CHORUS: Information-Theoretic Telescope Scheduling

The classic composite scorer asks: how good is this (target, node) pairing? CHORUS — Coverage-kernel Hierarchical Optimization for Reliability-weighted Utility of Samples — asks a different question entirely: how much scientific information does this observation deliver that the network would not otherwise have? Every coordination behaviour the network exhibits — redundancy avoidance, cadence shaping, longitude diversity, weather robustness — emerges as arithmetic from this single objective rather than from a set of hand-tuned multipliers.

CHORUS is the default live scheduler. The config key scheduler.chorus: true is set out of the box in cloud/config.yaml. The former per-node greedy packer is archived under cloud/archive/ and can be restored instantly by setting scheduler.chorus: false — no infrastructure restart required.

The hot path — T0 through T3 and Ring 0 — is 100% procedural and deterministic. No LLM calls occur during alert ingestion, composite scoring, or plan generation. Claude is used only in the Ring-1 advisory monitor (the same nightly weight-tuning loop described in Configuration), which is opt-in and ships disabled.

What CHORUS Replaces

Legacy hand-tuned mechanism	CHORUS emergent equivalent
`redundancy_decay = 0.55` geometric penalty	A second observation of an already-captured cell multiplies a residual that is already small — automatic diminishing returns, scaled by how likely the first observation was to succeed
Longitude-diversity recovery (`× sep/90° × 0.5`)	Observations at different longitudes touch different time cells → full marginal value, no recovery hack needed
`cadence_bonus_strength`	Time cells at cadence resolution: clustered samples hit the same cell, spread samples hit empty ones
`robustness_cloud_relax` for enclosure nodes	Enclosure/dew-heater raise `p_exec` (measured, not declared) — robust nodes win marginal-value ties in bad weather automatically
Trust multiplier `×(0.5 + 0.5 × trust)`	Reliability enters where it physically acts: p (data may not arrive), κ (data may be noisier than physics predicts), θ_out (data may be discarded)
`telescope_match` heuristic (+0.1 for wide field)	σ² model: FoV sets the comparison-star ensemble floor; aperture/cooling set the faint-end noise; the cooled scope wins faint targets because its information gain is 100× larger, not because a rule says so

Three First-Class Models

CHORUS is built on three models that replace the composite score’s individual heuristics:

Measurement Model

Per (node, target, time, exposure) predicted photometric variance σ², computed from the telescope’s actual optics, sensor, cooling, filter set, field of view, and sky background.

Delivery Model

Per-observation probability that data actually arrives and is accepted: p_o = p_sky × p_exec × p_accept, each factor maintained as a calibrated posterior.

Information Model

Each target owns a set of information cells — time bins, phase bins, event sub-windows, filter bands — with science value densities and precision requirements.

Information Cells

Each active target t owns a finite set of information cells U_t = {u₁ … u_m}. A cell is the atomic “thing worth knowing”, characterised by three quantities:

Locus x_u — a time interval, phase interval (for periodic targets), event sub-window (ingress/egress/mid for transits), and optionally a filter band
Value density ν_u ≥ 0 — the science utility of fully capturing this cell, set by the class template and modulated by campaign state and scarcity
Precision requirement σ_ref(u) — the photometric error at which the cell’s science is essentially achieved (e.g. 0.01 mag to resolve a 12 ppt transit; 0.1 mag to detect a CV outburst)

Cells replace the composite score’s coverage, cadence, time-criticality, and science terms simultaneously. A target’s total schedulable value tonight is Σ ν_u, and its cell structure encodes when and how precisely it needs observing.

Capture Coefficients

A candidate observation o (node n, start slot s, exposure plan e) captures a fraction of each cell it touches:

ρ(u, o) = g(σ_o, u) · k_t(x_u, x_o)     ∈ [0, 1]

g(σ, u)  = σ_ref(u)² / (σ_ref(u)² + σ²)     precision saturation
k_t(·,·)  = class-specific proximity kernel    temporal / phase locality

g is the exact Gaussian posterior variance reduction for a one-dimensional cell state with prior variance σ_ref². A measurement at σ = σ_ref captures 50%; at σ_ref/3 captures 90%; at 3σ_ref, only 10%. This is where telescope hardware differentiates continuously — a 200 mm cooled Newtonian at mag 16.5 might predict σ = 0.008 where a Seestar predicts σ = 0.25, giving capture coefficients of 0.975 versus 0.038 — a 25× value ratio. k_t is 1 when the observation sits inside the cell’s locus and decays with distance in time (aperiodic classes) or phase (periodic classes), with class-tuned length scales that are Ring-1 hyperparameters.

Delivery Probability

Each candidate observation succeeds — produces an accepted measurement — with probability:

p_o = p_sky(n, s..s+need)     calibrated per-slot clear probability
    × p_exec(n)               node executes and delivers, given clear sky
    × p_accept(n)             delivered data passes QC / AAVSO / cross-validation

p_exec and p_accept are posterior means of per-node Beta distributions maintained by the reliability ledger. Conditional on success, the measurement’s effective variance is the physics prediction inflated by the node’s measured efficiency:

σ_o² = κ_n · σ_phys²(n, t, s, e)

κ_n is the hardware-normalised skill factor — the ratio of delivered uncertainty to physics-predicted uncertainty, shrunk toward 1. A Seestar running at its limit has κ ≈ 1.05 (trust its σ); a scope with collimation problems has κ ≈ 6 (its 0.01 predictions behave like 0.025 in practice).

The Network Objective

Let A be the set of placed observations. Define per cell the residual — the probability-weighted fraction of the cell’s value still uncaptured:

r_u(A) = Π_{o ∈ A_t(u)} (1 − p_o · ρ(u, o))

The network objective is expected captured value plus an exploration bonus:

Φ(A) = Σ_t Σ_{u ∈ U_t} ν_u · (1 − r_u(A))   +   β · Σ_{o ∈ A} ξ(o)

The expectation over independent Bernoulli success indicators is exact and closed-form because of the product structure — no sampling, no simulation, fully deterministic. Theorem: Each term ν_u · (1 − Π(1 − p_o ρ_{u,o})) is a monotone submodular function of A. Therefore Φ is monotone submodular, and greedy maximization subject to the interval-scheduling and per-node capacity constraints inherits the classical near-optimality guarantees of submodular maximization over independence systems.

The Unified Scheduling Equation

The marginal value of a placement — the quantity the solver ranks at every step — is:

Δ(o | A) = Σ_{u touched by o} ν_u · r_u(A) · p_o · ρ(u, o)   +   β · ξ(o)

Read each term aloud and every current mechanism falls out:

ν_u — science value, urgency, brightness feasibility (via ρ → g)
r_u(A) — what is left: redundancy, cadence, diversity — all through the residual
p_o — weather, node reliability — the chance it actually happens
ρ(u, o) — how well this hardware captures this cell

One formula. No weight vector.

Scarcity Pricing

The composite score’s coverage_gap and time_criticality look backward (how neglected is it? how old is the alert?). CHORUS prices cells forward:

ν_u = ν_u^raw · S_u,     S_u = 1 / (1 + Σ_{d=1..H} γ^d · q_u(d))

q_u(d) is the probability the network could capture cell u on future night d — computed once per target per day by a deterministic sweep over visibility and climatological clear probability. γ ∈ (0, 1) is the horizon discount (default 0.93). H ≈ 45 nights. Consequences without special-casing:

A transit whose next visible event is in 43 days gets S ≈ 1 → full value tonight
A circumpolar LPV with 90 future chances gets S small → it competes fairly and becomes natural filler for new nodes
A target approaching solar conjunction automatically increases in value as q_u(d) collapses
Fresh transients get urgency from ν^raw set by the class template, not an age-decay curve

Node Reliability Vector

CHORUS maintains four conjugate posteriors per node, updated nightly by counting — no optimizer, no LLM:

p_exec   ~ Beta(a_e, b_e)    success = plan item attempted on a clear night → data delivered
p_accept ~ Beta(a_a, b_a)    success = delivered → aavso_submitted, non-outlier, good/acceptable
θ_out    ~ Beta(a_o, b_o)    cross-validation outlier rate
κ        ~ shrunk ratio       mean((σ_delivered / σ_phys_predicted)²) over recent accepted
                              measurements, shrunk toward 1 with m₀ = 8

Priors are Beta(3,3)-class — the principled form of “start at 0.5” — and every count decays with a ~60-night half-life so nodes can redeem themselves and regressions surface quickly. The legacy reliability_score and scheduler_trust_score columns are still written (a fixed monotone map of the posterior vector) so every existing UI, API, and member-app surface keeps working — but the planner never reads the scalar again. Why κ is the deep upgrade: today’s precision_factor = 1 − mean_unc/0.30 punishes small telescopes for physics and forgives large ones for sloppiness. κ compares each node to its own physics prediction. A Seestar running at its limit (κ ≈ 1.05) is treated as fully reliable; a C8 with collimation problems (κ ≈ 6) has its 0.01 mag predictions silently treated as 0.025 and loses the demanding faint-target assignments it cannot actually deliver.

Four Execution Tiers

CHORUS runs through four deterministic tiers on every planning cycle:

T0 LEDGER
T1 HORIZON
T2 SCORE
T3 PERFORM

Continuous + nightly — state update from evidence.Inputs: new measurements, incidents, AAVSO results, weather realizations.

chorus_node_ledger: Beta posterior counts for p_exec / p_accept / θ_out, κ ratio stats, per-site weather calibration (a, b), per-band extinction k_ext, monthly climatology
chorus_target_state: per-target cross-night residuals — EB phase-coverage vectors, CV hazard clocks, transient segment tracking, last-accepted-σ per band
Weather site calibration: logistic(a + b · logit(forecast_clear)) fit per site by counting realized outcomes — coastal nodes with chronically optimistic forecasts get honest probabilities within two weeks
Incident classifier provides attribution (weather failure → excluded from p_exec; collimation problem → added to κ) so reliability signals are not polluted by causes outside the node’s control

Daily, per target — scarcity sweep and cell compilation.For each active target, a deterministic sweep over the next H = 45 nights × capable nodes: analytic visibility, climatological p_sky, p_exec → q_u(d) → scarcity S_u. Then compile the class template + target_state into tonight’s cell list U_t with final ν_u and σ_ref(u). Cached in target_cells.This tier is also where campaign commitments live: a multi-night campaign is a set of pre-priced future cells. T1 raises tonight’s ν for cells whose future q is low given the campaign deadline — no separate campaign scheduler needed.

Per planning cycle — fleet-wide stochastic-coverage assignment.Opportunity generation (per node, parallel): dark window, alt/az curve, horizon mask, per-slot p_sky, per-slot σ_phys for each (target, exposure-candidate), feasibility (bright limit).Lazy cost-benefit greedy on Φ:

# 1. Prime a max-heap with optimistic Δ̂(o) for every opportunity
# 2. Pop o; recompute Δ(o | A) exactly against current residuals r_u
#    O(#cells touched); if still ≥ next heap key → commit (lazy = exact
#    under submodularity); update r_u ledgers, node occupancy, capacity
# 3. Stop when Δ_best < ε or occupancy/capacity exhausted
# 4. Seeded deterministic local search (same budget as today's annealing):
#    relocate / swap / drop-add moves accepted on exact Φ recomputation

Compatibility: for every (target, node) the best single-placement Δ normalised to 0–1 is written to scores.total with a component breakdown — so every existing scores-reading surface keeps functioning.

Per node — sequencing + contingency ladders → ObservationPlan.Sequencing keeps the current machinery — nearest-neighbour + 2-opt ordering, slew/filter/meridian-flip overhead model — with overhead now charged back into marginal values so badly-packed orderings are repaired by the local search.Contingency ladders (new): for each plan item, up to 2 alternates — the next-best placements from the same solved state tagged with trigger conditions (“if sky closed until slot s”, “if target unsolvable”). A late-start ladder precomputes the best truncated plan if observing begins at +1h, +2h, or +3h. Emitted inside the existing plan JSON as an additive contingencies object — old node agents ignore unknown keys.Incremental repair: alerts, a node dropping offline, or a hard forecast change do not trigger a full re-solve. Affected placements are removed, their r_u restored, and the greedy resumes from the heap — O(affected), retaining the near-optimality guarantee relative to surviving commitments.

Class Strategy Templates

Templates are declarative data — rows in class_templates, seeded from config, editable by Ring 2 with schema validation. The deterministic cell compiler reads them. Adding a science programme equals adding a template row.

Class	Cell structure
EB (eclipsing binaries)	32 phase bins from the ephemeris. ν^raw concentrated on primary/secondary eclipse bins (σ_ref 0.02–0.03), quadrature for the O’Connell effect, uniform low floor elsewhere. Phase ledger persists across nights — bins captured this season stay discounted. CHORUS sees zero marginal value sampling the same phase twice; it shifts to a node 90° west instead
EXOPLANET (transits)	Event sub-window cells: pre-ingress baseline (≥ 45 min), ingress, mid, egress, post-egress baseline. ν^raw ∝ depth-normalised timing value × scarcity. Partial coverage by different nodes composes correctly — node A takes ingress + mid, node B (300 km east) takes egress
CV (cataclysmic variables)	Quiescent: one detection-quality cell per hazard interval, ν^raw ∝ P(state change since last sample) = 1 − e^(−λ_cv · Δt). Outburst state: template swaps automatically to dense time cells with tight σ_ref — an automatic campaign escalation that fires before the next planning cycle
SN / transient	Time + band cells. Early cells (rise/peak/early decline) carry ν^raw far above late-decline cells — age enters through which cells still exist, not an exp(−age/12) fudge. Band-specific cells exist only when a filtered node is in the fleet; that node alone sees ρ > 0 on colour cells
LPV / Mira	Sparse time cells, wide σ_ref, huge future opportunity count → tiny S_u. The network’s ballast and nursery for new nodes

Three-Ring Tuning

The tuning system is elevated from “Claude nudges 30 weights” to a three-ring loop around a deterministic core:

Ring 0
Ring 1
Ring 2

Closed-form calibration — nightly, LLM-free.Everything that has a statistical estimator gets one and stops being an LLM knob:

Per-site forecast calibration (a, b) from logistic regression on forecast vs. realized outcomes
Per-node κ from shrinkage estimation over accepted measurements
Per-node/band extinction and zero-point drift
Class hazard rates λ for CV outburst probability
Monthly climatology tables

Pure counting/least-squares in T0. Deterministic, auditable, no trust region needed beyond sample-size gates. Today the Claude monitor spends delta budget nudging weather weights to compensate for miscalibrated forecasts — Ring 0 removes that error term at the source.

LLM-advised hyperparameters — nightly, evolved from today’s loop.The parameter surface shrinks from ~31 heuristic weights to ~15 genuinely judgment-shaped hyperparameters:

kernel_time_scale_h / kernel_phase_scale   sample locality per class
value_scale_* (EB, CV, transient, …)       relative programme priorities
scarcity_gamma, scarcity_horizon_nights    tonight vs the future
exploration_beta                           fleet-learning appetite
same_site_repeat_factor                    weather-redundancy conservatism
min_marginal, max_obs_per_target           breadth vs depth

Same tuning_state / weight_history machinery, same trust-region clamps, same admin notifications and rollback API.The decisive change — backtest gate: because the planner is deterministic and every night’s opportunity inputs are archived in chorus_run_archive, any proposed θ′ is replayed over the last 14 nights’ actual inputs, and the resulting plans are scored against realized outcomes. θ′ is applied only if backtested realized Φ ≥ current θ’s. The LLM proposes; arithmetic disposes.

Module Structure

cloud/chorus/
├── params.py       Ring-1 hyperparameters (DEFAULTS, BOUNDS, merged())
├── physics.py      Measurement model: sigma_phys per (node, target, slot, exposure)
├── cells.py        Cell templates, compiler, proximity kernels
├── horizon.py      T1 scarcity sweep per target
├── assign.py       T2 lazy submodular greedy + seeded local search
├── perform.py      T3 sequencing + contingency ladders
├── ledger.py       T0 reliability vectors, target state, Ring-0 calibration
├── planner.py      Orchestration: plan_network(), plan_single_node(), plan_shadow()
└── backtest.py     Ring-1 backtest gate and run archive

planner.plan_network() is the entry point called by scheduler.generate_all_plans() when scheduler.chorus: true. plan_shadow() runs the full pipeline and records telemetry without saving plans — the staged rollout path before flipping the flag live.

Guarantees and Budgets

Determinism: same DB rows, cached forecasts, and seed → same plans. All randomness is the seeded local-search RNG. No LLM anywhere in T0–T3 or Ring 0
Complexity: cells/target ≤ 64; opportunities ≈ nodes × 60 (unchanged query shape); marginal evaluation O(cells touched) with the residual ledger; lazy greedy ≈ O(N_opp log N_opp) pops in practice; T1 sweep O(targets × 45 × nodes) of trig, daily — comfortably inside the current planning cadence at 10³ nodes × 10³ targets
Approximation quality: Φ is monotone submodular → lazy greedy is exact greedy; near-optimality per submodular-maximization theory; the seeded local search only improves, never regresses
Cold starts: unknown specs → Seestar-anchored defaults; no forecast → site climatology; new target class → generic time-cell template; empty ledger → Beta(3,3)/κ = 1 priors — every fallback is the current system’s behaviour or better
Compatibility: ObservationPlan/PlanItem unchanged (additive contingencies, richer explanation); scores still written; legacy reliability columns mirrored; tuning_state/weight_history reused; plan_runs extended

Introduction

Node Setup

Cloud Server

Member App

Operations

CHORUS: Information-Theoretic Telescope Scheduling

What CHORUS Replaces

Three First-Class Models

Measurement Model

Delivery Model

Information Model

Information Cells

Capture Coefficients

Delivery Probability

The Network Objective

The Unified Scheduling Equation

Scarcity Pricing

Node Reliability Vector

Four Execution Tiers

Class Strategy Templates

Three-Ring Tuning

Module Structure

Guarantees and Budgets

Build docs developers (and LLMs) love

Introduction

Node Setup

Cloud Server

Member App

Operations

Documentation Index

​What CHORUS Replaces

​Three First-Class Models

Measurement Model

Delivery Model

Information Model

​Information Cells

​Capture Coefficients

​Delivery Probability

​The Network Objective

​The Unified Scheduling Equation

​Scarcity Pricing

​Node Reliability Vector

​Four Execution Tiers

​Class Strategy Templates

​Three-Ring Tuning

​Module Structure

​Guarantees and Budgets

Build docs developers (and LLMs) love

What CHORUS Replaces

Three First-Class Models

Information Cells

Capture Coefficients

Delivery Probability

The Network Objective

The Unified Scheduling Equation

Scarcity Pricing

Node Reliability Vector

Four Execution Tiers

Class Strategy Templates

Three-Ring Tuning

Module Structure

Guarantees and Budgets