sidereon_core/sp3/

continuity.rs

//! Continuity attestation for precise-ephemeris sample series.
//!
//! A merged orbit product is assembled per `(epoch, satellite)` cell from
//! several analysis centers. That is exactly the operation that can splice two
//! physically inconsistent arcs together while every input remains individually
//! well-formed. This module attests against that: it takes an ordered sample
//! series and either attests that it is continuous or reports each violation
//! with the epochs, the interval, and the magnitude that exceeded its bound.
//!
//! # Two checks, two jobs
//!
//! A single displacement-per-interval gate cannot do this work alone, and the
//! reason is quantitative rather than stylistic. Measured on a real GFZ ultra
//! product (satellite G01, 576 epochs at 300 s), adjacent-epoch ECEF chord
//! distances run 827-956 km, so the implied chord speed is 2757-3187 m/s. A
//! defensible upper bound for the class sits near 6 km/s (see [`OrbitClass`]),
//! which leaves several hundred kilometres of displacement per epoch pair
//! underneath the bound. A 500 m splice - a serious defect - moves the implied
//! speed by under 2 m/s, roughly 0.05% of the observed chord speed. It is
//! invisible to a speed gate by four orders of magnitude.
//!
//! So the two checks are deliberately separated:
//!
//! - [`ContinuityCheck::SpeedBound`] is a *gross corruption* gate. Its bound is
//!   a true physical upper bound for the orbit class (see [`OrbitClass`]), so it
//!   cannot false-positive on real data; it catches a record from the wrong
//!   satellite, the wrong day, or a corrupt field. It is insensitive by
//!   construction and is not asked to be otherwise.
//! - [`ContinuityCheck::HoldOutResidual`] supplies the sensitivity. Each interior
//!   sample is held out, predicted from its neighbours through the same
//!   sliding-window Lagrange substrate the product's own interpolator uses
//!   ([`super::interp::interpolate_precise_state`]), and compared against the
//!   stored record. On a clean arc the residual is the interpolator's own
//!   error - centimetres for GNSS MEO at 5-15 minute spacing. At a splice it
//!   jumps to the magnitude of the splice, which is what localizes the offending
//!   epoch pair.
//!
//! Run both. The bound gate is nearly free and rules out nonsense; the residual
//! check is the one that finds a spliced arc.
//!
//! # Frame
//!
//! Samples are ITRF/IGS ECEF, matching [`PreciseEphemerisSample`]. The bound is
//! therefore an *earth-fixed* bound, and [`OrbitClass`] derives it as such. Using
//! an inertial orbital speed here would be a category error: for a prograde MEO
//! satellite the earth-fixed speed is materially lower than the inertial speed
//! (the measurement above versus an inertial 3874 m/s for GPS), and for a
//! geostationary satellite it is near zero.
//!
//! # Ordering is this module's responsibility
//!
//! [`check_continuity`] sorts internally. A caller-ordered sequence that is
//! trusted is the failure this module exists to prevent, so shuffled input and
//! sorted input produce the identical verdict - there is a test that pins
//! exactly that. One ordered structure ([`OrderedSeries`]) feeds every check, and
//! it is built so that a zero or negative interval is *unrepresentable* in the
//! comparison path rather than merely rejected: duplicate epochs are split out
//! into [`ContinuityDefect::DuplicateEpoch`] during construction, after which
//! adjacent pairs are strictly increasing by construction and the pair iterator
//! is the only way to reach a comparison.
//!
//! Duplicates are reported, never silently deduplicated: two records for one
//! epoch is a real defect of the data, and which of them is "the" sample is not
//! this module's call to make.
//!
//! # This reports; it does not refuse
//!
//! [`check_continuity`] returns a [`ContinuityReport`] whether or not the series
//! is continuous. A caller may legitimately want the product together with its
//! defects - refusing is the caller's decision, made by consulting
//! [`ContinuityReport::attested`]. The bounds themselves are physical and are
//! never inferred from the data being validated: a check that can be widened
//! until it passes is not a check.

use std::collections::BTreeMap;

use crate::astro::constants::earth::OMEGA_E_DOT_RAD_S;
use crate::astro::constants::MU_EARTH;
use crate::constants::KM_TO_M;
use crate::id::GnssSatelliteId;
use crate::sp3::interp::{
    instant_to_j2000_seconds, interpolate_precise_state, precise_node_j2000_seconds_from_instant,
    NEVILLE_POINTS,
};
use crate::sp3::samples::PreciseEphemerisSample;
use crate::sp3::Sp3;
use crate::{Error, Result};

/// Inclusive evaluation window on the SP3 seconds-since-J2000 axis.
///
/// This identifies epochs the caller intends to evaluate. Continuity findings
/// outside the window can still influence it through the interpolation
/// neighbourhood, which is why queries also require a [`StencilExtent`].
#[derive(Debug, Clone, Copy, PartialEq)]
pub struct EpochWindow {
    from_j2000_s: f64,
    through_j2000_s: f64,
}

impl EpochWindow {
    /// Construct an inclusive evaluation window.
    ///
    /// Both endpoints must be finite and `from_j2000_s` must not be later than
    /// `through_j2000_s`.
    pub fn new(from_j2000_s: f64, through_j2000_s: f64) -> Result<Self> {
        if !from_j2000_s.is_finite() || !through_j2000_s.is_finite() {
            return Err(Error::InvalidInput(
                "SP3 continuity window endpoints must be finite".to_string(),
            ));
        }
        if from_j2000_s > through_j2000_s {
            return Err(Error::InvalidInput(
                "SP3 continuity window start must not follow its end".to_string(),
            ));
        }
        Ok(Self {
            from_j2000_s,
            through_j2000_s,
        })
    }

    /// Inclusive first evaluation epoch, seconds since J2000.
    pub fn from_j2000_s(self) -> f64 {
        self.from_j2000_s
    }

    /// Inclusive last evaluation epoch, seconds since J2000.
    pub fn through_j2000_s(self) -> f64 {
        self.through_j2000_s
    }
}

/// Time reach of the SP3 position interpolator's sliding node stencil.
///
/// Construct this with [`StencilExtent::for_sp3`]. The extent is derived from
/// the product interval and the same 11-node constant used by the position
/// interpolator, rather than accepted as a caller-supplied duration.
#[derive(Debug, Clone, Copy, PartialEq)]
pub struct StencilExtent {
    grid_origin_j2000_s: f64,
    interval_s: f64,
    before_s: f64,
    after_s: f64,
}

impl StencilExtent {
    /// Derive the interpolation reach for an SP3 product.
    ///
    /// The degree-10 Lagrange substrate uses 11 nodes centered on the query, so
    /// its nominal reach is five product intervals on either side. A non-finite
    /// or non-positive declared interval is rejected.
    pub fn for_sp3(sp3: &Sp3) -> Result<Self> {
        let interval_s = sp3.header.epoch_interval_s;
        if !interval_s.is_finite() || interval_s <= 0.0 {
            return Err(Error::InvalidInput(
                "SP3 stencil extent requires a positive finite epoch interval".to_string(),
            ));
        }
        let grid_origin_j2000_s = sp3
            .epochs_j2000_seconds()
            .first()
            .copied()
            .filter(|epoch| epoch.is_finite())
            .ok_or_else(|| {
                Error::InvalidInput(
                    "SP3 stencil extent requires at least one representable epoch".to_string(),
                )
            })?;
        let half_nodes = (NEVILLE_POINTS / 2) as f64;
        let half_width_s = half_nodes * interval_s;
        Ok(Self {
            grid_origin_j2000_s,
            interval_s,
            before_s: half_width_s,
            after_s: half_width_s,
        })
    }

    /// Nominal reach before an evaluated epoch, seconds.
    pub fn before_s(self) -> f64 {
        self.before_s
    }

    /// Nominal reach after an evaluated epoch, seconds.
    pub fn after_s(self) -> f64 {
        self.after_s
    }

    /// Union of nominal grid nodes the interpolator can select for any query in
    /// `window`.
    fn influence_bounds(self, window: EpochWindow) -> (f64, f64) {
        let pivot_at_or_before = |query: f64| {
            self.grid_origin_j2000_s
                + ((query - self.grid_origin_j2000_s) / self.interval_s).floor() * self.interval_s
        };
        (
            pivot_at_or_before(window.from_j2000_s) - self.before_s,
            pivot_at_or_before(window.through_j2000_s) + self.after_s,
        )
    }
}

/// Window-scoped continuity decision.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum WindowContinuityDecision {
    /// No recorded finding can enter an interpolation stencil for the window.
    Accept,
    /// At least one recorded finding can enter an interpolation stencil.
    Refuse,
}

/// A window-scoped decision that retains both influencing and global findings.
///
/// `all_defects` remains available for logging findings the caller accepted
/// around. Merge reports additionally populate `influencing_splices` and
/// `all_splices` through their own verdict helper.
#[derive(Debug, Clone, PartialEq)]
pub struct WindowContinuityVerdict<'a> {
    /// Accept or refuse the requested evaluation window.
    pub decision: WindowContinuityDecision,
    /// Defects whose time support intersects a stencil used by the window.
    pub influencing_defects: Vec<&'a ContinuityDefect>,
    /// Contributor-changing violations influencing the window.
    pub influencing_splices: Vec<&'a super::combine::MergeContinuityViolation>,
    /// Every defect in the underlying continuity report.
    pub all_defects: &'a [ContinuityDefect],
    /// Every contributor-changing violation in the merge report.
    pub all_splices: Vec<&'a super::combine::MergeContinuityViolation>,
}

impl WindowContinuityVerdict<'_> {
    /// Whether the requested window is accepted.
    pub fn accepted(&self) -> bool {
        self.decision == WindowContinuityDecision::Accept
    }
}

/// Orbit class supplying a physical earth-fixed displacement bound.
///
/// Each bound is `sqrt(mu / a_min) + omega_earth * r_max`, the inertial speed at
/// the class's tightest published semi-major axis plus the largest possible
/// earth-rotation transport term at its widest radius. That sum is a true upper
/// bound on earth-fixed speed for any geometry in the class, so the gate cannot
/// false-positive on physically real data. It is correspondingly loose - see the
/// module docs for why that is the correct trade for this check and where the
/// sensitivity actually comes from.
///
/// Bounds are constants of the orbit class. None of them is derived from the
/// series being validated.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum OrbitClass {
    /// GNSS MEO: GLONASS (a ~ 25 510 km) through Galileo (a ~ 29 600 km),
    /// covering GPS, BeiDou MEO, NavIC MEO, and QZSS's MEO-like arcs.
    MeoGnss,
    /// Geostationary and inclined-geosynchronous (a ~ 42 164 km), including
    /// BeiDou GEO/IGSO and QZSS.
    Geosynchronous,
    /// Low earth orbit from a ~ 6 678 km (300 km altitude) upward.
    Leo,
}

impl OrbitClass {
    /// Tightest published semi-major axis for the class, meters.
    const fn min_semi_major_axis_m(self) -> f64 {
        match self {
            Self::MeoGnss => 25_510_000.0,
            Self::Geosynchronous => 42_164_000.0,
            Self::Leo => 6_678_000.0,
        }
    }

    /// Widest radius for the class, meters, for the earth-rotation term.
    const fn max_radius_m(self) -> f64 {
        match self {
            Self::MeoGnss => 29_600_000.0,
            Self::Geosynchronous => 42_164_000.0,
            Self::Leo => 8_378_000.0,
        }
    }

    /// Physical earth-fixed speed bound for the class, meters per second.
    pub fn max_earth_fixed_speed_m_s(self) -> f64 {
        let mu_m3_s2 = MU_EARTH * KM_TO_M * KM_TO_M * KM_TO_M;
        (mu_m3_s2 / self.min_semi_major_axis_m()).sqrt() + OMEGA_E_DOT_RAD_S * self.max_radius_m()
    }
}

/// Which checks to run, and with what bounds.
#[derive(Debug, Clone, PartialEq)]
pub struct ContinuityOptions {
    /// Earth-fixed speed bound for the adjacent-pair gate. `None` disables the
    /// gate.
    pub speed_bound: Option<SpeedBound>,
    /// Hold-out interpolation residual tolerance in meters. `None` disables the
    /// residual check.
    ///
    /// This is the sensitive check. A tolerance well above the interpolator's own
    /// error at the product's sampling (centimetres for GNSS MEO at 5-15 minutes)
    /// and well below the smallest splice worth reporting is the useful range;
    /// 1.0 m is a defensible default for a merged GNSS orbit product.
    pub residual_tolerance_m: Option<f64>,
}

/// Source of the adjacent-pair speed bound.
#[derive(Debug, Clone, Copy, PartialEq)]
pub enum SpeedBound {
    /// Derive the bound from the orbit class.
    OrbitClass(OrbitClass),
    /// An explicit caller-supplied earth-fixed bound, meters per second.
    ExplicitMaxSpeed(f64),
}

impl SpeedBound {
    fn value_m_s(self) -> f64 {
        match self {
            Self::OrbitClass(class) => class.max_earth_fixed_speed_m_s(),
            Self::ExplicitMaxSpeed(bound) => bound,
        }
    }
}

impl ContinuityOptions {
    /// Both checks, with the class bound and a 1 m residual tolerance.
    pub fn for_orbit_class(class: OrbitClass) -> Self {
        Self {
            speed_bound: Some(SpeedBound::OrbitClass(class)),
            residual_tolerance_m: Some(1.0),
        }
    }
}

/// One continuity defect. Every variant names the satellite and locates itself
/// in time.
#[derive(Debug, Clone, PartialEq)]
pub enum ContinuityDefect {
    /// Two or more samples share one epoch. Reported, never deduplicated: which
    /// record is authoritative is not this module's decision.
    DuplicateEpoch {
        /// The satellite.
        sat: GnssSatelliteId,
        /// The repeated epoch, seconds since J2000.
        epoch_j2000_s: f64,
        /// How many samples carried this epoch (>= 2).
        occurrences: usize,
    },
    /// A satellite carried a single usable sample, so no adjacent pair and no
    /// hold-out prediction exist. Not a pass.
    SingleSampleSeries {
        /// The satellite.
        sat: GnssSatelliteId,
    },
    /// An adjacent pair implies an earth-fixed speed above the physical bound.
    SpeedBound {
        /// The satellite.
        sat: GnssSatelliteId,
        /// Earlier epoch of the pair, seconds since J2000.
        from_j2000_s: f64,
        /// Later epoch of the pair, seconds since J2000.
        to_j2000_s: f64,
        /// Elapsed interval, seconds. Strictly positive by construction.
        interval_s: f64,
        /// 3D chord displacement over the interval, meters.
        displacement_m: f64,
        /// Implied earth-fixed chord speed, meters per second.
        implied_speed_m_s: f64,
        /// The bound it exceeded, meters per second.
        bound_m_s: f64,
    },
    /// A sample disagrees with the arc its neighbours describe. This is the
    /// splice detector: `preceding_j2000_s` and `epoch_j2000_s` bracket the
    /// offending pair.
    HoldOutResidual {
        /// The satellite.
        sat: GnssSatelliteId,
        /// Epoch of the held-out sample, seconds since J2000.
        epoch_j2000_s: f64,
        /// Epoch of the preceding sample, seconds since J2000 - the other side
        /// of the offending pair.
        preceding_j2000_s: f64,
        /// 3D distance between the stored record and the value predicted from
        /// its neighbours, meters.
        residual_m: f64,
        /// The tolerance it exceeded, meters.
        tolerance_m: f64,
    },
}

impl ContinuityDefect {
    /// The satellite this defect concerns.
    pub fn satellite(&self) -> GnssSatelliteId {
        match self {
            Self::DuplicateEpoch { sat, .. }
            | Self::SingleSampleSeries { sat }
            | Self::SpeedBound { sat, .. }
            | Self::HoldOutResidual { sat, .. } => *sat,
        }
    }

    /// Whether this finding can enter any interpolation stencil used by the
    /// evaluation window.
    pub(super) fn influences(&self, window: EpochWindow, stencil: StencilExtent) -> bool {
        let (needed_from, needed_through) = stencil.influence_bounds(window);
        let support = match self {
            Self::DuplicateEpoch { epoch_j2000_s, .. } => Some((*epoch_j2000_s, *epoch_j2000_s)),
            Self::SingleSampleSeries { .. } => None,
            Self::SpeedBound {
                from_j2000_s,
                to_j2000_s,
                ..
            } => Some((from_j2000_s.min(*to_j2000_s), from_j2000_s.max(*to_j2000_s))),
            Self::HoldOutResidual {
                epoch_j2000_s,
                preceding_j2000_s,
                ..
            } => Some((
                epoch_j2000_s.min(*preceding_j2000_s),
                epoch_j2000_s.max(*preceding_j2000_s),
            )),
        };

        match support {
            Some((from, through)) => from <= needed_through && through >= needed_from,
            // The existing variant has no epoch. Querying the existing report
            // must therefore treat it conservatively rather than invent a
            // location or hide an unresolved input defect.
            None => true,
        }
    }
}

/// Which check produced a defect, for callers filtering a report.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum ContinuityCheck {
    /// Input well-formedness: duplicate epochs, single-sample series.
    Input,
    /// The physical earth-fixed speed gate.
    SpeedBound,
    /// The hold-out interpolation residual check.
    HoldOutResidual,
}

/// Result of a continuity check.
///
/// Absence of defects is the attestation; presence of defects is the structured
/// report. Both are the same type so a caller cannot accidentally handle only
/// one.
#[derive(Debug, Clone, PartialEq, Default)]
pub struct ContinuityReport {
    /// Every defect found, ordered by satellite then epoch.
    pub defects: Vec<ContinuityDefect>,
    /// Adjacent pairs the speed gate examined.
    pub pairs_checked: usize,
    /// Samples the hold-out residual check examined.
    pub residuals_checked: usize,
    /// Samples the residual check could not evaluate because the held-out
    /// neighbourhood was not interpolatable (a coverage gap, or too few
    /// neighbours). Reported rather than silently dropped: a caller must be able
    /// to tell "checked and clean" from "not checked".
    pub residuals_skipped: usize,
}

impl ContinuityReport {
    /// Whether the series is attested continuous: no defects of any class.
    pub fn attested(&self) -> bool {
        self.defects.is_empty()
    }

    /// Defects produced by one check.
    pub fn defects_from(&self, check: ContinuityCheck) -> impl Iterator<Item = &ContinuityDefect> {
        self.defects.iter().filter(move |defect| {
            let source = match defect {
                ContinuityDefect::DuplicateEpoch { .. }
                | ContinuityDefect::SingleSampleSeries { .. } => ContinuityCheck::Input,
                ContinuityDefect::SpeedBound { .. } => ContinuityCheck::SpeedBound,
                ContinuityDefect::HoldOutResidual { .. } => ContinuityCheck::HoldOutResidual,
            };
            source == check
        })
    }

    /// Findings that can influence evaluation in `window` through `stencil`.
    ///
    /// This filters the existing report. It does not rerun continuity checks or
    /// alter their defaults. A [`ContinuityDefect::SingleSampleSeries`] has no
    /// stored epoch, so it conservatively influences every window.
    pub fn defects_influencing(
        &self,
        window: EpochWindow,
        stencil: StencilExtent,
    ) -> Vec<&ContinuityDefect> {
        self.defects
            .iter()
            .filter(|defect| defect.influences(window, stencil))
            .collect()
    }

    /// Decide whether recorded defects can influence an evaluation window.
    ///
    /// The full report remains available in [`WindowContinuityVerdict::all_defects`]
    /// whether the result accepts or refuses the window.
    pub fn verdict_for_window(
        &self,
        window: EpochWindow,
        stencil: StencilExtent,
    ) -> WindowContinuityVerdict<'_> {
        let influencing_defects = self.defects_influencing(window, stencil);
        let decision = if influencing_defects.is_empty() {
            WindowContinuityDecision::Accept
        } else {
            WindowContinuityDecision::Refuse
        };
        WindowContinuityVerdict {
            decision,
            influencing_defects,
            influencing_splices: Vec::new(),
            all_defects: &self.defects,
            all_splices: Vec::new(),
        }
    }
}

/// One satellite's samples, sorted by epoch with duplicates already extracted.
///
/// Construction is the only way to obtain one, and construction sorts. After it,
/// `x` is strictly increasing, so every adjacent pair has a strictly positive
/// interval *by construction* - a zero or negative interval is unrepresentable
/// in the comparison path rather than checked for at each use.
struct OrderedSeries {
    /// Node epochs, seconds since J2000, strictly increasing.
    x: Vec<f64>,
    /// Node positions in file-native kilometres, matching the interpolation
    /// substrate's fit units.
    kx: Vec<f64>,
    ky: Vec<f64>,
    kz: Vec<f64>,
    /// Node positions in SI meters, for displacement arithmetic.
    pos_m: Vec<[f64; 3]>,
}

impl OrderedSeries {
    /// Sort `samples` by epoch and split out duplicates as defects.
    ///
    /// Non-representable epochs are dropped from the comparison path and counted
    /// as duplicates of nothing - they cannot be placed on the axis at all, so
    /// they are excluded here and surface as a short series.
    fn build(
        sat: GnssSatelliteId,
        samples: &[&PreciseEphemerisSample],
        defects: &mut Vec<ContinuityDefect>,
    ) -> Option<Self> {
        let mut placed: Vec<(f64, [f64; 3])> = Vec::with_capacity(samples.len());
        for sample in samples {
            let Some(seconds) = instant_to_j2000_seconds(&sample.epoch) else {
                continue;
            };
            if !seconds.is_finite() || !sample.position_ecef_m.iter().all(|c| c.is_finite()) {
                continue;
            }
            let Some(node) = precise_node_j2000_seconds_from_instant(&sample.epoch) else {
                continue;
            };
            placed.push((node, sample.position_ecef_m));
        }

        // The sort is this module's job, not the caller's: a shuffled input must
        // reach the checks in the identical order a sorted one does.
        placed.sort_by(|a, b| a.0.total_cmp(&b.0));

        let mut series = Self {
            x: Vec::with_capacity(placed.len()),
            kx: Vec::with_capacity(placed.len()),
            ky: Vec::with_capacity(placed.len()),
            kz: Vec::with_capacity(placed.len()),
            pos_m: Vec::with_capacity(placed.len()),
        };

        let mut index = 0usize;
        while index < placed.len() {
            let epoch = placed[index].0;
            let mut run = 1usize;
            while index + run < placed.len() && placed[index + run].0 == epoch {
                run += 1;
            }
            if run > 1 {
                // Duplicates are a defect of the data and are not resolved here.
                // Every record for the epoch is withheld from the comparison
                // path: silently keeping one would be picking an authoritative
                // sample, which is the caller's decision.
                defects.push(ContinuityDefect::DuplicateEpoch {
                    sat,
                    epoch_j2000_s: epoch,
                    occurrences: run,
                });
            } else {
                let (node, pos_m) = placed[index];
                series.x.push(node);
                series.kx.push(pos_m[0] / KM_TO_M);
                series.ky.push(pos_m[1] / KM_TO_M);
                series.kz.push(pos_m[2] / KM_TO_M);
                series.pos_m.push(pos_m);
            }
            index += run;
        }

        if series.x.is_empty() {
            return None;
        }
        Some(series)
    }

    fn len(&self) -> usize {
        self.x.len()
    }

    /// Every adjacent pair, in time order. The only path to a comparison, and
    /// every interval it yields is strictly positive.
    fn pairs(&self) -> impl Iterator<Item = (usize, usize)> + '_ {
        (1..self.x.len()).map(|index| (index - 1, index))
    }
}

/// Check an ordered ephemeris sample sequence for continuity.
///
/// Samples for any number of satellites may be supplied in any order; they are
/// grouped by satellite and sorted by epoch internally. The verdict is
/// independent of the order they arrive in.
///
/// This never refuses a series. Every finding lands in
/// [`ContinuityReport::defects`], and whether a product with defects is
/// acceptable is the caller's decision.
pub fn check_continuity(
    samples: &[PreciseEphemerisSample],
    options: &ContinuityOptions,
) -> ContinuityReport {
    let mut by_sat: BTreeMap<GnssSatelliteId, Vec<&PreciseEphemerisSample>> = BTreeMap::new();
    for sample in samples {
        by_sat.entry(sample.sat).or_default().push(sample);
    }

    let mut report = ContinuityReport::default();
    for (sat, sat_samples) in by_sat {
        // Each satellite's defects are collected and ordered on their own before
        // joining the report, so the report reads as one timeline per satellite
        // rather than interleaving satellites or check passes.
        let mut sat_defects = Vec::new();
        let Some(series) = OrderedSeries::build(sat, &sat_samples, &mut sat_defects) else {
            report.defects.append(&mut sat_defects);
            continue;
        };
        if series.len() < 2 {
            sat_defects.push(ContinuityDefect::SingleSampleSeries { sat });
            report.defects.append(&mut sat_defects);
            continue;
        }

        if let Some(bound) = options.speed_bound {
            check_speed_bound(sat, &series, bound, &mut sat_defects, &mut report);
        }
        if let Some(tolerance_m) = options.residual_tolerance_m {
            check_hold_out_residual(sat, &series, tolerance_m, &mut sat_defects, &mut report);
        }

        sat_defects.sort_by(|a, b| defect_sort_key(a).total_cmp(&defect_sort_key(b)));
        report.defects.append(&mut sat_defects);
    }
    report
}

fn check_speed_bound(
    sat: GnssSatelliteId,
    series: &OrderedSeries,
    bound: SpeedBound,
    defects: &mut Vec<ContinuityDefect>,
    report: &mut ContinuityReport,
) {
    let bound_m_s = bound.value_m_s();
    for (lo, hi) in series.pairs() {
        let interval_s = series.x[hi] - series.x[lo];
        let displacement_m = distance_m(series.pos_m[lo], series.pos_m[hi]);
        report.pairs_checked += 1;

        let implied_speed_m_s = displacement_m / interval_s;
        if implied_speed_m_s > bound_m_s {
            defects.push(ContinuityDefect::SpeedBound {
                sat,
                from_j2000_s: series.x[lo],
                to_j2000_s: series.x[hi],
                interval_s,
                displacement_m,
                implied_speed_m_s,
                bound_m_s,
            });
        }
    }
}

/// Hold out each interior sample and compare it against the arc its neighbours
/// describe.
///
/// The prediction runs through the same sliding-window Lagrange substrate the
/// product's own interpolator uses, so the residual on a clean arc is the
/// interpolator's own error rather than a second, differently-wrong model of the
/// orbit.
///
/// # Why the hold-out is by parity, not one node at a time
///
/// Deleting a single node from an otherwise uniform series does not leave a
/// series that is merely one sample shorter: it leaves one interval of twice the
/// nominal spacing, which the substrate correctly classifies as a *coverage gap*
/// and refuses to interpolate across. The evaluation then degrades to a
/// one-sided extrapolation, whose error grows with the polynomial degree and
/// reaches hundreds of kilometres at the arc's end - it would measure the
/// extrapolation, not the data.
///
/// Holding out every other sample instead keeps the retained series uniform (at
/// twice the spacing), so the substrate sees no gap and each held-out epoch is a
/// genuine interpolation bracketed by real neighbours. Two passes of opposite
/// parity cover every interior sample exactly once. This is the same decimation
/// hold-out the sample-source parity oracle uses.
///
/// Endpoints are never held out: with no neighbour on one side any evaluation
/// there is an extrapolation regardless of scheme.
fn check_hold_out_residual(
    sat: GnssSatelliteId,
    series: &OrderedSeries,
    tolerance_m: f64,
    defects: &mut Vec<ContinuityDefect>,
    report: &mut ContinuityReport,
) {
    let interior = series.len().saturating_sub(2);
    if interior == 0 {
        // Only endpoints exist; nothing can be held out with a neighbour on both
        // sides. Counted as skipped so the caller can see the check did not run.
        report.residuals_skipped += series.len();
        return;
    }

    for parity in [0usize, 1usize] {
        // Retained nodes: every sample whose index shares this parity. Held-out
        // nodes are the interior samples of the opposite parity.
        let keep: Vec<usize> = (0..series.len())
            .filter(|index| index % 2 == parity)
            .collect();
        let held: Vec<usize> = (1..series.len() - 1)
            .filter(|index| index % 2 != parity)
            .collect();
        if held.is_empty() {
            continue;
        }
        if keep.len() < 2 {
            // Too few retained nodes to define any fit for this parity.
            report.residuals_skipped += held.len();
            continue;
        }

        let x: Vec<f64> = keep.iter().map(|&i| series.x[i]).collect();
        let kx: Vec<f64> = keep.iter().map(|&i| series.kx[i]).collect();
        let ky: Vec<f64> = keep.iter().map(|&i| series.ky[i]).collect();
        let kz: Vec<f64> = keep.iter().map(|&i| series.kz[i]).collect();

        for index in held {
            let query = series.x[index];
            match interpolate_precise_state(sat, &x, &kx, &ky, &kz, &[], query) {
                Ok(state) => {
                    report.residuals_checked += 1;
                    let predicted = [state.position.x_m, state.position.y_m, state.position.z_m];
                    let residual_m = distance_m(predicted, series.pos_m[index]);
                    if residual_m > tolerance_m {
                        defects.push(ContinuityDefect::HoldOutResidual {
                            sat,
                            epoch_j2000_s: query,
                            preceding_j2000_s: series.x[index - 1],
                            residual_m,
                            tolerance_m,
                        });
                    }
                }
                Err(_) => {
                    // The retained neighbourhood is not interpolatable at this
                    // epoch - a real coverage gap in the product, not an artifact
                    // of the hold-out. Not a defect of the data, but not a pass
                    // either, so it is counted rather than dropped.
                    report.residuals_skipped += 1;
                }
            }
        }
    }
}

/// Epoch a defect is anchored at, for ordering a report as a timeline.
fn defect_sort_key(defect: &ContinuityDefect) -> f64 {
    match defect {
        ContinuityDefect::DuplicateEpoch { epoch_j2000_s, .. } => *epoch_j2000_s,
        ContinuityDefect::SingleSampleSeries { .. } => f64::NEG_INFINITY,
        ContinuityDefect::SpeedBound { from_j2000_s, .. } => *from_j2000_s,
        ContinuityDefect::HoldOutResidual { epoch_j2000_s, .. } => *epoch_j2000_s,
    }
}

fn distance_m(a: [f64; 3], b: [f64; 3]) -> f64 {
    let dx = b[0] - a[0];
    let dy = b[1] - a[1];
    let dz = b[2] - a[2];
    (dx * dx + dy * dy + dz * dz).sqrt()
}