# Persona: CZA residual + Supralateral coverage auditor Synthetic-audit dry-run, 2026-05-13. Source materials: `PHASE10_OPTICAL_AUDIT_HANDOFF.md`, `RICH_DISPLAY_OVERLAY_NOTES.md`, `PHASE10_EXPANSION_TRIAGE.md`, the eleven anchored photos and their JSON anchor files, plus a scan of `scripts/overlay_calibrate.py`. ## Top-line verdict - **§A (CZA opposite-sign residuals):** *Pushback.* This is **not** a clean route-reliability negative. The −19.3 / +21 px split is an artifact of a hardcoded atlas approximation (`CZA apex_y = sun_y − R46`) combined with a primitive-misidentification on p27. Re-run the CZA prediction against the literature refraction formula and the p2 residual collapses toward zero; the p27 measurement should be retracted, not used as evidence of route failure. - **§B (Supralateral coverage):** *Sound with caveat.* The committed set genuinely lacks visible supralateral on >1 photo, but supralateral is also intrinsically rare in any non-curated dataset (~4 days/yr observable vs ~100 for 22° halo; Schaefer / Lynch literature). p27 is the one candidate where supralateral may actually be present — and the team is currently misreading it as the CZA. Coverage gate is the right verdict on the wrong reasoning. --- ## §A — CZA-apex residual gate **Four-way verdict: not (i)/(ii)/(iii)/(iv) cleanly. It is mostly (ii) + primitive mis-identification on p27.** ### Atlas-side smoking gun `scripts/overlay_calibrate.py:381-384`: ```python # CZA — anchored to 46° halo top def cza_apex(c): anchored = WB_SUN[1] - WB_R46 # 60 return anchored + (0.85 - max(0.4, min(1.4, c))) * 200 ``` The atlas hardcodes the CZA apex at `sun_y − R46`, i.e. at angular distance 46° above the sun, with no `h`-dependence. This is only true at h ≈ 22° (where CZA is tangent to the 46° halo top by construction). At every other h, real CZA sits **above** that point. Literature CZA zenith distance is `γ` with `sin γ = √(n² − cos²α)`, n ≈ 1.31, α = sun altitude. Empirical anchor points (atoptics.co.uk, Wikipedia): | h | CZA altitude | CZA above sun | | ---: | ---: | ---: | | 0° | 57.8° | 57.8° | | 18.6° (p2) | ~64.6° | ~46.0° | | 22° | ~68° | 46° (tangent to R46) | | 32.2° | 90° (zenith) | — (degenerate, vanishes) | ### p2 (h = 18.6°, R22 = 182, sun = (567, 496)) - Atlas prediction (hardcoded "sun_y − R46"): y = 496 − 364 = **132**. - Literature prediction (CZA above sun = 46.4° → 46.4° × 182/22 = 383.7 px): y = 496 − 383.7 = **112.3**. - Observed apex (p2-anchor.json): y = **113**. - Residual under atlas: 113 − 132 = **−19 px** (matches team). - Residual under literature formula: 113 − 112.3 = **+0.7 px**. The −19.3 px residual on p2 is **almost exactly the atlas-vs-literature prediction gap at h=18.6°**. The team's `sun_px` and `R22_px` anchors are fine; the visual apex pick at (560, 113) is fine; the overlays (`p2.overlay.png`, `p2.rich-vocabulary.overlay.png`) visually confirm the predicted-CZA line (cyan) sitting ~20 px **below** the observed chromatic arc, which is exactly what the literature/hardcode gap predicts. **This is a stable, predictable, h-dependent atlas bias on the CZA primitive, not noise.** Treating p2 as evidence of "route reliability" was the wrong reading — the route was fine; the forward-prediction it was being tested against was simplified. ### p27 (h = 0.5°, R22 = 219, sun = (596, 559)) This is the more interesting case. At h ≈ 0.5°: - Atlas prediction: y = 559 − 438 = **121**. - Literature prediction: CZA above sun = 57.3° → 57.3° × 219/22 = 570 px; y = 559 − 570 = **−11** (off-frame at top). - "Observed apex" in p27-anchor.json: (599, 142). - Observed feature is 41.9° above sun (=417 px / 9.95 px/deg). The bright chromatic arc the team is calling the "CZA apex" in p27 sits at **~42° above sun**, well below the literature CZA prediction of ~57° above sun (off-frame). The actual CZA at h ≈ 0.5° would be **above the top of the frame** in p27. The chromatic arc visible in p27 at y ≈ 142 is therefore **not the CZA** — it is the upper rim of the 46° halo / supralateral arc complex (which at h ≈ 0 is tangent to the top of the 46° halo and is geometrically degenerate with the halo top). Atoptics.co.uk and the Cloud Atlas both note this degeneracy: at very low sun, supralateral starts "as a pair of arcs tangent to the sides of a 46° arc" and merges over the halo top; it is well known to be confused for the 46° halo itself. p27's `_meta.note` in the anchor JSON already admits the symptom: *"The CZA band is clear, but the flat apex makes the fitted math apex sensitive."* A real CZA at h=0.5° is not flat-apexed; it is a narrow, brilliantly chromatic, near-vertical-cusp smile high in the sky. A flat-apex chromatic band tangent to the 46° halo top is exactly the supralateral / 46° halo morphology. ### Reading the team's framing against this The team writes the +21 / −19 split as a "stable atlas bias has been falsified — the opposite signs mean the route is unreliable, not biased." That reading depends on both residuals measuring the same physical feature against the same atlas formula. **They don't.** p2's −19 px is the atlas-vs-physics gap on a correctly-identified CZA at h=18.6°. p27's +21 px is a different primitive (46° halo top / supralateral) being labelled CZA, against an atlas prediction that itself is already wrong by ~130 px on the real CZA at h=0.5°. The "opposite signs" cancel by accident, not by structure. ### Sub-question rejections - (i) **Anchor error on one photo:** weakly yes on p27, but not in `sun_px` / `R22_px` (those are defensible) — the error is in *which primitive is being labeled "CZA apex"*. Not the kind of anchor error the team's protocol is built to catch. - (ii) **Genuine atlas bias the team has not recognized:** *yes, this is the dominant reading on p2.* The hardcoded `sun_y − R46` is only correct at h ≈ 22°. Fix: replace with `sun_y − (90° − h − asin(√(n² − cos²(h)) / 1)) × (R22/22)` or equivalent. - (iii) **Photo-environment / ice-habit sensitivity the atlas legitimately ignores:** small contribution at most. Plate-crystal wobble (~1° oscillation, Mayor & Tape 1979 / Schaefer 1981 family of observations) widens the CZA but does not shift its centroid by 19 px at R22=182 (which would be ~2.3°). The smudge effect near h=32° is also irrelevant for p2 (h=18.6°) and p27 (h=0.5°). - (iv) **Within real-atmosphere variability:** no. 19 / 21 px on R22 = 182 / 219 corresponds to ~2.3° / ~2.1° in sky angle. Plate wobble + crystal-quality variation explains ~1° at most. The bulk is the atlas formula plus a labelling error. ### What changes the verdict - Re-run p2's CZA-apex residual against `CZA_above_sun(h) = 90° − h − arcsin(√(n²−cos²h))` (use n=1.31). I predict the residual collapses to <5 px. If it does, the "CZA route fails residual gate" finding retires and CZA-apex becomes a viable second inverse handle on the current calibration set (at least on p2). - For p27, re-do the primitive-ID call. The visible feature at y=142 is more likely the 46° halo top + supralateral merger than the CZA. Either record it as "CZA off-frame / not applicable" or, more productively, treat it as the first second-photo of *supralateral* visibility (see §B). --- ## §B — Supralateral coverage gate **Three-way verdict: mostly (i) [intrinsically rare] with a real (ii) sub-case [p27 is supralateral that the team is misreading as CZA].** ### What I actually examined I read every anchored photo in the committed Phase 10 set, looking specifically for a faint chromatic arc tangent to (and outside of) the 46° halo on the zenith side, or — at low h — a pair of arcs tangent to the sides of the 46° halo merging over the top. | photo | h | 46° halo visible? | supralateral visible? | | --- | ---: | --- | --- | | p1 (key) / p2 | 18.6° | yes (faint outer ring) | **yes** — large parabolic arc tangent to 46° halo top is *labelled supralateral* in the p1 key, distinct from the small chromatic CZA above | | p7 | 59.4° | no — h>32° cutoff | no — supralateral cutoff is also ~32° | | p13 | 6.83° | no (above frame) | no — top of frame is clean dark blue with no chromatic arc at 46° from sun | | p18 | low | no | no | | p19 | ~11° | no (R46 ≈ 540 px > frame) | no — bright feature at top is upper-tangent / suncave-Parry territory, sitting at R22 not R46 | | p20 | ~5° | no (cropped, R46 ≈ 910 px) | no | | p22 | ~5.7° | no (cropped) | no | | p25 | ~11.4° | no (cropped) | no | | p26 | ~9.0° | no (cropped) | no | | **p27** | **~0.5°** | **borderline — chromatic arc near R46 visible** | **probable yes — currently mislabelled as CZA** | | p30 | ~11.1° | no (cropped, top of 22° halo only) | no | ### Why supralateral is intrinsically rare in this dataset Atmospheric-optics literature is unambiguous: supralateral is rare. Schaefer / Lynch-family observation counts give ~4 days/year of visible supralateral against ~100 days/year for the 22° halo (10:1 selection penalty before any cropping or h-window filtering). The supralateral / 46° halo distinction is itself a famously hard call that has its own Cloud Atlas entry (*"Differentiation characteristics of the 46° halo and supralateral arc"*). On a curated atlas-photo set of 11 anchored frames, finding 1-2 supralateral-eligible photos is **consistent with literature base rates**, not bad luck. ### Why the team's coverage gate verdict is defensible *for the wrong reasons* The team correctly says supralateral is visible only on p2 on the committed set. They list p27 as a candidate-but-unmeasured. The correct atmospheric-optics reading is that the chromatic arc on p27 that the team is treating as CZA is, geometrically, *more likely* to be the supralateral arc (or 46° halo top — they merge at h≈0). A re-anchor with explicit supralateral-tangency labelling would plausibly give the team a second eligible photo — at which point the coverage gate **passes** and supralateral-position → h becomes measurable on this set. But the *route* still does not obviously work. Supralateral at h ≈ 0 sits at ~46° above sun (tangent to 46° halo top); at h = 18.6° it also sits at ~46° above sun on the zenith side. Its angular distance from the sun changes only ~0.5° over the entire h range from 0° to 22° — much less sensitive to h than parhelion-offset (which changes ~30° over that range). So even with coverage, supralateral-position → h is a **structurally weak inverse**: the signal-to-anchor-noise ratio is order-of-magnitude worse than parhelion offset. The team's "three layers of failure" framing might survive with a footnote: supralateral is degenerate-with-46-halo-top *and* has poor h-discrimination by construction. ### Sub-question dispositions - (i) **Intrinsically rare:** *yes,* literature-supported. ~4 days/yr vs ~100 for 22° halo. Curated atlas sets of 7-11 photos will routinely fail the coverage gate. - (ii) **Actually present beyond p2, missed by detection criterion:** *one case, p27.* What the team is calling CZA on p27 is more consistent with supralateral / 46° halo top. With a primitive-ID correction this *could* push the route to coverage. - (iii) **Genuinely absent in the calibration set as documented:** *substantially yes,* with the p27 caveat. p7 / p13 / p18-30 are all either supralateral-cutoff (h>32°) or cropped above the 46° halo region. Even an uncropped reshoot would have to thread a h<32°, cold-cirrus-or-diamond-dust, plate-crystal-dominant needle to add a second supralateral photo. --- ## Pushback / counterproposal 1. **The single-handle verdict's evidentiary chain for CZA-apex is compromised.** "Opposite-sign residuals on p2 and p27" is currently the load-bearing receipt for "CZA-apex fails the residual gate." On inspection, the −19 px is a hardcoded-formula bug at h=18.6° (CZA ≠ R46-above-sun outside h≈22°) and the +21 px is a primitive-ID error at h=0.5° (the team is measuring something else). Replace the atlas's CZA prediction with the refraction formula and re-anchor p27's chromatic arc as supralateral / 46° halo top before claiming CZA-apex is dead. CZA-apex on p2 alone may pass residual gate; the route may still fail coverage (only one eligible photo if p27 is reclassified), but the failure layer label changes. 2. **The atlas's forward-generation claim is over-claimed at very low h on the CZA primitive.** §2.4 of the handoff says forward generation is not under audit. It should be, at least for CZA. The hardcoded `sun_y − R46` mispredicts the CZA position by 130+ px at h=0.5°. That is forward atlas error, not inverse-route error. If the public framing says "rich in forward generation," that claim needs the CZA primitive specifically caveated, or the formula fixed. 3. **Supralateral coverage gate is the right verdict, but for a different reason than the team thinks.** The team is treating supralateral as "almost made coverage; needs one more lucky photo." Atmospheric-optics base rates suggest supralateral will routinely fail coverage on curated atlas sets of this size, even in expansion. A more honest framing is: *"supralateral is rare by construction; the coverage gate is a structural finding, not a selection-bias one."* This matters for the gravity-side framing — "three independent failure layers" implies three independent accidents; one of them is a base-rate near-certainty. 4. **The vocabulary on p27 needs reconciliation.** The same chromatic arc cannot be simultaneously "CZA" in the per-route residual table and "candidate supralateral" in the same row. Pick one. If the atlas's degenerate-at-low-h prediction is fixed, the right answer may be "neither pure CZA nor pure supralateral — a merged primitive that the atlas should explicitly label as such at h<5°." 5. **Concrete next test.** Re-anchor p2 against a refraction-formula CZA prediction. If the p2 y-residual drops below 5 px, file an addendum: CZA-apex route promotion blocked on *coverage* (single photo eligible after p27 reclassification), not residual. The single-handle verdict survives but its rationale for the CZA row changes from "residual gate" to "coverage gate." That is a smaller, cleaner result than the current claim. --- ## Sources retrieved - [Supralateral arc — Wikipedia](https://en.wikipedia.org/wiki/Supralateral_arc) - [Circumzenithal arc — Wikipedia](https://en.wikipedia.org/wiki/Circumzenithal_arc) - [Supralateral & Infralateral Arcs — Atmospheric Optics (Les Cowley)](https://atoptics.co.uk/blog/supralateral-infralateral-arcs/) - [Is it a 46° halo or a supra/infralateral arc? — Atmospheric Optics](https://www.atoptics.co.uk/blog/is-it-a-46-halo-or-a-supra-infralateral-arc/) - [Circumzenithal arc — International Cloud Atlas / WMO](https://cloudatlas.wmo.int/en/circumzenithal-arc.html) - [Differentiation characteristics of the 46° halo and Supralateral arc — Cloud Atlas](https://cloudatlas.wmo.int/en/differentiation-characteristics-of-the-46-degree-halo-and-Supralateral-arc.html) - [Circumzenithal Arcs vs Solar Elevation — Atmospheric Optics](https://atoptics.co.uk/blog/circumzenithal-arcs-vs-solar-elevation/) - [CZA — Effect of solar altitude — Atmospheric Optics](https://atoptics.co.uk/blog/cza-effect-of-solar-altitude/) - [Frequency analysis of the circumzenithal arc: Evidence for the oscillation of ice-crystal plates — JOSA 69(8), 1119 (1979)](https://opg.optica.org/josa/abstract.cfm?uri=josa-69-8-1119)