diff --git a/docs/aetheria-fauna-map.md b/docs/aetheria-fauna-map.md
index b35bab9d3..f3e6563fd 100644
--- a/docs/aetheria-fauna-map.md
+++ b/docs/aetheria-fauna-map.md
@@ -379,3 +379,89 @@ evidence) and `aetheria-fauna:question:habitat-no-pop` (how a member is carried
 23. `flow-moves-matter`: floating items, mines and vented clouds drift with the flow (`flow-moves-what-ruled`).
 24. `flow-slope-gradient-parity`: the brush-rendered heightfield and `Zone.GetHeight` agree (`flow-slope-terms`).
 25. `orbit-sync-helper`: the generic flying aid that holds a ship on the local orbital flow. Waits on an operator yes.
+
+## r4: placement is a trophic DAG
+
+Written by Imagination (agent imagination-aeth-trophic-dag, session self-2026-10-14-ag) against `origin/master`
+`7633408f` (the flow owner `FlowField`/`Zone.Flow` is on master) and CultLib `main` `6c902fd4`. The operator ruled
+`habitat-trophic-dag`: none of the r3 density drivers gives "the filament feeling"; placement is "a few layers of
+ecological abstraction, all deterministic, to author the various species with", whose trophic levels "form a DAG
+which we can evaluate in either shader passes or in C#". `voronoi-primitive` adds the weighted Voronoi she likes.
+Self relayed a correction on 2026-10-14, her words: "Parity between shader and C# is CultMath's whole raison
+d'etre". The target is revised to r4 ("Placement law"). The r3 rows B24-B27 and the habitat probe stand; B25's
+candidates are superseded as designs. Prior art: `docs/research/2026-10-14-trophic-dag-filaments-prior-art.md`
+(`TD:<line>`, tags [V] read, [S] search summary, [M] memory or derivation). The species the graph authors come from
+the lore branch `eureka/aetheria-fauna-lore` `74c7e212`, note `Open Water` (`OW`).
+
+### Body facts (r4)
+
+| # | Question | Result |
+|---|---|---|
+| B28 | What does CultMath already give a node library? | Integer PCG hashes `pcg`, `pcg3d`, `pcg4d` (Jarzynski and Olano), "integer-only, so dxc and C# agree bit for bit" (`packages/cultmath/src/CultMath/math.cs:393-426`, `shaders/CultMath.hlsl:396-426`). `cellular(float3)`: Worley F1 and F2 - F1 with analytic gradients, jitter from `pcg3d` of the integer cell, 3D, unweighted (`math.cs:849-975`, `CultMath.hlsl:440-503`). `smin_grad` (`math.cs:831-847`, `CultMath.hlsl:428-437`). `distance_to_segment` in C# only (`math.cs:319`; no HLSL twin). No weighted cellular, no diagram over explicit weighted sites, no site-graph gate. |
+| B29 | How does CultMath own parity? | Two legs, one owner each (`packages/cultmath/docs/design.md:202-206`): HLSL against C# by the mirror test, which compiles the text of `CultMath.hlsl` as C# and compares float32 bit patterns (`design.md:118-124`), plus a clean `dxc -T lib_6_3` compile (`design.md:114-116`); GLSL against C# by golden fixtures run on a device. The mirror proves the composition in the text, not that a GPU agrees (`design.md:119-121`); device HLSL runs are consumers' today (Asura `gpu-snoise-parity`; Aetheria `FlowFieldParityVerify`). CultMath ships a Unity compute smoke (`packages/cultmath/scripts/unity-smoke/`). Aetheria pins `cultmath-unity-v0.4.1` (`Packages/manifest.json`). |
+| B30 | Does Aetheria already keep a math twin outside CultMath? | Yes. `FlowField` uses CultMath's `math`, but its `Tri`, `Tri3` and `Tri3D` are Aetheria functions (`FlowField.cs:66-72`) whose HLSL twin is `Volumetric.cginc`, pinned by Aetheria's own `FlowFieldParityVerify` (`RelativeTolerance` 1.5e-4). That is a second parity owner beside CultMath. |
+| B31 | What is parked in CultMath that a DAG would use? | The tape: steps 2-5 (expression graph lowered to bytecode with C# evaluators, pruning, an HLSL interpreter, meshing) are parked until Asura is stable (`docs/cultmath-tape-target.md:3-8`, ruling `tape-target-unparks-when-asura-stable`). "Truth and lowerings" (`:84-92`): the field is a typed CultCache document, and the CPU evaluator and the HLSL interpreter are lowerings of it. Step 1 (intervals) and affine forms are on main. |
+| B32 | Do the candidates make filaments? (`docs/research/2026-10-14-trophic-dag-probe/`, README there; wells orbit, slope terms on, t = 0) | `skein` draws strands between neighbouring wells, bent by the flow (`density_skein.png`); `lattice` draws a fine cellular web, dense on the shoulders, dim elsewhere, with no long links (`density_lattice.png`); `skein-web` draws both: strands from well to well with a web hanging off them (`density_skein-web.png`, `layer_L2-krill.png`). Correlation with the B20 Physarum map at 64x32 blocks (this measures the envelope, not filaments: a block is 62 u, wider than a strand): band .512, lattice .359, skein-web .296, krill .277, skein .225, slack .171. Hosted krill at 16 u: band 2,075, skein-web 1,475, skein 639, lattice 419. |
+| B33 | Does the site graph pop as wells orbit? | The hard Gabriel graph over the six bodies changes its edge set 29 times in 1,400 s (one gas-giant orbit), each change a strand appearing or vanishing whole (TD:33 [M], now measured). The soft gate (empty-disc margin through smoothstep(-.15, .15)) moves by at most .00075 per 1/60 s. |
+| B34 | Do the candidates pop under the krill carriage? (`run1.log`, `win.log`, `cyc.log`; fade .1, 60 steps of 1/60 s from t = 100, flow read at the member's cycle start, cycle turns excluded) | Largest presence step: band .0035, slack .013, skein .054, lattice .124 (8 steps over .1), skein-web .493 (8 steps). The lattice steps are not discontinuities: a traced member's web value rises .03 per step for 5 steps, a thin weighted border sweeping a fixed candidate. Widening the search window to 7x7 changes nothing; lowering the weight boost to .6 removes the lattice steps (.047); reading the lattice drift at the member's cycle start, as the flow is read, removes them at full boost: lattice .011, skein-web .066, 0 steps over .1 (`cyc.log`). |
+| B35 | How fast do hosted sets turn over? | Members changed in 1 s, all terms / flow frozen at t's cycle (wells only): band .032 / .032; skein .244 / .106; lattice .594 / .449 (.262 with the drift at cycle start); skein-web .305 / .186 (.216 with the drift at cycle start); slack .089 / .089. The strands ride their wells at about 6 u/s across 16 u candidates, so a tenth of strand members change each second through the fade: motion, not popping (B34). |
+| B36 | What does a stencil predator cost? (Python, one evaluation) | krill .26 ms, minnows 3.19 ms (9 krill), sharks 29.3 ms (81 krill): each ring-stencil level multiplies the cost by 9. Hosted: minnows 274 of 5,432 candidates at 48 u; sharks 19 of 755 at 128 u; lanterns 36 of 3,063 at 64 u. |
+
+### Decisions made here, not forks
+
+- **The layers are the lore's web.** `OW` gives energy budgets (starlight, heat-light, gravity waves, mind-light),
+  a current with fronts, shear and slack, and the Skein: "a slime-mould web that grows toward food along the gravity
+  slope, linking well to well". The filament layer is therefore the Skein, a species of its own, and the layers
+  above read it. The DAG is donor-controlled: each level is a function of the levels below and never regulates
+  them (TD:56 [M]); a predator that thins its prey closes a cycle, which needs iteration (TD:56), so it is out.
+- **Strands link wells; the wells' Voronoi borders are slack.** In the adhesion model, filaments are borders between
+  void cells and the mass sits at the vertices (TD:38 [V]). Here the mass is the wells, so filaments between wells
+  are the dual: edges of a site graph, the graphs the Physarum agents approximate (TD:9, prior doc). The wells'
+  weighted Voronoi borders are where pulls cancel, which `OW` gives to the ambushers (lanterns, void spiders).
+  With multiplicative weights the border round a small well is an Apollonius circle (TD:20 [M];
+  `density_slack.png` shows the circles).
+- **The site graph's gate is soft.** B33: a hard Gabriel graph pops a whole strand 29 times per gas-giant orbit;
+  the soft gate is continuous. The graph is computed per tick from the orbit positions `Zone` already caches per
+  tick (B24), over the zone's bodies only; wormhole mouths and belts join as sites in their own cuts.
+- **Hunting radius is a stencil, or a widened kernel.** A predator reads its prey's density as the mean over a
+  fixed ring of taps: pointwise, exact by definition, the same in C# and HLSL. It costs 9x per level (B36), so a
+  stencil reads at most two levels down. Where the prey is a sum of Gaussian kernels (the Skein's strands) a
+  predator reads the same kernels widened instead, the exact blur of a Gaussian profile (TD:78 [M]). Grid-only
+  operators (blur of arbitrary fields, distance transforms, eikonal paths, jump flooding: TD:19, TD:78) are
+  presentation-only, never sim-visible.
+- **Fast drift is read at the member's cycle start.** `habitat-no-pop-ruled` reads the krill's flow at its cycle
+  start. B34 extends it, measured: the flow warp and the lattice web's drift are read at the member's cycle start;
+  the slope band and the site graph, which move slowly and continuously, are read now and carried by the fade.
+- **Nodes are CultMath functions; Aetheria composes.** Per Self's relay of the operator. Each primitive the DAG
+  needs is a CultMath function with an HLSL twin in `CultMath.hlsl`, pinned by CultMath's mirror test and dxc
+  compile (B29). Aetheria's `Habitat` is a composition of those calls and owns no math twin. Gaps to fill in
+  CultLib, not helpers in Aetheria: (1) a 2D weighted lattice cellular with the smooth-min blend (her node) on
+  `pcg3d` cells and zone time; (2) a weighted diagram over an explicit span of sites (F1, F2 and first-order border
+  distance, multiplicative and power weights); (3) the HLSL twin of `distance_to_segment`; (4) the soft Gabriel
+  gate over a site span. Gap (5): CultMath has no parity path for a consumer's composition, only for its own text
+  (B29), so a presenter that draws a composed layer (Skein glow, glim haze) waits on a CultMath-owned composition
+  check rather than a second `FlowFieldParityVerify`. B30's `Tri3D` twin is the existing instance of the same split.
+- **The search window follows the weight range.** A multiplicatively weighted lattice node needs its window to
+  cover the weight ratio (TD:20 [M]); the probe's 1.6x boost needed no more than 5x5 (B34). The CultMath node states
+  the weight range it supports instead of trusting the caller.
+
+### Questions (admitted in the mind)
+
+`aetheria-fauna:question:skein-filament-construction` (which construction is the Skein; images per option in
+`docs/research/2026-10-14-trophic-dag-probe/`) and `aetheria-fauna:question:trophic-graph-tape` (hand-written CultMath
+compositions now and the tape later, or unpark the tape for this).
+
+### Cut sequence (r4, one line each; each is mapped when it is about to run; r3 lines 4-25 stand after line 7)
+
+1. `fauna-flow-field`: on master (`FlowField`, `Zone.Flow`, `FlowFieldParityVerify`).
+2. `cultmath-trophic-nodes` (CultLib): gaps (1)-(4) above with HLSL twins, mirror tests and stated weight ranges;
+   a CultMath Unity tag. Waits on both questions.
+3. `fauna-trophic-habitat` (Aetheria): the CultMath pin bump; `Habitat` composes environment, Skein, glim and krill
+   in C# at candidates; per-species settings records; the r3 candidates and fade; tests for the r4 invariants; the
+   per-candidate cost measured. Replaces r3 line 2. Waits on 2.
+4. `fauna-krill-swarms`: as r3 line 3, on 3's krill hosting.
+5. `cultmath-composition-parity` (CultLib): gap (5), a CultMath-owned check that a consumer's C# composition and its
+   HLSL twin agree on a device; `FlowField`'s `Tri3D` moves under it. Waits on Self's scoping.
+6. `fauna-trophic-presenter`: the Skein and glim drawn in the nebula from the same composition. Waits on 3 and 5.
+7. `fauna-minnow-schools`, then predators by stencil and ambushers on slack (r3 lines 6-8), re-mapped as species of
+   the DAG per `fauna-bestiary-open` and `OW`.
diff --git a/docs/aetheria-fauna-target.md b/docs/aetheria-fauna-target.md
index ce78364c9..fecfa982a 100644
--- a/docs/aetheria-fauna-target.md
+++ b/docs/aetheria-fauna-target.md
@@ -1,16 +1,30 @@
 # Aetheria spaceborne fauna: target
 
-Campaign `aetheria-fauna`, target content r3 (r1 was admitted from the r0 draft at `f9705d32`, r2 by Self; r3 is
-admitted by Imagination). Repo `GameCult/Aetheria`, working branch `master`, cut branches
-`eureka/aetheria-fauna-<cut>`. Written by Imagination (agents imagination-aeth-fauna, imagination-aeth-fauna-r2 and
-imagination-aeth-fauna-r3, sessions self-2026-10-13-ag2 and self-2026-10-14-ag); r3 is against `origin/master`
-`b836af48`. Body facts and probes are in `docs/aetheria-fauna-map.md` (cited below as `B<n>`); prior art is
+Campaign `aetheria-fauna`, target content r4 (r1 was admitted from the r0 draft at `f9705d32`, r2 by Self; r3 and
+r4 are admitted by Imagination). Repo `GameCult/Aetheria`, working branch `master`, cut branches
+`eureka/aetheria-fauna-<cut>`; the DAG's node primitives land in `GameCult/CultLib` (CultMath). Written by
+Imagination (agents imagination-aeth-fauna, imagination-aeth-fauna-r2, imagination-aeth-fauna-r3 and
+imagination-aeth-trophic-dag, sessions self-2026-10-13-ag2 and self-2026-10-14-ag); r4 is against `origin/master`
+`7633408f` and CultLib `6c902fd4`. Trophic DAG prior art: `docs/research/2026-10-14-trophic-dag-filaments-prior-art.md`
+(`TD:<line>`); its probe: `docs/research/2026-10-14-trophic-dag-probe/`. Body facts and probes are in `docs/aetheria-fauna-map.md` (cited below as `B<n>`); prior art is
 `docs/research/2026-10-13-fauna-prior-art.md` (`PA:<line>`; `[M]` items are from memory and unverified),
 `docs/research/2026-10-13-fauna-placement-prior-art.md` (placement by simulation) and
 `docs/research/2026-10-14-fauna-placement-closed-form.md` (`CF:<line>`; its tags: `[V]` read, `[S]` search summary
 only, `[M]` memory or derivation, unverified). This is the target and the model page. Open forks are questions in
 the mind under `aetheria-fauna`.
 
+r4 applies `habitat-trophic-dag` (2026-10-14), after the r3 density drivers missed the look:
+
+> I'm not getting the filament feeling. I think we need a few layers of ecological abstraction, all deterministic, to
+> author the various species with. The trophic levels should form a DAG which we can evaluate in either shader
+> passes or in C#
+
+with `voronoi-primitive` (a weighted Voronoi node, her reference shader a sketch of the look) and her correction,
+relayed by Self: "Parity between shader and C# is CultMath's whole raison d'etre". Placement becomes a layered,
+donor-controlled trophic DAG whose filament layer is the lore's Skein, whose nodes are CultMath functions with HLSL
+twins, and which Aetheria composes ("Placement law" below; map section r4). The krill carriage of
+`habitat-no-pop-ruled` stands and is extended to every fast term (map B34).
+
 r3 applies `fauna-placement-ruled` (2026-10-13), against the recommendation to run a Physarum pass at generation:
 
 > Nothing we generate ahead of time would suffice, because the level is constantly changing. I'd imagine we can come
@@ -98,38 +112,56 @@ gather shows the shape of the wells and the currents, and where they are missing
 10. **Placement tells an ecological story, and the level writes it as it moves.** Where fauna are is a closed form
     of the gravity slope and the flow, evaluated at zone time whenever a query, presenter or sensor asks
     (`fauna-placement-ruled`). Wells orbit, gas giants and suns ripple their wells (B24), and the flow scrolls, so the
-    pattern moves with the level: a placement generated ahead would go stale. Fauna gather on the shoulders of wells,
-    not in the cores and not in flat space, and the flow writes texture into that band. The law is in "Placement
-    law" below.
+    pattern moves with the level: a placement generated ahead would go stale. Life follows the Skein, the
+    slime-mould web strung from well to well, and the energy the wells give off; predators follow their prey, and
+    ambushers wait in the slack between wells. Nothing gathers in the cores, and open flat space away from the Skein
+    is nearly empty. The law is in "Placement law" below.
 11. **No fauna in Sol.** Sol is a single flatspace zone with no fauna inside it; the strangeness begins at its edge.
 12. **Harm and harvest go through existing owners.** A fauna attack is damage through the path a weapon's hit
     takes; a harvest yields items through the economy's yield path; neither gets a fauna-only damage or loot rule.
 
 ## Placement law
 
-One law decides where fauna of a class are, from local quantities only (pointwise: the field and its derivatives at
-a point, CF:6, CF:56):
+Where fauna of a species are is decided by a **trophic DAG**: layers of fields, each a deterministic function of the
+layers below it and of world facts, evaluated at a point at zone time when a query, presenter or sensor asks
+(`habitat-trophic-dag`). Pointwise fields of slope and flow alone draw bands and blobs (B25); filaments need an
+input that is not local, and the DAG takes it from the zone's bodies, which every point can read (map r4).
 
-1. **A habitat density** in [0, 1] at a point, from the gravity slope there and the flow there. The slope term is a
-   band on the shoulders of the wells: the operator's own `Deposition(slope)` curve from her slime prefab (B20), zero
-   past the steep core and near zero in flat space. Which flow quantity shapes the band is the question
-   `habitat-density-driver`; the probe images are in the map (B25).
-2. **Candidates with fixed thresholds.** Each class has a lattice of candidate seed points, one per cell, jittered by
-   a hash of the zone seed and the cell, each with its own fixed threshold from the same hash. A candidate hosts a
-   member when the density at it is above its threshold. This is Horizon Zero Dawn's placement shape: a density map
-   discretised by a fixed threshold pattern, deterministic and "locally stable" (CF:33 [V]). Because each threshold
-   is fixed, raising the density never removes a member, and a member appears or leaves only when the density at
-   its own point crosses its own threshold (CF:40: the design is [V], the nesting is a reading [M], so it is pinned
-   here as an invariant instead of trusted). The member's identity is the cell, so it is a `ChunkId` with no stored
-   state.
-3. **No pop.** The density moves as fast as the flow scrolls (B25: under continuous evaluation a fifth of a
-   flow-shaped population changes in one second). A member never appears or vanishes at full presence; how it is
-   carried through a change is the question `habitat-no-pop`.
-4. **Predators by prey.** Classes that hunt read their prey's density, not a second map: the ideal free
-   distribution puts predators in proportion to prey (CF:49-50, [S]; composed pointwise, CF:53 [M]). Sharks on krill
-   shoulders are one product of two pointwise densities.
+| Layer | Fields (the first web, from the lore's Open Water; the bestiary stays open) | Reads |
+|---|---|---|
+| 0 Environment | Slope and the operator's `Deposition(slope)` band, the steep-core mask (`Zone.GetNormal`); the flow (`Zone.Flow`); the zone's bodies: positions from the per-tick orbit cache, gravity radius, kind; energy kernels round them: starlight inside a sun's light radius, heat-light on warm well floors. Later sources join here: gravity-wave rings (whales), mind-light round crews and stations (moths), wormhole mouths (upwelling), wrecks (succession). | World facts only |
+| 1 Structure | **The Skein**: strands between neighbouring bodies (a site graph with a soft gate, each edge a Gaussian strand, bent by a Zel'dovich warp of the flow, TD:39 [V]) and a weighted lattice Voronoi web hanging off them (`voronoi-primitive`). **Slack**: the borders of the bodies' weighted Voronoi, where pulls cancel. Which construction is the Skein is the question `skein-filament-construction`. | Layer 0 |
+| 2 Producers | Glim: energy times the Skein's feeding. | 0, 1 |
+| 3 Grazers | Krill: the Skein times a saturating response to glim (Holling II, TD:55 [S]). Minnows: krill over a hunting ring. | 0-2 |
+| 4 Predators and ambushers | Sharks: minnows over a wider ring, on the band. Lanterns and void spiders: slack times krill over a ring. | 0-3 |
 
-The law is pure and costs nothing per tick: it runs per candidate when asked, as `Zone.ChunkPose` does for rocks.
+1. **Operators.** A sim-visible layer uses only: pointwise arithmetic, remap curves, smoothstep, min, max and smooth
+   min, saturating responses; CultMath nodes (integer hash, weighted lattice cellular, weighted diagram over
+   explicit sites, segment kernel, soft site-graph gate); a **stencil** (the mean of a lower layer at the point and a
+   fixed ring of taps, at most two levels deep, 9x the cost per level, B36); and **kernel widening** where the prey
+   is a sum of Gaussian kernels (the exact blur, TD:78 [M]). Grid operators (blur of arbitrary fields, distance
+   transforms, eikonal paths, jump flooding, TD:19, TD:78), iteration and stored fields are presentation-only.
+2. **Donor control.** A layer never reads itself or a layer above it: predators follow prey and never thin it in
+   the law (TD:56 [M]). Thinning is a sim event (harvest, attack wear), not a placement term.
+3. **Candidates with fixed thresholds** (r3, kept). Each species has a lattice of candidate seed points, one per
+   cell, jittered by a hash of the zone seed and the cell, each with its own fixed threshold from the same hash; a
+   candidate hosts a member when its species' density there is above its threshold (Horizon Zero Dawn's shape,
+   CF:33 [V]; nesting pinned as an invariant, CF:40 [M]). The member's identity is the cell, a `ChunkId` with no
+   stored state. Candidate spacing is per species (16 u krill, 48 u minnows, 128 u sharks in the probe).
+4. **No pop.** Terms that move fast are read at the member's own cycle start (`habitat-no-pop-ruled` for the flow,
+   extended to the flow warp and the lattice web's drift, measured in B34); terms that move slowly and continuously
+   (the slope band, the soft site graph, B33) are read now and carried by the fade. A member never appears or
+   vanishes at full presence.
+5. **Nodes in CultMath, compositions in Aetheria.** Every node primitive is a CultMath function with an HLSL twin,
+   pinned by CultMath's mirror test (map B29); what CultMath lacks is a gap filled in CultLib (map r4, gaps 1-5),
+   never a helper in Aetheria. Each species' composition is C# in `ServerShared` (`Habitat`) calling those
+   functions, with its parameters in a per-species settings record; the sim evaluates only C#. A presenter that
+   draws a composed layer (the Skein's glow, glim haze) uses the composition's HLSL twin under a CultMath-owned
+   composition check. Whether compositions later become data on CultMath's parked tape is the question
+   `trophic-graph-tape`.
+
+The law costs nothing per tick: it runs per candidate when asked, as `Zone.ChunkPose` does for rocks; the site graph
+is per zone per tick over a handful of bodies.
 
 ## Scale classes
 
@@ -164,7 +196,8 @@ The rows follow the rulings `fauna-in-sim-ruled`, `fauna-identity-ruled` and `fa
 | **Swarm anchor** (later, sharks and whales) | Per field: a law that moves the field's frame across the flow. | Pure function of zone time plus sparse event records (fork `fauna-motion-model`). | `Zone`. Forbidden: per-member stepping. |
 | **Disturbance** (later) | `(member, time, push)`, sparse, as `ChunkWear` is. | Written when a hull passes through or a shot lands, then decays lazily against zone time. | `Zone`. It is read only by `Pose`. |
 | **Flow field** (new owner) | One law: `FlowField`, evaluated per zone by `Zone.Flow(position)` from the zone's world-law settings (`PlanetSettings.Flow`). | Settings authored in `Settings.asset`; time is zone time. Never stored per position. | `Zone`. Derived: every shader flow uniform (`_FlowScroll` and the rest). Forbidden: `VolumeSampling._flowScroll`, `ZoneEnvironment.Flow`, any frame-time accumulator. |
-| **Habitat** (new owner, a law) | `Habitat` in `ServerShared`: a class's `HabitatSettings`, a point's slope and flow quantities, a candidate's hashed seed point and threshold. | Never stored: evaluated at zone time per candidate when asked. | `Habitat` decides density and hosting; `Zone` supplies the local quantities from `GetNormal` and `Flow`. Forbidden: a generation pass, a saved or cached habitat map, a per-tick sweep. |
+| **Habitat** (new owner, a law: the trophic DAG) | `Habitat` in `ServerShared`: one composition per species over CultMath nodes, a species' settings record, a candidate's hashed seed point and threshold. | Never stored: evaluated at zone time per candidate when asked. | `Habitat` decides density and hosting; `Zone` supplies world facts (`GetNormal`, `Flow`, body positions from the per-tick orbit cache); CultMath owns every node and its HLSL twin. Forbidden: a generation pass, a saved or cached habitat map, a per-tick sweep, a math twin in Aetheria, a grid operator in a sim-visible layer. |
+| **Skein site graph** (derived) | Per zone: the soft gate of each pair of bodies (map r4). | Recomputed per tick from orbit positions; never saved. | `Habitat`, through a CultMath gate function. Forbidden: a hard (0/1) gate; a cached graph across ticks. |
 | **Attack** (later, per class) | `(member or swarm, ship, time)`, an event. | Raised by a class law when its trigger holds; applied through the ordinary damage path. | `Zone`. Forbidden: a fauna-only damage rule. |
 | **Harvest yield** (later) | Item kinds in the catalog, per fauna kind. | A member broken or netted by harvesting gear yields items through the economy's yield table; the field refills by respawn. | The catalog and the yield table. Forbidden: fauna-only loot code. |
 | **Fauna background kind** (aetheria-ew) | Entries of aetheria-ew's `BackgroundKind` for fauna classes (that target's row says "more by ruling"). | Static data. | `GameplaySettings`, per aetheria-ew. Its envelope gains a motion term per class (fork `fauna-disguise-path`). |
@@ -190,19 +223,33 @@ The rows follow the rulings `fauna-in-sim-ruled`, `fauna-identity-ruled` and `fa
 - `flow-step-free`: the flow at a position and zone time does not depend on step size or frame rate.
 - `fauna-none-in-sol`: Sol's zone hosts no fauna kind, so no candidate there is ever hosted.
 - `fauna-placement-closed-form`: whether a candidate hosts a member at zone time t is a pure function of the zone
-  seed, the class's habitat settings, and the gravity slope and flow at the candidate at t. Nothing about placement
-  is generated ahead, saved, cached across ticks or stepped.
-- `fauna-placement-story`: habitat density is zero in well cores, below every candidate's threshold in flat space,
-  and highest on well shoulders, and it changes when the slope or the flow at the point changes.
+  seed, the species' settings, the world facts at t (slope, flow at the member's cycle start, the bodies' positions)
+  and the lower layers evaluated at bounded points. Nothing about placement is generated ahead, saved, cached across
+  ticks or stepped.
+- `fauna-placement-story`: density is zero in well cores; along a Skein strand between two bodies it exceeds the
+  density at a point of equal slope off the strand; ambushers' density peaks on the slack borders; a predator's
+  density rises with its prey's within its hunting ring.
 - `fauna-placement-nested`: each candidate's threshold is fixed, so raising the density at a candidate never
   un-hosts it and lowering it never hosts it.
 - `fauna-placement-no-pop`: a member never appears or vanishes at full presence; every change of hosting is carried
-  through a fade.
+  through a fade. Within a member's cycle its presence moves by at most a stated bound per 1/60 s step as the bodies
+  orbit (the probe's worst was .066, map B34).
+- `trophic-dag-acyclic`: each layer reads only world facts and the layers below it; no layer reads itself or a layer
+  above it.
+- `trophic-dag-pointwise`: every sim-visible layer is evaluated at a point from world facts, the per-tick site
+  graph and a bounded number of evaluations of lower layers (stencils at most two levels deep); no grid, no
+  iteration, no stored field.
+- `trophic-nodes-in-cultmath`: every node primitive a layer calls is a CultMath function with an HLSL twin pinned by
+  CultMath's parity checks; Aetheria holds compositions only.
+- `skein-gate-continuous`: the Skein's site-graph gates are continuous in the bodies' positions, so no strand
+  appears or vanishes as the bodies orbit.
 
 ## Not in scope
 
 - Ambient presentation-only life (the slime trails) beyond leaving it untouched; the habitat law reuses its
   `Deposition(slope)` curve, but the presenter stays presentation.
+- Population dynamics: no layer is stepped or regulated by the layer above it; harvest and attack wear thin
+  members as sim events through `Zone.Wear`, not as placement terms.
 - Phantom positions (aetheria-ew `ew-where-lies-ruled`).
 - Ships drifting with the flow (`flow-moves-what-ruled`: ships do not; floating items, mines and vented clouds do,
   in a later cut).
@@ -214,4 +261,4 @@ Attacks and harvest are in scope as later cuts, designed per class (`fauna-inter
 
 ## Cut sequence
 
-The map's r3 cut sequence has one line per cut; each is mapped when it is about to run.
+The map's r4 cut sequence (with the r3 lines it keeps) has one line per cut; each is mapped when it is about to run.
diff --git a/docs/research/2026-10-14-trophic-dag-probe/README.md b/docs/research/2026-10-14-trophic-dag-probe/README.md
new file mode 100644
index 000000000..83ce043a0
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/README.md
@@ -0,0 +1,40 @@
+# Trophic DAG probe (2026-10-14)
+
+Serves rulings `aetheria-fauna:ruling:habitat-trophic-dag` and `:voronoi-primitive`, and the questions
+`aetheria-fauna:question:skein-filament-construction` and `:trophic-graph-tape`. Facts are map rows B28-B36 in
+`docs/aetheria-fauna-map.md`; prior art is `docs/research/2026-10-14-trophic-dag-filaments-prior-art.md` (`TD:<line>`).
+
+`trophic_probe.py` imports `habitat_probe.py` (the float64 transliteration of `Zone.GetHeight`/`GetNormal` and
+`FlowField`, in `../2026-10-14-fauna-habitat-probe/`) and adds what that probe lacked: the wells orbit, as
+`Zone.GetOrbitPosition` moves them (period = distance in seconds, `Settings.asset` `OrbitPeriod` exponent 1,
+multiplier 1; about 6.3 u/s for every planet). The flow's slope terms are on (swirl 6, slide 1.5, as B25g). Its hash
+is the probe's own integer hash, not CultMath `pcg3d`; images are qualitative evidence for a C# law, not the law.
+
+Filament candidates (krill habitat density, each times the steep-core mask):
+
+| Name | Construction |
+|---|---|
+| `band` | The operator's `Deposition(slope)` alone (r3's baseline, B25a). Control, not an option. |
+| `skein` | Strands: a Gabriel graph over the zone's wells (TD:31 [V]) with a soft gate (the empty-disc margin through a smoothstep), each edge a Gaussian strand of width 28 u + 3 % of its length, bent by a Zel'dovich warp of the flow, `x - 20 s * u(x)` (TD:39 [V]). |
+| `skein-hard` | `skein` with the hard 0/1 Gabriel gate, for the pop count. |
+| `lattice` | The operator's reference node: a lattice smooth Voronoi (260 u cells) with her hashed per-site multiplicative weight, raised by up to 1.6x near wells so the cells shrink on the shoulders; output is the border (her smooth-min gap, and F2 - F1 at width .1 cell), warped by the flow for 6 s, times the band widened (`band^.75`). Sites drift on zone time (.05 rad/s). |
+| `skein-web` | `skein` plus `lattice` hanging off the strands: the web is gated by a strand halo (4x width) or the band. |
+| `slack` | A multiplicatively weighted Voronoi of the wells (weight = gravity radius), distance to the cell border to first order, `(F2 - F1) / |grad(F2 - F1)|`: the saddles where pulls cancel (Apollonius circles round small wells, TD:20 [M]). |
+
+Trophic layers over `skein-web` (`layer_*.png`): `L1-glim` (starlight inside the sun's light radius plus heat-light on
+warm well floors, fed along the Skein), `L2-krill` (Skein times a Holling-II saturation of glim, TD:55 [S]),
+`L2-minnows` (Holling of krill averaged over the point and 8 taps on a 48 u ring), `L3-sharks` (minnows over a
+160 u ring, times the band), `L3-lanterns` (slack times krill over a 120 u ring).
+
+Images: `density_<candidate>.png` (zone 4000 u across, t = 0, absolute density, red = bodies), `members_<candidate>.png`
+(hosted krill candidates at 16 u, fixed thresholds .1 + .9h), `layer_<layer>.png`, `members_L2-minnows.png` (48 u),
+`members_L3-sharks.png` (128 u), `members_L3-lanterns.png` (64 u).
+
+Logs: `run1.log` (the full run, 1,211 s), `win.log` (search window and weight range against presence steps),
+`cyc.log` (the lattice drift read at the member's cycle start).
+
+To rerun: copy this folder and `../2026-10-14-fauna-habitat-probe/habitat_probe.py` into one scratch directory
+(the scripts write PNGs next to themselves), then `py -3 -u trophic_probe.py 256` (about 20 minutes),
+`py -3 -u winprobe.py`, `py -3 -u cycprobe.py`. `habitat_probe.py` reads the B20 Physarum map from
+`C:\aeth-wt\fauna-target-r3\docs\research\2026-10-13-fauna-placement-probe\output.txt`; edit the path if the
+worktree moved. Python 3 only, no packages.
diff --git a/docs/research/2026-10-14-trophic-dag-probe/cyc.log b/docs/research/2026-10-14-trophic-dag-probe/cyc.log
new file mode 100644
index 000000000..2cbf08084
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/cyc.log
@@ -0,0 +1,2 @@
+web at cycle start, lattice: presence step max 0.0113, 0 steps > .1 of 1500; members 435, changed in 1 s 0.262
+web at cycle start, skein-web: presence step max 0.0656, 0 steps > .1 of 1500; members 1475, changed in 1 s 0.216
diff --git a/docs/research/2026-10-14-trophic-dag-probe/cycprobe.py b/docs/research/2026-10-14-trophic-dag-probe/cycprobe.py
new file mode 100644
index 000000000..0bd8da727
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/cycprobe.py
@@ -0,0 +1,7 @@
+import sys; sys.argv=['x','64']
+import trophic_probe as T
+cands=T.cand_list(16.0); T.WEB_AT_CYCLE=True
+for name in ("lattice","skein-web"):
+    w,b,n=T.pop_probe(T.CANDS[name],cands,100.0,1500)
+    a=T.members(T.CANDS[name],cands,0.0); b1=T.members(T.CANDS[name],cands,1.0)
+    print(f"web at cycle start, {name}: presence step max {w:.4f}, {b} steps > .1 of {n}; members {len(a)}, changed in 1 s {len(a^b1)/max(1,len(a)):.3f}", flush=True)
diff --git a/docs/research/2026-10-14-trophic-dag-probe/density_band.png b/docs/research/2026-10-14-trophic-dag-probe/density_band.png
new file mode 100644
index 000000000..044373741
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/density_band.png
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3dc4ac288d82c01b1a72e6702bd2a46715e1dba4940db4154d295dcb8ffa8f54
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/density_lattice.png b/docs/research/2026-10-14-trophic-dag-probe/density_lattice.png
new file mode 100644
index 000000000..6cd74e11c
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/density_lattice.png
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/density_skein-web.png b/docs/research/2026-10-14-trophic-dag-probe/density_skein-web.png
new file mode 100644
index 000000000..d0a8371a7
--- /dev/null
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/density_skein.png b/docs/research/2026-10-14-trophic-dag-probe/density_skein.png
new file mode 100644
index 000000000..3950d7cc0
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/density_slack.png b/docs/research/2026-10-14-trophic-dag-probe/density_slack.png
new file mode 100644
index 000000000..dbdb2f316
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/layer_L1-glim.png b/docs/research/2026-10-14-trophic-dag-probe/layer_L1-glim.png
new file mode 100644
index 000000000..a2f35ad7d
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/layer_L2-krill.png b/docs/research/2026-10-14-trophic-dag-probe/layer_L2-krill.png
new file mode 100644
index 000000000..417729d54
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/layer_L2-minnows.png b/docs/research/2026-10-14-trophic-dag-probe/layer_L2-minnows.png
new file mode 100644
index 000000000..ee3241f29
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/layer_L3-lanterns.png b/docs/research/2026-10-14-trophic-dag-probe/layer_L3-lanterns.png
new file mode 100644
index 000000000..f3bc763b0
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/layer_L3-sharks.png b/docs/research/2026-10-14-trophic-dag-probe/layer_L3-sharks.png
new file mode 100644
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/members_L2-minnows.png b/docs/research/2026-10-14-trophic-dag-probe/members_L2-minnows.png
new file mode 100644
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new file mode 100644
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new file mode 100644
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/members_band.png b/docs/research/2026-10-14-trophic-dag-probe/members_band.png
new file mode 100644
index 000000000..18c76262e
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/members_band.png
@@ -0,0 +1,3 @@
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/members_lattice.png b/docs/research/2026-10-14-trophic-dag-probe/members_lattice.png
new file mode 100644
index 000000000..3f75174f6
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/members_lattice.png
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new file mode 100644
index 000000000..679501ad7
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new file mode 100644
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/members_slack.png b/docs/research/2026-10-14-trophic-dag-probe/members_slack.png
new file mode 100644
index 000000000..7371680c5
--- /dev/null
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diff --git a/docs/research/2026-10-14-trophic-dag-probe/run1.log b/docs/research/2026-10-14-trophic-dag-probe/run1.log
new file mode 100644
index 000000000..50dc816b4
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/run1.log
@@ -0,0 +1,27 @@
+grid 256, wells orbit (period = distance s), slope terms on, TAU 20.0 s, lattice 260.0 u
+gabriel over 1400 s: hard edge-set changes 29; soft gate largest step per 1/60 s 0.00075
+49109 krill candidates at 16 u
+  band wells-only (flow frozen at t's cycle): changed in 1 s 0.0323, 60 s 0.891
+band: corr physarumA 0.512; members 2075; changed in 1 s 0.032, 8 s 0.283, 60 s 0.891; presence step max 0.0035 (0 steps > .1, 2500 near-threshold candidates); 23s
+  skein wells-only (flow frozen at t's cycle): changed in 1 s 0.1064, 60 s 1.498
+skein: corr physarumA 0.225; members 639; changed in 1 s 0.244, 8 s 1.102, 60 s 1.549; presence step max 0.0536 (0 steps > .1, 2500 near-threshold candidates); 58s
+  skein-hard wells-only (flow frozen at t's cycle): changed in 1 s 0.1089, 60 s 1.495
+skein-hard: corr physarumA 0.225; members 643; changed in 1 s 0.244, 8 s 1.098, 60 s 1.546; presence step max 0.0536 (0 steps > .1, 2500 near-threshold candidates); 55s
+  lattice wells-only (flow frozen at t's cycle): changed in 1 s 0.4487, 60 s 1.871
+lattice: corr physarumA 0.359; members 419; changed in 1 s 0.594, 8 s 1.680, 60 s 1.874; presence step max 0.1236 (8 steps > .1, 2500 near-threshold candidates); 179s
+  skein-web wells-only (flow frozen at t's cycle): changed in 1 s 0.1864, 60 s 1.504
+skein-web: corr physarumA 0.296; members 1475; changed in 1 s 0.305, 8 s 1.144, 60 s 1.534; presence step max 0.4933 (8 steps > .1, 2500 near-threshold candidates); 217s
+  slack wells-only (flow frozen at t's cycle): changed in 1 s 0.0893, 60 s 1.756
+slack: corr physarumA 0.171; members 3942; changed in 1 s 0.089, 8 s 0.672, 60 s 1.756; presence step max 0.0132 (0 steps > .1, 2500 near-threshold candidates); 26s
+L1-glim: grid 256, corr physarumA 0.485; 18s
+L2-krill: grid 256, corr physarumA 0.277; 19s
+L2-minnows: grid 128, corr physarumA 0.360; 42s
+L3-sharks: grid 128, corr physarumA 0.403; 376s
+L3-lanterns: grid 128, corr physarumA 0.148; 42s
+members L2-minnows: 274 of 5432 at 48 u; changed in 1 s 0.124, 8 s 0.478; 52s
+members L3-sharks: 19 of 755 at 128 u; changed in 1 s 0.105, 8 s 0.526; 65s
+members L3-lanterns: 36 of 3063 at 64 u; changed in 1 s 0.139, 8 s 0.861; 31s
+cost krill: 0.26 ms per evaluation (Python)
+cost minnows: 3.19 ms per evaluation (Python)
+cost sharks: 29.26 ms per evaluation (Python)
+total 1211s
diff --git a/docs/research/2026-10-14-trophic-dag-probe/trophic_probe.py b/docs/research/2026-10-14-trophic-dag-probe/trophic_probe.py
new file mode 100644
index 000000000..8498ea222
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/trophic_probe.py
@@ -0,0 +1,307 @@
+"""Trophic DAG probe (Imagination, aetheria-fauna r4). Pure Python 3, no packages.
+
+Evaluates candidate filament nodes and a layered trophic DAG on the B20 zone (habitat_probe.py's transliteration
+of Zone.GetHeight/GetNormal and FlowField, float64), with the wells ORBITING as Zone.GetOrbitPosition moves them
+(period = distance seconds, Settings.asset OrbitPeriod exponent 1, multiplier 1). Writes per-layer density images,
+a members image per candidate, and prints per candidate: correlation with the B20 Physarum maps, hosted members,
+turnover in 1 s / 8 s / 60 s and the largest presence step per 1/60 s (fade band .1). Hashes are the probe's own
+integer hash, not CultMath pcg; images are qualitative evidence for the C# law, not the law.
+
+  py -3 trophic_probe.py [grid=256] [only=comma,list]
+"""
+import sys, os, math, time
+ARGS = sys.argv[1:]
+sys.argv = [sys.argv[0], "256"]
+import habitat_probe as H
+
+OUT = os.path.dirname(os.path.abspath(__file__))
+G = int(ARGS[0]) if ARGS else 256
+ONLY = ARGS[1].split(",") if len(ARGS) > 1 else None
+R = H.R
+H.FLOW.update(swirl=6.0, slope=1.5)          # flow-slope-terms-ruled: slope terms on (B25g's values)
+TAU = 20.0                                   # Zel'dovich warp time (s): strands bent by the flow, x -> x - TAU u(x)
+WEB_TAU = 6.0                                # the lattice web is warped less: its cells are smaller than a strand's run
+CYCLE = 8.0                                  # krill cycle period (s), FlowSettings.Period
+FADE = .1
+
+def smooth(a, b, v):
+    if a == b: return 1.0 if v >= b else 0.0
+    v = (v - a) / (b - a); v = 0.0 if v < 0 else 1.0 if v > 1 else v; return v * v * (3 - 2 * v)
+
+# ---------------- L0: environment (wells move) ----------------
+def set_time(t):
+    for (kind, m, d, ph), w in zip(H.BODIES, H.WELLS):
+        a = ph + (2 * math.pi * t / d if d > 0 else 0.0)
+        w["pos"] = (math.cos(a) * d, math.sin(a) * d)
+    pairs_cache.clear()
+
+def slope(x, z, t):
+    n = H.normal(x, z, t); return math.acos(max(-1.0, min(1.0, n[1]))) / (math.pi / 2)
+
+def band(s): return H.deposition(s) / 2.0      # the operator's Deposition(slope), [0, 1]; zero past slope .8
+def core(s): return smooth(.7, .8, s)          # steep core mask
+def envelope(b): return b ** .75           # the band, widened: where the web may live
+
+def flow_at(x, z, t, sc): return H.flow_xz(x, z, t, sc)
+
+# ---------------- L0.5 filament nodes ----------------
+pairs_cache = {}
+def pairs(hard):
+    """Per-zone site graph over the wells: Gabriel graph, gate soft (margin smoothstep) or hard (0/1).
+    Recomputed per tick from orbit positions (the zone already caches those per tick)."""
+    if hard in pairs_cache: return pairs_cache[hard]
+    W = H.WELLS; out = []
+    for i in range(len(W)):
+        for j in range(i + 1, len(W)):
+            a, b = W[i]["pos"], W[j]["pos"]; L = math.dist(a, b); m = ((a[0] + b[0]) / 2, (a[1] + b[1]) / 2); r = L / 2
+            margin = min([(math.dist(m, W[k]["pos"]) - r) / r for k in range(len(W)) if k not in (i, j)] or [9.0])
+            gate = (1.0 if margin > 0 else 0.0) if hard else smooth(-.15, .15, margin)
+            if gate > 0: out.append((a, b, L, gate, 28.0 + .03 * L))
+    pairs_cache[hard] = out; return out
+
+def seg_dist(p, a, b):
+    ax, az = b[0] - a[0], b[1] - a[1]; L2 = ax * ax + az * az
+    u = 0.0 if L2 == 0 else max(0.0, min(1.0, ((p[0] - a[0]) * ax + (p[1] - a[1]) * az) / L2))
+    return math.hypot(p[0] - a[0] - u * ax, p[1] - a[1] - u * az)
+
+def strands(q, hard=False, widen=1.0):
+    best = 0.0
+    for a, b, L, gate, sig in pairs(hard):
+        d = seg_dist(q, a, b) / (sig * widen); best = max(best, gate * math.exp(-d * d))
+    return best
+
+def warp(x, z, t, sc, tau=None):
+    ux, uz = flow_at(x, z, t, sc); tau = TAU if tau is None else tau; return (x - tau * ux, z - tau * uz)
+
+def well_slack(x, z):
+    """Multiplicatively weighted Voronoi of the wells (weight = gravity radius): distance to the cell border,
+    first order (F2 - F1) / |grad(F2 - F1)|. Borders are Apollonius circles round the small wells."""
+    ds = []
+    for w in H.WELLS:
+        dx, dz = x - w["pos"][0], z - w["pos"][1]; r = math.hypot(dx, dz) or 1e-6
+        ds.append((r / w["r"], dx / (r * w["r"]), dz / (r * w["r"])))
+    ds.sort()
+    (d1, gx1, gz1), (d2, gx2, gz2) = ds[0], ds[1]
+    gl = math.hypot(gx2 - gx1, gz2 - gz1) or 1e-9
+    return (d2 - d1) / gl
+
+LAT = 260.0      # lattice Voronoi cell (u)
+OMEGA = .05      # site drift rate (rad/s), zone time
+KW = .35         # smooth-min width (cell units), her w
+WEB_AT_CYCLE = False   # read the lattice web's drift at the member's cycle start (as the flow)
+WIN = 2          # search window half-size (cells); her reference uses 2
+BOOST = 1.6      # site weight raised near wells by up to this factor
+EW = .10         # border line half-width (cell units)
+def lattice_web(q, t):
+    """The operator's reference node: lattice smooth Voronoi, per-site multiplicative weight on distance, smooth-min
+    blend. Weight = her hashed .5-1, raised near wells so cells shrink there (denser web on the shoulders).
+    Output: 1 on cell borders, falling into the cells, from F1 minus the smooth minimum."""
+    if CUR_T0[0] is not None: t = CUR_T0[0]
+    px, pz = q[0] / LAT, q[1] / LAT; nx, nz = math.floor(px), math.floor(pz); fx, fz = px - nx, pz - nz
+    m = 8.0; f1 = 8.0; f2 = 8.0
+    for j in range(-WIN, WIN + 1):
+        for i in range(-WIN, WIN + 1):
+            cx, cz = nx + i, nz + j
+            ox, oz = H.hash01(cx, cz, 11), H.hash01(cx, cz, 12)
+            wt = ox * .5 + .5
+            sx, sz = (cx + .5) * LAT, (cz + .5) * LAT
+            prox = max(math.exp(-(math.dist((sx, sz), w["pos"]) / (2.2 * .103 * w["r"])) ** 2) for w in H.WELLS)
+            wt *= 1.0 + BOOST * prox
+            ox = .5 + .5 * math.sin(OMEGA * t + 6.2831 * ox); oz = .5 + .5 * math.sin(OMEGA * t + 6.2831 * oz)
+            d = math.hypot(i - fx + ox, j - fz + oz) * wt
+            if d < f1: f1, f2 = d, f1
+            elif d < f2: f2 = d
+            h = smooth(0.0, 1.0, .5 + .5 * (m - d) / KW)
+            m = m + (d - m) * h - h * (1 - h) * KW / (1 + 3 * KW)
+    gap0 = .25 * KW / (1 + 3 * KW)
+    soft = max(0.0, min(1.0, (f1 - m) / gap0))           # her smooth-min gap: 1 on borders, soft falloff
+    return max(soft ** 2, math.exp(-((f2 - f1) / EW) ** 2))   # F2 - F1 border line of width EW (cell units)
+
+# ---------------- candidate krill habitat densities (filament candidates) ----------------
+def env(x, z, t):
+    s = slope(x, z, t); return s, band(s), core(s)
+
+def D_band(x, z, t, sc):
+    s, b, c = env(x, z, t); return b
+
+def D_skein(x, z, t, sc, hard=False):
+    s, b, c = env(x, z, t); q = warp(x, z, t, sc)
+    return strands(q, hard) * (1 - c) * (.55 + .45 * b)
+
+def D_skein_hard(x, z, t, sc): return D_skein(x, z, t, sc, True)
+
+def D_lattice(x, z, t, sc):
+    s, b, c = env(x, z, t); q = warp(x, z, t, sc, WEB_TAU)
+    return lattice_web(q, t) * (1 - c) * envelope(b)
+
+def skein_web(x, z, t, sc):
+    """Strands between wells plus the lattice web hanging off them (web gated by a wide strand halo and the band)."""
+    s, b, c = env(x, z, t); q = warp(x, z, t, sc)
+    st = strands(q); halo = strands(q, widen=4.0)
+    web = lattice_web(warp(x, z, t, sc, WEB_TAU), t) * max(halo, b)
+    return max(st, .8 * web) * (1 - c), s, b, c
+
+def D_skein_web(x, z, t, sc): return skein_web(x, z, t, sc)[0]
+
+def D_slack(x, z, t, sc):
+    s, b, c = env(x, z, t); d = well_slack(x, z); return math.exp(-(d / 70.0) ** 2) * (1 - c)
+
+# ---------------- L1-L3: the trophic DAG over skein_web ----------------
+def glim(x, z, t, sc):
+    """Producers: starlight (sun's light radius) plus heat-light on warm well floors, fed along the skein."""
+    sun = H.WELLS[0]; light = math.exp(-(math.dist((x, z), sun["pos"]) / (300 * 14152 ** .25 * .5)) ** 2)
+    heat = sum(math.exp(-(math.dist((x, z), w["pos"]) / (.16 * w["r"])) ** 2) for w in H.WELLS[1:])
+    F, s, b, c = skein_web(x, z, t, sc)
+    return min(1.0, (.35 * light + .9 * heat) * (.3 + .7 * F) + .35 * F), F, b, c
+
+def holling(p, k=.25): return p * (1 + k) / (p + k)    # Holling II saturation, 0 -> 0, 1 -> 1
+
+def krill(x, z, t, sc):
+    g, F, b, c = glim(x, z, t, sc); return F * holling(g) * (1 - c)
+
+RING = [(math.cos(2 * math.pi * k / 8), math.sin(2 * math.pi * k / 8)) for k in range(8)]
+def stencil(f, x, z, t, sc, r):
+    """Prey density over a hunting radius: the mean of the prey field at the point and 8 taps on a ring of radius r
+    (pointwise: 9 evaluations of the layer below, no grid)."""
+    return (f(x, z, t, sc) + sum(f(x + r * cx, z + r * cz, t, sc) for cx, cz in RING)) / 9.0
+
+def minnows(x, z, t, sc):
+    s, b, c = env(x, z, t); return min(1.0, 1.6 * holling(stencil(krill, x, z, t, sc, 48.0)) * (.4 + .6 * b))
+
+def sharks(x, z, t, sc):
+    s, b, c = env(x, z, t); return min(1.0, 2.0 * stencil(minnows, x, z, t, sc, 160.0) * (.3 + .7 * b))
+
+def lanterns(x, z, t, sc):
+    return D_slack(x, z, t, sc) * min(1.0, 2.5 * stencil(krill, x, z, t, sc, 120.0))
+
+CANDS = {"band": D_band, "skein": D_skein, "skein-hard": D_skein_hard, "lattice": D_lattice,
+         "skein-web": D_skein_web, "slack": D_slack}
+LAYERS = {"L1-glim": lambda x, z, t, sc: glim(x, z, t, sc)[0], "L2-krill": krill, "L2-minnows": minnows,
+          "L3-sharks": sharks, "L3-lanterns": lanterns}
+
+# ---------------- rendering and measurement ----------------
+def grid(f, t, g):
+    set_time(t); sc = H.scroll(t); vals = []
+    for j in range(g):
+        row = []
+        for i in range(g):
+            x = ((i + .5) / g - .5) * 2 * R; z = ((j + .5) / g - .5) * 2 * R
+            row.append(None if x * x + z * z > R * R else f(x, z, t, sc))
+        vals.append(row)
+    return vals
+
+def save(vals, name, g):
+    px = [(0, 0, 0) if v is None else H.ramp(v) for r in vals for v in r]
+    H.mark_bodies(px, g); path = os.path.join(OUT, name + ".png"); H.write_png(path, g, g, px); return path
+
+def phys_corr(vals, g):
+    phys = [c for r in H.physarum_ascii("physarum A") for c in r]
+    bw, bh = g // 64, g // 32; blocks = []
+    for by in range(32):
+        for bx in range(64):
+            cell = [vals[y][x] or 0 for y in range(by * bh, (by + 1) * bh) for x in range(bx * bw, (bx + 1) * bw)]
+            blocks.append(sum(cell) / len(cell))
+    return H.corr(blocks, phys)
+
+def cand_list(C):
+    n = int(R / C); out = []
+    for j in range(-n, n):
+        for i in range(-n, n):
+            x = (i + H.hash01(i, j, 1)) * C; z = (j + H.hash01(i, j, 2)) * C
+            if x * x + z * z <= R * R: out.append((i, j, x, z, .1 + .9 * H.hash01(i, j, 3), H.hash01(i, j, 4)))
+    return out
+
+def cyc_scroll(t, ph):
+    """habitat-no-pop-ruled: the flow term is read at the member's own cycle start."""
+    t0 = t - ((t / CYCLE + ph) % 1.0) * CYCLE; return H.scroll(t0), t0
+
+CUR_T0 = [None]
+def density_at(f, c, t):
+    sc, t0 = cyc_scroll(t, c[5]); CUR_T0[0] = t0 if WEB_AT_CYCLE else None
+    try: return f(c[2], c[3], t, sc), t0
+    finally: CUR_T0[0] = None
+
+def members(f, cands, t, tref=None):
+    set_time(t)
+    if tref is None: return {(c[0], c[1]) for c in cands if density_at(f, c, t)[0] > c[4]}
+    return {(c[0], c[1]) for c in cands if f(c[2], c[3], t, cyc_scroll(tref, c[5])[0]) > c[4]}   # flow frozen at tref's cycle
+
+def presence(d, th): return smooth(th - FADE, th + FADE, d)
+
+def pop_probe(f, cands, t, nmax=2500):
+    set_time(t)
+    near = [c for c in cands if abs(density_at(f, c, t)[0] - c[4]) < .3][:nmax]
+    prev = {}; worst = 0.0; big = 0
+    for k in range(61):
+        tt = t + k / 60.0; set_time(tt)
+        for c in near:
+            d, t0 = density_at(f, c, tt); p = presence(d, c[4]); key = (c[0], c[1])
+            if key in prev and prev[key][1] == t0:          # cycle turns excluded (carried by the cycle fade)
+                step = abs(p - prev[key][0]); worst = max(worst, step); big += step > .1
+            prev[key] = (p, t0)
+    return worst, big, len(near)
+
+def gabriel_flips(T=1400.0, dt=1.0 / 60):
+    """Hard Gabriel edge-set changes, and the soft gate's largest step per 1/60 s, as the wells orbit."""
+    flips = 0; worst = 0.0; prev_h = None; prev_s = None; t = 0.0
+    while t <= T:
+        set_time(t); W = H.WELLS; hs, ss = set(), {}
+        for i in range(len(W)):
+            for j in range(i + 1, len(W)):
+                a, b = W[i]["pos"], W[j]["pos"]; r = math.dist(a, b) / 2; m = ((a[0] + b[0]) / 2, (a[1] + b[1]) / 2)
+                mg = min((math.dist(m, W[k]["pos"]) - r) / r for k in range(len(W)) if k not in (i, j))
+                if mg > 0: hs.add((i, j))
+                ss[(i, j)] = smooth(-.15, .15, mg)
+        if prev_h is not None:
+            flips += len(hs ^ prev_h); worst = max(worst, max(abs(ss[k] - prev_s[k]) for k in ss))
+        prev_h, prev_s = hs, ss; t += dt
+    return flips, worst
+
+def main():
+    t0 = time.time(); T = 0.0
+    print(f"grid {G}, wells orbit (period = distance s), slope terms on, TAU {TAU} s, lattice {LAT} u")
+    f, w = gabriel_flips()
+    print(f"gabriel over 1400 s: hard edge-set changes {f}; soft gate largest step per 1/60 s {w:.5f}")
+    cands = cand_list(16.0); print(f"{len(cands)} krill candidates at 16 u")
+    for name, fn in CANDS.items():
+        if ONLY and name not in ONLY: continue
+        t1 = time.time(); vals = grid(fn, T, G); p = save(vals, "density_" + name, G)
+        cr = phys_corr(vals, G)
+        a = members(fn, cands, T); b = members(fn, cands, T + 1); c8 = members(fn, cands, T + 8); c60 = members(fn, cands, T + 60)
+        n = max(1, len(a))
+        W2 = 600; px = [(10, 14, 30)] * (W2 * W2)
+        for c in cands:
+            if (c[0], c[1]) in a:
+                pi_, pj = int((c[2] / (2 * R) + .5) * W2), int((c[3] / (2 * R) + .5) * W2)
+                if 0 <= pi_ < W2 and 0 <= pj < W2: px[pj * W2 + pi_] = (235, 230, 170)
+        H.mark_bodies(px, W2); H.write_png(os.path.join(OUT, "members_" + name + ".png"), W2, W2, px)
+        a0 = members(fn, cands, T, T); w1 = members(fn, cands, T + 1, T); w60 = members(fn, cands, T + 60, T)
+        print(f"  {name} wells-only (flow frozen at t's cycle): changed in 1 s {len(a0 ^ w1) / max(1, len(a0)):.4f}, 60 s {len(a0 ^ w60) / max(1, len(a0)):.3f}")
+        wst, big, nn = pop_probe(fn, cands, 100.0)
+        print(f"{name}: corr physarumA {cr:.3f}; members {len(a)}; changed in 1 s {len(a ^ b) / n:.3f}, 8 s {len(a ^ c8) / n:.3f}, "
+              f"60 s {len(a ^ c60) / n:.3f}; presence step max {wst:.4f} ({big} steps > .1, {nn} near-threshold candidates); {time.time() - t1:.0f}s")
+    if ONLY is None or "layers" in ONLY:
+        for name, fn in LAYERS.items():
+            g = G if name.startswith(("L1", "L2-krill")) else G // 2
+            t1 = time.time(); vals = grid(fn, T, g); save(vals, "layer_" + name, g)
+            print(f"{name}: grid {g}, corr physarumA {phys_corr(vals, g):.3f}; {time.time() - t1:.0f}s")
+        # members per layer at its own candidate spacing
+        for name, fn, C in (("L2-minnows", minnows, 48.0), ("L3-sharks", sharks, 128.0), ("L3-lanterns", lanterns, 64.0)):
+            cs = cand_list(C); t1 = time.time(); a = members(fn, cs, T); b = members(fn, cs, T + 1); c8 = members(fn, cs, T + 8)
+            n = max(1, len(a)); W2 = 600; px = [(10, 14, 30)] * (W2 * W2)
+            for c in cs:
+                if (c[0], c[1]) in a:
+                    pi_, pj = int((c[2] / (2 * R) + .5) * W2), int((c[3] / (2 * R) + .5) * W2)
+                    for di in range(-1, 2):
+                        for dj in range(-1, 2):
+                            if 0 <= pi_ + di < W2 and 0 <= pj + dj < W2: px[(pj + dj) * W2 + pi_ + di] = (235, 230, 170)
+            H.mark_bodies(px, W2); H.write_png(os.path.join(OUT, "members_" + name + ".png"), W2, W2, px)
+            print(f"members {name}: {len(a)} of {len(cs)} at {C:.0f} u; changed in 1 s {len(a ^ b) / n:.3f}, 8 s {len(a ^ c8) / n:.3f}; {time.time() - t1:.0f}s")
+        # cost per evaluation (Python, relative): one krill vs one minnow vs one shark evaluation
+        set_time(T); sc = H.scroll(T)
+        for name, fn in (("krill", krill), ("minnows", minnows), ("sharks", sharks)):
+            t1 = time.perf_counter(); [fn(300.0 + k, 200.0, T, sc) for k in range(20)]
+            print(f"cost {name}: {(time.perf_counter() - t1) / 20 * 1e3:.2f} ms per evaluation (Python)")
+    print(f"total {time.time() - t0:.0f}s")
+
+if __name__ == "__main__": main()
diff --git a/docs/research/2026-10-14-trophic-dag-probe/win.log b/docs/research/2026-10-14-trophic-dag-probe/win.log
new file mode 100644
index 000000000..c9c905100
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/win.log
@@ -0,0 +1,6 @@
+WIN 2 BOOST 1.6 lattice: presence step max 0.1236, 8 steps > .1 of 1500 candidates
+WIN 2 BOOST 1.6 skein-web: presence step max 0.4933, 8 steps > .1 of 1500 candidates
+WIN 3 BOOST 1.6 lattice: presence step max 0.1236, 8 steps > .1 of 1500 candidates
+WIN 3 BOOST 1.6 skein-web: presence step max 0.4933, 8 steps > .1 of 1500 candidates
+WIN 2 BOOST 0.6 lattice: presence step max 0.0471, 0 steps > .1 of 1500 candidates
+WIN 2 BOOST 0.6 skein-web: presence step max 0.2361, 11 steps > .1 of 1500 candidates
diff --git a/docs/research/2026-10-14-trophic-dag-probe/winprobe.py b/docs/research/2026-10-14-trophic-dag-probe/winprobe.py
new file mode 100644
index 000000000..e836af667
--- /dev/null
+++ b/docs/research/2026-10-14-trophic-dag-probe/winprobe.py
@@ -0,0 +1,8 @@
+import sys; sys.argv=['x','64']
+import trophic_probe as T
+cands=T.cand_list(16.0)
+for win,boost in ((2,1.6),(3,1.6),(2,0.6)):
+    T.WIN, T.BOOST = win, boost
+    for name in ("lattice","skein-web"):
+        w,b,n=T.pop_probe(T.CANDS[name],cands,100.0,1500)
+        print(f"WIN {win} BOOST {boost} {name}: presence step max {w:.4f}, {b} steps > .1 of {n} candidates", flush=True)