# Mesa ↔ Geometry Crossover Note > _Filed 2026-05-13 from Mesa team to Geometry team. Status: load-bearing > for Phase 10/11 overlay tuning kickoff and for gravity-claim public > framing in `SUNDOG_V_GRAVITY.md`._ The mesa-optimization roadmap (`SUNDOG_V_MESA.md`) hit its v3.1/v3.2 gate in the in-vitro lane and produced a methodology surface that transfers cleanly into geometry. This note captures the transfer in a single place so Phase 10/11 doesn't have to rediscover it under time pressure. ## The one-liner The controller mesa cracked open has the same shape your sky does — **small-dimensional, entangled, holistically read, asymmetric under inversion** — and the methodological discipline that earned mesa its anchors is the same discipline that will earn the overlay protocol its strongest public claim. --- ## Five transferable findings ### 1. The field-shape has now been observed in two substrates Mesa headline after v3.1/v3.2: the basin-attractor mechanism lives in an **entangled 5D subspace at `net.7`** that resists every attempt to factor it — not into top SAE features (v2), not into top-k neurons by L2 (v3.2), not into PC1-alone or PCs-2-5-alone (v3.1). It is **read holistically or not at all.** That is structurally the same object Geometry's atlas committed to when it stopped treating arcs as independent features and started treating them as visible portions of a small set of complete implied circles. Both projects converged, from opposite ends, on the same shape: **small handful of generators, irreducibly entangled, only legible as a whole.** **Why it matters for gravity-language**: the field-not-reward framing in `SUNDOG_V_GRAVITY.md` now has both an **in-vitro receipt** (mesa) and an **in-the-wild receipt** (parhelion overlays). That is a quiet but real ratchet for the public claim — same shape, two substrates, independent methods. ### 2. Variance is not mechanism Mesa's PC1 carries **38.8% of the diff variance and almost no patch effect**. The most visually obvious component was not the load-bearing one. The team chased SAE features with `|corr| = 0.89` that produced zero patch effect. **Geometry analog** for Phase 10/11: the **brightest, easiest-to-overlay arc is not necessarily the most diagnostic** for the inverse inference `h = arccos(R₂₂ / parhelion_offset)`. A rich-display vocabulary pass that ranks primitives by visual contribution will mis-rank them by inferential contribution. **Action for Phase 10**: track overlay-fit residuals **per-primitive, not by total fit**. Explicitly record which optional arcs do inversion work versus which are decorative. The `do not promote` list in the current Phase 10 spec is the right shape; this finding sharpens what "do not promote" should mean. ### 3. Directional asymmetry is structural, not a quirk Mesa v3.1 found that the **basin-inducing direction generalizes** across held-out Medium pairs while the **basin-resisting direction is weaker and more policy-specific**. Forward and inverse are not symmetric. **Geometry analog**: today, `h → signature` runs cleanly forward (parhelion offset, halo radius, CZA visibility window all derived from sun altitude); the inverse `signature → h` runs through **one preferred route** — `arccos(R₂₂ / parhelion_offset)`. The mesa lesson is to **suspect that other inversion paths carry different residual profiles**: - CZA apex position → h (cutoff geometry; only valid for h < 32.2°) - Tangent-arc curvature → h (curvature is a non-monotone function of h) - Supralateral position → h (tangent to 46° halo top; geometric, not refractive) These are not equivalent for inversion accuracy. **Measure each explicitly** rather than assuming a unified inversion route. ### 4. Smoke gates and pre-registered negatives Mesa got **disproportionate value from spec'ing what failure looks like before running**. v3.2 deliberately stopped at the smoke gate and recorded a clean negative. That is a publishable result, not a wasted run. **Action for Phase 10**: pre-register, **for each candidate vocabulary primitive, the residual threshold below which it does not get promoted into the calibrated core**. The `do not promote` list in the current Phase 10 spec is already pointing this direction. The mesa pattern is to: 1. Make the failure condition **quantitative** (residual ≥ N pixels at anchor scale, across ≥ M of the calibration photos). 2. **Commit to honoring it** before the overlay run, in writing. 3. Treat the negative as a deliverable, not a non-event. ### 5. Non-linear attribution is mandatory for field-shaped objects The hardest-earned mesa lesson: if geometry ever tries to decompose the overlay fit into "which arcs contribute how much" via any **linear additive scheme**, mesa's v3.2 result predicts it will fail in a specific way — **partial delivery of the right basis still produces wrong downstream behavior.** **The atlas already dodges this by construction** (it does not claim linear decomposition into arc-importance scores; every visible arc is the upper portion of one full implied circle, all derived from a small shared parameter set). **Action**: bank this so future overlay metrics do not accidentally reintroduce the assumption. If a Phase 10/11 metric ever wants to report "arc X contributes 23% of the fit", flag it: this is the mesa trap surfacing in geometry. --- ## What lands where | Finding | Phase 10/11 deliverable | Gravity claim language | |---|---|---| | Same shape in two substrates | — | Add "in-vitro + in-the-wild receipt" pair to `SUNDOG_V_GRAVITY.md` field-shape section | | Variance ≠ mechanism | Per-primitive residual reporting in `RICH_DISPLAY_OVERLAY_NOTES.md` | — | | Directional asymmetry | New deliverable: per-inversion-route residual table at Phase 10 gate | Cite as structural property in falsification surface | | Pre-registered negatives | Quantitative `do not promote` threshold, committed before overlay run | — | | No linear attribution | Phase 11 metric review: reject any arc-importance score | Cite as why atlas is the right model class | --- ## Open questions for Geometry 1. Should Phase 10 add a `per-inversion-route` residual deliverable alongside the existing per-photo overlays? 2. Is the pre-registration of `do not promote` thresholds a Phase 10 blocker or a Phase 10 gate? 3. Does `SUNDOG_V_GRAVITY.md` want to absorb the "two substrates" framing as a separate appendix, or fold it into the existing field-shape section? ## Geometry resolution, 2026-05-13 1. **Yes: add the per-inversion-route residual deliverable.** It lives in `docs/calibration/RICH_DISPLAY_OVERLAY_NOTES.md` beside the per-photo notes rather than as a standalone document. The table measures parhelion offset, CZA apex, tangent-arc curvature, and supralateral position separately wherever each route is visible/applicable. 2. **Threshold pre-registration is a Phase 10 blocker for promotion.** An overlay run without written thresholds may still be exploratory, but it cannot promote primitives into calibrated defaults or logo language. 3. **Keep two-substrate convergence folded into the Gravity Claim for now.** It becomes a separate appendix only if Phase 10/11 produce enough quantitative route-residual evidence to make the two-substrate framing a public proof surface rather than a claim-section support beam. --- ## v3.8 addendum, 2026-05-13 Mesa Phase 6 v3.8 sharpens the crossover note rather than changing its direction. The per-PC decomposition and signed-effect map add three constraints Geometry should inherit during Phase 10/11: 1. **Do not equate variance, single-route sensitivity, and full mechanism.** PC1 is variance-heavy and now has the largest single-PC P->C max mean ablation cost, but PC1 alone still does not reproduce the K=5 patch. Geometry should report visual salience, route-local residual/sensitivity, and full-overlay fit as separate columns, never as one primitive importance score. 2. **Directional asymmetry has internal structure.** P->C is more component-partitioned and pair-specific; C->P is more component-shared and family-wide. Geometry's per-inversion-route residual table should preserve this possibility: one route can be photo- or primitive-specific while another route generalizes across the atlas. 3. **Active interference belongs in the `do not promote` logic.** Axis U's signed-effect map shows that some neurons help one direction while hurting the other. The geometry analogue is a primitive or route that improves one overlay target while worsening another; that case should be recorded as a conflict, not averaged into a global score. This addendum lands directly in `docs/calibration/RICH_DISPLAY_OVERLAY_NOTES.md` as a Phase 11 metric-review rule: no arc-importance percentages, no route aggregation that hides directional conflicts, and no promotion without per-route residuals. --- ## Geometry Phase 10 closeout, 2026-05-13 Phase 10 anchor-capture work (Tasks #52, #53, #54, #55) closed 2026-05-13. The closeout sharpens Finding #3 (Directional asymmetry is structural) more than this note originally hypothesized, and surfaces a new methodological vocabulary worth carrying back to mesa. > **Post-re-audit substantive update, 2026-05-14.** The closeout > below has been re-derived against the post-pass state of the > [Phase 10 attack campaign](PHASE10_ATTACK_ROADMAP.md) and verified > by the > [re-audit memo](calibration/PHASE10_OPTICAL_REAUDIT_MEMO.md). The > pre-audit "three independent failure layers" phrasing is retired > from this file in favor of **three structurally different failure > modes**: dataset/aspect-ratio coverage (CZA), atmospheric-physics > discrimination (supralateral), and hybrid coverage + detection-tooling > with verify-gate (tangent after Passes C2 + C4 + C5 + C6 landed > 2026-05-14: four literature-standard automated detectors miss the > signal on every photo, including Pass C6 matched-filter on > halo-subtracted b\* — the natural follow-up the C5 receipt named; > Pass C5 manual sample selection recovers on p2 with R\_uta\_obs / > R22 = 0.824 and RMS = 1.23 px but C6 falsifies the natural-extension > matched-filter on the same b\* substrate, putting the route in > C5↔C6 substrate tension; recommended specialist re-anchoring as > the verify gate; coverage gate fails at 1 / 3 photos; remaining > candidates are matched-filter on alternative substrates, > polarization filtering, or new calibration photos). The > two-substrate field-shape *pattern* survives unchanged; the inverse > direction is narrower than the pre-audit framing implied, in > directions that vary by route. The cross-substrate transfer of the > three-gate vocabulary is preserved; only the geometry-side route > verdicts are updated. ### Finding #3 outcome was sharper than hypothesized *(re-derived 2026-05-14)* The original Finding #3 framing predicted that CZA-apex, tangent-arc curvature, and supralateral position would carry "different residual profiles" than parhelion offset. The post-pass + post-re-audit geometry-side outcome is **stronger than the pre-audit verdict, in a narrower direction**: parhelion-offset remains the only promoted inverse handle, restricted now to a 3-photo strict-eligibility set, and the other three routes fail along three structurally different *failure modes* rather than along three independent measurement-stack gates. | route | gate outcome | failure-mode kind | | --- | --- | --- | | Parhelion offset → h | **promoted (post-hedged)** | 3-photo strict eligibility: p2 (h = 18.6°), p7 (h = 59.4°), p13 (h = 6.83°). Unambiguous bilateral peaks, valid geometry, ring-fit R22, non-trivial discrimination (p2, p7) or low-lever-but-supported (p13). | | CZA apex → h | **fails coverage gate** | **dataset / aspect-ratio.** After Pass A1b fixed the atlas formula bug and Pass A2 re-classified p27's chromatic feature as 46° halo top / supralateral merger, p2 is the only in-window photo with an independent CZA residual (+1.3 px). Every other anchored photo is either past the h = 32.2° disappearance threshold or has the literature CZA apex predicted above the top of the frame. | | Supralateral → h | **fails structural-discrimination gate** | **atmospheric physics.** Even at the two-photo eligibility threshold (p2 eligible-unmeasured + p27 measured post-A2), the predicted h-spread is ~0.3° (~2.5 px at p2 R22), below the typical 5–10 px visual-edge measurement noise on a chromatic-broadened halo arc. The route would not be a useful inverse handle even with perfect coverage. | | Tangent-arc curvature → h | **partially recovered on p2 under manual sample selection; coverage gate fails; C5↔C6 substrate tension flagged** *(Pass C1 + C2 + C4 + C5 + C6 landed 2026-05-14)* | **hybrid coverage + detection-tooling with verify-gate.** Pass C1 dropped p7. Three automated detectors fail (C2 wing-radial Lab b\* ridge, C4 wing-slope luminance-gradient curvature, **C6 matched-filter against parameterized arc model on halo-subtracted b\* — the natural follow-up the C5 receipt explicitly named**). **Pass C5 (manual sample selection) recovered the route on p2:** R\_uta\_obs / R22 = 0.824, RMS = 1.23 px — with methodology hedge. **Pass C6 falsified the C5→matched-filter extension**: correlation is negative across the entire R\_uta scan on p2, including at R\_uta values consistent with C5's manual fit. The route is in **C5↔C6 substrate tension**: either C5's gestalt signal is in a different substrate (untested: absolute b\*, L\* magnitude, chromaticity magnitude), or C5's tight fit is symmetry-bias artifact. Recommended specialist verify gate before further propagation. On p13 / p27 substrate-signal absence is unchanged. Coverage gate still fails (1 / 3 photos). Open questions: matched-filter on alternative substrates, polarization filtering, new calibration photos. | The careful taxonomy still matters, but the *type* of failure has sharpened. The pre-audit reading "CZA-apex reaches residual comparison and the residuals fail to replicate direction" was partly formula-bug artifact; post-A1b the p2 residual is sub-px and p27's chromatic feature was a different primitive altogether. The supralateral "only-one-eligible-photo" reading was correct but understated the structural physics-discrimination limit. The tangent "detection-degenerate" reading was correct as scoped to the column-peak protocol but was missing the p7-circumscribed-halo regime call. The atlas remains forward-rich for primitives the literature parameterizes from `h` alone (with hedges on the parhelic-circle rule and the 46° halo / infralateral visibility windows) and is inverse-narrow on the strict 3-photo parhelion-offset eligibility set. That is the same forward-rich / inverse-narrow asymmetric field-shape pattern mesa observed in-vitro, **now observed in-the-wild at numerical resolution with three different non-atlas reasons for the non-promoted routes' inverse-narrowness** (dataset coverage, atmospheric physics, detection tooling). None of the three failures implicates the atlas inversion math; the only route whose verdict was atlas-influenced was CZA, and Pass A1b corrected the underlying formula. ### Three-gate taxonomy is transferable back to mesa The residual / coverage / detection three-gate vocabulary is new methodological surface that didn't exist before the Phase 10 closeout. It is portable back to the mesa side: - **Residual gate analog (mesa):** ablation cost / dissociation thresholds, the v3.x family of "does the patch effect transfer at level X" tests. - **Coverage gate analog (mesa):** held-out pair availability and dimension matching — the Phase 6 v3.1 J3 Small-tier failure (256D basis applied to a 64D layer) is a coverage-gate failure in retrospect. - **Detection gate analog (mesa):** "are we measuring the right quantity at all?" The Phase 6 v2 SAE-feature failure (|corr| = 0.89 yet ~0% patch effect) and the v3.2 top-k L2-rank failure (correct basis, wrong ranking method, ~0% patch effect) are detection-gate failures in retrospect. We were measuring feature availability and L2 rank instead of feature use and ablation rank. The methodological rule worth carrying: **before claiming a substrate is wrong, classify the failure by detection, coverage, and residual gate.** Many cycles' worth of mesa "the substrate is wrong" candidates were really detection-gate calls in disguise. The same discipline applies in reverse: a geometry route that "doesn't work" can mean three substantively different things. ### Open questions filed, none blocking Phase 11 *(updated 2026-05-14)* Post-pass + post-re-audit, the three open questions resolve as follows: 1. **CZA coverage expansion.** *(Reframed from the pre-audit "lens-optics test for CZA-apex direction inconsistency", which assumed the pre-audit residual-gate framing that Pass A1b retracted.)* The post-A3 CZA verdict is coverage-gate-bound: only p2 is in-window with an independent residual. Reopening coverage requires new anchored photos in 5° < h < 32° where the literature CZA stays on-frame. Mesa #4-style falsification surface, now with a sharper question shape: *does the route hold up at a second in-window anchor?* 2. **Tangent-curvature tooling — wing-based / Lab b\* detector.** The campaign's optional Pass C2 was the pass that would have built and tested this; C2 was skipped per the recommended execution order. Passes C2, C4, C5, and C6 landed 2026-05-14. **C2** wing-radial Lab b\* ridge detector (`scripts/tangent_detector.py`) — not-recovered. **C4** gradient-based edge detector Persona 1 §5 named (`scripts/tangent_curvature.py`) — not-recovered. **C5** manual sample selection: 5 hand-anchored points on p2 fit a clean circle with R\_uta\_obs / R22 = 0.824 (within [0.7, 1.3]) and RMS = 1.23 px — **recovered on p2** with methodology hedge (possible symmetry bias). **C6** matched-filter against parameterized arc on halo-subtracted b\* (`scripts/tangent_matched_filter.py`) — the natural follow-up the C5 receipt named — **falsified the C5→matched-filter extension**: correlation negative across the entire R\_uta scan on p2; spurious half-R22 peak on p13; zero signal on p27. Four automated detectors now fail on p2's signal that C5 manual recovers, putting the route in **C5↔C6 substrate tension**: either gestalt signal in a different substrate (untested: absolute b\*, L\* magnitude, chromaticity magnitude), or C5's tight fit is hand-anchoring bias. On p13 only the apex is anchorable; on p27 sun-bloom prevents any anchoring; coverage gate fails at 1 / 3 photos. The failure-mode is **hybrid coverage + detection-tooling with verify-gate flagged**: recommended specialist re-anchoring of p2 before further propagation. Remaining open candidates: matched-filter on alternative substrates, polarization filtering, or new calibration photos, filed as Phase 10 backlog. 3. **Parhelic-belt-y replication.** Closed by Phase 10-FF ([`docs/calibration/PHASE10_BELT_Y_RESULTS.md`](calibration/PHASE10_BELT_Y_RESULTS.md)): p13's residual is photo-specific; the belt-y watch-list flag is retired. None gates Phase 11. ### Public framing constraint *(re-derived 2026-05-14)* The Phase 10 closeout retires any "atlas has multiple independent inverse routes converging" reading of the two-substrate convergence claim. The convergence survives: same field-shape pattern observed in two substrates, by independent methods. What gets retired is the implication of inverse-route redundancy and any "three independent accidents" reading of the non-promoted routes. The post-audit framing: > The atlas is forward-rich for primitives the literature parameterizes > from `h` alone, and inverse-narrow on the strict 3-photo > parhelion-offset eligibility set (p2, p7, p13). The three other > tested routes fail at three structurally different failure modes: > dataset / aspect-ratio coverage (CZA), atmospheric-physics > discrimination (supralateral), and hybrid coverage + detection-tooling > with verify-gate (tangent after Passes C2 + C4 + C5 + C6 landed > 2026-05-14: four literature-standard automated detectors miss the > signal on every photo; Pass C5 manual sample selection recovers on > p2 but Pass C6 matched-filter on the same b\* substrate falsifies > the natural-extension hypothesis, putting the route in C5↔C6 > substrate tension; coverage gate fails; recommended specialist > re-anchoring as the verify gate; remaining candidates are > matched-filter on alternative substrates, polarization filtering, > or new calibration photos). None of the three implicates the atlas > inversion math. > The mesa cliff is the same forward-rich / inverse-narrow asymmetric > field-shape pattern in the controller substrate. That is the sharpened public framing. The matching ratchet on the gravity ledger is in [`SUNDOG_V_GRAVITY.md`](SUNDOG_V_GRAVITY.md) forward/inverse asymmetry receipt; the matching specialist handoff is [`docs/calibration/PHASE10_OPTICAL_AUDIT_HANDOFF.md`](calibration/PHASE10_OPTICAL_AUDIT_HANDOFF.md) (rewritten 2026-05-14; previously stop-bannered). --- ## Follow-on, 2026-05-13: perception roadmap promoted The "structural transition" thread in this note — mesa's Phase 5→6 move from describing the cliff behaviorally to localizing it causally — has now seeded a structurally matched roadmap on the geometry side: [`SUNDOG_V_PERCEPTION.md`](SUNDOG_V_PERCEPTION.md). That doc reframes the atlas's "what it does NOT yet model" list as a prediction surface and instruments three candidate predictions ranked by apparatus cost: 1. Sub-visible parhelic circle continuation (smartphone + polarizer; Phase 1–4). 2. Intersection enhancement at predicted circle crossings (narrowband + long-exposure; Phase 5, reach). 3. Color-order inversion at arc tangencies (spectrometer; Phase 6, explicit reach). Phase 0 is locked at the smartphone-only apparatus tier with the predicted-curve software and pre-registration template inherited from mesa Phase 6 discipline. Phase 7 is the earned-language ratchet that would add a third receipt — *in-the-wild predictive* — alongside the existing in-vitro (mesa) and in-the-wild observational (atlas overlays) ones, on a Phase 4 positive verdict only. The five transferable findings above remain authoritative for Phase 10/11 of geometry; perception is a separate roadmap, not a successor. --- ## Phase 11 wave-2 addendum, 2026-05-14 The Phase 11 outreach campaign ran a second independent persona dispatch (wave-2) after wave-1's 15 patches landed; full record at [`docs/calibration/PHASE11_OUTREACH_SYNTHETIC_MEMO.md`](calibration/PHASE11_OUTREACH_SYNTHETIC_MEMO.md) §8. Wave-2 surfaced 3 send-blocking + 14 recommended findings on top of wave-1; all 17 patches landed in four user-approved batches the same day. The *post-re-audit substantive update* above pre-dates wave-2; this addendum absorbs the wave-2 findings with cross-substrate methodological reach. None of them weaken the two-substrate framing. ### Wave-2 W7 — chromatic-spread verification-gate miss Wave-1 §3a finding #8 patched `scripts/cza_formula.py` with a docstring claim that "the CZA disappearance altitude varies by ~0.1° across the visible chromatic spread, which is below this atlas's measurement precision." Wave-2 §8.4 re-derived from the script's own formula: | wavelength | n (ice) | h_disappear | | --- | --- | --- | | red (~670 nm) | 1.306 | 32.86° | | yellow (~589 nm) | 1.308 | 32.50° | | visible centroid | 1.31 | 32.19° | | violet (~404 nm) | 1.317 | 31.05° | Visible-band spread is **~1.8°**, not ~0.1°. Off by ~18×. The "below measurement precision" claim was also wrong: ~1.8° altitude uncertainty is well above the ~0.1° precision the photo-anchor JSONs work at. **Mesa methodological transfer.** This is a wave-1 verification-gate miss: the §5 standard ("persona claims about formulas must be backed by executable code or a specific cited literature line") should have caught the ~0.1° number during wave-1 consolidation, and didn't. The gate let a magnitude claim through because the magnitude wasn't re-derived from the underlying formula — only the qualitative direction was. Mesa's own verification gates across Phase 4 / 5 / 6 should treat **persona-quoted numerical constants as hypotheses to re-derive, not facts to propagate**. Audit-survived wording is only as strong as the consolidator's worst miss; the principle generalizes back to the basin-capture, cliff, and patch-success numerical claims that anchor Phase 7's earned envelope language. The wave-2 fix lands both at `scripts/cza_formula.py` lines 46-57 and at packet §1 row 5. ### Wave-2 W1 — p7 production-mechanism question Wave-2 Persona A flagged that the strict 3-photo parhelion-set includes p7 at h = 59.4°. Persona A's recall cited "Tape (1994) §3 and Greenler ch. 3" for the parhelia-low-to-moderate-`h` framing; that citation has since been verified to be **partly wrong** by direct read of Tape Ch 6 (on disk at `docs/calibration/AH-CH06/`). What Tape *does* directly support (Chapter 6, Display 6-4 text, verified): > *"As the sun rises in the sky, the upper and lower tangent arcs > bend toward each other at their extremities, and at a sun elevation > of 29° the two halos merge to form the circumscribed halo… For sun > elevations less than about 35°, the sides of the circumscribed halo > are normally imperceptible, and separate upper and lower tangent > arcs are seen."* So at h = 59.4° the circumscribed halo regime is structurally available, which confirms Pass C1's decision to drop p7 from *tangent-arc* eligibility, and makes "circumscribed-halo brightness at the parhelic-circle intersection" an available alternative interpretation for p7's parhelion anchor. What Tape Ch 6 does *not* support: the "parhelia don't form at high h" framing. Display 6-5 (h ≈ 39°) and Display 6-6 (h ≈ 72°) both show parhelion-related features. The plate-orientation parhelia treatment lives in Tape *Chapter 1: Halos From Plate Crystals*, which is **not on disk**. So the open W1 question for the specialist tier sharpens to: at h = 59.4°, is p7's bright spot a real plate-population parhelion, circumscribed-halo brightness, or ambiguous? Filed at handoff §2.8 with the updated literature anchors. **Mesa cross-substrate analog.** Mesa's Phase 4 basin-capture receipt shows canonical L-Reward has zero action-response to live `x_false` movement while ending preferentially at the training-time basin — that end-position is the load-bearing observable for the fixed- attractor reading. The geometry analog asks a sharpening question: **is the observable we measure actually produced by the mechanism we think it is, or by a different effect competing for the same observable?** Mesa's existing discipline (Phase 4 distinguishes action-response from end-position) already encodes this principle, and the geometry side now has a concrete worked example with **literature-confirmed structural availability of the alternative interpretation** — same bright spot, two production mechanisms (plate parhelion vs circumscribed halo), with Tape Ch 6 directly confirming that the circumscribed-halo regime starts at h ≈ 29° (i.e., the alternative-mechanism brightness *is* present at h = 59.4°). Worth banking as a methodological reminder for Phase 8 v2 replay design: when the replay shows continued attraction to the training-time basin, the replay shows the *effect*; whether the *mechanism* is internalized-basin or environment-feature is a separate question to keep posable. ### Wave-2 W4 — canonical vs project-original inverse handle Wave-2 Persona A surfaced that the literature standard tangent-arc inverse handle is **opening angle / arc extent** (Tape 1994 §6; Cowley tangent-arcs page), not circle-fit curvature. The project's tested inverse `R_uta / R₂₂ → h` was project-original framing, not canonical literature framing. Handoff §2.3 (v) already hedged this as an open framing question, but the wave-1 verdict tables treated it as settled. Wave-2 pulled the hedge up into the verdict tables across handoff §1 and packet §0. **Refinement of original Finding #3 (Directional asymmetry).** The forward/inverse asymmetry now has a sub-distinction inside the inverse direction: | inverse route | handle type | outcome | | --- | --- | --- | | parhelion-offset → h via `R₂₂ / cos h` | canonical literature | **promoted** (3-photo strict eligibility) | | CZA-apex → h via Bravais `arcsin(√(n² − cos²h)) − h` | canonical literature | **fails coverage gate** (dataset, not handle) | | supralateral → h | canonical literature | **fails physics-discrimination** (route-physics limitation, not handle) | | tangent-arc → h via `R_uta / R₂₂` circle-fit curvature | **project-original framing**, not canonical | **fails in C5↔C6 substrate tension** | The pattern: where the project used the canonical handle, routes either promoted or failed for a substrate-physics reason; where the project used an original handle, the route failed in a way that could be a real route failure *or* a measurement-of-the-wrong-shape failure. **Mesa cross-substrate analog and detection-gate refinement.** Geometry's three-gate vocabulary (residual / coverage / detection) ported back to mesa, and Phase 6 v2's `|corr| = 0.89` with ~0% patch effect was the original detection-gate lesson: feature *availability* ≠ feature *use*. Wave-2 W4 adds a deeper version: **the canonical literature inverse handle for a substrate may be a different geometric object entirely from the one being tested.** If mesa ever runs into a "negative on the substrate" result that survives detection-gate scrutiny, W4 says: re-check that the handle being tested is the canonical substrate-literature inverse, not a project-original framing dressed in canonical-looking notation. The `net.7` entangled 5D subspace is mesa's load-bearing basis; whether that 5D shape is the *canonical literature inverse* in the controller substrate (or project-original framing in canonical-looking notation) is a question mesa's existing infrastructure can't answer but the cross-substrate methodological surface now poses. ### What does not change Mesa's Phase 8 v1 public artifact (`mesa.html`) requires no update for wave-2: - §The Envelope (Phase 7 v1) class-balance (8/7/1/4/2) stands. - §The Cliff at `λ ≈ 0.953` stands. - §The Locus `net.7` patch-success receipt stands. - §What This Doesn't Say claim-boundary block stands. The gravity-ledger promotion summary and Candidate 2 *Current recommendation* (in `SUNDOG_V_GRAVITY.md`) stand. The two-substrate field-shape framing is intact. The wave-2 patches are concentrated on the *geometry-side public surfaces* (packet, handoff, brief, workbench HTML) and on the *cross-substrate methodological surface* (this addendum + the resolution-of-chromatic-spread record in the synthetic memo §8.4), not on mesa's earned claim language. ### Open items, none blocking mesa 1. ~~**Geometry W4 follow-up — Tape §6 opening-angle / arc-extent tangent inverse as a candidate Pass C7.**~~ **CLOSED 2026-05-14 — Pass C7 landed; receipt at [`docs/calibration/PASS_C7_OUTPUT.txt`](calibration/PASS_C7_OUTPUT.txt).** The canonical-handle reformulation tested C5's circle fit against HaloSim ray-tracing under the column-orientation tilt-dispersion assumption (0.1° per Cowley's HaloSim 22-deg-halo.sim defaults). **Verdict: C5's circle fit is geometrically inconsistent with the canonical literature arc curve at h = 18.6° — C5 places wings 1.2-5.6° too-far-radially, progressively with azimuth.** The C5↔C6 substrate tension resolves: C5 was likely the symmetry-bias artifact the C5 receipt hedged against, not a genuine recovery. The tangent route remains unpromoted *including* under the canonical handle. **Mesa transferable lesson:** the canonical-vs-project-original inverse-handle distinction in §Wave-2 W4 above is now empirically anchored on the geometry side; mesa's net.7 entangled-5D substrate analog should treat "canonical-handle test against an independent ground truth" as a discipline pattern worth importing if Phase 8 v2 work surfaces a similar handle-vs-substrate ambiguity. Net change to the gravity-ledger "in-the-wild receipt": none — forward/inverse asymmetry receipt was already 3-photo strict on parhelion-offset only; tangent route remains unpromoted, just now for *two* independent reasons (C6 + C7) rather than one (C6 with C5↔C6 tension flagged). 2. **Specialist reply on handoff §2.8 (p7 mechanism question).** External dependency. If specialist confirms mis-attribution, strict 3-photo wording cascades through handoff §1, packet §2 item 3, reaudit memo §94, brief §5; the gravity-ledger forward/inverse asymmetry receipt narrows from 3 photos to 2 (p2, p13). The cross-substrate pattern survives in narrower form either way. 3. **Outreach send sequence.** Tier-1 specialist handoff is ready; tier-2 editorial cover note (brief §10b) is ready; tier-3 Wikipedia-adjacent is now structurally unblocked by wave-2 W2/W13/W15 once `dist/sundog.html` is rebuilt and deployed to sundog.cc. None of these block mesa Phase 8 v2 work (best-cell / worst-cell replay, Phase 6 v2 Axis A redux at net.7, Phase 7 v2 cross-product + Large tier). ## Reference - `docs/SUNDOG_V_MESA.md` — the mesa roadmap, v3.1/v3.2 results - `docs/SUNDOG_V_GRAVITY.md` — gravity claim staging ledger - `docs/SUNDOG_V_GEOMETRY.md` Phase 10/11 — overlay tuning + logo toolkit - `docs/SUNDOG_V_PERCEPTION.md` — atlas-as-instrument roadmap (filed 2026-05-13)