Halo Vocabulary Legend

22 deg halo

The common ring around the sun and the scale reference for the atlas.

circle(sun, R22)

46 deg halo

A larger halo used as context for CZA, supralateral, and infralateral vocabulary.

circle(sun, R46)

Sundog / parhelion

Bright flanking spots on the parhelic circle. The offset recovers sun altitude when the anchors are eligible.

offset = R22 / cos(h)

Parhelic circle

The horizontal belt through the sun and parhelia. It is rendered, but not promoted as a hidden-state handle.

circle through sun and parhelia

Circumzenithal arc

The high smile-shaped arc. The current route is visibility-gated; pre-A1b anchors need rechecking before proof use.

visible when h < 32.196 deg

Supralateral arc

High arc near the 46 deg halo/CZA region. The inverse route failed coverage and structural-discrimination gates.

46 deg family context

Upper tangent arc

Column-crystal tangent vocabulary above the 22 deg halo. It remains useful for logo language, not inverse proof.

tangent-family candidate

Suncave Parry arc

A Parry-family cap near the upper tangent arc. It is optional vocabulary with weak photo support.

Parry-oriented family

Lower tangent arc

The lower counterpart of the upper tangent family, tied to low-altitude/observer geometry.

22 deg lower tangent family

Parry supralateral arc

Parry-family shoulders near the 46 deg top region. Coverage and weak evidence blocked promotion.

Parry + 46 deg family

Infralateral arcs

Lower-side 46 deg family vocabulary. Present as periphery language, not a calibrated inverse route.

46 deg lower-side family

Sun pillar

A vertical light column from plate-crystal reflection. The atlas renders it as stylized visual vocabulary.

plate-crystal reflection

Parry-family arcs

Includes suncave, sunvex, and Parry supralateral members. Some are optional labels today; the family still needs subrows and HaloSim receipts.

Pyramidal / odd-radius halos

Faint odd-radius rings from pyramidal ice crystals. HaloSim reproduces the family, but the atlas does not model it and the quantitative ring-isolation route topped out below promotion.

Lowitz arcs

Arcs from rotating plate orientations, historically contested and now photographically observed. Not modeled here yet.

Antisolar features

Anthelion, anthelic arcs, paranthelia, and 120 deg parhelia live opposite or far around from the sun.

Sub-horizon halos

Subsun and subparhelia require aircraft, mountain, or below-horizon observer geometry.

Circumhorizon arc

A high-sun plate-crystal arc sometimes called a fire rainbow. It is outside the current sundog-facing regime.

Hidden state

The decisive quantity the system does not get to inspect directly: sun altitude, target position, pole angle, local field, obstacle geometry, or player intent.

Trace

The indirect signal left in the world: parhelion offset, detector intensity, shadow, pressure field, deformation, local acceleration, or behavior wake.

Transformation

The rule that makes the trace usable. Sometimes it is closed form, like R22 / cos(h); sometimes it is a bounded controller or measured operating envelope.

Boundary

The point where the trace stops being enough. A credible indirect route names the boundary where it should fail instead of smoothing that failure into a story.

Choreography

A periodic three-body orbit where all bodies share a single closed inertial-frame trajectory — the same wire — phased thirds of a period apart.

Strict vs relative

A strict choreography returns to the same wire each period. A relative choreography returns rotated by 2π/3 in SO(3). The σ₃ detector splits 25 → 21 strict + 4 relative.

σ₃ detector

A gauge-invariant test that compares an orbit's third return to itself. Distinguishes strict-from-relative choreographies by rotation angle, blind to the catalog's labels.

rotation-angle metric on σ₃·X vs X

G.2 catalog

Li & Liao (2025) supplementary-A table of three-body periodic orbits at m₃ = 1. The 21 strict G.2 single-curve choreographies are the K_facet test's input set.

K_facet

A pre-registered structural-zero test on the strict G.2 catalog. For each row it asks whether the standard D₃ block is absent in the kernel by construction.

Structural-zero receipt

The named artifact class. A row earns one when ci = di = 0 by construction — not by tolerance, not by post-hoc pruning. 20 of 21 rows returned receipts in v0.3h.

Audit chain

A receipt-first, closure-relative, three-stage pipeline: sentinel/Γ runner → adaptive-floor reprocessor → bridge audit. Constants and outcome categories are registered before interpretation.

Adaptive floor (three guards)

Stage 2 picks the smallest pre-registered floor satisfying all three: D₃ leakage ≤ 1e-3, gap ratio ≤ 1e-3, first-rejected singular value ≥ 1e-3. No row-specific knobs.

floor ladder: 1e-8 → 1e-5

D₃ representation

The standard real D₃ block is a structured T/S/E decomposition. A valid representation is what the audit chain looks for; an invalid one — e.g. T(2) + S(6) + E(1) with odd E — is what trips the bridge audit.

Γᵢ (Gamma_i)

The per-orbit audit operator. A Γᵢ failure would indicate an orbit-specific defect inside the chain. O_617 is not a Γᵢ failure — the defect is downstream, in the bridge representation.

Opposite-strict

A catalog row whose orientation is admitted by the opposite-strict admission test, with admission residual 1.01e-8 for O_617. The canonical residual 1.62e-1 is diagnostic-only for an opposite-strict row, never an admission residual.

Bridge direction (defective-D3)

At the bridge-admitted kernel, O_617's representation is not a valid standard real D₃ block. The Jordan-chain test amplifies (90.04) and the order-3 relation fails (‖σ₃³ − I‖∞ = 3.96e-2). The defect lives here, in the bridge representation — not in admission, not in the audit chain.

Named quarantine

A row held back from being counted for or against the prediction, with a specific representation-level reason given. O_617 is the sole quarantine in v0.3h. Naming the quarantine is the discipline — absorbing it into a clean number would not be.

Shadow projection

A local, gauge-invariant readout that extracts an algebraic quantity from a small spacetime stencil without reconstructing a globally consistent potential. The shape the Sundog method asks of any verifier: small stencil, exact invariance.

Plaquette holonomy

The Shadow Faraday realisation of P_shadow: the line integral ∮ A around the boundary of a coordinate plaquette. By Stokes it equals the flux ∫ F; the gauge term drops out around any closed loop.

Gauge invariance (Sundog sense)

The readout is unchanged under A → A + dλ by an algebraic identity, not by approximate cancellation. In EM that follows from the holonomy of an exact form vanishing on any closed loop.

Structural zero (vs tolerance threshold)

The closure residual is zero by an algebraic identity, not by being below a numerical floor. Distinguished from tolerance-based guarantees that report no observed violation across many test cases.

Named quarantine

A pre-registered failure class paired with the branch it forces. Shadow Faraday names five: regularity, topology, monopole, operator-stencil commutator, motional EMF. A surprise without a pre-registered class is a Branch C bounded failure.

Branch A · clean structural zero

All registered clean-domain residuals evaluate to exact algebraic zeros. The strongest landing. Shadow Faraday earned Branch A on the registered classical-vacuum domain.

Branch B · named quarantine

One precisely-named survivor — boundary at infinity, Aharonov–Bohm phase, monopole insertion, a registered topological obstruction. Closure is conditional; the failure is articulate.

Branch C · bounded failure

A surviving global-reconstruction, gauge-choice, nonlocal, or unregistered residual inside the registered clean domain. The bound is publishable; the prior is updated.

Two-tier operator

Phase 2 retained both P_shadow^point (algebraic zero-out object, equal to Fμν in the smooth limit) and P_shadow^stencil (locality receipt). Public claims must not blur the two.

Admissibility rule

The five-clause registered condition on (S, ∂S): oriented C² surface, contractible in U, static in the working frame, plaquette mesh covering S without overlap or gap, mesh respects orientation.

Reading-2 witness

A constructive witness in the Postulate-1 idiom: pairs of trajectories that agree on a Sundog-style signature to within ε_K also agree on the proxy-action objective. The "Reading 2" regime is where standard determining-modes signals fail to reconstruct full state but a smaller signature suffices for control.

Regime generality (G value)

Whether a witness that holds at one Grashof number G on a Kolmogorov-flow cell also holds at a second. The NSE C1 witness now replicates at G = 200 and G = 300; that's the current span.

Portable objective

A control objective designed to transport across Grashof regimes — held-out-quantile rather than a fixed-percentile threshold pinned to one cell.

Damp fraction

A portability-gate quantity. The G=300 adjusted damp fraction is 0.2688, well above the v6 0.004 vacuity that motivated the regime-generality pivot.

Witness pair

A pair of trajectories that compose the Reading-2 witness. The G=300 twin-state lock is certified with 942,834 unique pairs, 100% witness coverage.

Bounded-null synthesis

A named outcome class: pre-registered lanes that returned null verdicts with the specific substrate causes identified. Bounded nulls are receipts, not silent failures. Riemann and Yang-Mills publish bounded-null syntheses.

Failure-mode taxonomy (cross-substrate)

The eight named ways a cross-substrate generalization fails: marginal (body barely resists its shadow), numerical wall (shadow unmeasurable with current tooling), bounded-null (shadow carries no separating structure), vacuous (rigidity trivially satisfied), cost-bounded (envelope blocks promotion), convergence-to-null (needs a reframing, not another sweep), conditional (rigid only after naming the held-fixed coordinate), deflationary (over-attribution corrected). Cataloguing the mode, not just the negative, is what turns each wall into a design constraint. The public map lives on Generality, with each lane ledger carrying its own scope fence.

Review-gated (status tag)

A lane whose next move depends on an external review pass. NSE C1, Riemann, and Yang-Mills are currently review-gated. The badge stays prominent on public pages until the gate closes.

Cost hold (status tag)

A lane whose safety floor is positive but whose cost has not been adjudicated. P-vs-NP v5: safety green, cost-unresolved.

UNPROMOTED

A lane whose witness is in hand but whose promotion criteria are not all met. Public copy carries this badge to refuse collapsing a witness into a theorem-facing claim. NSE C1 remains UNPROMOTED until criterion (c) closes.

Body-resistance (the axis)

How much a body (full state) resists reconstruction from its shadow (a lossy projection) — the axis used to compare public cross-substrate lanes. Two exact poles bound it: Faraday (resistance zero by the Bianchi identity — the shadow reconstructs the body) and Kakeya (resistance maximal — the direction-shadow cannot compress the set below full dimension). The marginal substrates (NSE C1, Mesa, shell) sit between, near-zero by low dimension.

Kakeya bridge (body-resistance, not regime-2)

The Kakeya conjecture read on the body-resistance axis: the line direction is the fiber-label / shadow; "informationally incompressible at ambient dimension" is maximal body-resistance. Polson–Zantedeschi (2026) formalize this via conditional Kolmogorov complexity and the Lutz point-to-set principle — the same body/shadow split Sundog uses, reached independently. Honest fence: this is the body-resistance half only. That framework has no control-sufficiency notion, so Kakeya is not a Reading-2 / regime-2 witness — its direction-shadow is "sufficient for the direction" only trivially (it is the direction).

Adaptive-fibering obstruction

Body-resistance is exact only when the shadow is identifiable — each body maps to one shadow-label. When a point lies on many fibers (many directions through one point), an adversarial oracle can pick whichever direction minimizes description length, undermining the clean split. This identifiability boundary is why Kakeya is resolved in R³ (Wang–Zahl; sticky/Lipschitz neutralizes it) yet open for n ≥ 4.