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+\documentclass[10pt]{article}
+
+\usepackage[margin=1in]{geometry}
+\usepackage{booktabs}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{amsthm}
+\usepackage{graphicx}
+\usepackage{xcolor}
+\usepackage{hyperref}
+\hypersetup{
+  pdftitle={Counterfactual Action Atlas: Learning Local Causal Geometry for Vision-Language-Action Control},
+  pdfauthor={DoVLA-CIL Working Draft},
+  pdfsubject={CIL-Atlas diagnostic draft with measured CTT rollout and utility-energy selector diagnostics},
+}
+
+\title{Counterfactual Action Atlas: Learning Local Causal Geometry for Vision-Language-Action Control}
+\author{DoVLA-CIL Working Draft}
+\date{\today}
+
+\newcommand{\cil}{\textsc{CIL}}
+\newcommand{\atlas}{\textsc{CIL-Atlas}}
+\newcommand{\ctt}{\textsc{CTT}}
+\newcommand{\bench}{\textsc{CILBench}}
+\newcommand{\dovla}{\textsc{DoVLA}}
+\newcommand{\pptc}{\ensuremath{\mathrm{PPTC}}}
+\newcommand{\outcomeptr}{\ensuremath{\mathrm{OutcomePTR}}}
+
+\newtheorem{definition}{Definition}
+\newtheorem{theorem}{Theorem}
+\newtheorem{proposition}{Proposition}
+
+\begin{document}
+\maketitle
+
+\begin{abstract}
+Vision-language-action policies are usually trained from demonstrations that
+show what the robot did, but not what would have happened under nearby actions.
+We introduce the Counterfactual Action Atlas, a same-state interventional
+framework for measuring local do-action geometry and for auditing whether a
+deployment-clean generator actually reaches positive tangent support. A
+\bench{} chart restores the identical state and instruction, executes multiple
+action chunks, and measures which tangents cause recovery, progress, failure,
+collision, or success. The current six-task diagnostic shows why this object
+matters: direct h=16 behavior cloning reaches 29.74\% success,
+deployment-clean residual transport reaches 38.90\%, its top-8 proposal oracle
+reaches 44.35\%, and the hidden same-state no-expert chart reaches 56.99\%.
+This decomposes failure into proposal-support and selector gaps. The current
+\atlas{} implementation evaluates Causal Tangent Transport (\ctt{}), which
+starts from measured train positive tangents and learns
+$T_{\phi}(z_s,z_t,\xi_s^+)\rightarrow \xi_t^+$, transporting a positive
+do-action tangent from a nearby source chart into the current target chart.
+Measured validation and test rollouts confirm the support story but not yet a
+final deployment method: on test charts, the generated proposal oracle reaches
+50.69\% success and \outcomeptr{}@8 reaches 52.78\%, while the selected action
+falls to 22.22\%, exposing an unsolved calibrated-dominance problem. We keep
+the metric boundary explicit: \outcomeptr{} is reported only after generated
+candidates are rolled out, while distance-only support diagnostics are
+\pptc{}. These runs are therefore diagnostic evidence for the Atlas thesis and
+the next selector/generator gate, not an unqualified SOTA claim.
+\end{abstract}
+
+\section{Introduction}
+
+Standard imitation collapses a state into one demonstrated action. For
+manipulation this is the wrong unit of supervision. The same visual state and
+instruction may admit a successful lateral correction, a smooth no-op, a
+collision, a wrong-object move, and a recovery tangent. The missing information
+is not merely more demonstrations or a larger decoder; it is measured
+same-state interventional geometry:
+\[
+  \text{for the same }(s,\ell),\quad
+  \text{which } do(a_i) \text{ causally improves or destroys the outcome?}
+\]
+
+The current diagnostic makes this geometry visible. Clean residual transport
+improves success by 9.16 points over the direct h=16 policy. However, the
+proposal oracle inside the clean top-8 prefix is only 5.45 points above the
+deployed selector, while the gap from that proposal oracle to the hidden
+same-state no-expert chart is 12.64 points. The bottleneck is therefore support:
+the method must generate actions that lie on positive causal tangent support,
+not merely rescore a fixed candidate set.
+
+This draft follows one spine. \atlas{} turns robot action learning from one
+demonstrated action per state into local causal action geometry: for the same
+visual state and instruction, what action tangents actually cause recovery,
+progress, failure, collision, or success? \bench{} defines the chart primitive.
+Causal Action Regret decomposes deployment failure into proposal support and
+selector terms. \ctt{} is the current transport generator inside the Atlas: it
+transports measured train positive tangents into target charts. Baselines such
+as residual retrieval, generic CVAE/flow generation, and Gaussian field search
+are kept as diagnostics for why noise-initialized or off-manifold proposal
+search is insufficient.
+
+\paragraph{Contributions.}
+\begin{itemize}
+  \item We define \bench{}, a same-state interventional chart format for VLA
+  manipulation, with train-only outcome visibility and evaluator-only
+  validation/test outcomes.
+  \item We implement canonical metrics that separate measured outcomes from
+  geometry proxies: BranchCAR, \outcomeptr{}@K, SelectorRegret@K,
+  SupportGap, \pptc{}@K, NegativeNear, and proxy support distance.
+  \item We introduce \atlas{}, an object-centric representation hypothesis for
+  local causal action geometry. The current implementation is \ctt{}, a
+  transport operator
+  $T_{\phi}(z_s,z_t,\xi_s^+)\rightarrow\xi_t^+$ that starts from measured
+  positive source tangents rather than ambient noise.
+  \item We provide leakage-audited chart exports, data accounting, local
+  positive-memory baselines, residual/gated \ctt{} proxy comparisons, and
+  measured validation/test generated-candidate rollouts. We report them
+  honestly as geometry and gate evidence, not as final deployment success.
+\end{itemize}
+
+\section{Related Work}
+
+\paragraph{VLA policies and fine-tuning.}
+OpenVLA demonstrates that open VLA backbones can be fine-tuned for generalist
+manipulation from large robot datasets~\cite{kim2024openvla}. OpenVLA-OFT
+shows that parallel decoding, action chunking, continuous actions, and simple
+regression objectives substantially improve fine-tuning efficiency and LIBERO
+performance~\cite{kim2025openvlaoft}. These methods improve the base policy
+that produces $a_b$ in our framework. They do not by themselves provide
+same-state alternatives or measured do-action contrasts.
+
+\paragraph{Test-time sampling, verification, and abstention.}
+RoboMonkey scales VLA inference by sampling candidate actions and selecting
+with a VLM-based verifier~\cite{kwok2025robomonkey}. VeriSpace adds 3D-aware
+scene encoding and spatially grounded action reasoning for verifier-based
+selection~\cite{zhao2026verispace}. BOKBO highlights a safety failure of
+best-of-$K$: when all candidates are bad, the verifier-best action can still be
+unsafe, motivating calibrated abstention~\cite{singh2026bokbo}. \ctt{} is
+orthogonal: it targets proposal support by transporting measured positive
+tangents before scoring or abstention.
+
+\paragraph{Counterfactual robot data and benchmarks.}
+CAST uses counterfactual language/action labels to improve instruction
+following without new intervention rollouts~\cite{glossop2025cast}. In
+contrast, \bench{} measures $Y\mid do(a),s,\ell$ through same-state action
+execution. ManiSkill3 supplies GPU-parallel simulation and rendering for
+scalable manipulation experiments~\cite{tao2024maniskill3}; VLABench stresses
+long-horizon language-conditioned manipulation~\cite{zhang2024vlabench};
+RoboTwin~2.0 targets scalable bimanual data generation~\cite{chen2025robotwin2};
+and LIBERO studies lifelong transfer across language-conditioned manipulation
+suites~\cite{liu2023libero}. These benchmarks motivate broader evaluation once
+the current CTT support gate is passed.
+
+\section{CILBench}
+
+\subsection{Same-State Charts}
+
+A \bench{} group is a local chart
+\[
+  C(s,\ell)=\{(o,\ell,a_i,y_i)\}_{i=1}^{K},
+\]
+where every branch executes $do(a_i)$ from the same restored simulator state
+$s$, observation $o$, and instruction $\ell$. Because the state is fixed, a
+within-chart difference
+\[
+  Y(a_i)-Y(a_j)
+\]
+is a same-state causal contrast between interventions $do(a_i)$ and $do(a_j)$.
+This is not subjective preference data. It is measured intervention data for
+robot action chunks.
+
+Each branch stores an action chunk, branch family, rollout trace reference, and
+outcome vector
+\[
+  y_i=[s_i,p_i,c_i,v_i,q_i,e_i,r_i],
+\]
+for terminal success, dense progress, contact quality, safety violation,
+task-stage quality, smoothness, and recovery. A scalar utility $U(y_i)$ is used
+for ranking and CAR, while reports should keep the components visible.
+
+\subsection{Splits and Leakage Contract}
+
+The train split is the only split allowed to expose outcomes to retrieval,
+generation, and utility training. Validation and test chart DBs are
+evaluator-only: their outcomes may be loaded by metric scripts, but their
+indexes are not retrieval indexes and must not be loaded by deployment-time
+proposal or selection code. This is the contract required for a
+deployment-clean method: no same-state validation rewards at inference, no
+expert proposals, and no hidden simulator state at selection time.
+When calibration rollouts target train charts, retrieval must also exclude any
+source chart with the same chart id or restored-state hash as the target; this
+prevents a train-only calibration set from copying the exact target positive
+tangents it is supposed to evaluate.
+
+\begin{table}[t]
+\centering
+\caption{Scripted chart data accounting. Counts are generated by
+\texttt{scripts/build\_data\_accounting.py}. Train rows expose outcomes for
+training; validation/test rows expose outcomes only to evaluator scripts.}
+\label{tab:data-accounting}
+\scriptsize
+\input{../runs/data_accounting/table}
+\end{table}
+
+The current leakage audit over \texttt{data/cil\_charts/\{train,val,test\}}
+passes with zero violations. The train index contains 2,044 charts and 32,704
+rows; the complete split export contains 2,873 charts and 45,968 rows.
+
+\section{Metrics}
+
+For one chart, let $a_b$ be the base action and let $U(\cdot)$ be measured
+utility when outcomes are available. Branch Causal Action Regret is
+\[
+  \mathrm{BranchCAR}=U(a^*_{\mathcal A})-U(a_m),
+  \qquad
+  a^*_{\mathcal A}=\arg\max_{a\in\mathcal A} U(a).
+\]
+
+\paragraph{Measured proposal metrics.}
+Generated candidates may be called successful only after they are rolled out or
+otherwise evaluated by the benchmark. Outcome-positive proposal recall is
+\[
+  \outcomeptr@K=
+  \mathbb{1}\left[\exists \hat a_k\in P_K:
+  U(\hat a_k)>U(a_b)+\epsilon\right].
+\]
+Selector Regret inside the measured proposal prefix is
+\[
+  \mathrm{SelectorRegret@K}
+  =U(a^*_{P_K})-U(a_{\mathrm{selected}}).
+\]
+Support Gap is
+\[
+  \mathrm{SupportGap}
+  =U(a^*_{\mathrm{hidden\ chart}})-U(a^*_{P_K}).
+\]
+These metrics are invalid for distance-only candidates.
+
+\paragraph{Proxy geometry metrics.}
+When generated candidates have not been rolled out, this draft reports support
+geometry as \pptc{}:
+\[
+  \pptc@K(\tau)=
+  \mathbb{1}\left[
+  \min_{\hat\xi_k\in P_K,\xi^+\in \Xi^+}
+  d_{\mathrm{RMS}}(\hat\xi_k,\xi^+) \le \tau
+  \right].
+\]
+NegativeNear@K reports the fraction of generated tangents within threshold of a
+measured negative tangent. PosCloserThanNeg and proxy support distance summarize
+whether the generated set lies nearer to positive support than to negative
+support. These are geometry diagnostics, not outcome success.
+
+\section{Counterfactual Action Atlas}
+
+\atlas{} is the local causal geometry learned from same-state charts. Its
+deployment object is not a single action label, but a field over candidate
+tangents: which nearby action corrections are positive, negative, recoverable,
+unsafe, or unsupported for the current observation and instruction. The current
+implemented generator is \ctt{}, a positive-tangent transport method. It does
+not start from Gaussian noise and then optimize a learned field off-manifold.
+It starts from measured train positives:
+\[
+  \Delta U_i = U(a_i)-U(a_b),\qquad
+  \xi_i^+=\psi(a_i-a_b)\quad \text{if } \Delta U_i>\epsilon .
+\]
+For a source chart token $z_s$, target chart token $z_t$, and measured source
+positive tangent $\xi_s^+$, the model predicts
+\[
+  \hat\xi_t^+=T_{\phi}(z_s,z_t,\xi_s^+).
+\]
+The implemented residual and gated residual \ctt{} variants are
+\[
+  \hat\xi_t = \xi_s^+ + \Delta_{\phi}(z_s,z_t,\xi_s^+),
+\]
+\[
+  \hat\xi_t =
+  g_{\phi}(z_s,z_t,\xi_s^+)\odot\xi_s^+
+  +(1-g_{\phi}(z_s,z_t,\xi_s^+))\odot
+  \Delta_{\phi}(z_s,z_t,\xi_s^+).
+\]
+
+\paragraph{Training loss.}
+The current implementation trains on outcome-visible train charts. For each
+nearby same-task source-target pair, it minimizes one-sided positive alignment,
+a negative boundary penalty, and a cycle consistency term:
+\[
+  \mathcal L =
+  \lambda_+\min_{\xi_t^+\in\Xi_t^+}\|\hat\xi_t-\xi_t^+\|_2^2
+  + \lambda_-\max(0,m-d(\hat\xi_t,\Xi_t^-))
+  + \lambda_c\|T_{\phi}(z_t,z_s,\hat\xi_t)-\xi_s^+\|_2^2.
+\]
+The first implementation uses exported base-action summaries as chart features.
+This is an engineering limitation, not the intended Atlas representation. The
+next chart export should include visual-language tokens, target/distractor
+object tokens, robot/contact-region tokens, and object-centric tangent frames.
+
+\paragraph{Deployment plan.}
+At test time, \atlas{} should sample or retrieve positive tangents, decode them
+into candidate action chunks, score their causal utility, and execute only if a
+calibrated lower confidence bound says the best tangent dominates the base
+action. The current \ctt{} implementation retrieves nearby train positive source
+tangents, transports them into the current chart, and decodes the public 21D
+tangent summary as three residual keyframes with linear interpolation into an
+action chunk. This is an auditable engineering decoder, not a lossless
+reconstruction of the hidden branch action.
+
+\input{../paper/sections/theory}
+
+\section{Current Evidence}
+
+We evaluate six ManiSkill manipulation diagnostics with clean rows that do not
+use same-state validation proposals, same-state validation rewards, or expert
+proposals at deployment. Same-state rows are diagnostic oracles that reveal
+local chart geometry.
+
+\input{tables/main_results}
+\input{tables/car_decomposition}
+
+Table~\ref{tab:car-decomposition} is the central diagnostic. It says that the
+current residual baseline learns a useful local utility field, but the larger
+remaining bottleneck is proposal support.
+
+\subsection{Baselines and Failure Modes}
+
+\input{tables/source_score_sweep}
+\input{tables/selector_calibration}
+
+Residual transport V0, utility-weighted residual retrieval V1, negative-margin
+reranking, barycentric chart synthesis, CVAE generators, and flow generators are
+diagnostic baselines. V1 does not beat V0. Negative-margin reranking does not
+replace local positive support. Raw-action CVAE and spline flow variants can be
+safe under NegativeNear, but collapse strict positive support. These failures
+motivate \ctt{}: positive support should be transported from measured positive
+chart tangents, with negative tangents defining boundaries, rather than sampled
+from ambient noise.
+
+Previous distance-only memory and local-atlas diagnostics must be read as
+\pptc{}, not \outcomeptr{}. The train-only positive memory reaches 11.83\%
+\pptc{}@16 at threshold 0.20 and 41.94\% at threshold 0.40. Local-atlas
+retrieval reaches 23.66\% \pptc{}@16 at threshold 0.20 and 52.69\% at threshold
+0.40, with 5.33\% NegativeNear at threshold 0.20. These numbers support the
+local organization of positive tangents, but they are not measured rollout
+success.
+
+\subsection{CTT Smoke Artifact}
+
+\begin{table}[t]
+\centering
+\caption{First residual \ctt{} proxy smoke on train self-target charts. This
+table is an artifact check, not validation/test performance and not
+\outcomeptr{}. The 0.20 NegativeNear value exceeds the current safety gate, so
+the run should not be claimed as method success.}
+\label{tab:ctt-smoke}
+\scriptsize
+\input{../runs/ctt_residual_smoke_proxy/table}
+\end{table}
+
+The first residual \ctt{} smoke trains on 16 train charts and evaluates
+train self-target proxy geometry. It reaches perfect \pptc{} in this small
+self-target setting, but NegativeNear@16 at threshold 0.20 is 10.10\%, above
+the local-atlas reference of 5.33\% by more than one point. Therefore the gate
+for rollout is not passed. The correct conclusion is that the code path and
+artifact contract now exist; the method still needs a safer validation-scale
+transport run before any outcome claim.
+
+A gated residual smoke run is safer in this same tiny setting
+(50.00\% \pptc{}@16 at threshold 0.20 and 5.73\% NegativeNear@16 at threshold
+0.20), but it is still train self-target proxy evidence. It is a candidate for
+the next validation-scale proxy sweep, not a paper result.
+
+\subsection{Validation Proxy Gate}
+
+\begin{table}[t]
+\centering
+\caption{Validation proxy comparison on 69 validation charts with measured
+positive tangents, using train-only source positives. The gate column is
+proxy-only: it requires no more than one point higher NegativeNear@0.20 than
+local-atlas and improvement on \pptc{}@0.20, \pptc{}@0.40, or mean positive
+distance. Passing this gate permits rollout evaluation; it is not
+\outcomeptr{} or measured success.}
+\label{tab:ctt-val-proxy}
+\scriptsize
+\resizebox{\linewidth}{!}{\input{../runs/ctt_val_proxy_comparison/table}}
+\end{table}
+
+Table~\ref{tab:ctt-val-proxy} is the first three-seed validation support-geometry
+artifact. Residual \ctt{} lowers mean positive distance relative to local-atlas
+and keeps NegativeNear@0.20 within the one-point safety slack, but it does not
+beat local-atlas on \pptc{} coverage. Gated residual \ctt{} lowers mean positive
+distance further, but the three-seed NegativeNear@0.20 average exceeds the
+safety slack, so it fails the proxy gate. The honest interpretation is that
+residual \ctt{} is eligible for measured rollout, while the support/safety
+tradeoff remains unresolved.
+
+A one-seed base-context diagnostic appends deployment-visible task and
+instruction hashes to the base-action chart token. It reaches 62.32\%
+\pptc{}@0.40 and 1.82\% NegativeNear@0.20 on the same 69 validation charts, but
+still trails the local-atlas \pptc{} rates. A follow-up non-destructive
+RGB-reference export, \texttt{data/cil\_charts\_rgb\_refs}, passes leakage audit
+and exposes 32D deterministic RGB-stat observation embeddings in every split.
+Across three seeds, the corresponding \texttt{base\_context\_obs} row reaches
+24.64\% \pptc{}@0.20, 64.25\% \pptc{}@0.40, 3.43\% NegativeNear@0.20, and mean
+positive distance 0.4347. This is the strongest current \ctt{} proxy row on
+support geometry while staying inside the local-atlas safety slack, but it
+remains proxy-only and still does not beat local-atlas \pptc{}. We therefore
+treat it as rollout-eligible representation evidence, not as a
+visual-language/object-centric or measured outcome claim.
+
+\subsection{Measured Rollout Harness}
+
+The first measured \ctt{} rollout artifact now exists:
+\texttt{scripts/eval\_ctt\_generated\_rollout.py} generates train-positive
+transport candidates, decodes them into action chunks, restores the validation
+state, executes base plus generated candidates in ManiSkill, and writes measured
+rows consumable by \texttt{scripts/eval\_metrics.py}. On CPU backends it falls
+back to sequential same-state restores because ManiSkill does not allow
+multi-environment CPU vectorization.
+
+A one-chart smoke run at K=2 verifies the measured path and restore accuracy
+(\texttt{runs/ctt\_residual\_rollout\_direct\_smoke\_seed0\_v3}), but it does
+not support a method-success claim: \outcomeptr{}@2 is 0.0000 and the generated
+candidates underperform the measured base action on that chart. This negative
+smoke is useful because it protects the paper from reclassifying \pptc{} proxy
+evidence as outcome success.
+
+\begin{table}[t]
+\centering
+\caption{Measured residual \ctt{} rollout on 69 validation positive-support
+charts across three train seeds, K=8. Generated candidates are decoded and
+executed from restored simulator states; these are measured outcome metrics,
+not \pptc{} proxies.}
+\label{tab:ctt-val-rollout}
+\scriptsize
+\resizebox{\linewidth}{!}{\input{../runs/ctt_val_rollout_comparison/table}}
+\end{table}
+
+Table~\ref{tab:ctt-val-rollout} is the first non-proxy \ctt{} validation
+evidence. Across 207 measured rows, \outcomeptr{}@8 is 0.4589 with a 95\%
+bootstrap interval of [0.3913, 0.5314]. This shows that transported positive
+tangents often find actions that beat the base action. At the same time,
+selected success is only 24.15\%, below the measured base success of 28.50\%.
+The proposal oracle is 37.68\%, the hidden same-state chart oracle is 66.67\%,
+the success support gap is 29.47 points, and the success selector gap is 13.53
+points. The validation result supports the paper's support-gap story more than
+it supports an unqualified deployment claim.
+
+\begin{table}[t]
+\centering
+\caption{Measured validation rollout for the proxy-positive
+\texttt{base\_context\_obs} visual-stat chart token, across three train seeds,
+K=8. The RGB-stat chart token improves support-side validation metrics, but the
+selected action still fails to beat the base action.}
+\label{tab:ctt-base-context-obs-val-rollout}
+\scriptsize
+\resizebox{\linewidth}{!}{\input{../runs/ctt_base_context_obs_val_rollout_comparison/table}}
+\end{table}
+
+Table~\ref{tab:ctt-base-context-obs-val-rollout} tests whether the proxy
+improvement from \texttt{base\_context\_obs} survives measured rollout. It does
+improve support-side validation metrics over Table~\ref{tab:ctt-val-rollout}:
+\outcomeptr{}@8 rises from 45.89\% to 50.24\%, proposal-oracle success rises
+from 37.68\% to 40.58\%, and the success support gap falls from 29.47 to 27.54
+points. The selector failure remains: selected success is 24.15\%, below the
+27.54\% base success, and the success selector gap grows to 16.43 points. Thus
+deterministic visual statistics help proposal support, but they do not solve
+deployment-clean action selection.
+
+\begin{table}[t]
+\centering
+\caption{Measured residual \ctt{} rollout on 48 test positive-support charts
+across three train seeds, K=8. The generated proposal oracle crosses the
+internal 50\% support target, but the selected action fails because the current
+score/dominance rule chooses poor candidates.}
+\label{tab:ctt-test-rollout}
+\scriptsize
+\resizebox{\linewidth}{!}{\input{../runs/ctt_test_rollout_comparison/table}}
+\end{table}
+
+Table~\ref{tab:ctt-test-rollout} gives the current clean test gate. Across 144
+measured rows, \outcomeptr{}@8 is 52.78\% with a 95\% bootstrap interval of
+[44.44, 60.42], proposal-oracle success is 50.69\%, and hidden chart oracle
+success is 72.92\%. This is the strongest evidence so far that learned
+positive-tangent transport can improve proposal support. However, selected
+success is 22.22\%, below the measured base success of 28.47\%, and the success
+selector gap is 28.47 points. The immediate next method step is therefore not
+another proxy generator claim; it is calibrated causal dominance and utility
+selection that refuse to execute generated actions unless they confidently
+dominate the base.
+
+\begin{table}[t]
+\centering
+\caption{Measured test rollout for the \texttt{base\_context\_obs} visual-stat
+chart token, across three train seeds, K=8. Support and score-only selection
+improve relative to the base-action chart token, but selected success remains
+below base.}
+\label{tab:ctt-base-context-obs-test-rollout}
+\scriptsize
+\resizebox{\linewidth}{!}{\input{../runs/ctt_base_context_obs_test_rollout_comparison/table}}
+\end{table}
+
+Table~\ref{tab:ctt-base-context-obs-test-rollout} shows the held-out effect of
+the leakage-audited RGB-stat token. It raises \outcomeptr{}@8 from 52.78\% to
+53.47\%, proposal-oracle success from 50.69\% to 51.39\%, and score-only
+selected success from 22.22\% to 27.08\%. The selected action is still below
+the measured base success of 29.17\%, so this remains support evidence plus a
+selector diagnostic rather than a deployment claim.
+
+\begin{table}[t]
+\centering
+\caption{Validation-calibrated dominance fallback evaluated on the measured
+test rollout. The threshold and conformal residual quantile are fit on
+validation rows only; test outcomes are used only for reporting. The fallback
+reduces coverage but does not yet repair selector transfer.}
+\label{tab:ctt-dominance}
+\scriptsize
+\resizebox{\linewidth}{!}{\input{../runs/ctt_dominance_val_to_test/table}}
+\end{table}
+
+Table~\ref{tab:ctt-dominance} tests the decision rule requested by the method:
+execute a generated tangent only when a calibrated lower confidence bound on
+$F(a)-F(a_b)$ exceeds a threshold. On validation, the auto threshold improves
+selected success from 24.15\% to 30.92\% at 39.61\% coverage. On test, however,
+the same calibrated rule reaches only 25.00\% selected success at 39.58\%
+coverage, still below the 28.47\% base success. A stricter fixed $\tau=0$
+variant falls back 87.50\% of the time and reaches 27.78\%, nearly the base
+rate but still not an improvement. This makes the next failure mode precise:
+the proposal set contains useful actions, but the current utility-energy margin
+does not transfer as a reliable dominance certificate.
+
+\begin{table}[t]
+\centering
+\caption{Learned dominance fallback trained on validation measured rows and
+evaluated on held-out test rows. Features are deployment-visible candidate
+features: utility-energy scores, score margins to base, rank, and tangent
+norms. This improves over the base test success but remains far below the
+paper gate.}
+\label{tab:ctt-learned-dominance}
+\scriptsize
+\resizebox{\linewidth}{!}{\input{../runs/ctt_learned_dominance_val_to_test/table}}
+\end{table}
+
+Table~\ref{tab:ctt-learned-dominance} asks whether a small learned calibrator
+can repair the selector without new rollouts. A ridge dominance model trained
+only on validation measured rows reaches 30.56\% held-out test selected success
+at 24.31\% coverage, improving over the 28.47\% base policy and the 22.22\%
+score-only selector. This is a real selector improvement, but it is still far
+from the 47--50\% target and leaves a 25.69-point success selector gap. The
+evidence therefore narrows the bottleneck: transported proposals contain useful
+actions, and lightweight dominance helps, but the final method needs a stronger
+train-only utility-energy model and richer visual/object-centric chart tokens.
+Additional validation-selected ridge variants that fit success, success-weighted
+utility margin, or the transported 21D tangent code are logged as diagnostics;
+their held-out test selected success ranges from 29.17\% to 29.86\%, so they do
+not replace the best learned-dominance row. Deployment-visible context features
+based on task id, instruction hashes, source task id, and same-task flags also
+reach only 29.17\% held-out selected success. Full train-only utility-energy
+checkpoints are negative across three seeds: when
+\texttt{eval\_dominance\_selector.py} recomputes candidate scores from
+\texttt{runs/utility\_energy\_full\_seed\{0,1,2\}}, held-out selected success is
+27.08\%, 28.47\%, and 23.61\%, below the learned ridge selector.
+
+\begin{table}[t]
+\centering
+\caption{Best validation-calibrated dominance diagnostic so far: learned
+context dominance over the measured \texttt{base\_context\_obs} visual-stat
+rollout rows. The calibrator is fit on validation measured rows only and
+evaluated on held-out test rows.}
+\label{tab:ctt-base-context-obs-learned-dominance}
+\scriptsize
+\resizebox{\linewidth}{!}{\input{../runs/ctt_base_context_obs_learned_dominance_context_val_to_test/table}}
+\end{table}
+
+Table~\ref{tab:ctt-base-context-obs-learned-dominance} combines the visual-stat
+proposal set with validation-calibrated context dominance. It reaches 32.64\%
+held-out selected success at 50.69\% coverage, improving over the RGB-stat
+score-only selector, the measured base action, and the previous learned
+dominance row. The gain is real but not sufficient: proposal-oracle success is
+51.39\%, hidden chart oracle success is 72.92\%, and the success selector gap
+remains 24.31 points. The remaining problem is still reliable deployment-clean
+dominance, not merely generating more nearby tangents.
+
+The feature-source audits turn this negative result into a concrete engineering
+target. In the original \texttt{data/cil\_charts} indexes, scene ids and
+instructions are present, but observation embeddings and raw observation
+references are absent. The new \texttt{data/cil\_charts\_rgb\_refs} export adds
+leakage-audited observation refs and deterministic RGB-stat embeddings, and
+the three-seed \texttt{base\_context\_obs} proxy and measured rollout rows
+improve support and learned selected success. Therefore the current \ctt{}
+chart encoder has a useful visual-stat diagnostic path, but it is still missing
+the learned visual-language or object-centric geometry needed to close
+SupportGap and SelectorGap.
+
+\section{Reproducibility Artifacts}
+
+The current draft is backed by explicit artifacts:
+\begin{itemize}
+  \item \texttt{cil/metrics.py} and \texttt{scripts/eval\_metrics.py} enforce
+  the measured/proxy metric split.
+  \item \texttt{scripts/export\_cil\_charts.py},
+  \texttt{scripts/build\_data\_accounting.py}, and
+  \texttt{scripts/audit\_cil\_charts.py} produce split indexes, accounting, and
+  leakage reports.
+  \item \texttt{cil/models/ctt.py}, \texttt{scripts/train\_ctt.py}, and
+  \texttt{scripts/eval\_ctt\_proxy.py} implement the first transport path.
+  \item \texttt{cil/chart\_features.py} centralizes deployment-visible chart
+  feature construction, and
+  \texttt{scripts/audit\_chart\_feature\_sources.py} audits whether chart
+  indexes expose observation embeddings or raw observation references.
+  \item \texttt{scripts/slurm/render\_six\_task\_chart\_observations.sbatch}
+  and \texttt{scripts/slurm/reexport\_rgb\_ref\_cil\_charts.sbatch} produce the
+  non-destructive RGB-reference chart export used for visual-stat diagnostics.
+  \item \texttt{scripts/export\_chart\_observation\_embeddings.py} creates the
+  deterministic 32D RGB-stat observation embeddings, and
+  \texttt{scripts/slurm/train\_ctt\_feature\_proxy.sbatch} runs feature-mode
+  CTT proxy sweeps such as \texttt{base\_context\_obs}.
+  \item \texttt{scripts/eval\_ctt\_generated\_rollout.py} and
+  \texttt{scripts/slurm/eval\_ctt\_generated\_rollout.sbatch} implement the
+  measured generated-candidate rollout path, including a self-source exclusion
+  flag for train-split calibration and metadata loading for deployment-visible
+  chart features such as \texttt{base\_context\_obs}.
+  \item \texttt{scripts/build\_ctt\_rollout\_comparison.py} aggregates
+  measured validation/test rollouts and reports selected success, proposal
+  oracle success, hidden chart oracle success, success support gap, and success
+  selector gap.
+  \item \texttt{scripts/eval\_dominance\_selector.py} calibrates a dominance
+  fallback rule on validation measured rows and evaluates it on held-out test
+  measured rows; it can use rollout row scores or recompute scores from a
+  train-only utility-energy checkpoint.
+  \item \texttt{scripts/eval\_learned\_dominance\_selector.py} trains a small
+  validation-calibrated dominance model over deployment-visible candidate
+  features and evaluates it on held-out measured test rows; it also logs
+  feature/target ablations, including context metadata and tangent-code
+  variants, for selector diagnostics.
+  \item \texttt{scripts/eval\_chart\_positive\_memory\_proxy.py} and
+  \texttt{scripts/build\_ctt\_proxy\_comparison.py} generate the local-atlas
+  baseline and validation proxy gate table.
+  \item \texttt{scripts/check\_tangent\_reconstruction.py} verifies that the
+  exported 21D tangent codes are deterministic summaries of \texttt{delta\_action}.
+  \item \texttt{scripts/train\_utility\_energy.py} and
+  \texttt{scripts/calibrate\_dominance.py} implement the utility/scoring and
+  dominance-calibration path.
+  \item \texttt{scripts/summarize\_ctt\_runs.py} generates
+  \texttt{runs/summary\_ctt.csv} and \texttt{runs/summary\_ctt.md}.
+  \item \texttt{paper/notes/theory\_ctt.md} and
+  \texttt{paper/sections/theory.tex} state the theory obligations.
+\end{itemize}
+
+\section{Limitations and Next Steps}
+
+This draft is not an unqualified SOTA claim. The current \ctt{} evidence
+includes validation and test measured generated-candidate rollouts, but the
+selected action fails the internal paper gate even when the test proposal oracle
+passes 50\%. The missing method component is calibrated dominance and a better
+utility selector, not another proxy-only support plot. The first standalone
+train-only utility-energy checkpoints and context-metadata ridge variants do
+not solve this transfer problem, so the chart token must move beyond base-action
+summaries and coarse task metadata toward exported visual-language and
+object-centric geometry. The RGB-reference export now provides a leakage-audited
+visual-stat token and improves measured support plus validation-calibrated
+selected success, but this does not qualify as the needed learned object-centric
+representation because the best held-out selected success is only 32.64\% and
+the selector gap remains large. Related work experiments, external
+benchmarks, real robot near-miss recovery, unsafe-contact measurement, and a
+dominance rule that approaches the internal success gate remain to be completed
+before submission.
+
+The next experimental step is concrete: replace the current weak train-only
+utility-energy selector with visual-language/object-centric chart features,
+rerun held-out measured dominance selection, and add unsafe execution and
+fallback-rate metrics. Proxy evidence may open the rollout gate; it cannot
+replace rollout measurement.
+
+\section{Conclusion}
+
+Same-state counterfactual charts reveal a support gap that ordinary
+demonstration learning and verifier-only candidate selection cannot see.
+Counterfactual Action Atlas turns that observation into a method program: learn
+local causal action geometry, generate positive do-action tangents on support,
+select them only under calibrated dominance, keep the metric boundary between
+outcome and proxy evidence explicit, and evaluate deployment-clean improvements
+only after generated candidates are measured.
+
+\bibliographystyle{plain}
+\bibliography{references}
+
+\end{document}