# Sundog Promo Highlights This document is for broadcasts, landing pages, pitch decks, interviews, release notes, and short-form public writing. It is intentionally more provocative than the research docs. Use it as a message bank. Do not treat every sentence here as a paper claim. The academic claim remains narrower: photometric mirror alignment without target-position access, tested with matched MuJoCo experiments and baselines. ## Core Hook Sundog turns indirect signals into usable control. Where conventional systems ask for full world state, Sundog asks a stranger question: what if the shadow, the torque, the occlusion, the deformation, or the disturbance already contains enough structure to act? ## Short Positioning Lines - Alignment does not always require direct sight. - A system can learn where to aim by reading what the world does back to it. - Sundog is a theory of useful partial information. - We are building software that treats indirect signal as first-class input. - The future of simulation is not always more fidelity. Sometimes it is better structure. - H(x) is the promise that the halo around a process can be more useful than a direct measurement of the thing itself. - We are not trying to render the whole world. We are trying to find the part of the world that matters. - Sundog compresses certain physical behaviors into forms that agents can use. - The theorem begins where ordinary perception gives up. - The most useful signal is not always the most obvious one. - Twenty structural-zero receipts and one quarantine that explains itself. - Receipt-first, closure-relative. No row-specific knobs. Outcome categories pre-registered. ## One-Paragraph Promo Sundog is a research and product program for transforming indirect observable phenomena into usable software control. In the core experiment, a controller aligns a reflected beam without target-position access, using only sparse photometric feedback and joint state. In product systems, the same idea appears as roguelike agents acting under occluded state, verb-field NPC behavior, graph telemetry that makes softbody motion analyzable frame by frame, and a three-body dynamics workbench where a sensor-limited controller uses only local gravitational field readings to improve survival in a regime where a naive controller fails. The claim is simple and dangerous: some systems do not need to see the target directly. They can align by reading the structure of the disturbance. ## Broadcast-Ready Version Last year, Sundog was a theorem-shaped provocation: alignment may emerge from the relationship between action, projection, and environmental response. This year, it is a working program. The core repo now contains a defensible mirror-alignment experiment: a controller with no Cartesian target access reaches terminal accuracy comparable to a target-aware analytic baseline in the tested MuJoCo setting. EyesOnly extends the idea into procedural agent play under occluded state. Dungeon Gleaner pushes it into verb-field NPC behavior, where unmet needs diffuse across satisfier nodes instead of relying on scripted idle planners. Money Bags brings it into softbody terrain systems, where torsion, torque, center of gravity, deformation, and recovery become graph-readable telemetry. The three-body workbench pushes the pattern into chaotic dynamics: a sensor-limited controller that reads only local gravitational field gradients — not the positions or masses of the primaries — improves survival in a bounded near-escape operating pocket where a naive local baseline fails. The full state is 18-dimensional. The controller uses three. The direction is bigger than any one demo: software systems that do not need perfect state to behave intelligently. Systems that can act from the halo. ## Hooks By Audience ### For Researchers - What if indirect feedback can match direct-state control in constrained alignment tasks? - Sundog reframes alignment as a measurable relationship between action and environmental response. - The interesting result is not magic. It is the trade: less privileged state, slower acquisition, comparable terminal accuracy. - The theorem is broad, but the current paper claim is narrow enough to attack. - v0.3h ran 21 strict G.2 single-curve choreographies through a three-stage audit (sentinel/Gamma, adaptive-floor, bridge-audit) with pre-registered outcome categories and no row-specific knobs. Twenty rows returned structural zeros; one (O_617) was quarantined because its bridge direction sits outside the valid D3 representation. The audit chain is intact; the theorem-facing result is not closed. ### For Game Developers - Sundog is a way to make systems feel reactive without giving them impossible information. - It helps turn cheap approximations into coherent player-facing behavior. - It gives agents a way to act from partial, compressed game state. - It gives physics-heavy prototypes a telemetry language for motion that would otherwise look like noise. ### For Simulation Engineers - More fidelity is not always the winning move. - Sundog asks which projection of a physical process is control-relevant. - If the approximation preserves the actionable structure, the system can be cheaper, more legible, and easier to tune. - The future stack may combine high-fidelity simulation where needed with Sundog-style transforms where full fidelity is waste. ### For AI / Agent Builders - An agent does not always need the full state. It needs the right compressed signal. - Occlusion is not only a limitation. It can be a design surface. - Stop-conditioned action batches are a practical bridge between reactive agents and unstable environments. - Alignment may be less about telling an agent where the target is and more about giving it a world whose responses can be read. #### The Stack-Invariance Argument For the recurring class of question that runs *"how can a prompt-level artifact possibly do alignment-relevant work on a stock inference stack when the agent does not see its own residual stream?"* — this is the sharpest position currently available. Drafted in dialogue with Claude, in response to a Sōtō-Zen-practitioner-and-CS-engineer Reddit mod who pressed for the chatbot-agent translation of the cap-set / unit-distance substrate-rhyme. > If the result generalises across that many lineages with no model > access, something stack-invariant is happening, and the most > parsimonious explanation we have is that the artifact is keeping the > relevant low-dim subspaces aligned in each model's residual stream. The line is doing three jobs at once: 1. It treats the chat experiment's 0-unsafe-accepts-across-5,670-trials number as *evidence for a causal hypothesis*, not as a marketing trophy. The number was published as a falsifier; this is how to speak about it without overclaiming. 2. It names the property the result is actually evidence of — *stack-invariance* — rather than "alignment" in the universal-theorem sense. The chat anchor does not prove alignment is solved. It proves that something the artifact does survives translation across four training lineages, which is a smaller and defensible claim. 3. It hands the explanation to mechanistic-interpretability readers in their own vocabulary — low-dim subspaces in the residual stream — without borrowing the credit. If the line lands with a mech-interp audience, it is because their literature already supports the substrate-shadow framing; we are pointing at their evidence, not inventing ours. Use this line when the audience is technical and skeptical, when a mod or reviewer asks for the chatbot-agent translation, or when a quotable position is needed for a citation rail. It is paired with the substrate-rhyme framing on [`sundog.cc/unit-distance`](https://sundog.cc/unit-distance) and with the chat experiment ledger in [`docs/SUNDOG_V_CHAT.md`](../SUNDOG_V_CHAT.md). Do not use it alone — the 0 / 5,670 number is the empirical anchor that lets the line stand up, and the cap-set / unit-distance overlays are the mathematical existence proofs that make the substrate-shadow operator legible. ## Provocative Statements Use these when the context rewards sharpness. Pair them with evidence if the audience is technical. - Direct perception is overrated. - Full state is a luxury, not a requirement. - The shadow can be a sensor. - The disturbance is the data. - The halo is cheaper than the object. - The system does not need the truth. It needs a transform that preserves the part of truth that matters. - Physics can be compressed without becoming fake. - Some behaviors are expensive only because we insist on simulating the wrong layer. - A good approximation is not a shortcut. It is an argument about what matters. - Occlusion is not failure. It is an interface. - Alignment is not always a coordinate. Sometimes it is a resonance. - We are building systems that can infer from the wake they leave behind. - The future of game AI is not omniscient agents. It is agents that know how little they know. - A beam can be aligned without seeing the target. That should bother people. - The next generation of simulation tools will not just compute physics. They will decide which physical signatures are worth keeping. - The most boring result of the year is also the strongest: structural absence, by construction. - We name our quarantines. We do not absorb them. - The shadow of chaos can be a compass. - Three-body dynamics are hard because no closed-form solution exists. Sundog asks whether you need one. - Full state is 18-dimensional. You need three. - The most chaotic systems still cast shadows before they break. - A tidal sensor in a gravitational field is already enough to tell you something useful. ## Product Highlights ### Sundog Core Highlight: > A sparse photometric controller aligns a reflected beam without direct target > coordinates, matching the terminal accuracy of a target-aware analytic > baseline in the tested MuJoCo setup. Why it matters: - proves the program has a measurable core; - gives researchers a compact artifact to inspect; - shows the trade clearly: less privileged state, more acquisition time; - anchors the broader theorem in a real experiment. ### EyesOnly / Gone Rogue Highlight: > Gone Rogue shows Sundog as procedural control under occlusion: an agent can > act from compressed state, plan in batches, and stop when volatility returns. Why it matters: - moves the idea from lab controller to live game engine; - treats partial information as a design feature; - makes the agent feel reactive without giving it authorial omniscience; - creates a path toward matched-seed agent studies. ### Dungeon Gleaner Highlight: > Dungeon Gleaner shows Sundog as physical compression: glass, reflection, hose > pressure, kinks, spray, splatter, and torch response become coherent gameplay > without full physical simulation. Why it matters: - converts expensive physical motifs into cheap player-readable systems; - treats visual and mechanical coherence as the target, not exhaustive fidelity; - gives the pressure washer a physics signature players can feel; - opens a route to performance claims once benchmarked. ### Money Bags Highlight: > Money Bags shows Sundog as softbody interpretation: rig topology, torsion, > torque, deformation, symmetry, and recovery become telemetry instead of > chaos. Why it matters: - extends the theorem beyond optics; - makes frame-by-frame simulation data inspectable; - gives softbody design a graph vocabulary; - creates a path toward predicting recovery and controllability from motion signatures. ### Three-Body Dynamics Workbench Highlight: > In the tested planar restricted setup, a sensor-limited controller using only > local gravitational field readings improves survival over passive and naive > local baselines in a robust high-velocity near-escape pocket. Full state is > 18-dimensional. The controller reads three. Why it matters: - pushes the Sundog pattern into a classically hard dynamical regime; - demonstrates that indirect dynamical signatures (tidal tensor, local acceleration) can support useful control in three-body dynamics without primary-position or mass access; - maps the operating envelope and failure boundary explicitly: low-velocity and equal-mass cells are known harms, not hidden caveats; - shows the workbench as a living demonstration that claims discipline and honest failure maps are part of the result, not footnotes. ### Pushable Occluder (falsification slate) Highlight: > Pushable Occluder is the program's first deliberate falsification surface: > a pushable block that occludes the beam until moved. A flat photometric > controller is predicted to fail because the indirect signal does not > expose the preparatory push as a usable gradient. The verdict surface is > `BOUNDARY FOUND`, not `BUSTED` — the theorem stands; the method's honest > upper limit is reached. Why it matters: - demonstrates the program is willing to publish a measured negative result, not only positive demos; - clarifies the theorem boundary: indirect signal is not enough when the useful gradient appears only after a preparatory action; - gives the highlights rail its first stamp-interrupting card and earns the rail's broader MythBusters rhythm; - roadmap lives at [`PUSHABLE_OCCLUDER_ROADMAP.md`](../PUSHABLE_OCCLUDER_ROADMAP.md); rail integration in [`HIGHLIGHTS_RAIL_ROADMAP.md`](../site/HIGHLIGHTS_RAIL_ROADMAP.md). ### Isotrophy K_facet (useful negative → audit-chain receipt) Highlight: > A σ₃ isotropy detector reconciled the 21 strict equal-mass three-body > choreographies from the Li–Liao 10,059-orbit catalog, and cleanly split off > 4 relative ones (a 2π/3 global rotation; 25 gauge-invariant vs the > literature's 21), rendered as a doctor's-office bead-maze. That is a > detector and literature-count win, not theorem evidence. The proposed > daughter-count theorem test was then retired at its cheap K1 precheck, when > under v0.2 it reduced to the equivariance-only null (K_facet = 0). Why it matters: - it is the discipline working, not a result: the cheap falsifier ran before the multi-hour sweep, the operator was retired instead of patched, and the boundary is published; - it is explicitly not a proof of Sundog; K_facet = 0 does not mean "no piano-trios exist," and the 4 relatives are outside the strict single-curve convention, not literature errors; - the durable part is the detector / literature reconciliation (21 strict + 4 relative = 25 gauge-invariant), inspectable in the bead-maze render at `public/media/isotrophy-bead-maze.svg` (served at `/media/isotrophy-bead-maze.svg`); - the v0.2 path is closed; v0.3a/b/h are the fresh derivation and pre-registration the discipline asked for. Workbench: [`sundog_v_isotrophy.md`](../isotrophy/sundog_v_isotrophy.md); handoff: `docs/isotrophy/archive/isotrophy_handoff_note.md`. #### v0.3h update — structural-zero receipt + named quarantine Update, 2026-05-22: > K_facet v0.3h ran the 21 strict G.2 single-curve choreographies at m3 = 1 > through a three-stage audit chain (sentinel/Gamma -> adaptive-floor -> > bridge-audit) with pre-registered outcome categories and no row-specific > knobs. **Twenty rows returned `no_bridge_present`**: the standard D3 > sector is structurally absent, so `c_i = d_i = 0` by construction, not by > tolerance or post-hoc pruning. **One row (O_617) was quarantined**, not > failed: it is a clean opposite-strict row, but its bridge direction sits > outside the valid D3 representation (`sigma3^3-I = 3.96e-2` at the > bridge-admitted kernel), not in the audit chain itself. Why it matters: - the audit chain produced **structural-zero receipts** as a named class of Sundog artifact — evidence with the property that the absence is by construction rather than by measurement; - the quarantine of O_617 demonstrates the discipline working as designed: the chain caught its own out-of-scope case, located the representation defect at the bridge boundary, and refused to absorb the anomaly into a clean number; - **the load-bearing claim is "20/21 structural zeros plus one quarantined O_617 defective-D3 bridge," not "a closed 21/21 theorem-facing result."** Promo copy must preserve that distinction; - the receipt-first, closure-relative methodology with adaptive-floor + bridge-audit is a generalizable template — it is the first time the Sundog audit-chain discipline has produced a publishable result on theorem-adjacent mathematics rather than a MuJoCo controller; - writeups: `docs/isotrophy/kfacet/kfacet_v03h_writeup.md` (methodology + result) and `docs/isotrophy/kfacet/kfacet_v03h_o617_deep_dive.md` (the six-probe attribution of the O_617 defect to upstream σ₃ admission). Both are internal pending a public-facing companion that strips implementation detail and preserves the discipline + result + boundary. ### Sundog vs. Yang-Mills (useful negative → audit-chain receipt + reviewer packet) Headline candidate (for the eventual `generality.html` YM card / subpage): > **4 probes, 1 bounded null** — Sundog's small-loop gauge-invariant > shadow did not earn a relative-locality certificate on a registered > SU(2) 3D 12³ × β-slate `{2.0, 2.4, 2.8}` ensemble. The bounded null is > the receipt, and the discipline that produced it is the story. Also slotted in `public/data/high-stakes-generality-gallery.json` ▸ `projects.yang_mills` as `chartHeadline` (terse, 24 chars, status-matrix-card slot) and `pageHeadline` (sentence-length, hero slot for the eventual subpage). Highlight: > Across **four pre-registered probes** — bare small-loop mean/variance > (vocab v1), APE-smeared mean/variance at frozen `(α, N_sm) = (0.5, 10)` > per P0 amendment 1 (vocab v4), bare connected 2-point correlator at a > frozen 5-class displacement slate (vocab v5), and the v1 signature > re-scored against a new per-config spatial-variance held-out target > `σ²_W33` (target vocab v2) — the within-β k-NN bin-purity@5 against > per-β tertile labels landed within ±0.04 of the 0.333 chance baseline. > All four probes failed both registered promotion gates (absolute > bin-purity ≥ 0.5 and margin over `CTRL_RAND` ≥ 0.10). The synthesis > receipt is filed; the lane is paused at a bounded cell-local null; a > lattice-gauge-theorist external review packet is drafted and > owner-pending send. Why it matters: - it is the discipline working, not a result on Yang-Mills: every probe was filed as a dated spec before its runner ran, the smearing parameters were frozen by P0 amendment 1 with an explicit anti-scope-creep clause (no retune after a receipt is filed), and the PAUSE-and-synthesize disposition was pre-stated as the v4 fallback default in the v3 probe spec **before** the v3 run started; - it is explicitly **not** a Clay claim, a mass-gap claim, a confinement proof, or a continuum-limit statement. Public-language boundary in `docs/prereg/yang-mills/P0_DOMAIN_AND_RECEIPT_LOCK.md` §"Public Language Boundary" forbids those phrasings on every output of this lane, including any future `yang-mills.html` card or subpage; - the v1 implementation produced a **receipt-quality methodology save**: an early draft of APE smearing used the heatbath-staple traversal order, breaking gauge invariance after smearing; `CTRL_GAUGE_RAND` fired `YM-P1-NEG-A gauge_leakage` before any rank-locality score could be interpreted, the bug was fixed, and the corrected implementation produced the v1 receipt numerics. The seven-entry leakage controls battery did exactly the work it was designed to do; - the durable artifacts are the four phase-2 receipts, the bounded-null synthesis, and the external-review packet: - synthesis: [`receipts/2026-05-29_SU2_3D_phase2_bounded_null_synthesis.md`](../yang-mills/receipts/2026-05-29_SU2_3D_phase2_bounded_null_synthesis.md); - external review packet: [`docs/yang-mills/EXTERNAL_REVIEW_PACKET.md`](../yang-mills/EXTERNAL_REVIEW_PACKET.md) and email cover-letter draft: [`docs/yang-mills/EXTERNAL_REVIEW_EMAIL_DRAFT.md`](../yang-mills/EXTERNAL_REVIEW_EMAIL_DRAFT.md); - SVG card already regenerated by `npm run generality:public-media` at `public/media/generality-yang-mills.svg` (status chip now reads `REVIEW GATED`, not `DRAFT HANDOFF`); - it is a generalizable template for the rest of the math-ledger lanes (Riemann was the first; Yang-Mills is the second; Navier-Stokes C1 reviewer email is still owner-pending): pre-register every probe, pre-state every fallback, freeze every "amendment-able" parameter at the amendment that admits it, and PAUSE the lane when the registered evidence base is sufficient for a bounded-null conclusion rather than shopping for a positive across signature / target combinations. Promo-copy guardrails (binding on every YM-derived output, mirroring the riemann section's discipline): - the load-bearing claim is **"four pre-registered probes, one bounded cell-local null on the registered SU(2) 3D 12³ × β-slate × 32-configs envelope, lattice-gauge-theorist review packet pending,"** not "we tried Yang-Mills and failed" and not "we have a Yang-Mills result"; - `chartHeadline` and `pageHeadline` in the gallery data are the authoritative short / hero phrasings — promo copy should match or be rewritten only with the same scoping; - the four-receipt matrix in [`yang-mills/EXTERNAL_REVIEW_PACKET.md`](../yang-mills/EXTERNAL_REVIEW_PACKET.md) §"Four-Receipt Summary" is the authoritative numerical surface; promo copy should not invent additional metrics; - the bounded null is the **result**, not a setback. Frame it as "Sundog discipline produced a publishable named null on a hard substrate before any p-hunting could happen," not as "we hit a wall and stopped." #### Pending external-review surface gate Same hygiene rule as Isotrophy K_facet v0.3h: the YM card and any future subpage are admissible only when they carry a clear "external review pending" banner OR "external review returned: " banner once the lattice-gauge-theorist reply is filed. The `generality-yang-mills.svg` REVIEW GATED status chip already encodes this for the gallery; a future `yang-mills.html` page must inherit the same posture in copy. ## Future Bets These are forward-looking statements. They are useful for pitch language, but they should be marked as roadmap or research direction. ### Bet 1: Agents Will Need Less World State Future agents will not always be fed complete world models. They will operate through compressed, uncertain, and partial views. Sundog is positioned for that world because it treats indirect feedback as the primary signal, not a degraded backup. ### Bet 2: Cheap Physics Will Become More Valuable High-fidelity simulation will remain essential, but many product systems do not need truth at every layer. They need coherence, controllability, and legibility. Sundog-style transforms can identify the physical signature worth preserving and discard the rest. ### Bet 3: Game AI Will Move Away From Omniscience The most interesting game agents will not be those that know everything. They will be those that act convincingly from limited knowledge. Occlusion, partial state, and stop-conditioned planning can make agents feel more alive because they are not cheating with perfect information. ### Bet 4: Telemetry Will Become A Design Medium In softbody systems, physics traces are often treated as debugging exhaust. Money Bags points toward a different future: telemetry as a design surface. Torsion, deformation, symmetry, and recovery can become the language designers use to tune feel. ### Bet 5: The Most Interesting Signal Is Often A Derivative The direct object may be expensive or impossible to observe. The change in its projection may be cheaper and more useful. This is the spirit of `H(x)`: look for the relationship between action and environmental response. ## Big Future Claims To Explore These are intentionally bold. They are not yet proven. - Sundog could become a general method for designing agents that act under occlusion. - Sundog-style transforms could reduce the cost of selected simulation effects by preserving only control-relevant signatures. - Softbody systems may become easier to tune when interpreted through graph alignment rather than raw physics state. - Procedural games may feel more authored when their agents know less, not more. - The right indirect signal may outperform a noisy direct measurement. - Future engines may expose "signature layers" alongside physics, rendering, and AI. - The most powerful design move may be choosing what not to simulate. ## The Gravity Claim This is the most outlandish public framing in the program. It is intentionally hard to falsify cheaply, and it points at a horizon experiment that would cost real resources to run. Use the language here only in venues that can also carry the boundary text below. The full staging ledger is [`docs/SUNDOG_V_GRAVITY.md`](../SUNDOG_V_GRAVITY.md). ### The claim, named tightly > Sundog is gravity for agents under partial observability: a geometry-derived > background field that deflects policy without ever being a target. Sister formulations: > Reinforcement learning gave agents a reward to optimize. Sundog gives them a > field to fall through. The first invites Goodhart. The second has no metric > to corrupt. > An agent that reads tidal gradients cannot reward-hack gravity. The mass is > where the mass is. > Optimization made the agent face the target. Sundog makes the target part of > the geometry the agent moves in. ### The Goodhart sidestep Reward optimization places the objective inside the agent — a learned value function, a critic, a numerical target the agent can corrupt. Signature control places the objective inside the environment's geometry. The tidal tensor at a point is a function of the masses, not the agent's policy. You cannot gradient-hack a tidal field. You can only move through it. This is the original unhinged intuition of the Sundog program, restated as a structural argument about threat models rather than a slogan. It is not a proof of adversarial robustness. It is a falsifiable claim that signature-driven control and reward-driven control should behave differently under hostile conditions, with the experiments to test that difference deliberately listed and deliberately expensive. ### The empirical anchor (Phase 5 v4) The Sundog mesa roadmap has now produced a quantitative receipt that the Goodhart-sidestep argument is more than rhetoric. In the shadow-field navigation environment, matched-architecture PPO trained on an L-Mixed objective `R = (1 − λ) · J_signature(s) + λ · R_canonical(s, a)` with a calibrated modest false-basin shaping term (β = 2.0, x_false = (-2.5,-2.5), σ_false = 1.5) exhibits a sharp cliff in basin-internalization protection. The cliff localizes at **λ ≈ 0.952588**, sitting between λ = 0.95 (basin not internalized; competent task performance) and λ = 0.97 (basin internalized; old-basin attractor visible under live x_false interventions at the Phase 4 receipt threshold). The cliff is sharp: the basin-position intervention metric `old_basin_pref` flips from sub-threshold to above-threshold across this 0.02 window without an intermediate regime. Two things to notice. First, the protective threshold is small in absolute terms — 5%, not 50%. Second, the threshold is binary in the measured window: there is no broad middle regime between collapse and protection. ### The mechanical anchor (Phase 6 v1 → v3.8) Phase 6 opened the box, and what's inside has a shape worth naming. The behavioral cliff has a causal locus in the actor's final hidden activation (`net.7`), and the circuit at that locus is **a small handful of generators, irreducibly entangled, only legible as a whole**. Ten rounds of mechanistic probing landed on the same shape from different directions: - **v1.** Layer-level activation patching localizes the cliff causally to `net.7` (the actor's final hidden layer); earlier layers do not. - **v3 (axis-H).** PCA on per-step matched-seed activation diffs at `net.7` compresses the relevant subspace to **5 principal components, capturing 97.4% of the diff variance and reproducing v1's full-layer patch effect.** The "huge dimension" claim shrinks to a small handful. - **v3.1.** Those 5 components are **entangled** — neither PC1 alone nor PCs 2-5 alone reproduce the patch; all five are jointly necessary. There is no offset/mechanism factorization. - **v3.2.** Top-32 neurons by aggregate L2 in the basis (12.5% of `net.7`, 33.6% of L2) deliver **0% of patch effect**. Linear additive top-k restriction destroys the mechanism even when the basis is correct. - **v3.3.** Per-neuron zero-ablation finds **no single critical neuron** (max ablation cost ≤ 0.10 in either direction). The mechanism is genuinely distributed at the single-neuron level. - **v3.4.** **Set-level** substrate-restricted ablation of v3.3's P→C and C→P top-32 critical sets dissociates patch_success functionally: each direction's substrate preferentially disrupts its own direction and slightly *improves* the other (functional opposition, not null). Bootstrap confirms the cross-direction ranking overlap is statistically stable at 0.049 (95% CI [0.016, 0.085]). Single neurons are weak, but *direction-specific neuron substrates* are functionally separable. - **v3.5.** Cross-policy ablation rankings on J1 + J2 inverted the obvious-prediction substrate-identity-generalization story: P→C critical neurons are heterogeneous across held-out pairs (Jaccard 0.255 / 0.067) even though P→C behavior transfers; C→P critical neurons are unexpectedly stable across held-out pairs (Jaccard 0.422 / 0.684) even though C→P behavior doesn't transfer. - **v3.6.** Functional mask-transfer test using the cliff-pair C→P top-32 mask in Axis P on J1/J2 confirms the v3.5 substrate identity is operationally meaningful: J1 dissociation +0.151, J2 +0.508. The C→P substrate is shared at both ranking-identity and functional levels across the controller family. (P→C exploratory mask-transfer from v3.5 was weak/ambiguous; the asymmetry holds.) - **v3.7.** Pair-specific own-mask functional ablation closes the three-layer cross-policy table. J1's own P→C mask dissociates J1's P→C patch by +0.128; J2's own P→C mask dissociates J2's P→C by +0.253. So **basin induction is anatomically real within each policy** — the v3.5 P→C ranking is not noise, it just doesn't transfer across pairs. C→P own-mask sanity-checks also confirm (J1 +0.208, J2 +0.392), though J2's own C→P mask interestingly underperforms the cliff-pair-derived mask transferred to J2 (+0.508), suggesting the cliff pair carries a *cleaner* C→P ranking signal than within-policy ablation does. - **v3.8.** Per-PC decomposition and signed-effect analysis close the crossover-friendly version of the result. P→C is more component-partitioned than C→P (`0.322` vs `0.430` mean off-diagonal PC top-32 Jaccard), while C→P signed structure transfers more strongly across held-out pairs under both thresholds. The stale "PC1 is offset only" line is retired: PC1 has the largest single-PC P→C max mean ablation cost (`0.0148`), but that cost is floor-level and PC1 still cannot reproduce the K=5 patch alone. What's left after those five rounds is a structural claim, not a score-table artifact: > The basin-attractor circuit at the actor's final hidden activation > is a 5-dimensional entangled subspace, read holistically or not at > all. The behavioral cliff at `1 − λ ≈ 0.048` is the threshold at > which that circuit appears in the policy weights; below the > threshold, the training process does not assemble it. **Two complementary structural findings stack with the headline.** *Anatomical separation and functional opposition.* v3.4's substrate- restricted ablation (Axis P) confirms that the basin-inducing and basin-resisting sub-circuits at `net.7` are not just non-overlapping but **functionally opposed**: ablating the P→C critical top-32 neurons drops P→C patch_success by 0.077 *and improves* C→P by 0.097 — a dissociation of 0.174. Ablating the C→P critical top-32 neurons drops C→P by 0.579 *and improves* P→C by 0.083 — a dissociation of 0.662. Each substrate preferentially disrupts its own patch direction; the cross-direction effect is *negative*, not null. v3.4's Jaccard bootstrap (Axis Q) confirms the v3.3 P→C/C→P top-32 overlap is statistically stable at 0.049 (95% CI [0.016, 0.085]) — robust near-disjointness, though the CI still brackets chance-level (0.067) so the stronger "anti-correlated" reading is unearned. The basin-resisting substrate is also **more anatomically tight** within the cliff pair than the basin-inducing one (C→P dissociation 0.662 is ~4× the P→C dissociation 0.174). *The cross-policy generalization story has three layers, not two.* v3.5 ran zero-ablation on two held-out pairs (J1 = L-Sig-Terminal-M vs L-Reward-M, J2 = L-Mixed-M-λ=0.9 vs λ=0.99) and computed Jaccard between cliff-pair critical sets and held-out critical sets; v3.6 followed up by running the cliff-pair C→P top-32 mask through v3.4 Axis P on those same held-out pairs to test functional transfer. Together they distinguish **three layers** of cross-policy generalization that earlier framings collapsed into one: 1. **Subspace-level behavioral transfer:** the cliff-pair 5D PCA basis as a control surface. v3.1 found this transfers strongly on P→C (J1/J2 ≥ 0.94) and weakly on C→P (J1 = 0.16, J2 = 0.63). 2. **Neuron-identity substrate transfer:** Jaccard between cliff- pair top-32 critical neurons and held-out top-32 critical neurons. v3.5 found P→C identity does *not* generalize (Jaccard 0.255 / 0.067 — at chance) while C→P identity generalizes strongly (Jaccard 0.422 / 0.684). 3. **Functional mask transfer:** ablating the cliff-pair top-32 critical set during patching on held-out pairs. v3.5's exploratory P→C mask transfer was ambiguous (J1 dissociation +0.113, J2 +0.096 with noisy cross-drop). v3.6's cliff-pair C→P mask transferred cleanly to both J1 (+0.151 dissociation) and J2 (+0.508 dissociation). The clean updated reading, after the v3.8 closeout: > **Basin induction is family-wide at the 5D subspace/control-surface > level and anatomically grounded within each policy, but the > anatomical substrate identity is pair-specific.** Different policies > route the same direction through different neurons (v3.5 Jaccard > 0.255/0.067 across cliff-pair vs J1/J2); each pair's own P→C > top-32 mask is functionally real within that pair (v3.7 DD1/DD2: > J1 +0.128, J2 +0.253). The cliff-pair P→C mask doesn't transfer > functionally to held-out pairs (v3.5 weak/ambiguous) precisely > because the anatomy is pair-specific even though the geometric > direction is shared. > > **Basin resistance is shared at both substrate identity and > function across Medium policies.** The same neurons are critical > for C→P patching across the controller family (v3.5 Jaccard > 0.422/0.684), and the cliff-pair C→P mask functionally dissociates > basin-resistance in every held-out pair (v3.6 +0.151/+0.508); the > own-pair C→P masks also work (v3.7 DD3 +0.208, DD4 +0.392). The > reason v3.1's behavioral C→P transfer was weak is *not* that the > substrate is policy-specific — it is that the cliff-pair-derived > substitution activation pattern isn't the precise operational > target each policy needs at the shared substrate. The basin-attractor circuit at net.7 thus carries one shared neuron substrate (C→P) and one shared activation-space direction (P→C) through the same 5D subspace, with the two halves generalizing through different mechanisms. v3.8 adds the internal anatomy: P→C is more partitioned across the five PCs and pair-specific at neuron identity, while C→P is more shared across PCs and across Medium held-out pairs. That is the part that crosses cleanly into the geometry program: do not collapse variance, local sensitivity, and full multi-component mechanism into one "importance" score. *The L2-overlap retroactively explains v3.2.* v3.4 also bootstrapped the v3.3-critical / v3.2-L2-rank overlap: the C→P critical set substantially overlaps the L2-rank top-32 (Jaccard 0.333, 95% CI [0.280, 0.391]) while the P→C critical set does not (Jaccard 0.049, CI [0.032, 0.123]). The basin-resisting circuit lives at *high-L2* neurons; the basin-inducing circuit does *not*. v3.2's L2-rank-based top-k restriction was always going to fail more on the basin-inducing direction specifically — a structural reason the v3.2 negative result took the asymmetric shape it did. *The attractor lives in the weights, not in perception.* Clean and basin-position-intervened patch batteries are bit-identical for all logged fields. The learned feed-forward policies do not observe live `x_false` at inference; the cliff policy is computing, not perceiving, its basin. The behavioral receipt from Phase 4 is now mechanistic. **Six methodological lessons stack out of the ten rounds.** Each was earned by a method that failed to surface mechanism on its own or that overturned an obvious prior, and each is a documented reason the obvious-reach toolkit doesn't work here: 1. **Feature-availability rankings are not mechanism rankings.** A sparse-autoencoder feature with |correlation| = 0.89 against the per-episode basin outcome produced zero patch effect (v2). The SAE picked a policy-identifier feature, not a mechanism feature. 2. **Variance is not mechanism, and local sensitivity is not full mechanism.** PC1 carries 38.8% of the diff variance, fails to reproduce the patch alone, and nevertheless has the largest single-PC P→C max mean ablation cost in v3.8. Variance rank, local ablation sensitivity, and full multi-component patch effect are separate observables. 3. **Linear additive top-k restriction destroys mechanism, even with the right basis.** Capturing 33.6% of basis L2 in the top-32 neurons delivers 0% of patch effect (v3.2). Partial delivery of the right basis is not partial mechanism. 4. **Single-neuron ablation does not surface a critical subset.** No neuron has ablation cost above 0.10 in either direction (v3.3). The mechanism is genuinely distributed at the single-neuron level. 5. **Set-level substrate-restricted ablation does surface structure that single-neuron methods missed.** v3.4 found that the direction-specific top-32 ablation-rank sets dissociate patch_success functionally — even though each single neuron in those sets is weak (v3.3), the set as a whole carries direction-specific mechanism. 6. **Subspace behavioral transfer and neuron-identity transfer can point in opposite directions.** v3.5 found that basin-inducing behavior transfers across the controller family while its neuron-identity does not, and basin-resisting shows the opposite pattern. *Behavioral transferability under a basis* and *neuron- identity stability* are independent properties of a circuit, not two views on the same property. Reasoning that conflates them will misread the structure. Together: **for field-shaped circuits, non-linear holistic and set-level methods are mandatory**, and *behavior* and *substrate- identity* must be tracked as separate observables. Linear analysis methods (probes, SAE features, top-k subspace restriction, top-k neuron restriction, single-neuron ablation) all fall short individually; set-level ablation along basis-derived rankings recovers structure but only at one layer at a time; cross-policy transfer reveals that the two layers can carry different family- wide patterns. This is itself a publishable finding about the methodology of mechanistic interpretability under field-shaped objectives. **The same shape, observed in two substrates.** The mesa-trap program's headline shape — *small handful of generators, irreducibly entangled, only legible as a whole* — is structurally the same object the Sundog geometry program independently committed to in its parhelion atlas. The atlas stopped treating arcs as independent features and started treating them as visible portions of a small set of complete implied circles, governed by a small shared parameter set and read holistically. Two independent methods from opposite ends of the program — controllers in-vitro, sky photography in-the-wild — converged on the same shape. The crossover is documented in [`MESA_CROSSOVER_NOTE.md`](../MESA_CROSSOVER_NOTE.md); the gravity claim now has both an in-vitro receipt and an in-the-wild receipt for the field-not-reward framing. **Atlas-side single-handle receipt *(Phase 10 closeout 2026-05-13, re-audited and ratcheted 2026-05-14)*.** The crossover earned an additional atlas-side mechanistic anchor at numerical resolution: the atlas is **forward-rich on the primitive classes the literature parameterizes from `h` alone, and inverse-narrow on a strict 3-photo eligibility set**. Four candidate `signature → h` inversion routes were tested. **Parhelion-offset** survived promotion on the strict 3-photo eligibility set (p2 h = 18.6°, p7 h = 59.4°, p13 h = 6.83° — photos with unambiguous bilateral peaks, valid geometry, and an independently fittable 22° halo). The other three failed at three structurally different **failure modes**: **CZA** on **dataset / aspect-ratio coverage** grounds (only p2 is in-window with an independent residual at +1.3 px after the atlas formula correction; every other anchored photo is past the h = 32.2° disappearance threshold or has the literature CZA apex predicted above the top of the photo); **supralateral** on **atmospheric-physics discrimination** grounds (the h-signal across the route's eligibility window is below visual-edge measurement noise even with perfect coverage); and **tangent-arc curvature** on **detection-protocol tooling** grounds (column-peak detection fails on the post-C1 sampled set with three distinct degeneracy modes; Passes C2 + C4 + C5 + C6 landed 2026-05-14 — a wing-radial Lab b\* ridge detector with 22°-halo-radial-profile subtraction (`scripts/tangent_detector.py`), a wing-slope luminance-gradient curvature detector with circle fit (`scripts/tangent_curvature.py`), and a matched-filter detector against a parameterized arc model on halo-subtracted b\* (`scripts/tangent_matched_filter.py`, the natural follow-up the Pass C5 receipt named) all returned not-recovered on every photo, but manual sample selection from visual crops (`scripts/test_tangent_manual.py`) recovered the route on p2 with R\_uta\_obs / R22 = 0.824 and RMS = 1.23 px. p13 (washed) and p27 (sun-bloom) yield no usable manual anchoring. C6's falsification of the natural-extension matched-filter on the same b\* substrate that C5 found a circular fit on puts the route in C5↔C6 substrate tension — either the gestalt signal C5 picked up is in a different substrate, or C5's tight fit is hand-anchoring symmetry-bias artifact; recommended specialist re-anchoring as the verify gate. Tangent route fails coverage gate at 1 / 3 photos under hybrid coverage + detection-tooling. Remaining candidates: matched-filter on alternative substrates (absolute b\*, L\* magnitude, chromaticity magnitude), polarization filtering, or new calibration photos for coverage expansion, filed as Phase 10 backlog). This is an atlas-side / single-handle receipt, not a new universal proof surface: the shape we observed is the same forward-rich / inverse-narrow asymmetry the mesa side exhibits in-vitro, now at in-the-wild numerical resolution. The closeout retires a soft overclaim that was at risk of slipping into public language: **do not frame the atlas as "multiple independent inverse routes converging."** One handle is promoted (post-hedged); three others fail at three different failure modes, none of which implicates the atlas inversion math. The failure-mode taxonomy itself (dataset, physics, tooling) is the methodological deliverable that travels back to mesa as a classification rule. Provenance: synthetic optical audit + attack campaign + re-audit memo at [`docs/calibration/PHASE10_OPTICAL_REAUDIT_MEMO.md`](../calibration/PHASE10_OPTICAL_REAUDIT_MEMO.md); attack roadmap at [`docs/PHASE10_ATTACK_ROADMAP.md`](../PHASE10_ATTACK_ROADMAP.md); audit-survived public-framing sentence in [`docs/SUNDOG_V_GRAVITY.md`](../SUNDOG_V_GRAVITY.md) forward/inverse asymmetry receipt. This is in-vitro evidence in a 2D continuous-control environment with a synthetic Goodhart-prone shaping surface. It is not a deployment guarantee. It is, however, the cleanest mechanistic anchor the program has produced: the behavioral cliff has a representational explanation, the explanation is shaped like a small handful of generators read holistically, the basin-inducing and basin-resisting sub-circuits are anatomically separable, and the methodology of reaching that explanation is itself documented as a published lesson stack. The full trail is at [`docs/SUNDOG_V_MESA.md`](../SUNDOG_V_MESA.md); result notes at [`PHASE6_RESULTS.md`](../mesa/PHASE6_RESULTS.md) (v1), [`PHASE6_V2_RESULTS.md`](../mesa/PHASE6_V2_RESULTS.md) (v2+v3), [`PHASE6_V31_RESULTS.md`](../mesa/PHASE6_V31_RESULTS.md), [`PHASE6_V32_RESULTS.md`](../mesa/PHASE6_V32_RESULTS.md), [`PHASE6_V33_RESULTS.md`](../mesa/PHASE6_V33_RESULTS.md), [`PHASE6_V38_RESULTS.md`](../mesa/PHASE6_V38_RESULTS.md), [`PHASE7_V3_RESULTS.md`](../mesa/PHASE7_V3_RESULTS.md), and [`PHASE6B_RESULTS.md`](../mesa/PHASE6B_RESULTS.md). ### The envelope (Phase 7 v1) Phase 7 took the same 22-policy zoo behind the empirical and mechanical anchors and ran it through the operating-envelope cross-product: probe slate, intervention battery, selection-pressure curriculum, and the Phase 6 mechanistic annotation, joined into a single classification per cell. The result is a *mapped envelope*, not a triumphalist sweep. Class balance across the 22 cells, from [`docs/mesa/PHASE7_RESULTS.md`](../mesa/PHASE7_RESULTS.md) v1: | class | count | reading | | --- | ---: | --- | | hold | 8 | signature-shaped controller resisted the basin | | collapse | 7 | reward-anchor-class fixed-attractor formed | | fragile | 1 | nominally attached but breached on probe slate | | incompetent | 4 | did not reach competence floor | | ambiguous | 2 | below hold threshold, no fixed-attractor collapse | Of the 20 non-ambiguous cells, 8 are claim-support `hold` cells and 7 are `collapse` cells. The same Phase 5 v4 cliff at `λ ≈ 0.952588` defines the boundary between the two pockets, and Phase 6 v1's `net.7` mechanistic annotation lands exactly on the protected/collapsed pair (`λ = 0.95` / `λ = 0.97`) that defines the boundary. The earned wording — the strongest sentence Phase 7 v1 supports directly: > In the tested shadow-field navigation family at Small and Medium > capacity, terminal-signature and mixed-signature controllers preserve > field attachment across a mapped pocket of selection pressure, with a > sharp Medium breach at `λ ≈ 0.953`. Above that boundary, high-reward > mixed policies collapse into the same fixed-attractor class as > reward-trained controllers; Phase 6 localizes the behavioral cliff to > an entangled 5D subspace at the actor's final hidden layer. This is a *partially holds* outcome — the roadmap's pre-named third result, not the maximalist "gravity-claim earned" or the pessimistic "gravity-claim falsified." The protected pocket is real but bounded. The collapse pocket is also sharp, and the program owns both honestly. The Medium `λ = 0.5` cell sits in the fragile column rather than hold, which prevents overclaiming the Medium mixed curve as uniformly protected; the two ambiguous Small low-`λ` rows do not support the claim and are not promoted. The boundary stays hard: this is an *in-vitro operating-envelope map* in a 2D continuous-control environment with a synthetic Goodhart-prone shaping surface. It is not universal mesa immunity, not foundation-model behavior, not deployed-system robustness. The horizon experiments in [`SUNDOG_V_GRAVITY.md`](../SUNDOG_V_GRAVITY.md) — adversarial signature benchmark, spacecraft trajectory under unmodeled perturbation, the side-channel defense stretch — remain unrun and would each ratchet the envelope further. The earned floor is what the in-vitro result earns, no more. ### The Large extension (Phase 7 v2 -> v3) The Large-tier follow-up changes the public read without turning the mesa result into a universal claim. Phase 7 v2 first mapped a six-policy Large cliff-subset and found a U-shaped profile along the Medium `lambda` spine: weak terminal alignment at `lambda = 0.95` and `lambda = 0.97`, recovery at `lambda = 0.99`, and a pure-reward crater at `lambda = 1.00`. The open caveat was whether `lambda = 0.99` really avoided the old basin or merely collapsed onto a co-pointing attractor. Phase 7 v3 ran the causal intervention battery on those same checkpoints and closes that caveat. The load-bearing update: - `lambda = 0.99` Large is genuine basin-attractor avoidance (`sig_resp_L2 = 0.579`, `bp_obp = 0.459`), not just high terminal alignment. - The U-trough cells (`lambda = 0.95`, `lambda = 0.97`) are **field-coupled, under-budget**: they retain healthy signature response but do not navigate effectively at the tested mixture weight. - The pure-reward endpoint is **bootstrap-collapse**: a degenerate fixed trajectory at the old basin, not harmless undertraining. Public sentence: > At Large, the L-Mixed family remains field-coupled across the measured > `lambda = 0.90` through `0.99` spine, but competence is not monotone: > the trough is field-coupled and under-budget, `lambda = 0.99` recovers > with intervention-confirmed basin-attractor avoidance, and pure reward > collapses into a degenerate old-basin trajectory. Boundary sentence: > This is still a six-cell Large extension, not a full Large envelope: > mostly single-seed cells, one PPO value-coefficient setting, no Large > probe-slate extension yet, Path-B hparams untested, and no clean > Phase-6-style transferable basin-circuit analog. Phase 6b tightens that last boundary. A Large mechanism side-thread tried single-layer cross-policy activation injection between the `lambda = 0.99` recovery cell and the `lambda = 0.97` trough cell. It falsified that protocol: patching was destructive at every MLP layer, so there is no simple Large `net.9` analogue of the Medium `net.7` basin circuit under that test. This does not weaken the v3 labels; it prevents us from selling the Large trough/recovery boundary as a clean copy of the Medium mechanism. ### The three-body wedge The three-body workbench is the audience-conceptualizable entry point because the gravity is literal. A controller reads the tidal tensor of a real gravitational potential and maintains regime in a near-escape pocket without being told w