Perpetual Settlement as a Second Genus

Chapter VIII completed the listed-options family: a vector of mechanical strips, each settled by an auction in the options that enter it. This chapter is the book’s contribution: the perpetual family, written so a twenty-four-hour book inherits the same three jobs. A published index I_t — density print, realized clock, or dual F — a mark, a funding rule, a cash session. FloatNet is the registry in which that combination becomes payable. The two genera together are the replacement program.

Culmination

Three trajectories meet here. The market form is continuous: matching, marking, and cash on a published interval, already the native clock of the books FloatNet studies. The instrument form is the perpetual: a position that stays open while funding pins its mark to an index. The analytic form is a full-distribution coordinate — a density print on [0, 1] together with the path’s own quadratic variation, ranked into the same unit. Dated variance strips gave the twentieth century a public vol number. Twenty-four-hour perps gave the twenty-first a cash clock that runs while the position lives. FloatNet gives both a signed freeze a wrapper can carry from venue to venue.

That is combinatorial evolution in the strict sense. Each piece existed. The listed strip, the perpetual, the density tape, the realized path, the quorum, the registry. The payable object is their joint: a dual-input index F, frozen, attested, funded against. Chapter VIII supplied the strip family. This chapter supplies F, the freeze, and the funding indenture.

Two genera

Genus I is the dated family. VIX options and VX futures cash-settle to the Special Opening Quotation, built from an opening auction in SPX (or SPXW) options thirty days out. Live VIX interpolates two tenors on mids; the SOQ uses opening prints, a single expiry, and a published wing rule. UX options deliver into the front VX future. Notes and funds add the roll as a product. Chapter VIII’s successor — a published vector Φ of piecewise-linear g, each settled by an auction in the same options that enter the strip — is that family made full-distribution.

Genus II is the perpetual family. Alignment is continuous funding of the mark toward a published index, plus a session cash clock that realizes PnL while the position stays open. The underlier is that index: a versioned density print, a realized-vol clock, or the dual primitive this chapter writes. The challenge mechanism is the methodology of the index, the construction of the mark, and the funding rule — executable by trading the perp and the hedge the index names. Basis is mark minus index, paid as funding. Term lives in the funding interval. Surveillance lives in the index booklet, the mark rule, and the venue’s insurance book.

Two clocks, one unit

The Q-clock

The implied, risk-neutral clock is a versioned functional of a named surface or density tape. On this publisher it is the datafi.live unsigned print, already on [0, 1], signed as (unsigned − 0.5) × 2, with a named feed version. Chapter IV’s estimator facts — wing liquidity, mid versus open, interpolation versus single-expiry, the variance premium baked into Q — become, for a perpetual, inputs to be versioned and lagged. The Q-clock on a twenty-four-hour book is a freeze of that tape, attested by the quorum.

The P-clock

The physical clock is a versioned quadratic-variation estimator of the named path. Sampling frequency, window, and jump treatment live in the booklet. On this publisher the P-clock is twenty-four hours of close-to-close hourly log-returns on the Hyperliquid perps that share the Core book’s twenty-four-hour path — BTC, ETH, HYPE — ranked in the prior thirty daily windows, equally weighted. Rank places P in the same unit as Q. Path dependence is the information the clock is built to carry. Chapters IV and VIII treated realized variance as commentary on the premium. Genus II promotes it to a first-class settlement input, versioned beside Q.

Dual-input design

F is a published map from two versioned numbers in a common unit, at a matched horizon, with a named lag, into one index a mark can fund toward. The design work is units, horizon, lag, the vector of F, the disagreement flag, and which member lists.

A common unit

The Q-clock on this tape is the datafi.live unsigned print, on [0, 1]. The P-clock enters the same unit by rank: the last twenty-four hours of close-to-close hourly quadratic variation on a named perp, ranked in the prior thirty non-overlapping daily windows. Rank 1 is the jumpiest day in the lookback. Rank is fully determined by the window and the lookback. Variance units remain available as a later member of a P-vector; this booklet’s listed mix lives on the unit interval, where the density tape already lives.

Matched horizon, named members

Core 1D Q matches a 1D P. The P-clock on Core is BTC, ETH, and HYPE on Hyperliquid, equally weighted — the three members that share the Core book’s twenty-four-hour path. GOLD, SILVER, and CL enter the Q-clock of the same freeze; the booklet records the membership of each clock. Horizon match is a methodology sentence, written once.

Point-in-time lag

Q is the last sealed freeze. P is quadratic variation on [t − 24h, t), right-open, so the incomplete hour waits for the next freeze. Each clock is complete before the funding interval it prices. A change of lag is a methodology amendment, versioned like Cboe’s booklet date.

Staleness of Q is a fallback event, already designed in Chapter VIII: the alternate is F1, announced, versioned. The listed vector stays F0–F3. The fallback stack lives beside the vector, as it does for dated strips.

Disagreement as information

Let δ_t = |u^Q_t − u^P_t|. Booklet band 0.25. When δ exceeds the band the freeze carries a flag — the analogue of health gates H1–H2, published with the print. Funding continues to pay F2. Dual clocks that move apart are the premium F3 is built to display. The flag is that display, made visible to every reader of the freeze.

Why F2 lists

F0 moves with the density model. F1 moves with twenty-four hours of three perps; a spike in one coin is averaged across three names and ranked in thirty days. F2 averages those two motions, so the listed underlier is the more stable object a funding book can pin to. F3 isolates the residual those two motions leave — the premium a second money line can quote. Sampling of P is hourly close-to-close, a complete choice: later members of a P-vector (Parkinson, realized kernel, jump-robust) are versioned additions to the family. A twenty-four-hour perp tape has a single session; that is the partition the booklet records.

Five fulfillments

A perpetual settlement that a venue rulebook can adopt, written as five positive objects.

1. A published index I_t, versioned, in a named unit. Dual-input F with both clocks in the booklet; F2 the listed member.
2. Mark construction and a funding rule that pin the mark to that index on a published interval. Premium is mark relative to index; funding pays that premium as cash.
3. A cash session that realizes PnL while the position remains open. Daily is the classical clock; hourly or eight-hour sessions are booklet parameters of the same genus.
4. Q-inputs that are freezes of a public tape, lagged and named. P-inputs that are ranked quadratic variation on the same horizon. Wing prints and Wednesday opens remain the challenge mechanism of Genus I, available as a lagged, versioned term if a later F-member calls them.
5. Mechanical, public rules for a density or lattice primitive: freeze, signers, clocks, and funding inputs written at the same standard as a variance strip. The density print is listable as Genus II because those rules exist.

What FloatNet realizes

FloatNet’s construction console freezes both clocks together. The Q-clock is the live print at datafi.live — the GM! Core book print, mean of the current 1D member cells, unsigned in [0, 1], signed as (unsigned − 0.5) × 2, named feed version. The P-clock is twenty-four-hour hourly quadratic variation on Hyperliquid BTC, ETH, and HYPE, ranked in a thirty-day lookback. The listed freeze is F2. Signers attest F2. F0, F1, and F3 travel with the freeze. Hyperliquid is the matching venue; funding is how a perp on F2 pays; the registry record is the legal pointer. Analysis, instrument, and market close on one number.

Genus I continues on the same publisher. P3 tail mass, P4 curve, P6 term, P7 shortfall are mechanical strips, each settled by an auction in the options that enter the strip, each a Float Line with a Float Strip. IBIT opening prints and a Deribit delivery window are Genus I clocks. Dated futures, prediction-market contracts, and note indentures point at those prints. Perpetuals point at F2. One quorum, two indentures, a wrapper that carries the print that matches its clock.

Surveillance, statute, book

Genus I surveillance is the opening auction: weights, wing, tradable open. Genus II surveillance is the freeze, the mark, and the funding interval. The booklet states how old a freeze may be and names the alternate (F1). Caps, clamps, and insurance are venue rules, disclosed with the product. Impact limits and last-trade rules are the mark’s analogue of a tradable open. Auto-deleveraging and insurance funds are the venue’s analogue of a clearinghouse assessment, and they live in the venue rulebook. The publisher writes I_t. The venue writes mark and funding. That split is how a calculation agent stays a publisher, and how a venue stays a book.

How the two families run together

1. Keep publishing Genus I strips. The VIX complex, IBIT openings, and Deribit delivery windows remain the hedge and the legal object for dated claims.
2. Publish I_t as a freeze. Signers attest F2. Readers recompute. The live tape at datafi.live is the public coordinate; the freeze is the settlement object a funding book pins to.
3. Name the clocks in the first paragraph of the Genus II booklet: F2 listed; F0, F1, F3 published; lags and versions of u^Q and u^P frozen.
4. The venue publishes mark and funding. The registry holds the freeze. Publisher and book stay two sentences.
5. Write the mechanical freeze for a density print to the same standard as a variance strip. Then the density print lists as Genus II, and the family of F is the published surface of that listing.