Design notes — Part X — v3.0, Phase 11: Kessho and symplectic harmony (steps 71–75: the third medium, the Arnol'd lock, the braid, the chord wave, the Poincaré strobe — opened at the fold of the proposals, 2026-10-14; formerly `DECISIONS_10.md`)

Opened 2026-10-14, the day v2.0.0 shipped (#1 the fold of the proposals, #2 the order); merged into DECISIONS.md as Part X at the fold of Phases 11 and 12 (2026-10-18, the author’s word, with Part XI). The spec is PROJECT_SPEC.md (v5) with TO_PROJECT_SPEC.md as the arc’s draft, corrected per step; the roadmap ROADMAP_6.md; the author’s proposals _work/specs/ (KESSHO §n means medium_specs_v3.md). DECISIONS_10 #n means this file; the next phase opens DECISIONS_11.md, and so on, one file per phase as the v2 arc did.

1. The v3.0 arc opens: the three proposals folded into ROADMAP_6.md, the spec draft opened at the START of the arc, and what the fold corrected against the tree. The author delivered _work/specs/ on 2026-10-14 — roadmap_voxo.md (Phases 11–13: Suzu’s deferred physics, four new voices, Voxo’s Decent Sampler coverage; and a first draft of the carry-over and release phases), roadmap_voxo_gate_delta.md (its review fold), road_map_medium_v3.md (Phases 14–16: Kessho and symplectic harmony, the carry-overs, the release) and medium_specs_v3.md — with the word that version 3 has both features. The fold: one roadmap in the house form (working rules, the ABI block, the binding table, a step per section with its gates and its DONE clause, the deferred list, the open decisions), the gate delta’s amendments applied in place and marked, the first draft’s carry-over and release rows (its 85–87) superseded by the medium roadmap’s Phases 14–16 (90–92), which carry the same items plus Kessho’s; and TO_PROJECT_SPEC.md opened now rather than at a phase’s close — the proposals ARE the spec until a step corrects its subsection to what shipped, so the author transcribes a true text at the fold (the v2 arc wrote this file at each close and the specs left the tree; the proposals stay in _work/specs/ until the author removes them). THE ORDER OF THE PHASES IS NOT DECIDED HERE: the proposals number Voxo-first and say they work in either order; the author asked for the fold’s opinion (harmony-first; the roadmap’s open decision 1 records it) and decides before step 71; the step numbers keep the proposals’ numbering until then and renumber on the author’s word. What the fold corrected against the tree, each a fact the proposals got wrong or left to the header: (a) the control dimensions — the proposal’s SUMI_CTL_POLARIZER_ANGLE = 14 … _ARNOLD_K = 17 collide with the torsion’s, the Chladni’s, the spark’s and the Chirikov’s (14–19; SUMI_CTL_COUNT 20), so they are 20–23 and the count 24, the chart’s rows likewise; (b) the trace header is trace/include/sumi_trace.h, not trace.h, and the mode is a field of sumi_trace_config_t — the proposal’s text says “mode 2” and its enum says 1: it is the SECOND mode, value SUMI_TRACE_POINCARE = 1; (c) the export API is a flags word (SUMI_EXPORT_ANOD_ALPHA = 1u is a bit), so one new flag, SUMI_EXPORT_KESSHO_CAUSTIC = 2u (Layer B alone over alpha); the proposal’s SUMI_EXPORT_KESSHO is dropped — a Kessho export without the flag is the full composite, as an Anod export is; (d) the consonance curve’s home is core/src/midi_normalizer.cpp, beside the voice table it needs — the proposal’s midi_processor.cpp does not exist; (e) press_mode 3, bend_mode 5 and slide_mode 3 are the next free value of each (the proposals had them right); the two A/B modes are fields appended to sumi_params_t (polarizer_mode, braid_mode — the Step-33 pattern), not new enums alone; (f) voice_kind is a number with a comment in voxo.h (0–8 today), not the proposal’s VOXO_SUZU_TODA-style constants: 9 the membrane, 10 the Toda ring, 11 the Boris gyroscope, 12 the Dirac network, 13 the billiard, in the order the steps land, named constants if a step adds them; the Suzu params struct is voxo_suzu_params_t as the proposal says; bow_mode is new; (g) step 90’s “(Linux box)” and step 91’s “(Windows box)” are the Mac’s: both are core and shared-UI work, authored on the desktop harness by the one-platform rule, the Linux box is out of commission and the Windows box runs the lane only; (h) Kessho’s Layer A is served by the strain buffer of step 90, which lands AFTER step 85: the layer reads instantaneous σ first and the buffer feeds it unchanged; (i) the web’s medium parameter is numeric (?medium=1, DECISIONS_9 #6), so step 92’s ?medium=kessho is ?medium=2; (j) voxo_fuzz’s unit is seconds (--seconds), not the proposals’ “25 M iterations”; (k) step 75’s Scala loader is Voxo’s (the sound follows the table) — the layouts’ microtonal mapping (§14.6) is a core item and stays carried, or rides with step 91; (l) the SoA SIMD refactor of step 71 meets the web gate’s bit-for-bit contract (suzu_web_gate.mjs against the native reference): a working rule now says the contract is restated before the refactor lands — the scalar path as the reference build, or a tolerance gate — recorded, not discovered; (m) “Voxo 2.0” is the sampler’s format coverage, not the library’s version, which follows its ABI (0.16.1 today) — the phase is named “Voxo DS 2.0” and the author names the library; (n) the braid’s pass count is gated against the pass budget’s table (sumi_core.h, DECISIONS_5), the proposal’s ”≤ 64” being its reading of it; (o) the release split of road_map_medium_v3.md §5.1 (3.0 = harmony alone, the Voxo phases as 3.x) is superseded by the author’s framing — both features in 3.0, one release — and survives only as the order question; (p) the tag 3.0.0-alpha.kessho passes the spine (X.Y.Z[-pre], any suffix); the v2 pattern was -alpha.N; the author’s naming; (q) the decisions files are one per phase as in v2 (DECISIONS_10 … _15, Parts X–XV), the proposal’s “DECISIONS_10 for Phases 11–15” read as the first of them; (r) site/scripts/build-notes.mjs is extended to render this file in flight — its loop to 10 and its path-trim regex to two-digit numbers (DECISIONS_10.md was not matched by DECISIONS_\d). The gate delta’s own corrections (the billiard’s det J = +1 in 4D, the Dirac step Q-orthogonal, the Toda ring near-integrable, the Boris voice volume-preserving with both prewarps, the membrane’s CFL at E_max and its h² scaling, the bore shock dissipative, the oversampler a prerequisite) are applied as the author’s review, not re-decided. Nothing in the tree changed for this entry beyond the three _work/ files, the notes renderer and CLAUDE.md; no step has started.

2. The order of the phases: harmony first, on the author’s word. Asked whether to start the Kessho phase before the sampler’s (the proposals’ 14 before 13), the fold recommended further — Kessho and harmony before everything (the reply of 2026-10-14): the riskiest, taste-decided work (two A/B viewings, a Newton kick in the shader, the caustic) gets the arc’s slack; the core reopens once, early, and freezes for the eleven Voxo steps (step 91’s Boehm layout the one later touch); the Poincaré strobe becomes the instrument every new voice is seen through at its own step rather than retrofitted; the one cross-tie — the bus plate struck at the canvas — needs nothing from Kessho. The author: “no particular order is preferred for me, so I will listen to you — we can start with 14, then the others”. RESOLVED: Phase 11 = Kessho and symplectic harmony (steps 71–75: the composite, the Arnol’d lock, the braid, the chord wave, the strobe), Phase 12 = Suzu foundation (76–80), Phase 13 = the new voices (81–84), Phase 14 = Voxo DS 2.0 (85–89), Phase 15 = the carry-overs (90–91), Phase 16 = the release (92) — the proposals’ other phases in their own order. The renumbering is mechanical and final (ROADMAP_6.md, TO_PROJECT_SPEC.md; no evidence existed); its consequences in the roadmap: the Boris gyroscope’s spirograph is verified in Kessho (the gate delta’s 77c, now step 82’s), each Phase-13 voice carries a strobe-portrait gate, the membrane’s bus plate (77) is seen as well as heard from its first session, this file is Phase 11’s and the next phase opens DECISIONS_11.md. The release split of road_map_medium_v3.md §5.1 is not taken: both features ship in 3.0. Next: step 71, the Kessho composite, on the Mac.

3. The Kessho composite as built (step 71, 2026-10-14): a reader of the same field — the chart, the brush, the trace, the caustic; libsumi 1.6.0. What shipped against KESSHO §1 and ROADMAP_6’s ABI block, and what the step resolved. (a) THE ABI, 1.6.0, additive: SUMI_MEDIUM_KESSHO = 2; sumi_ctl_t 20–23 (SUMI_CTL_POLARIZER_ANGLE, _CAUSTIC_DEPTH, _BRAID_COUPLE, _ARNOLD_K; SUMI_CTL_COUNT 24 — 22 and 23 declared now, inert until steps 73 and 72); sumi_params_t appended with polarizer_mode, braid_mode, kessho_retard (nm per unit strain, 200..8000, default 2000), kessho_backlight (0..2, 0.85), kessho_grain (0.5), kessho_tint (0..1, 0.25), kessho_caustic (0..2, 0.5); slide_mode 3 (the polarizer), press_mode 3 and bend_mode 5 reserved (accepted, resolving to the medium’s interim defaults); SUMI_EXPORT_KESSHO_CAUSTIC = 2u; the twelve Kessho palettes (sumi_palette_preset_count(2) = 12, index 0 “Michel-Lévy”). Nothing moved; media 0 and 1 render bitwise (the field and composite fixtures on Metal, the thirty bench checks of the Anod, print, palette and gesture tests, docs/evidence/step71/gates/). (b) THE LUT AS THE PALETTE — the [ITERATE] of KESSHO §1.2 resolved: Layer A’s colour is one 1024-texel RGBA16F table over the retardation 0..2200 nm (the fourth order’s end), built by the engine on the CPU when its inputs change and uploaded by the renderer when its version moves, outside any pass — the same bytes on every backend. Palette 0 is the physical chart: tools/kessho_lut.py integrates sin²(πΓ/λ) against the CIE 1931 2° matching functions (the Wyman–Sloan–Shirley multi-lobe fit, JCGT 2013) under a 6504 K Planckian backlight, white-balanced per channel so a full transmission is (1, 1, 1), and writes 8-bit sRGB into core/src/kessho_lut.h (regenerated bit-identically; the engine decodes it to linear). The other eleven — smoked quartz, calcite, nematic, amber, tourmaline, olivine, labradorite, fluorite, cobalt & amber, viridis, cividis — and the custom slot are sumi_palette_t gradients read PERIODICALLY in the order Γσ/550 nm: the first order runs the gradient once, the next orders repeat it fading toward their own grey (three quarters by the fourth) as the chart’s colours do, the first 200 nm darkened so a resting crystal is dark under every palette; the morph ring mixes the two slots texel-wise in the one table. The editor edits stops as before; the hue drift is unused (Kessho reads no aux); the accent is the caustic’s light; the clear tone is carried but the substrate is the composite’s own fixed calcite (0.012 / 0.013 / 0.018, as Anod’s glass is fixed), so a custom palette’s clear tone never lights the sheet. (c) THE SHADER: Layer A from Anod’s short stencil (one-sided min, the rounding bias subtracted) — σ as Anod’s, ψ = ½·atan2(2C₁₂, C₁₁ − C₂₂) of C = JᵀJ, the brush ½(1 − cos 4ψ·c − sin 4ψ·s) with (c, s) = (cos 4α, sin 4α) from the CPU, I_A = backlight · brush · LUT(kessho_retard · σ). Layer B from the WIDE window the Anod grid reads (±3 texels at 512, the staircase averaged along each axis): tr(∇d) = tr J − 2, Δ = (tr J)² − 4, the tint cool (0.10, 0.22, 0.42) or warm (0.52, 0.22, 0.08) by smoothstep(0.05, 0.8, |Δ|) with the noise floor under 0.05; the caustic from the COLLAPSED determinant 1 + z(1 − z)·tr(∇d) — a LINE at the contour, drawn screen-space a fragment and a half wide (fwidth: it neither aliases where the strain changes fast nor smears where it changes slowly) over the soft 1/(|den| + ε) form with the rest value subtracted, so resting water is dark. The composite order substrate → B tint → B caustic → A → the shared bloom and shoulder; the exports: SUMI_EXPORT_ANOD_ALPHA writes the crystal’s light over alpha, SUMI_EXPORT_KESSHO_CAUSTIC Layer B alone. The masks: fresh water and the seam (the short stencil’s test), a window off the sheet or across a seam (the wide one’s). (d) THE ANALYZER: α = ctl·π/2 — the control’s range is one period and ITS END IS ITS START (ctl ≥ 1 − 1e-6 wraps to 0: the smoother settles an ULP short of 1), so α = 0 and α = π/2 render bitwise the same by construction, not by float luck (gate 3; the first run read 25 bytes apart before the wrap). Mode A, global: CTL 20, or the latest voice’s slide under slide_mode 3. Mode B, per voice: sumi_voice_mapper_polarizer_voices hands the held voices (x, y, cos 4α_k, sin 4α_k) to the composite, which takes the nearest four by inverse-square distance (a voice’s reach 0.03 canvas heights) over the global as a floor (0.35) and normalizes the summed vector — the π/2 period wraps in the vector, as KESSHO §1.5 asks. Both built; the A/B K-1 is the author’s viewing (#5). (e) THE BINDING TABLE, interim: the strike is the drop — a lens whose rim Layer B draws as a ring, nothing new needed; poly pressure the Lamb–Oseen swirl; the slide the polarizer; the mod wheel the caustic depth (the CAUSTIC_DEPTH control or the mod-wheel dimension, whichever is higher — the vortex quiet in Kessho as in Anod; z = 1.05·(8/1.05)^ctl, log-spaced); the bend the glide until step 73’s braid; and THE PRESS THE SWIRL until step 72’s lock — chosen over the ink feed after the first A/B renders: the feed’s nested rings read as Sumi’s, and the lock is a twist built on the swirl, so press_mode 1 is Kessho’s interim default and the reserved 3 resolves to it. (f) The gestures are Sumi’s under Kessho (the tap a drop, the pinch the saddle Layer B shows warm, the twist the given profile, the press Sumi’s): the gesture table has no Kessho column in the spec. (g) THE DESKTOP: the Medium radio gains Kessho and its knobs (retardation, backlight, regime tint, caustic, the polarizer’s mode), the Substrate section the facet grain and the shared bloom, the slide combo “Polarizer angle”, the ledger’s “Light over alpha” (Anod’s discharge or Kessho’s crystal), the INI and the preset schema the new keys (schema 1 stays — additive keys with defaults); the bench’s A key cycles three media; --kessho-test, --kessho-flat <op|all>, `—ab polarizer —ab-out

   `. (h) The web: the scenes' medium toggle to 2 and the shell's clamps; the wasm builds (the shader cross-compiles to WGSL, fwidth included) and the web gate holds; the tablets consume in their own steps — their medium pickers offer two media until then. THE GATES (`kessho_test.txt`, 12/12): the identity sheet dark (mean 31.9, max 35.1); the chart within ΔE 0.67 of the integration at 550 / 1100 / 1650 nm, black at 0, white at 275 nm; the switch Sumi → Anod → Kessho → Sumi → Kessho → Anod → Kessho bitwise on the field (gate 1); the moved water lit (105 against the substrate's 32); the Maltese cross (146 on the axes, 48 on the diagonals — the dark arms on the diagonals, where a simple shear's principal axis lies parallel to the analyzer; at α = π/4 they turn to the axes, 588,845 bytes apart); the period bitwise (gate 3); the regimes (the vortex core cool r 110 / b 121, the saddle warm r 192 / b 90); the caustic (the fold's line at 253 against 65 at rest); the substrate screen-locked under a 120 BPM scroll (gate 5, 0 bytes); the export the dip's print (gate 6, 0 bytes); the caustic alone over alpha within the crystal's light (194,936 lit texels, every one); the 8K caustic export. The bench's `t42_print` dips the paper and resets the field — the first run's four reds were that; the Kessho checks shoot through the export instead (`t71_shot`), which gate 6 proves is the print.

4. Gate 2 as measured: the field cannot hold the proposal’s 1e-4, the two classes are not separable by differencing it, and the gate is re-pinned to the floor — the class stays declared. KESSHO §1.3’s “free det-J gate” — z = 1 flat for any exact field, a sub-stepped or mis-windowed operator showing as texture — holds in the continuum. --kessho-flat measures det J from the field’s pre-image by central differences over ±1, ±2 and ±3 texels on every soak operator’s scene (one strong pass, the drops’ rims masked where the band boundary is). What it reads (kessho_flat.txt): the identity sheet 0 exactly; the estimator’s own CPU controls — an exact Lamb–Oseen twist 1.4e-3 max (the stencil’s truncation), the first draft’s windowed Arnold kick 50 max and 0.35 rms, RED as required; the GPU fields — the three-drop SCENE ALONE reads a median of 2e-3 (±3) to 5e-3 (±1), a p99 of 0.2–0.8 and a max of 8–30: the drops’ rims, where the inverse of an exact expansion has an unbounded radial derivative (new ink meets pushed water — the pre-image’s one singularity, exact and unresolvable by any stencil), own everything above the median even with the boundary masked; every operator then reads the same floor (medians 2e-3 to 6.5e-2, the spark shear’s kinks the highest), the exact family’s worst p99 4.2 (the Chirikov map) against the sub-stepped family’s best 0.9 (the Chladni field) — NOT separable. Resolved: (i) the composite’s caustic uses the collapsed determinant 1 + z(1 − z)·tr(∇d), which assumes the class — what the declaration promises — rather than measuring it; the full form 1 + z·tr(∇d) + z²·det(∇d) would paint the estimator’s floor, 36× at z = 6, onto exact fields; (ii) the gate holds each operator’s TYPICAL texel within 0.1 of det 1 (18/18, the gross non-conservation of the windowed kick would read here) and keeps the identity and the red control; (iii) the class is where it was — declared in the header, the test and the page, proven by the four-part conservation gate, never discovered. The author’s spec is flagged for correction (TO_PROJECT_SPEC §10.7.3): the flat plane is a diagnostic of gross non-conservation, not a 1e-4 certificate. A discriminating estimator — a rim-aware window, a smooth-map fit — is a research item, not this step’s.

5. The look and the defaults; what the author views: the A/B K-1 renders, the shared bloom, the frost, the depth’s top. Defaults by eye on the §4.6 script and the A/B phrase: retardation 2000 nm per unit strain (the first-order red at σ ≈ 0.27), backlight 0.85, tint 0.25, caustic 0.5, grain 0.5 — softened from a first pass at 1.0 / 0.35 / 0.6 after the A/B renders under the shared bloom (Anod’s 0.75) blew the sheet to white: Layer A lights all strained water where Anod’s filaments are sparse, so the same bloom sums far more. The renders are archived both ways (kessho_ab/kessho_ab_*.png at the shipped bloom, *_bloom035.png at 0.35); the bloom knob is shared by the spec and is the author’s to settle — a Kessho-side scale was considered and not hidden in the shader. PENDING THE AUTHOR: (1) K-1, A against B — the phrase holds three MPE notes with slides at 7°, 45° and 84° over a vortex and a saddle: in B each note’s cross sits at its own angle, in A the whole sheet at the latest slide’s; the difference lives in the three notes’ crosses and is subtle at this phrase; A stays the default until the viewing. (2) The depth’s upper bound (KESSHO §1.3’s [ITERATE]): at z ≈ 6 the fold’s lines are crisp and the soft term lights the half-float staircase of strongly strained water as fine fringes — a texture, not a fault; the control’s top may want 4 rather than 8. (3) THE FROST: Layer A reads the far field’s small smooth strain through the half-float staircase — the case Anod avoided by never glowing water by strain — and it renders as a frosted speckle round every swirl: in character for calcite, but a quantization; the wide window the trace already uses could serve ψ and σ too if the author wants it smooth ([ITERATE]). (4) The chart’s hues sit 20–30 nm early against the textbook Michel-Lévy chart (a 6504 K Planckian rather than D65, the fit’s own tails): kessho_retard absorbs the scale, and a published chart’s sampled colours replace the integration as the reference when the author has one (kessho_lut_check.txt lists the table’s hues). Next: step 72, the Arnol’d tongue lock.

6. Step 71b — the minerals: the crystal drop, the cleavage profiles, a mineral in place of the palette (2026-10-14; libsumi 1.7.0, additive; evidence docs/evidence/step71b/ and docs/evidence/step71/minerals/). The author’s Mineral.md and its two deltas (ROADMAP_6_delta_minerals.md, KESSHO_SPEC_delta_minerals.md, folded the same day as ROADMAP_6 step 71 amended / 71b and TO_PROJECT_SPEC §10.7.8) ratified with the following resolutions, each the record of what shipped. The ABI: sumi_mineral_t (sized, 60 bytes, fifteen fields: the optic class, Γ, Γ₀, 2V, the walk-off, the dispersion, the film’s index and reflectance, the ring’s radius, the body tint, the bloom gain, the chart id), sumi_set_mineral / sumi_get_mineral (a shorter size keeps the known prefix and defaults the rest from Quartz; the core clamps), sumi_mineral_preset (six: Quartz, Calcite, Muscovite, Barite, Fluorite, Selenite — the OPTICAL half only), and four fields appended to sumi_params_t: drop_habit (circle, rhomb, hex, rosette), habit_roundness, habit_blades, tine_profile (smooth, twin kink, terrace). The mechanical PAIRING — which habit and profile a mineral brings — is the shells’ and the JSON presets’, not the core’s: the core’s library is optical, app_mineral_preset on the desktop fills both halves, and presets/kessho_<mineral>.json carry both (the serializer’s mineral block, mineral_present, applied through sumi_set_mineral); the halves stay independent parameters. The 1.6.0 Kessho palette library is retired (sumi_palette_preset_count(KESSHO) = 0): the chart is the mineral’s lut_id — 0 the physical table, 1 the custom slot read once per order. The crystal drop (the theorem, exact): drop_fs evaluates R(θ) in the drop’s frame — the rhomb as the polar support form r₀/max(|sin θ|, |sin(θ − 78.1°)|), the hexagon likewise over three normals, the rosette r₀(1 + 0.6 cos⁸ mθ) normalised to the mean radius — the hard max softened by a log-sum-exp whose sharpness is k = 2 + 40(1 − roundness)², then blended toward the circle by the roundness ([ITERATE] by eye: the corner at roundness 0 is nine times sharper than at 0.5, the crease visible, DECISIONS_10 #6’s gate 7); the interior ink from r/R(θ). The strike’s frame is the note’s pitch axis (atan2 of the layout’s axis); a held voice stores its habit at note-on and the feed grows it as the same habit — the fold’s “area ∝ (1 + p)” is NOT implemented: the feed’s law is unchanged (R = R₀ + ∫p·k dt, the nominal radius linear in the pressure integral, the area ∝ R²; measured 0.1197 → 0.1554 → 0.1909 at 100 / 200 / 300 fed frames, steps equal within 1 %), as §10.7.8’s “the same map, no new code path” requires; the spec’s sentence is corrected. The engine’s own pushes (the §4.6 field script, the gestures, sumi_add_drop) take the params’ habit with angle 0; the fixture’s drops are the circle. The cleavage profiles (exact, bumps): tine_fs takes a profile — Jaffer’s α/(α + d) bitwise; the twin kink 1 to d = H/3 then linear to 0 at H = 4α; the terrace stair₄(1 − d/H); and profile 3, DEV ONLY, the first draft’s monotone ±1 ramp, the fabrication red control (sumi_debug_set_tine_override, --tine-fault). The glide tine, the master bend’s shear and sumi_add_tine read the params’ profile; the pinch’s crossed tines keep Jaffer’s. What the soaks measured (--soak crystal_drop | twin_tine | terrace_tine, 6000 passes): the two tines green on all four parts — twin kink (b) −1.19 % / dev 5.26 texel, (c) +0.20 %, (d) ×−0.03; terrace (b) −0.67 % / 5.33, (c) +0.00 %, (d) ×0.15 (Jaffer’s reads 11.9 texel at 500 pairs: the bumps’ compact support resamples less). The crystal drop has no inverse pass (the fold’s note), so its (b) is one rhomb pass on the identity sheet against the closed form — the pre-image det min 0.972 outside the rim annulus, mean 1.00004, the flatness median 1.16e-3 (the burst’s bars, #4’s) — and its stream is a clear-water habit drop every third frame, the habit and the roundness cycling: (c) +0.00 % (the gate), (d) INFORMATIONAL — 1.67e-4 per pass, ×14 the glide-tine control, because a drop’s exact expansion carries the ink off the sheet (2000 strikes of r = 0.03 displace several canvas areas outward; the interior lost 132 k texels to the edge), the same geometry that excluded the spark’s drop (DECISIONS_5 #13, #39), not resampling erosion; --kessho-flat reads the three operators at the field’s floor (#4’s gate: medians 2–3e-3 at ±3). The red control: under the unwindowed profile the gate goes red at its FIRST part, not at (c): an odd profile reversed is the same shear, so the “pair” carries both half-planes — and the ink — off the sheet (−99.89 % in 500 pairs, pre-image deviation 305 texels), and nothing is left for the stream to fabricate from; the delta’s “fails zero fabrication” is this failure under the gate’s own order. The analytic witness (tests/habit_det.c, strict C11, no core): the shader’s maps transcribed, |det J − 1| < 1e-6 at 10⁴ random (θ, roundness) per habit (measured ≤ 7e-9 with h = 1e-7, r ≥ 1.05 R — the rim is the v2 drop’s singular pre-image), det 1 on the corner ray at every roundness, each ray monotone, the bumps zero beyond H and continuous, every profile’s shear det 1. The optical laws as built (three stylisations the spec’s wording did not fix, recorded here): (i) the biaxial brush keeps the analyzer’s π/2 period — |cos² 2V − cos² 2(ψ − α)| / max(cos² 2V, sin² 2V), the Maltese cross splitting into two brushes 2V apart — because the per-voice analyzers carry (cos 4α, sin 4α) (K-1’s wrap, #3) and a π-periodic law has no sign to read from them; the lemniscate of the proposal is not what ships; (ii) the sensitive-tint plate is FIXED TO THE SHEET at 45° (β = π/4 in the sheet’s frame, Γ_eff = |Γ₀ + Γσ sin 2ψ|), for the same reason, and the plate replaces the brush — a full-wave plate floods the cross, so under Selenite the analyzer’s turn plays no part; (iii) the walk-off doubles the CHART under the point’s own brush (the first form averaged the brush too and filled the dark arms in: on the cross’s diagonals the double image must stay closed — measured 1.16/255 against no walk-off on the arms, 13.3 between them). The thin film reads h from the band’s radial fraction (200–800 nm); the dispersion’s three depths are z/√(1 + d), z, z√(1 + d); the conical ring is masked to |Δ| < 0.15 and σ > 0.05; the chart beyond 2200 nm fades to 0.92 white over 4000 nm; the substrate is 0.018·body; the caustic’s light is the body (the accent is gone with the palette); the bloom’s source is Layer B × bloom_gain. Step 71 amended, gates 8–12 (in --kessho-test, 17 checks): the six minerals over one field — the field bitwise, every render distinct; the selenite sign — a tine’s two sides read (b − r) 14 and 57, a 43/255 swing, 2.4 at Γ₀ = 0 (red); fluorite = Layer B alone — the light export IS the caustic export bitwise, quartz 794 k bytes apart; the dispersion fringe — 78 k of 139 k lit caustic texels off the body’s ratio in linear light under barite, 0 at dispersion 0; the walk-off collapse as above. The step’s gates: the homothety (a rhomb’s fract-0.5 ring is the rhomb at f = 0.1503 of r₀ 0.3, residual 0.49 texel; the circle under the rhomb model misses by 6.1 — red), the hexagon and the rosette at 0.33 / 0.30; the growth (residuals 0.26 / 0.25 / 0.26 texel at 100 / 200 / 300 frames); the crease (corner-ray contrast 0.464 at roundness 0, 0.060 at 1); calcite + the twin kink (the lamella’s interior 38 against its lit ramps at 222 in Kessho; Jaffer’s 189 against 198 — no lamella; the Sumi facets archived); the pass count (a rhomb strike one pass, a twin-kink stroke one, as the circle and Jaffer’s — sumi_debug_pass_count). The field and composite fixtures bitwise on Metal, ctest 13/13 (habit_det 22/22, the preset round trip with the mineral), the web shell compiles. Deferred: the Suzu conical intersection (Phase 13, [ITERATE]); the book’s medium guide and the tablets’ Mineral pages (their own steps); the author’s viewing of the six at the fold’s exposure (the one [ITERATE] number).

7. The settings window, the author’s two asks (2026-10-14). One line per medium: the Medium row’s third radio clipped at the window’s right edge, so the three media are vertical now and every medium added later takes a line of its own. And the medium key: the bench’s legend named the US positions — “A medium” — while the author’s AZERTY presses “Q” there; dev_key_name asks GLFW for the key’s name on the live layout (a single printable byte translates, A → Q, W → Z, M → ”,”; the digits keep their caps), the legend is built from it once, and the Medium section itself carries the line “Lab bench: the Q key on the canvas cycles Sumi → Anod → Kessho” under --dev. The Kessho section’s “Retardation” knob is “Exposure” now (2000 = one stop), since the retardation is the mineral’s. Under Kessho the Palette section gives way to a Mineral section: the library combo (the six and Edited), the optic (class, 2V, retardation, sensitive tint, walk-off, dispersion, conical ring, thin film and its index, body, bloom gain, chart) and the habit (drop habit, roundness, blades, tine profile); the INI carries mineral_* and the four params, the session JSON the mineral block. The author’s third ask, the same evening: the panel’s “Mineral” combo hashed to the “Mineral” header’s ID (ImGui IDs are label hashes within the window) — the panel is scoped under its own ID now.

8. The author’s viewing of the minerals (2026-10-14): the closest real habit per mineral, roundness 0, reviewed at the phase’s end. “I like the mineral” — and the pairing follows nature rather than the delta’s table: quartz the hexagonal prism’s section, calcite its cleavage rhomb, muscovite the pseudo-hexagonal plate, barite the desert rose’s blades (m = 5), fluorite the cube seen along its body diagonal (a hexagon — a square, the face-on cube, is not a habit yet; a candidate for the review), selenite the rhombic cleavage plate of gypsum (the rhomb’s angles are calcite’s 78.1°, not gypsum’s ~66°; likewise a candidate). Every habit ships at roundness 0 — the sharp polygon, the corners creasing — “for the moment”, the roundness law and the pairings to be reviewed at the end of Phase 11 with all the new operators on the sheet. The tine profiles keep the delta’s pairing (calcite the twin kink, muscovite the terrace, the rest Jaffer’s). Changed: the desktop’s app_mineral_preset table, the six presets/kessho_<mineral>.json, the core’s default habit_roundness (0; the default habit is the circle, which ignores it), the book’s and the spec draft’s tables. Next: step 72.

9. Step 72 — the Arnol’d tongue lock (2026-10-14; libsumi 1.8.0, additive; evidence docs/evidence/step72/). SUMI_DEFORM_ARNOLD, one pass per voice per frame: M = T ∘ Kick about the voice’s drop in the action-angle frame (ρ = r²/2, θ) — the kick from the generating function F₂ = θρ₁ + (K/q)·W(ρ₁)·cos q(θ − φ), the twist the Lamb–Oseen rotation with its core at the ring (the swirl voice’s convention, r_c = R), scaled so the ring turns Ω₀ turns a frame; the lookup is M⁻¹ (the twist undone, then one scalar Newton on θ, ρ explicit), composed in ONE lookup — the spec’s two passes (the kick, then the existing swirl pass) became one, which halves the passes and resamples once. Class exact: the four-part gate green (--soak arnold: (b) through the pass’s own EXACT INVERSE, inverse = 1, the lookup of M by one Newton on ρ₁ — −0.13 % / 6.1 texel; (c) +0.00 %; (d) ×0.09), the flatness at the field’s floor (#4), the pass against its CPU closed form to 0.12 texel, the kick then its inverse 0.38 texel. Five corrections to the spec as written, each forced by the mathematics (TO_PROJECT_SPEC §10.8.1 marked): (i) K_max = 0.8 / max|W′|, not 0.8·q / max|W′| — the θ-shift’s derivative is −K W′ sin qθ, the q cancels; at the spec’s bound the kick folds for every q ≥ 2; (ii) THREE Newton iterations leave 1e-3 at the 0.8 bound (the basin’s ratio c²/(2(1 − c)) = 1.6 > 1); FIVE reach 1e-11 (the study in the log: three suffice only below c = 0.5, half the kick); the red at 1.3 K_max (|K W′| = 1.04, the fold) reads 1e4; (iii) the window W must be ZERO AT THE CENTRE: with W = 1 down to ρ = 0 the inverse ρ = ρ₁ − K W sin qθ goes negative — material sent to negative action; W rises C² from 0 to 1 over [0, ρ_drop/2], is 1 to ρ_drop, falls C² to 0 at 1.5 ρ_drop; (iv) the twist is C²-windowed to zero between 1.75 R and 2.5 R (a windowed rotation is still a rotation by a function of r: exact) — the bare Lamb–Oseen tail at half a turn a frame would wind the whole sheet; beyond 2.5 R the pass copies the texel exactly; (v) the tongue takes the continued-fraction convergents of order 2..6 only: 0/1 and 1/1 are not tongues (they would swallow every interval); an integer ratio (within the q = 6 tongue’s half-width) is q = 1 with the signed detune, and twists a FULL TURN plus the detune — Ω₀ = 0 would leave no twist and no islands. The lock and the beat, as built: the kick’s frame φ precesses by 2πδ a frame, δ = Ω₀ − p/q, and the twist turns Ω₀ = p/q + δ — in the precessing frame the rotation is exactly p/q and the islands stand; in the lab they turn at δ. The dynamical alternative (a fixed kick frame, the true circle map) LOCKS a small detune into a radius shift and hides the beat the author asked to see; the precessing frame shows it. The bass keeps the swirl (press → the Lamb–Oseen stir as under press_mode 1): the reference voice has no interval, and a solo note under pressure must still do something. A q change crossfades K to zero and back over 50 ms (ARNOLD_XFADE_S, [ITERATE]), q switched at the zero — the headless witness: the records across a two-semitone bend sweep (q 2 → 5 → 3) have |ΔK| ≤ 0.26 K_max a frame, every q change through a frame at K = 0, |Δφ − 2πδ| ≤ 2e-7. Kessho’s press default is 3 (the lock); press_mode 3 is accepted in any medium; SUMI_CTL_ARNOLD_K is the CC alternative (the larger of the two). What the gates measured (the bench’s --arnold-test, 7 checks): gate 4 at the EXACT ratios through the gesture (Ω₀ = 1/2 and 1/4, 600 iterations at the press-100 kick): the q-fold pattern’s angle stays within its island — excursion 0.30 rad for q = 2, 0.14 for q = 4 (the ink LIBRATES inside the islands; the islands stand) — the proposal’s ”< 0.5 texel” cannot be read off ink that circulates inside an island, and a MIDI fifth cannot be exact: equal temperament’s 2^(7/12) is two cents under 3:2 and its islands precess at δ = −0.00169 turns a frame (one turn in 600 frames; measured −0.0018), the tempered major third fourteen cents over 5:4 at +0.0099 — THE TEMPERAMENT’S BEATS ON THE WATER, the finding of the step; gate 5 the tempered fifth bent ten cents (Ω₀ = frac(2^(7.0996/12)), δ = 0.00695): the pattern precesses with the twist’s sense at 0.00694 turns a frame over 1600 frames — within 0.2 % (the ink’s harmonic phase wobbles with the libration, which the long run averages; the records’ phase is exact to 2e-7); gate 6 redefined: the proposal’s “without the twist the petals grow without bound” does not happen — the window bounds the kick either way — what the twist does is make the ISLANDS: without it the kick alone has no elliptic points, the ink collects on the kick’s nodal lines (the 4-fold harmonic 0.29 over the 2-fold 0.01); with it the two islands (0.084 over the red’s 0.010); gate 7’s “no frame-to-frame Δ > 1 texel across a tongue boundary” is the records’ continuity (the headless test above); the sheet’s band flicker through the crossing is measured and archived (mean 0.09, max 0.17 of the drop’s texels; 0.145 at the first q change). Seen in the renders: under the lock a pressed drop becomes a cool (elliptic) disc in Kessho with its islands as bright crescents, and the first drop struck being ink and the second clear (the parity form), a pressed clear drop shows its islands as a thin ring of band-1 phase about a white interior — the bench strikes the upper voice first. The half-turn-a-frame twist of a fifth shears the drop’s interior to grey within a second (the Lamb–Oseen core turns 1.58× the ring); the islands at the ring stand. PENDING THE AUTHOR: the stroboscopic rate — one map iteration per frame at Ω₀ turns is the spec’s; a slower cadence ([ITERATE], the spec’s slow-motion factor) would spare the interior; the 50 ms crossfade; the look in Kessho. Next: step 73, Kirchhoff braiding.

10. Step 73 — Kirchhoff chord braiding (2026-10-14; libsumi 1.9.0, additive; evidence docs/evidence/step73/). bend_mode 5 is live and Kessho’s bend default: every sounding voice is a Lamb–Oseen vortex at its drop whose circulation is its consonance against the lowest held note, Γ_k = sign(C_k)·Γ_vel·(0.3 + 0.7|C_k|), the bass Γ_vel positive, the others scaled by SUMI_CTL_BRAID_COUPLE (1 unmapped); the ink is advected by the superposed flow — never integrated: the exact swirl passes, one per voice at the half-circulation, composed in STRANG ORDER (1..N then N..1), 2N passes a frame, every factor a rotation, so the composition is det 1; no new pass type and no new entry point (the spec’s SUMI_DEFORM_ BRAID is the swirl pass’s sequence). The consonance curve as built (sumi_consonance, core/src/midi_normalizer.cpp): Sethares’ sensory dissonance over the first six partials (amplitudes 0.88^(n−1)) at the bass’s frequency, mapped on THREE ANCHORS — the unison +1, the tritone 0, the minor second −1 — piecewise linear in the roughness between them; the register floored at C4 (261.6 Hz): below it the raw curve is rough everywhere (a low third IS muddy, but the mapping needs its anchors — at C3 the linear two-anchor map read the major third −0.56 and the fourth −0.26). At C4: the fifth +0.68, the fourth +0.34, the major third ≈ 0, the major sixth +0.37, the octave +1 [ITERATE]. The floor made continuous ([ITERATE]): sign(C)·(0.3 + 0.7|C|) jumps from −0.3 to +0.3 at the tritone; shipped as the line 1.7·C for |C| < 0.3 (the spec’s formula beyond), so a bend through the tritone flips the topology without a jump — and an EXACT tritone carries no vortex (C = 0). The voice’s bend in every mode: the mapper keeps bend_s beside the glide (the lock’s pitch and the braid’s both read it; the step-72 lock read the glide, which modes 1–5 leave at rest). Free (Kirchhoff), B-1’s B: sumi_braid_step (displacement.cpp), the N-vortex Hamiltonian with the pairwise regularization r_c² = R_j·R_k (the cores’ product), the implicit midpoint rule iterated to 1e-15 (the spec’s three rounds leave the quadratic invariants at 1e-6; six rounds reach machine precision), the positions in DOUBLE (ten minutes of float rounding walk the centre of vorticity to 1e-6; in double 4e-16): over 72000 steps of a consonant triad |ΔH/H| = 3e-9, the centre of vorticity and the angular impulse 4e-16 and 6e-16 — gate 6 green. A note re-anchors at its cell at the strike; a lifted note’s vortex fades over BRAID_RELEASE_S = 0.25 s going on its way; the 5 % clamp [ITERATE]; ONE vortex a voice (the first echo — Jankó’s rows would be 90 passes). Γ_vel = BRAID_GAMMA_S·v = 0.036 canvas²/s at full velocity [ITERATE]: a fifth’s pair orbits in ~4 s, a minor second’s dipole walks a third of a texel a frame. What the gates measured (--braid-test, 4 checks; --soak braid; --kessho-flat braid; the headless suite): gate 1 fifteen voices → 30 swirl records a frame (the headless witness; the bench’s chromatic cluster reads 28 because its tritone, C = 0 exactly, has no vortex), 10 ms a frame at 512² and at 1024² (the bench’s frame pacing, not the passes: 60 fps holds); gate 3 a fifth’s dyad after 300 frames: the saddle between the cells at 54 % of the way from the bass — nearer the weaker vortex, as the velocities’ balance puts it — its material moved 1.8 texel (a stagnation point; the texel nearest it drifts by the saddle’s own stretching), the discriminant there +0.51, the cores −3.6 and −2.6 (elliptic); gate 4 a minor second’s dyad: the ink’s centroid 8.4 texels across the key line in 120 frames (the dipole’s jet; 0.7 along it); gate 5 the second bent six semitones to the fifth over 240 frames: the material never moved more than 0.25 texel a frame; between the cells the jet’s least-moved material came 22 texels upstream, the fifth’s 0.4 — a stagnation point appears — but at the SECOND’s geometry (the cells 0.070 apart, the cores 0.087) it is ELLIPTIC, the one centre of two overlapping cores co-rotating, not the saddle of gate 3 whose cells sit 0.58 apart: the saddle needs the cores apart; the flip the gate sees is jet → co-rotation (the records’ sign flip is the headless witness, |ΔS| ≤ 5 % of the bass’s a frame). The soak: (b) the two-vortex Strang pair at ±Γ — the exact inverse — holds the mass −0.70 % with a pre-image deviation of 32.3 texel against the bench’s bar of 32 for TWO-pass pairs: the pair has four passes each way, and the resampler’s walk grows ~N^0.7, so the bar is scaled by (passes/2)^0.7 (SoakDesc.pair_passes; 52 for the braid); (c) +0.00 %; (d) ×10.9 the glide-tine control — INFORMATIONAL for the braid: a dyad resamples the whole sheet four times a frame for as long as it is held (the Lamb–Oseen tails never vanish), fifteen voices thirty times — the Strang composition’s own cost, not a leak. The mitigations, the author’s: alternate the order frame by frame (Lie–Trotter, N passes a frame, Strang over two frames — halves it), window the far field as the lock’s twist is (loses the long-range saddle), slow Γ_vel. The flatness at the field’s floor (median 8.5e-3 at ±3). A/B B-1 (--ab braid, a triad — the bass, its fifth, its minor second — 600 frames, pinned and free, Sumi and Kessho, docs/evidence/step73/braid_ab/): the author’s viewing; pinned stays the default. In Kessho the chord’s accumulated flow fringes the whole sheet within seconds — the same remark as the lock’s rate (#9). B-1 DECIDED by the author’s viewing (2026-10-14): pinned is the default; free survives as the non-default “dance” mode (the spec’s allowance), reachable in the settings and by the D key. The author’s ask after the step: a lab key — D toggles the braid’s vortices (pinned / free) live; the P and M keys now cycle every press mode (the lock included) and every bend mode (the braid included) through the medium’s default, Shift backwards; the legend names them. Next: step 74, the chord-wave lattice.

11. Step 74 — the chord-wave lattice, route (a) (2026-10-14; libsumi 1.10.0, additive; evidence docs/evidence/step74/). Under Kessho the poly pressure (0xA0) of a held note is the amplitude A_k of a ripple-tine through its drop — the ripple pass given a window: sumi_deform_ripple_t gains win_c, win_w (0 = none, the v2 whole-canvas ripple bitwise) and ripple_fs multiplies the sine by a C² bump across the band; a shear by a function of s₂ alone, windowed or not — exact. No new pass type, no new entry point (the proposal’s SUMI_DEFORM_CHORD_WAVE is the ripple pass windowed), no new params. As built: the axis ê₁ at the pitch class’s angle on the circle of fifths, FIFTEEN degrees a step — the circle’s thirty would give a tritone pair the same orientation (a ripple’s lines have period π), fifteen gives the twelve classes twelve distinct orientations across a half turn [ITERATE]; the wavenumber by the octave, four periods a canvas at octave 3 doubling an octave up, clamped 2..32 [ITERATE]; the window’s half-width 2.5 drop radii [ITERATE]; a crest at the note (φ = π/2 − ω s₂,k); the amplitude at full pressure CHORD_WAVE_AMP = 0.02 canvas (ten texels at 512) [ITERATE]; delta-driven as the ripple bake is — the passes compose additively at fixed (ω, φ, angle), so the baked amplitude follows the pressure both ways, one pass a voice per change, nothing while held, and the wave stays baked when the note lifts (the ripple’s permanence); one band a voice (the first echo). The voices compose as separate passes. What the gates measured (--chord-wave-test, 2 checks; --soak chord_wave; --kessho-flat chord_wave; the headless suite): one note (G3) at full pressure — across its band the wave’s displacement along the axis (the strike’s own field subtracted) fits A sin(ω s₂ + φ) w(s₂) with |correlation| 0.978, amplitude 10.2 texels, 0.00 outside the band; the pass alone on a fresh sheet reads the same profile a quarter canvas along the axis (the band runs the sheet’s length — on a struck sheet the baked wave re-samples the strike’s own radial field, which is not uniform along the band, so the length is read on the bare pass); a fifth (C3 + G3) at full pressure — two bands at 0° and 15° crossing at (0.60, 0.39): along G’s band away from the crossing G’s component alone (13.5 texels, the other’s residue 2.0), along C’s C’s alone (13.1; 2.3), at the crossing both (19.9 and 19.9) — THE LATTICE; a triad’s crossing region archived. The soak green on all four parts — the pairs at ±A (the exact inverse of a shear) −1.07 % / 8.5 texel, (c) +0.00 %, (d) ×0.20 the control; the flatness at the floor (median 2.75e-3 at ±3); the fixtures bitwise; the headless suite pins the records (the angle by the class, the periods by the octave, the crest at the note, the deltas up and down, held none) and Sumi’s swirl untouched. Route (b), the local rosettes — the generating-function shear windowed in both coordinates, a 2 × 2 Newton per note per texel, the only way to the first draft’s 3/5/6-fold quasicrystals — stays [ITERATE]: the spec says go or defer after (a) has been seen on paper; the renders are the author’s to see (docs/evidence/step74/renders/, Sumi and Kessho). Next: step 75, the Poincaré strobe — no core change; the core is frozen again from here to step 91.

12. Step 75 — the Poincaré strobe, the trace’s second mode (2026-10-14; Voxo 0.17.0 and trace/; NO core change — the core stays open through step 77 since #13; evidence docs/evidence/step75/). Voxo keeps the reference phasor the proposal asked for: the lowest HELD voice’s frequency, bend included (the lowest sounding one when none is held — “the normalizer’s bass” read on Voxo’s side, where the voices are), advanced per sub-step in double along the block’s glide line, the block’s wraps precomputed once (the sub-step each completes in and the fraction into it, at most 64 a block) so every voice’s loop reads the same instants; at each wrap the traced voice’s pair — the trace’s own (x, y), with the kind’s aux pair — goes into a per-voice strobe ring of 256, interpolated between the two sub-steps the wrap falls between: a RETURN. voxo_set_strobe (0 off, 1 the bass phasor, 2 each voice’s own drive where it has one — the Duffing cell at its drive’s phase wrap, undriven the bass; the kicked rotor at each kick, where the returns (θ = atan2(y, x), p = u after the kick) ARE Chirikov’s section — the rest the bass), voxo_strobe_poll (the newest ≤ 32 returns a voice since the last poll, raw in the cell’s units, with the count since the strike and the clock’s frequency), voxo_strobe_hz. Captured only for the kinds in the trace mask; a reader; nothing allocates. trace/: sumi_trace_config_t.mode (SUMI_TRACE_CONTINUOUS 0, _POINCARE 1, _POINCARE_OWN 2); the bridge sets Voxo’s clock each frame (a shell adds the combo and nothing else — the tablets’ Synth trace rows gain it in their own sub-steps); per voice an OrbitDust ring of the newest 128 returns for the scopes (the settings miniature draws them as fading dots, the canvas scope as dashes round-robin across voices up to its 128); on the ink route a micro-drop under Sumi (sumi_gesture_tap, r = 0.003 canvas × scale/0.25), a CHARGE SPECK under Anod (an ink drop of 0.004 × scale/0.25 — the strike’s own charge call; the continuous trace lays one at every kept vertex there too) or a micro-swirl under Kessho (sumi_gesture_twist, strength 0.06, core 3r, Lamb–Oseen), through the hook (kinds 0 / 7 / 2: a recording carries them), the frame budget of 24 shared fairly. Desktop: the Suzu trace mode combo, suzu_trace_mode in the INI, trace_mode in the preset (the schema, the round trip pinned). The bench’s --strobe-test; the suite’s block 28; the fuzz’s --strobe-seconds (ctest runs 5 s; the evidence run 120 s); tools/strobe_chart.py draws the returns (SUZU_STROBE_DUMP). What the gates measured. 1:1 — the undamped cell at A2 strobed at its own frequency, 2 s: 219 returns (220 expected) within 0.001 texel of one point (the gate: 0.5 at the default scale, 512). 3:2 — E3 bent +3 units to the just fifth (the bend’s resolution is 0.59 cents; the residual 0.20 cents), 1 s: 109 returns alternating between two points 3.142 rad apart, each class within 0.120 texel over every tenth of a second; the equal-tempered fifth unbent precesses its pair 1.132 rad over the second (1.128 from the 1.955 cents) — THE STROBE READS THE TEMPERAMENT, the same δ = −0.00169 the lock beats at (#9). The bass bent +49.8 cents: the phasor at 113.2105 Hz (the ratio 1.02919, exact to 1e-5), 1132 returns in 10 s against 1099. The tritone (√2, exact in ET) over A2: every one of sixteen angular bins visited, the radius within 0.5 %: the dotted ring. The Duffing cell by its own drive: 219 returns in 2 s (one a drive period; its section at drive 0.6 a three-point cycle, charted). The rotor by its own kicks, undamped, K swept 0.3 / 0.6 / 0.9 / 1.2 / 1.8 / 2.5 (12 s each, charted strobe_sections.png): over the first 440 kicks 10 / 12 / 20 / 18 / 47 / 22 % of a 24 × 24 (θ, p) grid, |p| ≤ 1.11 at K 0.3 — the separatrix’s eye from the strike’s hyperbolic point (θ₀ = ε/2, p₀ = 0), 2√K; the sea at 1.8. Bit-identical with the strobe on and off for kinds 0, 1, 4, 5, 7 (three bent voices, polled every block), zero global allocations and the malloc zone’s blocks unchanged across the loop; the fuzz’s strobe run 120 s, 0 blocks differing from the unstrobed twin. On the live core (--strobe-test, 8 checks, Sumi, Kessho and Anod renders archived): the scope route alone leaves the field bit-identical to the untraced run; the ink lands under both media; through the hook the bass alone on one point (95 stamps within 0.001 texel), the just fifth on two sides of its cell (47 + 46 stamps, every one within 0.011 rad of the pair’s axis, the pair precessing 0.0011 rad a return — the residual’s rate), the tritone’s 95 round all sixteen bins; the rotor’s dust inked. The fixtures bitwise on Metal; the web wasm’s gate GREEN; the preset round trip 40/40. What the strobe found (it is the instrument Phases 12–13 will hold every voice to, and it began on the rotor): (1) the rotor’s section is Chirikov’s map only approximately — the retune’s re-basing at each kick is not exactly area-preserving in (θ, p) — and at K 2.5 the undamped rotor SINKS into a period-4 cycle within ten seconds (the occupancy by thirds 22 → 7 → 6 %), while a damped one’s amplitude is in float noise by six (its T60 of 3 s); the gate reads the first 440 kicks and prints the thirds — Phase 12’s rotor, [ITERATE]. (2) The strobe fuzz found two Voxo faults, fixed in 0.17.0 with their checks in block 28: a patch of ANOTHER VOICE KIND over sounding notes rendered the old bodies (cells under the trumpet’s bore were NaN in two blocks, and a NaN never leaves the bus) — a kind change ends the voices, the same kind’s knobs stay live; and the flute at B5 bent +47 semitones in one jump (17.6 kHz) was NaN in its block — the jet’s receptivity band past the SVF’s range, the bore at four cells — so the jet and the bore are built for the pitch up to rate2/16 (6 kHz at 48 kHz, above any flute’s top) and saturate there, as the chain’s pitch does at its CFL bound. And THE BREAKER: a non-finite block never leaves the bus — the voices end, the reverb and the delay clear, the block goes out as silence, voxo_stats_t.breaker_trips counts it (the lab’s forced-unstable chain trips it; the next note sounds; the suite’s four red controls — the chain’s CFL, the loop’s passivity, the bore’s CFL, the valve’s junction — now read the trip as their red, since a blow-up no longer reaches the output). (3) The ink route floods at the clock’s rate: every return a drop at a stationary point composes — 876 of three texels in 4 s made one drop of 0.18 canvas — so the stamps are a texel and a half and the ink route keeps about INK_RATE = 23.7 returns a second per voice (a credit of 23.7/clock a return, a stamp when it reaches one — a FRACTIONAL stride, because every N-th return aliases the section: a 2-cycle inked every tenth return is one point, measured on the bench; and not a round rate, so no equal-tempered pitch divides it), the scopes every return [ITERATE] — the author’s eye on the rate and the micro sizes. The author’s viewing (2026-10-14): the rate is right, and in Sumi and Kessho the micro stamps make the strobe read better than the continuous segments; in ANOD both modes are imperceptible — the medium’s rule: only CHARGED material glows by strain, and the water draws only its grid where the displacement exceeds a texel; the trace’s tines and the strobe’s micro-swirls land on water around a charge a third of the strike’s radius (the step-59 figure read because its demo’s charges were torn into streamers the tines then strained). An Anod stamp must be the medium’s own event; the author chose the CHARGE SPECK for both modes (over the micro-spark, an episode per return): an ink drop of two texels glowing at the charge’s base (0.22) and brightening under the chord’s own strain — the strobe’s returns and, in the continuous mode, one speck along the orbit at the same ink rate (a speck at every vertex flooded: 5040 in 4 s charged discs far past the orbits; the bridge has no clock, so the continuous credit runs per frame at an assumed 60 fps), kind 7 through the hook; the bench’s Anod renders (strobe_anod.png, trace_anod.png) are the author’s to view. Open for the author: the tablets’ mode row; the rotor’s symplecticity (Phase 13 now, #13). Next: the phase close — the fold of this file as Part X (after the commit, the author’s word), the pre-release tag v3.0.0-alpha.1 the author’s — and step 76, Anod finished, under DECISIONS_11.md.

13. The phase order, re-resolved: the carry-overs directly after Kessho, Voxo last — the author’s word (2026-10-14, after the strobe’s Anod viewing; _work/specs/ROADMAP_6_delta_phase_order_and_spark.md, folded into ROADMAP_6.md in place). Phase 12 is now the carry-overs (steps 76, 77: Anod’s deterministic seed, the strain buffer, the Chirikov grid and the spark reading params.anod_glow_mode — the delta’s addition, born of the viewing in #12 where Anod showed neither trace mode; then the Boehm layout, the split surface, preset-next), Phase 13 Suzu’s foundation (78–82), Phase 14 the voices (83–86), Phase 15 Voxo DS 2.0 (87–91), Phase 16 the release (92). Why: the phase holds the only two core changes outside Phase 11, so the arc gets ONE contiguous core-open window, steps 71–77, and one freeze, 78–92, across all eleven Voxo steps, instead of reopening at the old 91 after nine frozen steps; Kessho’s Layer A reads the accumulated σ from its second session; the seed makes every later voice’s strobe portrait gateable bitwise in Anod (the step-75 bench ran its bitwise gates in Sumi for want of it); the Lichtenberg operator (recorded at 76, 76b or 4.0) has a seed to stand on before the freeze. The corrections at the fold (the agent’s, accepted): the machines stay the Mac for both steps (the delta said “unchanged: Linux box, Windows box”; the roadmap had already moved them, the Linux box being out since 2026-10-05); the roadmap’s open decisions are 20 (the order) and 21 (Lichtenberg), 19 being the crystal-drop theorem; two cross-references the delta’s table missed — decision 10 (the web gate’s contract, step 78) and decision 11 (step 82 Voxo’s loader, the core side with 77); and the step-75 records’ “frozen from here to step 91” become “open through step 77”. The spark reading must state whether ridges light on water or only on charge — today only charge glows, which is why #12’s Anod stamps are charge specks; the step’s A/B should show the trace both ways. The release tags follow the phases: alpha.1 (11), alpha.2 (12, the carry-overs), alpha.3 (13), alpha.4 (14), alpha.5 (15), rc.N (16). The decisions files stay one per phase (DECISIONS_11 is Phase 12’s, the carry-overs). Next: step 76, on the Mac, the core open.