-bootstrap of Bitcoin's own daily log returns preserves volatility clustering and drawdown geometry.

May combine two claims.

Out of sample (2025-26), the power-law signal beats buy-and-hold on Sharpe while cutting maximum drawdown by ten points (-41% versus -51%), and it is the only signal that does both.

“Out of sample (2025-26), it beats buy-and-hold on Sharpe while cutting maximum drawdown by ten points (-41% versus -51%), and it is the only signal that does both (the Mayer z edges buy-andhold on Sharpe alone).”

May combine two claims.

The crossover requires the moderate entry threshold (z < 0 or +0.25; the deepest threshold remains slightly negative).

“The crossover requires the moderate entry threshold (z < 0 or +0.25; the deepest threshold remains slightly negative), a threshold dependence we flag rather than bury.”

May combine two claims.

RSI-14's 30-day IC across epochs runs +0.28 → +0.14 → +0.17 → -0.02: decay to statistical zero, robust to every RSI period from 7 to 30.

“RSI-14's 30-day IC across epochs runs +0.28 → +0.14 → +0.17 → -0.02: decay to statistical zero, robust to every RSI period from 7 to 30.”

May combine two claims.

Across three mature epochs and two price sources the sign never flips and the magnitude never weakens, while every comparator flips, fades, or both.

“What we do advance is model-free: across three mature epochs and two price sources the sign never flips and the magnitude never weakens, while every comparator flips, fades, or both;”

May combine two claims.

A purely halving-anchored cash rule (hold Bitcoin except during the historical top-to-bottom window, roughly 525 to 900 days after each halving, using only the known halving calendar and a one-day lag) beat buy-and-hold on total compounded return in all four cycles, cut every cycle's maximum drawdown, and compounded to roughly fifty times buy-and-hold's terminal wealth over the full history.

“A purely halving-anchored cash rule (hold Bitcoin except during the historical top-to-bottom window, roughly 525 to 900 days after each halving, using only the known halving calendar and a oneday lag) beat buy-and-hold on total compounded return in all four cycles, cut every cycle's maximum drawdown, and compounded to roughly fifty times buy-and-hold's terminal wealth over the full history.”

May combine two claims.

At the 180-day horizon several indicators invert: the Pi ratio's IC swings to +0.49 in E4, and the Mayer z and RSI flip sign relative to their 2017-era values.

“At the 180-day horizon several indicators invert: the Pi ratio's IC swings to +0.49 in E4, and the Mayer z and RSI flip sign relative to their 2017-era values.”

May combine two claims.

The halving-anchored cash rule survives leave-one-cycle-out, a window optimized on any three cycles still beating buy-and-hold out of sample on the fourth (ratios 1.7 to 4.1).

“and the rule survives leave-one-cycle-out, a window optimized on any three cycles still beating buy-and-hold out of sample on the fourth (ratios 1.7 to 4.1).”

May combine two claims.

A random cash mask of identical duration beats buy-and-hold only four percent of the time and never approaches the realized multiple.

“a random cash mask of identical duration beats buy-and-hold only four percent of the time and never approaches the realized multiple;”

May combine two claims.

The clock's regularity consists of six retrospectively identified turns: three mature-cycle tops at 525/546/534 days after their halvings (range 21 days) and three completed bottoms at 406/364/366 days after their tops (range 42 days).

“The clock's regularity consists of six retrospectively identified turns: three mature-cycle tops at 525/546/534 days after their halvings (range 21 days) and three completed bottoms at 406/364/366 days after their tops (range 42 days).”

May combine two claims.

Aligned at a random offset, the correlation collapses to 0.02, and only 2.8% of random alignments match the halving alignment.

“Aligned at a random offset instead, the correlation collapses to 0.02, and only 2.8% of random alignments match the halving alignment”

May combine two claims.

At the tops, the radius shrinks every revolution (bottom-side readings are noisier: -1.46, -0.61, -1.17).

“At the tops, the radius shrinks every revolution (the bottom-side readings are noisier: -1.46, -0.61, -1.17).”

May combine two claims.

Ethereum's mechanical cycle tops land near the BTC halving phase, at 553, 546, and 489 days after the BTC halving, against Bitcoin's 525/546/534, with the 2021 tops falling on the same day.

“Ethereum's mechanical cycle tops themselves land near the BTC halving phase, at 553, 546, and 489 days after the BTC halving (against Bitcoin's 525/546/534), with the 2021 tops falling on the same day.”

May combine two claims.

Pooling every (phase, forward-90-day-return) pair across cycles, average forward returns are strongly positive from the halving to about day 520, turn negative from roughly day 520 to 900, and turn positive again afterward.

“pooling every (phase, forward-90-day-return) pair across cycles, average forward returns are strongly positive from the halving to about day 520, turn negative from roughly day 520 to 900, and turn positive again afterward”

May combine two claims.

The bottom-side minima end the era far higher than they began (MVRV 0.56 → 1.15; Puell 0.31 → 0.53), though not monotonically.

“The bottom-side minima end the era far higher than they began (MVRV 0.56 → 1.15; Puell 0.31 → 0.53), though not monotonically (Figure 5).”

May combine two claims.

The CLOCK values at the mature tops are 525, 546, 534; the angle does not move.

“Read down the CLOCK column at the mature tops: 525, 546, 534.The angle does not move.”

May combine two claims.

Not one of 10,000 block-bootstrapped Bitcoin histories reproduces the tops' 21-day cluster under the deterministic construction, while 38% reproduce the bottoms' 42-day cluster.

“not one of 10,000 block-bootstrapped Bitcoin histories reproduces the tops' 21-day cluster under the deterministic construction, while 38% reproduce the bottoms' 42-day cluster.”

• AssumptionThe authors state this as an assumption: Circular block-bootstrap of Bitcoin's own daily log returns preserves volatility clustering and drawdown geometry.

May combine two claims.

Distances from the three Bitcoin tops to the nearest M2-YoY peak are +227, -253, and -67 days, mixed in sign and ranging from 67 to 253 days, versus the halving clock's ±10 days.

“Distances from the three Bitcoin tops to the nearest M2-YoY peak are +227, -253, and -67 days: mixed in sign and ranging from 67 to 253 days, versus the halving clock's ±10 days (Figure 8), an order of magnitude looser.”

May combine two claims.

Under the US presidential-election cycle, the three mature tops span 68 days; under a fixed four-year calendar they span 1,423 days; and of 2,000 random four-year clocks, none matches the halving's 21-day spread.

“Under the US presidential-election cycle, also four-yearly, they span 68 days; under a fixed fouryear calendar they span 1,423 days, because the tops follow the halving's actual, lengthening spacing rather than a fixed period; and of 2,000 random four-year clocks, none matches the halving's 21-day spread.”

May combine two claims.

The sign flips almost exactly at the mechanically dated top window (525-546 days) and again near the bottom.

“The sign flips almost exactly at the mechanically dated top window (525-546 days) and again near the bottom.”

May combine two claims.

As of the Coin Metrics data freeze (May 23, 2026; price $76,620), CLOCK is 763, SPRING is -0.53, 229 days after the October 2025 top.

“As of the Coin Metrics data freeze (May 23, 2026; price $76,620): CLOCK 763, SPRING -0.53, 229 days after the October 2025 top.”

May combine two claims.

The mature tops cluster at 535 ± 10 days (±2%); as a fraction of their varying halving gaps they sit at 0.374 / 0.379 / 0.366.

“The mature tops cluster at 535 ± 10 days (±2%); as a fraction of their varying halving gaps they sit at 0.374 / 0.379 / 0.366 (the last computed against the protocol-expected 1,458-day gap to the next halving).”

May combine two claims.

The fitted exponent stabilizes early and converges to n = 5.61 on Bitstamp data (5.67 on Coin Metrics), consistent with the value near 5.8 reported from full-sample fits.

“The fitted exponent stabilizes early and converges to n = 5.61 on Bitstamp data (5.67 on Coin Metrics), consistent with the value near 5.8 reported from full-sample fits (Figure 2).”

May combine two claims.

Hochberg across all 36 cells, no single cell survives at q = 0.05 or q = 0.10; the smallest individual p in the grid belongs to RSI in its 2016-2020 golden era (p = 0.015), a cell whose signal subsequently died.

“Hochberg across all 36 cells, no single cell survives at q = 0.05 or q = 0.10.The smallest individual p in the grid belongs to RSI in its 2016-2020 golden era (p = 0.015), a cell whose signal subsequently died.”

May combine two claims.

Realized volatility does not peak at a consistent halving-day: the peak phases are 157, 585, and 394 days, and the volatility-versus-phase shape correlates at only 0.15 across cycles, indistinguishable from the random-offset placebo (p = 0.19).

“Realized volatility does not peak at a consistent halving-day: the peak phases are 157, 585, and 394 days, and the volatility-versus-phase shape correlates at only 0.15 across cycles, indistinguishable from the randomoffset placebo (p = 0.19).”

May combine two claims.

Sliding the same-width cash window across the cycle, the edge is sharply localized to the true bust phase and loses everything when placed on the boom.

“Sliding the same-width cash window across the cycle, the edge is sharply localized to the true bust phase and loses everything when placed on the boom;”

May combine two claims.

The power-law signal's Sharpe edge over buy-and-hold improves monotonically across epochs (-0.99 → -0.41 → -0.26 → +0.12) and crosses positive in the current cycle.

“But the power-law signal's Sharpe edge over buy-and-hold improves monotonically across epochs (-0.99 → -0.41 → -0.26 → +0.12) and crosses positive in the current cycle (Figure 7).”

May combine two claims.

The power-law deviation's nominal HAC statistics are large in both recent epochs (E3: t = -2.69; E4: t = -2.63), and it is the only cell in the grid with same-sign nominal significance in both.

“Its nominal HAC statistics are large in both recent epochs (E3: t = -2.69;E4: t = -2.63),and it is the only cell in the grid with same-sign nominal significance in both.”

May combine two claims.

The regularity survives the most hostile defensible specification at p ≈ 10−3 and the headline specification at 10−5 to 10−6.

“The regularity survives the most hostile defensible specification at p ≈ 10⁻³ and the headline specification at 10⁻⁵ to 10⁻⁶.”

• AssumptionThe authors state this as an assumption: Under the uniform null, each top is uniformly distributed on a window of width W_top days after its halving, and each bottom uniformly on W_bot days after its top.
• AssumptionThe authors state this as an assumption: The two gap families (top-to-halving and bottom-to-top) are disjoint random variables under the uniform null, so the joint probability is their product by construction.

May combine two claims.

The February 2021 M2-growth peak preceded the April 2021 secondary top by six weeks, and the 2022 curve inversion coincided with that bear market.

“the February 2021 M2-growth peak preceded the April 2021 secondary top by six weeks, and the 2022 curve inversion coincided with that bear market.”

May combine two claims.

The three mature tops sit 77,901 to 79,596 blocks after their halvings (a 1,695-block band by the mempool point-lookups, 1,723 by the mechanical dating on the daily height series, agreeing within end-of-day sampling).

“The three mature tops sit 77,901 to 79,596 blocks after their halvings (a 1,695-block band by the mempool point-lookups, 1,723 by the mechanical dating on the daily height series, agreeing within end-of-day sampling).”

May combine two claims.

The halving out-separates its look-alikes more widely than in days, a 1,723-block band against 12,775 for the US election clock and 209,158 for a fixed calendar.

“The halving out-separates its look-alikes more widely than in days, a 1,723-block band against 12,775 for the US election clock and 209,158 for a fixed calendar.”

May combine two claims.

In days, a fixed four-year clock at a random phase never matches the halving's top cluster, so phase carries the signal; in blocks, a fixed 210,000-block clock at a random offset matches it 98.5% of the time, because the halving is an exact period, not a drifting one, and the tops recur on it regardless of phase.

“In days, a fixed four-year clock at a random phase never matches the halving's top cluster, so phase carries the signal; in blocks, a fixed 210,000-block clock at a random offset matches it 98.5% of the time, because the halving is an exact period, not a drifting one, and the tops recur on it regardless of phase.”

May combine two claims.

The first-cycle top sits at 0.693 of the mature mean in days but 0.801 in blocks, because the 2011 to 2013 chain ran about 15% fast (170 against 147 blocks per day at maturity); roughly a third of its apparent earliness is the young chain outrunning the calendar.

“The first-cycle top sits at 0.693 of the mature mean in days but 0.801 in blocks, because the 2011 to 2013 chain ran about 15% fast (170 against 147 blocks per day at maturity); roughly a third of its apparent earliness is the young chain outrunning the calendar.”

May combine two claims.

In block phase, the deterministic top construction is reproduced by zero of 10,000 block-bootstrap paths, exactly as in calendar days; the conservative selection-symmetric construction falls from 11 to 3 per 10,000.

“In block phase the deterministic top construction is reproduced by zero of 10,000 block-bootstrap paths, exactly as in calendar days; the conservative selection-symmetric construction falls from 11 to 3 per 10,000.”

May combine two claims.

The three bottoms' blocks-after-halving span is reproduced by 1.7% of paths in day phase and only 0.16% in block phase, a tenfold sharpening that survives conditioning on the cycle structure (3.7% to 0.3%).

“the three bottoms' blocks-after-halving span is reproduced by 1.7% of paths in day phase and only 0.16% in block phase, a tenfold sharpening that survives conditioning on the cycle structure (3.7% to 0.3%).”

May combine two claims.

The top-to-bottom gap that Section 4.5 found process-intrinsic is reproduced by about 40% of null paths, unchanged, so bear duration still carries no clock evidence.

“The top-to-bottom gap that Section 4.5 found process-intrinsic is reproduced by about 40% of null paths, unchanged, so bear duration still carries no clock evidence.”

May combine two claims.

The hostile four-top variant that forces the 2013 top into the mature set widens the null from zero to 8 per 10,000 in days but only to 3 per 10,000 in blocks: the native coordinate is more robust to the first cycle.

“the hostile four-top variant that forces the 2013 top into the mature set widens the null from zero to 8 per 10,000 in days but only to 3 per 10,000 in blocks: the native coordinate is more robust to the first cycle.”

Classified as probably not a substantial claim.

The cycle turns are identified retrospectively by a fixed mechanical rule (an all-time high followed by a ≥45% drawdown), not from a real-time forecasting record.

“These turns are identified retrospectively by a fixed mechanical rule (an all-time high followed by a ≥45% drawdown), not from a real-time forecasting record.”

May combine two claims.

The Bitcoin monetary schedule is a constant in the protocol, SubsidyHalvingInterval = 210000 blocks, fixed at block zero and executable by no one's discretion.

“The schedule is not a policy that an institution maintains; it is a constant in the protocol, SubsidyHalvingInterval = 210000 blocks, fixed at block zero and executable by no one's discretion.”

• cites Satoshi NakamotoNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim.

No discretionary dating is involved at any point.

“No discretionary dating is involved at any point.”

May combine two claims.

Among all candidate coordinate systems examined (price levels, price-derived oscillators, on-chain ratios, monetary aggregates, the yield curve), the protocol's time structure is the only one whose relationship to Bitcoin's dynamics is stable across eras, and the only one knowable in advance.

“Our claim is positional: among all candidate coordinate systems examined (price levels, price-derived oscillators, on-chain ratios, monetary aggregates, the yield curve), the protocol's time structure is the only one whose relationship to Bitcoin's dynamics is stable across eras, and the only one knowable in advance.”

May combine two claims.

The compression of indicator extremes explains why threshold indicators fail in sequence ordered by threshold aggressiveness, and predicts that recalibration cannot help: a threshold fit to past amplitude is a bet that damping has stopped.

“The compression of indicator extremes (top-side maxima declining monotonically across five oscillators in all four epochs; bottom-side minima ending the era higher than they began) explains why threshold indicators fail in sequence ordered by threshold aggressiveness, and predicts that recalibration cannot help: a threshold fit to past amplitude is a bet that damping has stopped.”

May combine two claims.

The block-height series is validated by two independent ground-truth checks: the four protocol halving heights are reached within one day of their known dates, and eleven mempool.space point lookups at the dated turns agree to a constant sampling offset.

“Two independent ground-truth checks validate it: the four protocol halving heights (210,000 / 420,000 / 630,000 / 840,000) are reached within one day of their known dates, and eleven mempool.spacepointlookups at the dated turns agree to a constant sampling offset (median 75 blocks above the noon-sampled lookups, which cancels in every range statistic).”

May combine two claims.

Under two time-anchored coordinates, days since halving and power-law deviation, Bitcoin's history traces a damped spiral: the amplitude is dying, the clock is not.

“We summarize the asset's state in two time-anchored coordinates, days since halving and power-law deviation, under which Bitcoin's history traces a damped spiral: the amplitude is dying, the clock is not.”

May combine two claims.

Price-anchored signals decay to noise while a time-anchored structure does not, which suggests that what is being arbitraged away is amplitude, not timing.

“Price-anchored signals decay to noise while a timeanchored structure does not, which suggests that what is being arbitraged away is amplitude, not timing.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

PlanB's (2019) Stock-to-Flow model related price to programmed scarcity and gained wide attention before its post-2021 predictions failed by an order of magnitude.

“PlanB's (2019) Stock-to-Flow model related price to programmed scarcity and gained wide attention before its post-2021 predictions failed by an order of magnitude;”

• cites PlanB's (2019)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The halving is defined in blocks, one every 210,000, not in days, and the chain does not run at a fixed 144 blocks per day, so days since halving and blocks since halving are two different clocks.

“The halving is defined in blocks, one every 210,000, not in days, and the chain does not run at a fixed 144 blocks per day, so”

May combine two claims.

The SPRING compression is Table 3's compression in trend-deviation units, and it is why every amplitude-calibrated indicator has died or will die.

“This is Table 3's compression in trend-deviation units, and it is why every amplitude-calibrated indicator has died or will die.”

Classified as probably not a substantial claim. May combine two claims.

The placebo probabilities in Section 5.8 come from random-offset permutation nulls of the same discrete-event family exempted in Section 4.3, not the autocorrelation-robust per-signal p-values that the rotation null disqualifies.

“The placebo probabilities in this section (the 2.8% above and the volatility p = 0.19) come from random-offset permutation nulls of the same discrete-event family exempted in Section 4.3, not the autocorrelation-robust per-signal p-values that our rotation null disqualifies”

Classified as probably not a substantial claim. May combine two claims.

The turns are ex post; they are dated by the mechanical rule of Section 3, applied to history; no one called them publicly in advance.

“First, the turns are ex post.They are dated by the mechanical rule of Section 3, applied to history; no one called them publicly in advance.”

May combine two claims.

The case still rests on the tops, and the cadence is not the surprise; the phase-lock is.

“The case still rests on the tops, and the cadence is not the surprise; the phase-lock is.”

Classified as probably not a substantial claim.

The persistent-regressor calibration caveat applies to the horse-race t-statistics, so the horse race is read as a relative statement rather than calibrated significance.

“The persistent-regressor calibration caveat of Section 4.3 applies to these t-statistics with full force, so we read the horse race as a relative statement (which regressor survives joint conditioning with stable direction) rather than as calibrated significance.”

May combine two claims.

The fifty-fold figure is overwhelmingly a compounding artifact of avoiding four single-asset crashes; the honest per-cycle out-of-sample edge is the two-to-fourfold range.

“The fifty-fold figure is overwhelmingly a compounding artifact of avoiding four single-asset crashes; the honest per-cycle out-of-sample edge is the two-to-fourfold range;”

Classified as probably not a substantial claim.

No parameter anywhere in this paper is estimated with future data.

“No parameter anywhere in this paper is estimated with future data.”

May combine two claims.

Monetary turning points are confirmable only months after the fact, while the halving schedule has been public since 2009.

“monetary turning points are confirmable only months after the fact, while the halving schedule has been public since 2009.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

This construction was independently reconstructed from scratch by a second analyst on independently pulled data, with corroborating results under both constructions.

“This construction was independently reconstructed from scratch by a second analyst on independently pulled data, with corroborating results under both constructions.”

May combine two claims.

The clock governs the cycle's direction and shape, not its volatility.

“The clock governs the cycle's direction and shape, not its volatility.”

May combine two claims.

Four discriminating tests are available, and all four point the same way.

“Four discriminating tests are nonetheless available, and all four point the same way.”

May combine two claims.

Design (a) of Section 4.4 produces too few events to evaluate: the power-law rule fired six times in fifteen years (positive in every epoch, with two stop-outs), so the economic evidence rests on design (b).

“Design (a) of Section 4.4 produces too few events to evaluate: the power-law rule fired six times in fifteen years (positive in every epoch, with two stop-outs), so the economic evidence rests on design (b).”

Classified as probably not a substantial claim. May combine two claims.

The inclusion rule is asymmetric and the unfavorable variant is reported.

“Third, the inclusion rule is asymmetric and we report the unfavorable variant.”

May combine two claims.

We do not advance the power-law cell as calibrated inference, because the rotation null of Section 4.3 shows that configuration arises by persistence artifact with probability 0.21, and that the NW statistic's true size here is 0.17-0.33, not 0.05.

“We do not advance this as calibrated inference, because the rotation null of Section 4.3 shows that configuration arises by persistence artifact with probability 0.21, and that the NW statistic's true size here is 0.17-0.33,not 0.05.”

May combine two claims.

A coin with no halving of its own still turns near the BTC halving phase, which points to the halving as a market-wide clock rather than only a Bitcoin-supply effect.

“A coin with no halving of its own still turns near the BTC halving phase, which points to the halving as a market-wide clock rather than only a Bitcoin-supply effect.”

May combine two claims.

Macro's relationship to Bitcoin is era-dependent and ex post, sharing the instability of every price-anchored signal, while the time structure is era-stable and ex ante.

“It is that macro's relationship to Bitcoin is era-dependent and ex post, sharing the instability of every priceanchored signal, while the time structure is era-stable and ex ante.”

May combine two claims.

Because the date-to-height map is fixed by the chain and independent of price, the turn-timing battery rescores in the protocol's own coordinate without circularity, on the height-covered span ending May 23, 2026.

“Because the date-to-height map (Section 3) is fixed by the chain and independent of price, the turn-timing battery rescores in the protocol's own coordinate without circularity, on the height-covered span ending May 23, 2026.”

Classified as probably not a substantial claim. May combine two claims.

The test postdates the observation; like any analysis of a noticed pattern, the null test was designed after the clustering was seen.

“Second, the test postdates the observation.Like any analysis of a noticed pattern, the null test was designed after the clustering was seen.”

May combine two claims.

On balance the native coordinate strengthens the tops result's robustness and its separation from look-alike clocks, dissolves the bottom-anchor puzzle, and recovers partial bottom structure, at the cost of the shape and volatility overlays.

“On balance the native coordinate strengthens the tops result's robustness and its separation from look-alike clocks, dissolves the bottom-anchor puzzle, and recovers partial bottom structure, at the cost of the shape and volatility overlays.”

May combine two claims.

The bottom-anchor question of Section 4.5 is resolved mechanically: measuring a block-defined cycle in days created it, and in blocks it dissolves.

“The bottom-anchor question of Section 4.5 is thereby resolved mechanically: measuring a block-defined cycle in days created it, and in blocks it dissolves.”

May combine two claims.

The height target is fixed by protocol arithmetic; only its calendar arrival depends on realized block times.

“The height target is fixed by protocol arithmetic; only its calendar arrival depends on realized block times.”

May combine two claims.

In the coordinates of that clock, the asset's history is a damped spiral, with turns at 525-546 days after each halving and 364-406 days after each top, a retrospective regularity whose chance probability ranges from 5×10−6 to 1×10−3 across every timing-free null and construction tested, including a 2025 top that arrived on schedule while every famous indicator was silent and global liquidity

“In the coordinates of that clock, the asset's history is a damped spiral, with turns at 525-546 days after each halving and 364-406 days after each top, a retrospective regularity whose chance probability ranges from 5×10⁻⁶ to 1×10⁻³ across every timing-free null and construction we tested against it, including a 2025 top that arrived on schedule while every famous indicator was silent and global”

May combine two claims.

In block coordinates the same bottom maps to a height band of 968,910 to 973,934 (128,910 to 133,934 blocks after the April 2024 halving at height 840,000), computed and logged on July 21, 2026, before the window opens.

“In block coordinates the same bottom maps to a height band of 968,910 to 973,934 (128,910 to 133,934 blocks after the April 2024 halving at height 840,000), a supplementary and sharper-unit statement of the same call, computed and logged on July 21, 2026, before the window opens.”

May combine two claims.

The macro alternatives behave no better, flipping sign era to era and failing a joint test against the calendar.

“The macro alternatives behave no better, flipping sign era to era and failing a joint test against the calendar.”

May combine two claims.

The height target needs no estimate of the halving's uncertain calendar date, which is the very source of imprecision the calendar version cannot avoid.

“the height target needs no estimate of the halving's uncertain calendar date, which is the very source of imprecision the calendar version cannot avoid.”

May combine two claims.

Top-phase alignment is what the deterministic null never reproduced in 10,000 paths (and the conservative variant reproduced in fewer than 0.25% of them), and it is where the thesis lives or dies.

“top-phase alignment is what the deterministic null never reproduced in 10,000 paths (and the conservative variant reproduced in fewer than 0.25% of them), and it is where the thesis lives or dies.”

May combine two claims.

The halving schedule is the most public focal point in the asset's culture; if enough participants expect cycle behavior in halving-time, front-running and herding can synchronize the turn, a Schelling clock.

“the schedule is the most public focal point in the asset's culture; if enough participants expect cycle behavior in halving-time, front-running and herding can synchronize the turn, a Schelling clock (Schelling, 1960).”

• cites Schelling, 1960Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The halving's exact day is not yet set: it depends on realized block times and has historically arrived somewhat before the naive ten-minute estimate, so a calendar window pinned now would inherit an error we do not control and cannot honestly pre-register.

“The halving's exact day is not yet set: it depends on realized block times and has historically arrived somewhat before the naive tenminute estimate, so a calendar window pinned now would inherit an error we do not control and cannot honestly pre-register.”

May combine two claims.

The block clock times the cycle's discrete turns, including the return-by-phase sign flip, which lands on the 77,901 to 79,596-block top band; it does not organize the continuous path between the turns any better than the calendar does.

“The block clock times the cycle's discrete turns, including the return-by-phase sign flip, which lands on the 77,901 to 79,596-block top band; it does not organize the continuous path between the turns any better than the calendar does.”

May combine two claims.

The amplitude is dying; the clock is not.

“The amplitude is dying; the clock is not.”

May combine two claims.

The case still rests on the tops, and the phase-lock, not the cadence, is still the surprise.

“The case still rests on the tops, and the phaselock, not the cadence, is still the surprise.”

May combine two claims.

The bottoms are not merely inheriting the tops' phase-lock; each turn is independently anchored to the halving, tops and bottoms occupying separate tight bands near 78,000 and 132,000 blocks.

“so the bottoms are not merely inheriting the tops' phase-lock; each turn is independently anchored to the halving, tops and bottoms occupying separate tight bands near 78,000 and 132,000 blocks.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based). May combine two claims.

A self-fulfilling cycle anchored to a constant in the source code is still a cycle anchored to the source code, and its timing is still knowable decades ahead.

“a self-fulfilling cycle anchored to a constant in the source code is still a cycle anchored to the source code, and its timing is still knowable decades ahead.”

May combine two claims.

The cycle's profitability is dying on schedule with maturation, while its timing has never been more precise.

“The cycle's profitability is dying on schedule with maturation, while its timing has never been more precise.”

May combine two claims.

The two halves of the paper are one phenomenon: diminishing amplitude is the asset converging toward its adoption trend; fixed period is the trend's clock.

“The two halves of the paper are one phenomenon.Diminishing amplitude (returns, volatility, indicator extremes, SPRING at tops) is the asset converging toward its adoption trend; fixed period is the trend's clock.”

May combine two claims.

Every price-anchored description of Bitcoin's market cycle is dying, in a measured, monotone, mechanistically explicable way: the oscillation's amplitude compresses every cycle, so thresholds go silent in order of aggressiveness and continuous indicators decay toward noise or invert.

“Every price-anchored description of Bitcoin's market cycle is dying, in a measured, monotone, mechanistically explicable way: the oscillation's amplitude compresses every cycle, so thresholds go silent in order of aggressiveness and continuous indicators decay toward noise or invert.”

May combine two claims.

What remains is the one structure that was never estimated from price at all, because it was never estimated from anything: a constant written into the protocol at block zero and announced by its author in January 2009 as 'the amount cut in half every 4 years.'

“What remains is the one structure that was never estimated from price at all, because it was never estimated from anything: a constant written into the protocol at block zero and announced by its author in January 2009 as”

• cites Nakamoto, 2009Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.