POLYMARKET · PREDICTION MARKET · ELON MUSK # TWEETS JUNE 13 - JUNE 15, 2026?

Will Elon Musk post 115-139 tweets from June 13 to June 15, 2026?

YES · live

0.1¢

NO · live

100.0¢

▸ Advanced metrics · M2M bundle

polymarket · elon-musk-of-tweets-june-13-june-15-115-139 · fresh · feed 0s old

24h sparkline · 60 pts▼ —

realized vol (ann.)

7.83%

max drawdown

80.00%

sharpe

—

ulcer index

66.42%

RMS drawdown

pain index

63.31%

mean drawdown

mod. VaR 95%

0.00%

Cornish-Fisher

martin ratio

—

ret / ulcer

CDaR 95%

80.00%

cond. drawdown

gain/pain

0.50

Σgain / Σ|loss|

sterling

—

ret / CDaR

omega (θ=0)

0.50

upside/downside

roll spread

21.8 bps

implied (price-only)

bars used

2000

store

spread

—

24h Δ

—

flow lean

—

carry

flat

signalNEUTRALconfidence 20%

Same bundle via M2M API: /api/m2m/pm-elon-musk-of-tweets-june-13-june-15-115-139/bundle · venue execution: polymarket →

LIVEPOLL0SRCFRESH8ms⏱--:--:-- UTCNEXT8.0sUP0s--:--HIST0/30

▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC FRESH·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC FRESH·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·

YES · live

0.1¢

NO · live

100.0¢

YES price · live 24h

25 ticks · last 0.05¢

YES / NO split · live

Σ 100.00% · fair

Σ-sides total = 100.00% (tight rounding)

H(p) entropy = 0.006 / 1.00 bits (1%) · informative — one side favoured

YES

0.1%0.1¢2000.00×▬ +0.00pp

100.0%100.0¢1.00×▬ +0.00pp

Σ 100.00% · arb gap 0.00pp

Per-tick activity · |Δp| in basis points · live

Σ 90bp moved · peak 15bp · n=24 ticks

Live numerics · pulse on poll

LIVE NUMERICS8 metrics·POLL 0

⏱snapshot age

8ms

▲YES mid

0.05¢ (0.05%)

▼NO mid

99.95¢ (99.95%)

ΣΣ sides

100.00%

⚖arb gap

0.000pp

$24h vol $

$32.4k

≋liquidity $

$46.2k

◳history points

25 ticks (live)

§1 · 24h price history (YES + NO tokens)

YES price · CLOB mid

25 YES observations from clob.polymarket.com · last 0.05¢

NO price · CLOB mid

25 NO observations from clob.polymarket.com · last 99.95¢

§2 · Distribution of Δp

Histogram of hourly increments

n=24

Q-Q plot · standardised Δp vs N(0,1)

reference line = identity (perfect normality). Heavy upper-right tail = fat positive tail.

§3 · Sample moments

Descriptive statistics · 5-number summary · shape diagnostics

SAMPLE MOMENTS · N=25RIGHT-SKEWED (G₁=0.91)

μ MEAN0.25¢95% CI: [0.17¢, 0.32¢]

σ STD DEV0.20ppσ² = 0.040 · CV = 81.07%

med MEDIAN0.25¢Q₁ 0.05¢ · Q₃ 0.35¢

FIVE-NUMBER SUMMARY · BOX PLOTrange 0.70pp · IQR 0.30pp (1.349σ→0.27pp)

SKEWNESS · G₁0.907right-skewed

−3−10+1+3

EXCESS KURTOSIS · G₂-0.209mesokurtic · normal-like

−30+2+4+6

μ ↔ median≈ equal · symmetric|μ−med| / σ = 0.02

σ × 1.349 ↔ IQRconsistent with normalratio = 0.90

range ↔ σconcentrated (range < 4σ)range / σ = 3.51

μ = mean YES probability · σ = standard deviation · 95% CI = μ ± 1.96·SE. Skew/kurt diagnose departure from normality.

§5 · Time-series structure

Regime & autocorrelation diagnostics

TIME-SERIES STRUCTUREREGIME: MEAN-REVERTING · ADF rejects unit root

ρ(1) AUTOCORR-0.027within white-noise band

ρ(2) AUTOCORR-0.234lag-2 not significant

H · HURST EXPONENT1.088strongly persistent

OLS TREND · t-STAT-11.468significant @ α=0.05

HURST EXPONENT [0, 1]strongly persistent · H = 1.088

H = 1.088STRONGLY PERSISTENT

0
anti-persistent0.45
mean-reverting0.5
random walk0.55
persistent1
strongly trending

AUTOCORRELATION FUNCTION · ρ(k) for k=1..5WHITE NOISE · no significant lags

OLS TREND · t-STAT · [-5, +5]SIGNIFICANT @ 1% (|t|=11.47)

−5 reject−1.960 retain H₀+1.96+5 reject

REGIME CLASSIFICATIONMEAN-REVERTING · ADF rejects unit rootfrom Hurst + ρ(1) joint diagnosis

PREDICTABILITY · score 1.00very high · strong structure|ρ(1)| + 2·|H − 0.5| heuristic

TREND SIGNIFICANCESIGNIFICANT @ 1% (|t|=11.47)α=0.05 critical |t|=1.96 · α=0.01 |t|=2.58

ρ(k) = lag-k sample autocorrelation · H = R/S Hurst exponent · t = OLS-trend t-statistic. Significance bands at ±2/√n approximate the 95% white-noise envelope. α=0.05 critical |t|=1.96; α=0.01 |t|=2.58.

§6 · Microstructure

Market quality · two-sided pricing · activity

MICROSTRUCTURE · MARKET QUALITYPERFECT · ARB-FREE Σ=100.00%

MARKET ID2506622

SLUGelon-musk-of-tweets-june-13-june-15-115-139

CATEGORYElon Musk # tweets June 13 - June 15, 2026?

TWO-SIDED PRICINGFAVOURS NO (100¢)

PRIMARY · YES0.05¢implied prob 0.05% · decimal odds 2000.00×

COUNTER · NO99.95¢implied prob 99.95% · decimal odds 1.00×

0.05¢

99.95¢

Σ-SIDES ARBITRAGE TESTPERFECT · ARB-FREE Σ=100.00%

0%50%100% · target110%

Σ = 100.00% · |1 − Σ| = 0.000pp

24H ACTIVITY · LIQUIDITYACTIVE

24H VOLUME32.39k USD 24h

LIQUIDITY46.22k USD

MARKET QUALITYPERFECT · ARB-FREE Σ=100.00%|1−Σ| ≤ 0.5pp ⇒ fair · > 2pp ⇒ inefficient

PRICING SKEWFAVOURS NO (100¢)|primary − counter| = 0.999 · entropy 0.006 bits

LIQUIDITY DEPTHACTIVE100k+ deep · 10k+ active · 1k+ modest · 100+ thin

Σ-sides = YES + NO implied probabilities. Perfect arb-free Σ = 100%. |1−Σ| > 2pp suggests synthetic outright arbitrage.

§7 · Position sizing & edge analysis

Probability split · YES vs NO · Kelly · entropy · arbitrage

FAIR MARKET · no edge

Probability scale (YES)

0%25%50%
fair75%100%

Implied decimal odds

YES2000.00×(0¢)NO1.00×(100¢)

Kelly bet-size (% of bankroll) K* = 0.00%

K* full

0.00%

½K half

0.00%

¼K quarter

0.00%

Entropy H(p̂) = 0.006 bits (1% of max) · informative — one side strongly favoured

0 (certain)0.250.50.751.00 (max)

Σ-sides = 100.00% · |1 − Σ| = 0.00pp · tight cross-venue rounding

K* full = (b·p − q)/b · ½K and ¼K are conservative fractions of the full-Kelly bet. Entropy in bits — log₂(2)=1 is maximum uncertainty for a binary market.

§8 · Time decay & θ projection

Time decay & theta projection

⏱ URGENCY · HIGHresolves 2026-06-15 16:00 UTC

0days

22hrs

56min

YES →$1.00(P = 0.1%)

NO →$0.00(P = 100.0%)

current: $0.0005 · expected return per side: $1.00 on YES hit · $0.00 on NO hit

Theta progression · θ ∝ σ / √t_remainingθ_now = 0.977 pp/day

now22.94h left

0.977 pp/day×1.00

−25%17.21h left

1.128 pp/day×1.15

−50%11.47h left

1.382 pp/day×1.41

−75%5.74h left

1.954 pp/day×2.00

−90%2.29h left

3.090 pp/day×3.16

θ approximation: σ/√T (expected daily move magnitude). The cone shows ±√(p̂(1−p̂)) widening as time decays, funneling to {0, 1} at resolution. Theta accelerates as √(t_left)→0.

§9 · Hourly return heatmap

24-hour signed Δp grid · green = up · red = down

1 up bars · 9 down · best 0.10% · worst -0.15% · typical |Δ| 0.038%

§10 · Equity curve & underwater drawdown

Cumulative compounded return + running peak-to-trough

final equity 0.9930 (-0.70%) · max DD -0.70% · time-under-water 24/25 bars

§11 · Rolling-window statistics (w = 6 bars)

Rolling annualised Sharpe ratio · green positive · red negative

latest -60.415 · range [-111.06, 0.00] · μ -47.149 · positive Sharpe = excess-return-per-risk earned by buying-and-holding through this window

Rolling annualised volatility (%)

latest 2.42% · range [2.42%, 7.05%] · μ 4.89% · σ̂ scaled to annualised (×√8760)

Rolling lag-1 autocorrelation ρ(1)

latest 0.417 · |ρ| > 0.3 ⇒ regime with persistence (ρ > 0) or reversal (ρ < 0) · |ρ| ≤ 0.1 = consistent with random walk

§12 · Hypothesis tests (α = 0.05)

Formal inference at 5% significance

2 of 5 REJECT · mixed evidence2 reject·3 pass·1 n/a·α = 0.05

𝒩

Jarque-Bera

FAIL TO REJECTns

H₀: Δp ~ Normal(μ, σ²)

STATISTIC

0.5627

p-VALUE (log scale)

0.7548

10⁻⁴10⁻³10⁻²10⁻¹1

Ljung-Box(h=5)

FAIL TO REJECTns

H₀: No serial autocorrelation up to lag 5

STATISTIC

8.3520

p-VALUE (log scale)

0.1366

10⁻⁴10⁻³10⁻²10⁻¹1

Dickey-Fuller (τ_μ)

REJECT H₀*

H₀: p has a unit root (non-stationary)

STATISTIC

-3.3660

p-VALUE (log scale)

0.0131

10⁻⁴10⁻³10⁻²10⁻¹1

Wald-Wolfowitz runs

N/An/a

H₀: Sign sequence of Δ is random

STATISTIC

—

p-VALUE (log scale)

—

KPSS (μ stationarity)

REJECT H₀**

H₀: p IS level-stationary

STATISTIC

0.8538

p-VALUE (log scale)

0.0053

10⁻⁴10⁻³10⁻²10⁻¹1

Variance ratio q=3

FAIL TO REJECTns

H₀: Δp is a random walk · VR = 1

STATISTIC

-1.0742

p-VALUE (log scale)

0.2827

10⁻⁴10⁻³10⁻²10⁻¹1

Each row states an explicit null H₀, the test statistic, an approximated p-value, and the decision. REJECT means evidence against H₀. KPSS complements ADF (rejecting both ⇒ ambiguous; rejecting one ⇒ clean verdict).

§13 · Spectral analysis (DFT periodogram)

Power spectrum of Δp · ‖X̂(k)‖²/n

dominant period ≈ 3.00h (freq 0.333) · concentrates 42.0% of total energy · Σ|X̂|²/n = 3.667e-6

▸ Depth section using sovereign-store price series (2138 bars · effective 1753005 bars/year) — annualisation reflects native polling cadence, not upstream timeframes.

§14 · Honest position analytics

A binary-market analytics module framed in horizon time (days to resolution, not annualised). Estimators that need a model probability q as a first-class input (Kelly, KL divergence, Bayesian posterior, Mark-to-Market MC) only render when q is provided externally. Sweep an exploratory q at the interactive simulator →

§15 · Horizon returns

Returns · per bar / per day / per horizon

Horizon 1.0 d · σ/bar 0.006pp · expected |Δp| over horizon 0.03ppterminal variance p(1−p) = 0.0005 · n = 2138✓ n = 2138

μ per bar

-0.000pp

average Δp · drift

σ per bar

0.006pp

one-bar volatility · logit-free

Per-day movedaily

0.03pp

σ × √24

Per-horizon move1d

0.03pp

σ × √22.94293916666667

Terminal variancebinary

0.0005

p(1−p) at resolution

Current pricep

0.1¢

latest snapshot

Note: annualised Sharpe/Sortino are omitted — they are not meaningful for a bounded fixed-horizon binary contract that snaps to {0, 1} at resolution.

Annualised metrics are intentionally omitted — they don't apply to bounded probability series that resolve at a fixed date.

§16 · Tail risk

VaR · ES · max drawdown

VaR₉₅ 0.01pp · ES₉₅ 0.01pp · method parametric · drift-correcteddrift -0.000pp/bar · quantised: yes · median step 0.05pp · unique ratio 0.00✓ n = 2138

VaR 95%

0.01pp

1.645·σ (parametric) of Δp

ES 95%

0.01pp

mean of the tail

Max drawdown

80.0pp

peak 0.3¢ → trough 0.1¢

Median step

0.05pp

price bucket granularity

Price series is bucketed (cent grid). Empirical quantiles collapse to grid points — parametric N(0, σ²) used instead.

Empirical quantiles unless the price series is bucketed (PM cent grid), in which case parametric N(0, σ²) is used to avoid grid collapse.

§17 · Odds conversion

Odds conversion · every dialect a bettor thinks in

Implied probabilityP

0.1%

= price

Decimal oddsEU

2000.000

total return per $1

AmericanUS

+199900

$100 wins $199900

FractionalUK

1999.00 / 1

profit per $1 risked

Profit per $100stake

+$199900.00

clean dollar framing

underdog (+)favorite (-)your price

Price → implied probability → decimal odds → American moneyline → fractional. Five views of the same number, plus the moneyline curve.

§18 · Binary entropy

Binary entropy · uncertainty as bits of information

Market entropyH(p)

0.006 bit

max 1.0 at p = 0.5

Your entropyH(q)

0.006 bit

Δ +0.000 bit vs market

Surprise · YES−log₂ p

10.97 bit

self-information

Surprise · NO−log₂(1−p)

0.00 bit

self-information

Market entropy only — model entropy requires an external q.

§19 · Model-dependent surfaces

§ Edge / Kelly / KL · no model probability provided

External model required

The position-economics, Kelly, KL-divergence, Bayesian and Monte-Carlo surfaces require a model probability q as input — a number independent of the market price p.

The previous build defaulted q to a tape-momentum heuristic derived from p; that produces apparent edge that is structurally guaranteed to be small and is not a useful skill signal. The auto-derived path has been removed.

To explore these surfaces with a hypothetical q, open the interactive simulator and drag the MODEL P(YES) slider. To wire a real model, POST to the NOSTRADAMUS hook (TBD) or pass ?q=… on the simulator URL.

§∞ · Provenance & attestation

Upstream (snapshot): gamma-api.polymarket.com
Upstream (history): clob.polymarket.com
YES token ID: 52156126825734883942022990172011672732000733097736942649166378493351858489890
NO token ID: 56004211583378640492821585582237989773248727080236968009538272290015638125474
Snapshot fetched: 2026-06-14 17:03:25 UTC
Snapshot age: 8ms
History points: 25 CLOB mids
Page rendered: 2026-06-14 17:03:25 UTC
Storage policy: no persistence — fetched on every request
SHA-256 attestation: 1e15de0e59f04a475b174964a569c04a6add4ea5ab6bb1083272a4dbae3e35ec · deterministic hash of source snapshot
Open data licence: CC0 / public domain

§∞-2 · Related markets · explore more

HL PREDGermany94.3¢HL PREDSpain89.5¢HL PREDUruguay66.9¢POLYMARKETWill Australia win the 2026 FIFA World Cup?0¢POLYMARKETWill Scotland win the 2026 FIFA World Cup?0¢POLYMARKETWill Curaçao win on 2026-06-14?2¢HL PERPBTC-USD perpetual$63,941.5 HL PERPETH-USD perpetual$1,662.85 HL PERPHYPE-USD perpetual$60.14

Also see: /arb opportunities · RSS feed · more in Elon Musk # tweets June 13 - June 15, 2026?

Market depth

▸ live order book · Polymarket YES

Depth within 1bp

bid $0 · ask $0

Depth within 5bp

bid $0 · ask $0

Depth within 10bp

bid $0 · ask $0

Depth within 50bp

bid $0 · ask $0

Mid price

—

(best bid + best ask) / 2

Spread

—

(bestAsk − bestBid) / mid

Imbalance (whole book)

-1.000

ask-heavy

Imbalance (top-5)

-1.000

ask-heavy top-of-book

Slippage scenarios

▸ live book walk · Polymarket YES

Simulating a market order at three notionals against the live book. Slippage = avg execution price vs. mid, in basis points. Worst fill = price of the deepest level touched. Live JSON: /api/asset/pm-elon-musk-of-tweets-june-13-june-15-115-139/slippage?size=10000&side=buy

Side	Notional	Avg fill	Slippage	Worst fill	Levels	Status
BUY	$1.00K	—	—	—	—	ERR
BUY	$10.00K	—	—	—	—	ERR
BUY	$100.00K	—	—	—	—	ERR
SELL	$1.00K	—	—	—	—	ERR
SELL	$10.00K	—	—	—	—	ERR
SELL	$100.00K	—	—	—	—	ERR

Risk metrics

▸ sovereign store · 2,138 barsperiods/year ≈ 1.75M

Realized vol (annualised)

6009.67%

σ per bar = 0.045390

Mean return (annualised)

-132024.01%

μ per bar = -0.000753

Sharpe (rf=0)

-21.97

annualised; risk-free assumed zero

Max drawdown

80.00%

peak 0.00 → trough 0.00 over 639 bars

/api/asset/pm-elon-musk-of-tweets-june-13-june-15-115-139/risk · same metrics, JSON