# Phase 3.5 -- Deterministic Low-Capacity Learner Family Reflection Roadmap: [`../../SUNDOG_V_ARC.md`](../../SUNDOG_V_ARC.md) Phase 3 spec: [`PHASE3_SUFFICIENCY_SPEC.md`](PHASE3_SUFFICIENCY_SPEC.md) Filed: **2026-05-28 (PT)** Status: **REFLECTION ONLY -- NO EXECUTION OR VERDICT ADMISSION**. This document names the three-receipt convergence under the Phase 3 deterministic-low-capacity-learner family as a methodological finding, scopes what kind of learner Phase 3 would need to produce a non-trivial sufficiency verdict, and surveys Phase 4 branch options. It does not admit any new learner, change any binding receipt's verdict, or relax any discipline rule. Public-language constraints from Pass D and the Phase 0-2 receipts remain in force. ## Why This Document Phase 3 has filed three binding receipts under three distinct deterministic low-capacity learner families: | receipt | learner version | candidate construction | | --- | --- | --- | | first | `nn_output_transfer_v1` | nearest-input output-transfer (conditioning outputs only) | | second | `nn_delta_transfer_v1` | + same-shape `delta_overlay` synthesis | | third | `candidate_combinator_v1` | + per-pair bijective colormap fit, seven non-identity D4 variants, cross-pair cell unions (delta_overlay retained) | All three receipts produced verdict **task hardness / decoder failure** under the frozen Pass C verdict gates. The third learner is empirically a strict superset of the first two on slot-1 and slot-2 metrics, and its verdict was the same as the first two. The convergence is itself a finding, distinct from any single receipt's verdict, and it shapes what Phase 3 would need to do next to produce evidence about signature sufficiency rather than evidence about the learner family. The reflection here is preregistered to keep that distinction frozen: the convergence is **not** a sufficiency-failure conclusion, **not** a support-on-registered-subset conclusion, and **not** a public claim about ARC. It is a learner-class observation, and the next admitted work must follow from that observation, not from a re-interpretation of the existing receipts. ## What The Three Receipts Showed The numerically stable observations across all three LODO `k_ge_3` receipts (105 instances, 102 active after Pass B trivial-task suppression): | metric | nn_output_transfer_v1 | nn_delta_transfer_v1 | candidate_combinator_v1 | | --- | ---: | ---: | ---: | | `signature_only.rep_exact_slot1` | `0.000` | `0.010` | `0.000` | | `signature_palette.grid_exact_any_slot` | `0.000` | `0.000` | `0.000` | | `signature_palette.rep_exact_slot1` | `0.000` | `0.010` | `0.000` | | `signature_palette.rep_sim_best` | `0.784` | `0.803` | `0.789` | | `metadata_only.rep_exact_slot1` | `0.039` | `0.010` | `0.039` | | `metadata_only.rep_sim_best` | `0.939` | `0.942` | `0.942` | | `raw_grid_lowcap.grid_exact_any_slot` | `0.000` | `0.010` | `0.010` | | `raw_grid_lowcap.rep_sim_best` | `0.912` | `0.920` | `0.922` | | `metadata_only.coverage_failure_rate` | `0.951` | `0.941` | `0.941` | | `signature_palette.coverage_failure_rate` | `1.000` | `0.990` | `0.990` | | `raw_grid_lowcap.coverage_failure_rate` | `1.000` | `0.990` | `0.990` | | `signature_only.coverage_failure_rate` | `1.000` | `0.990` | `0.990` | | `metadata_only - signature_palette` gap on `rep_sim_best` | `0.155` | `0.139` | `0.153` | (See the binding receipts under `results/arc/phase3-sufficiency/`, `results/arc/phase3-sufficiency-nn_delta_transfer_v1/`, and `results/arc/phase3-sufficiency-candidate_combinator_v1/`, hashed in the respective verdict amendments in [`PHASE3_SUFFICIENCY_SPEC.md`](PHASE3_SUFFICIENCY_SPEC.md).) What is stable across the three receipts: 1. **Exact-rate floor.** Every learner-arm exact metric is below the Pass C decisive thresholds for "support". `grid_exact_rate_any_slot` never exceeds `0.010`. `rep_exact_rate_slot1` never exceeds `0.039`. 2. **Coverage floor.** Every grid-bearing arm reports coverage failure on at least `0.99` of LODO `k_ge_3` instances under `nn_delta_transfer_v1` and `candidate_combinator_v1`; under `nn_output_transfer_v1` coverage is exactly `1.0` for all arms except `metadata_only`. The held-out outputs are nearly always outside the learner's candidate pool, regardless of which deterministic primitive set we extend the pool with. 3. **The signature-vs-metadata `rep_sim_best` gap.** `metadata_only` leads `signature_palette` on `mean_output_rep_similarity_best` by `0.139` to `0.155` across the three receipts. This is the decisive metric in the Pass C ladder for every receipt, and it has the same sign and roughly the same magnitude every time. 4. **Verdict.** All three receipts trigger the Pass C task-hardness condition (every grid-bearing arm has `grid_exact_rate_any_slot < 0.03`; every representation arm has `rep_exact_rate_slot1 < 0.05`) and the Pass C sufficiency-failure condition (signature_palette materially trails metadata_only on the first decisive metric). Task hardness preempts sufficiency failure under the same learner-class reasoning each time. ## What The Receipts Did Not Show The three receipts are silent on the following questions: 1. **Is the signature representation sufficient for ARC-style abstraction?** The decisive metric in the verdict ladder (`rep_sim_best`) is computed inside a learner class whose candidate pool overwhelmingly does not contain the held-out output. The metric gap therefore reflects how the candidate-identity rules for each arm trade off against chance-collision probability, not how well each representation captures the underlying rule. 2. **Is `metadata_only` actually sufficient?** Its `rep_exact_slot1` hits are coincidence: two grids with the same shape, palette, density, and color histogram receive the same 28-dim identity vector. Three to five such collisions in 102 LODO `k_ge_3` instances does not establish that the metadata representation captures the rule, only that its identity rule is coarse enough to be chance-hit more often than the signature's. 3. **Would a more capable learner reveal a different result?** The three filed receipts cannot answer this. They have all been pulled from the same "rank conditioning-derived candidates by arm distance, emit at most two" family, with progressively richer deterministic synthesis primitives. None of them learns anything per-task in the gradient-descent sense; none of them can synthesise an output grid that is not a deterministic function of the conditioning data alone. ## Why A Fourth Deterministic-Low-Capacity Learner Would Likely Converge Again The next-learner reservation in PHASE3_SUFFICIENCY_SPEC.md named a third candidate, `finite_program_selector_v1`, that was not filed. Under the same deterministic-low-capacity discipline (no fitted parameters, no optimizer, no cross-task weights, candidates emitted from frozen primitives applied to conditioning data), program selection would have the same structural property: - the candidate pool is bounded by the number of frozen DSL programs times the number of source conditioning configurations; - ARC tasks are explicitly designed so that the registered rule is novel per task, not a member of any frozen pre-listed DSL; - the Phase 0 `oracle_copy_floor_lodo_rerun` rows in every receipt already report `0/115` exact for `dsl_lite_v0`, `dsl_lite_v1`, `dsl_lite_v2`, `tiny_learned_v0`, `identity_copy`, and `random_valid` -- the most natural seed DSL is already shown to be exhausted by the registered subset. Either the program search would re-discover a primitive already in `candidate_combinator_v1` (D4, colormap, cell union, delta-overlay, output-copy) and add nothing, or it would need a DSL strictly richer than Phase 0's set, which is the substantive design change. A program selector inside the current discipline is therefore not expected to escape the convergence. The signature-vs-metadata gap on `rep_sim_best` is even more directly attributable to the learner class. Every receipt's gap is driven by `metadata_only`'s coarser candidate-identity rule producing systematically larger best-similarity values than `signature_palette`'s finer identity rule, regardless of what the underlying primitive set is. This gap is not evidence about representation sufficiency; it is evidence about how arm-distance ranking interacts with identity-rule coarseness inside this learner class. ## What Kind Of Learner Would Produce A Non-Trivial Verdict To break the convergence pattern, the next learner family would need at least one of the following structural changes, all of which are outside the current Pass C "deliberately small first learner" constraint: 1. **Per-task gradient-trained mapper.** A small MLP that fits an `input_rep -> output_rep` mapping on `k - 1` conditioning pairs and applies it to the query input. This learner can synthesize an output representation that is not a deterministic function of the conditioning outputs alone, and so its candidate pool is unbounded by the conditioning-data primitive set. Requires admitting fitted parameters, a seed slate, a training budget, and an early-stop rule. 2. **Program induction over an unfrozen DSL.** A search that learns the DSL primitives from the conditioning data instead of receiving them frozen, in the spirit of Dreamcoder-style approaches. Inside the "no pretrained model" rule this is feasible but would require a primitive-induction operator definition and a substantial Pass A extension. 3. **Iterative refinement learner.** Start from a deterministic candidate (e.g. `output_copy` or `delta_overlay`) and edit until the resulting input-output pair under the conditioning representation matches a metric computed against the conditioning pairs. Requires admitting an edit operator with a search budget. 4. **Representation-conditioned generative model.** A model that emits output candidates conditioned on the representation arm. Outside the "no pretrained model" rule unless the model is trained per task from scratch. The first option is the smallest step inside the spirit of the existing Pass C admission. Option 3 is the next-smallest, because the edit operator can be a frozen primitive set and the search can be bounded. Options 2 and 4 are larger lifts. Any of these would require: - a new Pass C-style admission amendment in PHASE3_SUFFICIENCY_SPEC.md pinning learner architecture, hyperparameters, seed slate, fitting budget, and (for stochastic learners) the reproducibility envelope; - a new runner script set following the established naming pattern; - a new receipt directory under `results/arc/`; - the freeze-marker commit discipline currently in force. ## Phase 4 Branch Options This reflection names four candidate next moves. Each is consistent with the discipline already in force; the choice is the operator's. ### Branch A -- Admit A Stochastic Per-Task Mapper Smallest step beyond the current learner family. A new Pass C-style admission amendment files a `per_task_mlp_v1` or `per_task_linear_v1` learner with: - a fixed shallow architecture; - a seed slate; - a per-task training budget capped under the repo's ten-minute rule (or staged as an external command if it exceeds that); - the same Pass A representation arms and Pass B instance handling. The candidate pool would no longer be conditioning-derived. If a fitted mapper produces materially higher exact rates than the cheap baselines on LODO `k_ge_3`, Phase 3 finally has signal about representation sufficiency rather than about candidate-pool structure. If it does not, the convergence extends to the gradient-trained class and the representation question survives more learner families. ### Branch B -- Pass C Threshold Revision Across all three receipts, `shape_exact_rate_slot1` ranges over `0.51` to `0.61` and `palette_exact_rate_slot1` over `0.43` to `0.48`, both well above chance. The current Pass C verdict table treats these as tie-breakers below the exact-rate tier; they never reach decisiveness in practice. A Pass C amendment could operationalise the consistent shape/palette recovery as its own admissible verdict tier ("structural support"), reflecting that representation arms do recover non-trivial structural information about held-out outputs even when they cannot reconstruct them. This is a threshold-only change; it does not admit any new learner. The risk is that "structural support" becomes a moving goalpost. The amendment must therefore freeze the threshold band based on these three receipts before any later receipt is generated, and explicitly tie the verdict to the existing three receipts' numbers, not to any future learner's. ### Branch C -- Pause Phase 3, Return To Gravity Ledger Three task-hardness verdicts is itself a defensible stopping point on the Phase 3 deterministic-low-capacity branch. The Sundog program continues elsewhere; this reflection becomes the canonical characterisation of what Phase 3 did and did not show. The Phase 3 receipts and PHASE3_SUFFICIENCY_SPEC.md remain binding; no new learner work is admitted; the program returns to Gravity Ledger items outside ARC. The risk is that the Phase 3 lane is read by an outside reader as a sufficiency-failure conclusion. The reflection above and the Pass D public-language drafts already cover that risk in writing, but pausing without filing Branch A or Branch B leaves the question hanging on the lane's public face. ### Branch D -- Different Sufficiency Framing Entirely The current Phase 3 framing scores `input_rep -> output_rep` mapping under a fixed candidate-emission learner. An alternative framing could score the representation arms directly on properties of the representation itself (e.g., does the representation predict the correct shape and palette of the held-out output without producing a candidate grid?). The three receipts' consistent shape/palette recovery above chance is the empirical motivation. Implementing this would require a substantial Pass A or new "Phase 3 alt" spec. This is the largest design change of the four branches and is the least mechanically continuous with the existing receipts. ## Discipline Carries Nothing in this document admits any of the following. The previous binding constraints remain in force: - no edits to Pass A arm schemas, Pass B instance handling, Pass C verdict ladder thresholds, or Pass D receipt schema without a new append-only amendment in `PHASE3_SUFFICIENCY_SPEC.md`; - no public-evaluation grid inspection (Phase 6 only); - no Kaggle notebook prep, Kaggle private or semi-private splits; - no sufficiency, dimensionality, palette-dependent, or partial-support claim from any Phase 3 receipt; - no description of any Phase 3 receipt as evidence on the public-evaluation split or as an ARC solve. This reflection cites the three binding receipts by their filed artifact hashes; it does not re-interpret them and does not propose any re-run that would replace those receipts. Each branch above, if filed, must produce its own receipt under a learner-version-suffixed path and must not overwrite the existing receipts. The public-language drafts in Pass D and the verdict amendments remain the canonical phrasing for any external citation of Phase 3 results. ## Pre-Registered Stance If the operator chooses Branch A: a new Pass C-style admission amendment for a stochastic per-task learner is filed under PHASE3_SUFFICIENCY_SPEC.md, following the same template as the `nn_delta_transfer_v1` and `candidate_combinator_v1` admissions. If the operator chooses Branch B: a new Pass C threshold-revision amendment is filed defining the structural-support verdict tier, explicitly bound to the three filed receipts and not to future unfiled receipts. If the operator chooses Branch C: no further amendment is filed; this reflection becomes the canonical characterisation and the lane status is "Phase 3 paused after deterministic-low-capacity convergence". If the operator chooses Branch D: a new spec (likely `PHASE3_ALT_FRAMING_SPEC.md` or similar) is filed alongside PHASE3_SUFFICIENCY_SPEC.md, with its own Pass A--D structure. This document does not pre-commit to any branch. The operator's choice of branch becomes the next admitted Phase 3 work after this reflection is committed. ## Post-Blackwell / Compact-7 Addendum Filed: **2026-05-28 (PT)**. Subsequent Phase 3 amendments used this reflection's branch menu to test whether a stronger or narrower full-grid control could open a meaningful signature-vs-full-grid comparison. Those later receipts do not replace the three deterministic-low-capacity receipts above; they add a separate full-grid-control calibration layer: - V1 Blackwell runner: `signature_palette` and the matched full-grid control both floored at zero exact matches, so no sufficiency comparison was interpretable. - V2 public-training raw-grid control: `full_grid_control_floor` under freeze marker `79C5B060`, with zero exact matches on both held-out lanes. - Compact-7 diagnostic: `compact_full_grid_control_floor` under freeze marker `50EAEBBF`, with zero exact matches despite `shape_exact_slot1 = 1.000`. The compact-7 residual audit names a qualitatively new failure mode: **dominant-color mode collapse**. Predictions often match output shape and background mass while omitting the target object palette/content; 13 of 13 held-out compact-7 predictions use at most two slot-1 colors, while targets use 3--9 colors. After compact-7, the narrowed deterministic full-grid-control path is closed. No further raw-grid capacity bump, extra seed, or additional task-distribution narrowing in this learner family is admitted as a Phase 3 reopen path. The remaining reopen paths are: - **Branch A**: admit a stochastic per-task learner with a new Pass C-style amendment and receipt path. - **Branch D**: admit a different framing, such as structured edit prediction or residual learning, with its own Pass A--D contract. Branch C remains available as a pause state. Branch B is closed by the V2 and compact-7 receipts. Branch A has now been selected for spec work in `PHASE3A_STOCHASTIC_PER_TASK_SPEC.md`. That file freezes `per_task_coord_mlp_v1` as the first stochastic per-task learner contract, but does not admit execution until runner wiring and a freeze-marker amendment are filed. ## Post-Phase-3A Addendum Filed: **2026-05-28 (PT)**. Phase 3A has now filed its binding 20-shard receipt under `per_task_coord_mlp_v1`. The verdict is `branch_a_full_grid_floor`: `raw_grid_per_task` scored zero exact tasks on both held-out lanes, so the arena did not open and no `signature_palette_per_task` vs. `raw_grid_per_task` sufficiency comparison is licensed. The named Phase 3A failure character is **conditioning starvation + shape-generalisation failure**. This is distinct from V1/V2's noise-dominated failure and compact-7's dominant-color mode collapse. The receipt closes this reflection's Branch A in the filed stochastic per-task learner family. Current reflection status: - Branch A: closed in the filed `per_task_coord_mlp_v1` learner family by `branch_a_full_grid_floor`. - Branch B: closed in the deterministic narrowed-task-class lane by compact-7. - Branch C: no longer the active next move after the filed Branch A receipt. - Branch D: untouched and the only remaining admissible Phase 3 reopen path. Any Branch D move requires its own pre-registered spec, arena gate, learner or framing contract, receipt path, and public-language constraints. ## Branch D Spec-Filed Addendum Filed: **2026-05-28 (PT)**. Branch D has now started in `PHASE3D_DIFFERENT_FRAMING_SPEC.md`. The filed contract is `structured_edit_residual_v1`: model the output as an input-derived baseline canvas plus a residual edit mask and edit colors. The spec preserves the full-grid-control discipline by requiring `raw_grid_edit` to open a non-baseline arena before any `signature_palette_edit` sufficiency comparison. This addendum does not admit execution. Branch D remains in execution hold until runner tooling and a freeze-marker amendment are filed. ## Post-Phase-3D Addendum Filed: **2026-05-28 (PT)**. Phase 3D has now filed its binding 20-shard receipt under `structured_edit_residual_v1`. The verdict is `branch_d_full_grid_edit_floor`: `raw_grid_edit` scored zero non-baseline exact tasks on both held-out lanes, so the non-baseline edit arena did not open and no `signature_palette_edit` vs. `raw_grid_edit` sufficiency comparison is licensed. The named Phase 3D failure character is **edit-color-rule failure**. This is distinct from V1/V2's noise-dominated failure, compact-7's dominant-color mode collapse, and Phase 3A's conditioning starvation + shape-generalisation failure. The structured-edit receipt decomposes the bottleneck: shape/canvas and edit-mask signal are nontrivial, but the per-task edit-color rule does not recover exact output colors. Current reflection status: - Branch A: closed in the filed `per_task_coord_mlp_v1` learner family by `branch_a_full_grid_floor`. - Branch B: closed in the deterministic narrowed-task-class lane by compact-7. - Branch C: characterised by the deterministic-low-capacity and Blackwell floor receipts. - Branch D: closed in the filed `structured_edit_residual_v1` framing by `branch_d_full_grid_edit_floor`. All four PHASE3_5_REFLECTION branches plus the filed Branch D framing are now characterised. Any further Phase 3 reopen requires a new pre-registered Branch D variant or a new Branch E spec with its own arena gate, verdict discipline, receipt path, and public-language constraints. ## Branch D Bottleneck Variant Addendum Filed: **2026-05-28 (PT)**. The first Branch D variant is now filed in `PHASE3D_EDIT_COLOR_RULE_VARIANT_SPEC.md`. It targets the edit-color-rule bottleneck named by the Phase 3D receipt. The variant keeps the structured-edit baseline and edit-mask components fixed, and replaces only the edit-color MLP with a deterministic color-rule bank selected from conditioning residuals. This addendum does not admit execution. The variant remains in execution hold until runner tooling and a freeze-marker amendment are filed. ## Post-Edit-Color-Rule Variant Addendum Filed: **2026-05-28 (PT)**. The `structured_edit_color_rule_v2` binding receipt is now filed. Its verdict is **`branch_d_color_rule_full_grid_floor`**: the raw-grid color-rule arm did not open the non-baseline exact arena, so no `signature_palette_edit_color_v2` vs. `raw_grid_edit_color_v2` sufficiency comparison is licensed in this variant. This closes the first Branch D bottleneck variant in its filed framing and marks the sixth Phase 3 full-grid-control floor. The result is diagnostically useful because the bottleneck shifted into measured slices: - `edit_mask_failure`: **41%** of failures; - `color_rule_selection_failure`: **16%** of failures, including the largest locked-accuracy regret slice; - `color_rule_bank_coverage_failure`: **9%** of failures. Further Phase 3 work requires a new pre-registered reopen spec. The admissible next moves are now narrowed to a mask-targeted Branch D variant, selection-refinement Branch D variant, rule-bank extension Branch D variant, or Branch E spec. This addendum admits no execution. ## Mask-Targeted Branch D Variant Addendum Filed: **2026-05-28 (PT)**. The next Branch D variant is now filed in `PHASE3D_MASK_TARGET_VARIANT_SPEC.md`. It targets the largest bottleneck slice named by the edit-color-rule receipt: `edit_mask_failure` at 41% of failures. The variant keeps the structured-edit baseline picker and deterministic edit-color rule bank fixed, and replaces only the edit-mask predictor with a conditioning-derived mask-candidate bank. This addendum does not admit execution. The mask-targeted variant remains in execution hold until runner tooling and a freeze-marker amendment are filed. ## Post-Mask-Target Variant Addendum Filed: **2026-05-28 (PT)**. The `structured_edit_mask_target_v3` binding receipt is now filed. Its verdict is **`branch_d_mask_target_full_grid_floor`**: the raw-grid mask-targeted arm did not open the non-baseline exact arena, so no `signature_palette_edit_mask_v3` vs. `raw_grid_edit_mask_v3` sufficiency comparison is licensed in this variant. This closes the second Branch D bottleneck variant in its filed framing and marks the seventh Phase 3 full-grid-control floor. The result is a clean within-framing negative: replacing the learned mask MLP with a deterministic mask-candidate bank did not lift the mask bottleneck. Mask-stage labels still dominated, and the inherited learned mask candidate still won a non-trivial share of selections. With both structured-edit bottlenecks probed by deterministic banks and both floored, Branch E is now the live frontier. A smaller selection-targeted Branch D variant remains possible, but it would still be within the same baseline + mask + color composition. ## Phase 3E Signature-Fiber Certificate Addendum Filed: **2026-05-28 (PT)**. `PHASE3E_SIGNATURE_FIBER_CERTIFICATE_SPEC.md` is now filed. It asks whether registered ARC contexts contain exact or near `signature_palette` context-fiber collisions with incompatible required behavior. This is a certificate lane, not a decoder lane: it can find a finite-context insufficiency witness or license a later Branch E program-selector runner, but it does not train a solver. ## Post-Phase 3E Certificate Addendum Filed: **2026-05-29 (PT)**. The Phase 3E signature-fiber certificate binding receipt is now filed. Its verdict is **`phase3e_deferred_label_vacuity`**. The receipt found no registered `signature_palette` fiber collision and no near cross-task structure: zero exact-output collisions, zero representation-level collisions, zero cross-task pairs within the frozen radius, and minimum cross-task context distance `0.207`. The deferral is caused by two facts: - the registered context fibers are singletons at the frozen radius, so there is no locality structure to certify positive or negative; - the Branch D-derived `program_sketch_v1` oracle is prior-blind on 68% of primary contexts, covering `color_role` and `objectness` but not `counting`, `local_completion`, `spatial_transform`, or `symmetry`. This does not block Branch E, because no collision witness was found. It also does not license Branch E via `phase3e_fiber_locality_positive`, because no fidelity-passing neighborhoods exist and the oracle is vacuous on most primary contexts. A future certificate would need a framing-agnostic program-sketch oracle, a larger registered context universe, or both. ## Program-Sketch Oracle v2 Addendum Filed: **2026-05-29 (PT)**. `PHASE3E_PROGRAM_SKETCH_ORACLE_V2_SPEC.md` is now filed. It targets the specific weakness named by the Phase 3E binding receipt: the inherited `program_sketch_v1` oracle was a Branch D edit-composition labeler, so it was prior-blind on the non-local-edit priors (`counting`, `local_completion`, `spatial_transform`, and `symmetry`). The v2 spec is deliberately a certificate-labeling repair, not a solver. It freezes nine framing-agnostic transformation facets plus anti-vacuity, anti-prior-laundering, and anti-solver-leakage gates. If those gates pass, a future runner may rerun the Phase 3E fiber certificate using the same frozen signature geometry thresholds (`epsilon_primary = 0.05`, `epsilon_strict = 0.025`, `epsilon_loose = 0.10`, k=3). No execution is admitted by this addendum. ## Post-Program-Sketch Oracle v2 Addendum Filed: **2026-05-29 (PT)**. The Phase 3E program-sketch oracle v2 binding receipt is now filed. Its verdict is **`phase3e_v2_deferred_sparse_fibers`**. The run was deterministic, pinned to `gitCommit 3B1B76D2` and runnerSha256 `6163C208`, and completed in about 8 s on `U_primary=25`. The result separates the two v1 deferral causes. The v2 oracle repairs the label-vacuity defect: anti-vacuity is `0.00`, anti-prior-laundering violations are 0%, anti-solver-leakage stays below the frozen thresholds (`unique_core=0.36`, `exact_lookup=0.04`), and the four v1-blind priors are now non-vacuous with 6-7 of 9 facets populated per primary context. The geometry does not move: 0 exact collisions, 0 representation-level collisions, 0 near pairs, minimum cross-task distance `0.207`, and 0% fidelity-passing neighborhoods. Therefore Phase 3E v2 is still deferred, but now solely because the registered context universe is too sparse at the frozen signature radius. The next certificate path is a Phase 0 register expansion; a Branch E solver remains possible only on independent capability grounds under a new pre-registered solver spec. ## Phase 0 Context-Expansion Spec Addendum Filed: **2026-05-29 (PT)**. `PHASE0_CONTEXT_EXPANSION_FOR_FIBERS_SPEC.md` is now filed as the Phase 0 register-amendment path for the Phase 3E v2 sparsity result. It keeps `program_sketch_v2`, `d_context_signature_palette`, `epsilon_primary = 0.05`, `epsilon_loose = 0.10`, and k=3 frozen, and pre-registers a balanced expansion target of 108 public-training tasks (18 per prior). It admits no execution: the original 36-task register remains binding until a future expansion receipt files the candidate queue, manual inspection log, expanded register, leak-check coverage, and freeze-marker amendment. ## Post-Context-Expansion Certificate Addendum Filed: **2026-05-29 (PT)**. The Phase 0 context expansion and expanded Phase 3E v2 certificate are now filed. The expansion receipt returned **`phase0_fiber_expansion_admit`**: the register was expanded to 108 public-training tasks, exactly 18 per prior, from a frozen candidate queue with 0 hard-exclusions and 0 discipline tripwires. The expanded certificate returned **`phase3e_v2_expanded_oracle_regression`**. `U_primary` increased from 25 to 336, but the v2 oracle's anti-solver-leakage gate failed on the larger register: `core_sketch_exact_lookup_fraction` rose from 0.04 to 0.351 against the frozen 0.20 threshold. Vacuity and prior-laundering still passed. The fiber geometry remained sparse: minimum cross-task distance contracted only from 0.207 to 0.196, with 0 near pairs and 0% fidelity-passing neighborhoods at `epsilon_primary = 0.05`. The expanded receipt therefore neither promotes nor blocks signature sufficiency or a Branch E solver. It falsifies the assumptions that the v2 anti-leakage gate transfers unchanged to a larger register and that a 3x balanced expansion populates the absolute-epsilon fibers. ## Relative-Locality Certificate Spec Addendum Filed: **2026-05-29 (PT)**. `PHASE3E_RELATIVE_LOCALITY_CERTIFICATE_SPEC.md` is now filed. It keeps the absolute-epsilon receipts intact and asks a separate rank-local geometry question on the 108-task expanded register: whether cross-task nearest neighbors under `signature_palette_context` are more `program_sketch_v2` coherent than signature-only, metadata-only, raw-grid, random, prior-stratified random, and permutation controls. The spec does not retune `epsilon_primary = 0.05`; it records that the fixed radius is empty and moves the primary test to rank cuts k=1/3/5/10, with k=5 primary. The expanded oracle leakage regression is carried as an explicit caveat rather than erased. No execution is admitted by this addendum. ## Post-Relative-Locality Certificate Addendum Filed: **2026-05-29 (PT)**. The Phase 3E relative-locality certificate binding receipt is now filed. Its verdict is **`phase3e_relative_locality_negative`**. The run used the 108-task expanded register (`U_primary=336`), freeze-marker `f7850f0`, runnerSha256 `3DD2C97A`, k=1/3/5/10 with k=5 primary, and 5 seeds x 1000 permutations. The result contains a real but unusable rank signal. `signature_palette_context` is above prior-stratified random at k=5 (`p=0.0002`), so the rank order is not pure noise. But it is essentially tied with `metadata_only` (`delta=+0.006`, with sign flipping negative by k=10), below `raw_grid_context` (`delta=-0.036`), below the positive random-margin bar (`delta_vs_uniform=+0.072 < 0.15`), and has a hard-incompatibility rate of 0.285, above the 0.25 negative gate. This closes the Phase 3E locality-certificate program as a certificate lane: absolute fibers are empty on 36 and 108 tasks, expanded absolute geometry triggers oracle regression while staying sparse, and relative rank locality is negative. The remaining live path is Branch E on capability grounds under its own pre-registered solver spec, or recording the certificate negative as the durable finding. ### Branch E opened and closed-positive (2026-05-29) Branch E was filed and executed as a deterministic program-search solver ([`PHASE3_BRANCH_E_PROGRAM_SEARCH_SPEC.md`](PHASE3_BRANCH_E_PROGRAM_SEARCH_SPEC.md)), explicitly on **capability grounds**: it selects programs by train-pair consistency over a frozen primitive library (structural transforms + the imported Branch D color-rule bank + simple deterministic mask families + candidate- combinator candidates), never by `signature_palette` geometry. The four Phase 3E certificate verdicts are cited as a no-collision / no-locality **boundary**, not as a geometric-selector motivation. Binding verdict (pinned `6886074`, deterministic, U_primary=336): **`branch_e_capability_demonstrated`** — the first non-zero exact-match result in the program. It cleared the established non-trivial floor (≥2 distinct held-out tasks solved exactly on both `test_lodo` and `pttest`: `be94b721` via `extract_largest_component`, `f25fbde4` via `crop_bbox>>scale`; validation diagnostic also 2) that all seven prior decoder/learner-family floors hit at zero. The result is **modest** (2 distinct tasks per gated lane, ~3% instance rate, structurally simple tasks; 3 of 4 solves are depth-2 compositions) and is **not** a Blackwell-sufficiency proof, an ARC solve, or any eval/Kaggle claim — Phase 6 still gates that. The methodological reading: *searching* a fixed primitive library succeeds (modestly) where *learning* the transforms from scratch floored, which is the expected come-apart between the capability question and the learning/representation question the seven floors + four certificates characterized. A Branch E v2 (deferred intricate mask families + deeper composition) is the natural next probe of whether the rate rises above this floor-clearing baseline. Branch E v2 was executed (pinned `a307340`, deterministic): verdict **`branch_e_v2_capability_replicated`**. Admitting the deferred intricate deterministic mask families + the morphology cross-product + depth-3 composition **did not lift** the capability — v2 retained both v1 gated solves on both lanes but solved zero new tasks (material-lift gate not met), and the enlarged search space slightly *reduced* validation (2→1 per lane) via top-2 crowding (train-consistent-but-test-wrong programs displacing the correct one). So the deterministic program-search capability is **bounded near the v1 ~3% baseline**; more deterministic primitives/depth do not crack new held-out tasks in the registered universe. A materially higher rate would need a different solver class (learned ranker, richer object-centric language, or LM proposer), each under its own pre-registered spec; otherwise this is the durable deterministic-search bound.