{ "capcard_version": "3.1.0", "id": "ai.capcard.monogate", "name": "Monogate", "type": "library", "description": "Open-source mathematics stack built on the EML operator eml(x, y) = exp(x) - ln(y). Includes the Pfaffian-cost analyzer (eml-cost) with three prediction functions for SymPy compile-time, float64 numerical precision loss, and PyTorch per-layer activation behavior. Cross-validated against a Lean 4 formalization with 50 EML-original theorems across 17 files (14 of 17 files carry zero sorry; the remaining 3 carry 5 documented sorries total — 4 blocked on the same Mathlib o-minimal / Khovanskii zero-count gap, 1 standard approximation bound deferred to a future Float64 file).", "version": "2.5.0", "license": "MIT", "homepage": "https://monogate.org", "repository": "https://github.com/agent-maestro/monogate", "lean_repo": "https://github.com/agent-maestro/monogate-lean", "related_sites": { "research": "https://monogate.org", "developer": "https://monogate.dev", "interactive": "https://1op.io", "paper_notes": "https://monogate.org/paper", "theorems": "https://monogate.org/theorems", "explorer": "https://monogate.dev/lab", "pypi": "https://pypi.org/project/monogate/", "pypi_eml_stdlib": "https://pypi.org/project/eml-stdlib/", "npm": "https://www.npmjs.com/package/monogate", "arxiv": "https://arxiv.org/abs/2603.21852", "eml_stdlib_repo": "https://github.com/agent-maestro/eml-stdlib" }, "authors": [ { "name": "Monogate Research", "url": "https://monogate.org", "based_on": "Odrzywolek (2026), arXiv:2603.21852" } ], "capabilities": [ { "id": "universality.eml", "name": "EML universality", "category": "scientific_claim", "description": "The single binary operator eml(x, y) = exp(x) - ln(y) generates every elementary function as a finite tree from the constant 1 alone. Lean-formalized as the IsEMLElementary predicate in Universality.lean.", "status": "proven_machine_verified" }, { "id": "barrier.infinite_zeros", "name": "Infinite Zeros Barrier (T01)", "category": "scientific_claim", "description": "Real EML trees have finitely many zeros on any closed bounded interval where they are real-analytic, while sin(x) has infinitely many. Therefore sin is not an element of EML(R). Parts A, B, C, C-prime are closed in Lean. Part D (sin_not_in_eml, sin_not_in_real_EML_k) carries 2 documented sorries pending o-minimal / Wilkie 1996 machinery not yet in Mathlib.", "status": "proven_partial" }, { "id": "routing.superbest_v5", "name": "SuperBEST v5.3 routing table", "category": "construction", "description": "Routing table mapping 10 positive-domain arithmetic operations to F16 expressions, achieving 14n / 80.8% savings vs the 73n naive baseline, plus a general-domain 8-op basket at 16n / 74.2% savings vs the 62n naive baseline. Library, blog, browser, and capability-card surfaces are synchronized from monogate.superbest.", "status": "proven_machine_verified", "constraints": { "total_nodes": 14, "naive_total": 73, "savings_percent": 80.8, "positive_total_nodes": 14, "positive_naive_total": 73, "positive_savings_percent": 80.8, "general_total_nodes": 16, "general_naive_total": 62, "general_savings_percent": 74.2, "canonical_source": "python/monogate/superbest.py" } }, { "id": "lower_bound.add", "name": "SB(add) >= 2", "category": "lower_bound", "description": "No single F16 operator equals (x, y) -> x + y for all real x, y. Exhaustive 16-witness refutation in AddLowerBound.lean.", "status": "proven_machine_verified" }, { "id": "lower_bound.sub", "name": "SB(sub) >= 2", "category": "lower_bound", "description": "No single F16 operator equals (x, y) -> x - y for all real x, y. SubLowerBound.lean, 16-case refutation.", "status": "proven_machine_verified" }, { "id": "lower_bound.mul", "name": "SB(mul) >= 2", "category": "lower_bound", "description": "No single F16 operator equals (x, y) -> x * y for all real x, y. MulLowerBound.lean, derivative obstruction route + witness refutation.", "status": "proven_machine_verified" }, { "id": "lower_bound.div", "name": "SB(div) >= 2", "category": "lower_bound", "description": "No single F16 operator equals (x, y) -> x / y for all real x, y. DivLowerBound.lean.", "status": "proven_machine_verified" }, { "id": "tool.estimate_time", "name": "estimate_time(expr) compile-time predictor", "category": "tool_function", "description": "Predicts SymPy compile wall-time across simplify/factor/cse/lambdify proxies from the Pfaffian profile. Regression model fit on 202 expressions (cross-domain-3 R v2). 5-fold CV R^2 by proxy: simplify 0.68, factor 0.76, cse 0.83, lambdify 0.84.", "status": "empirically_confirmed" }, { "id": "tool.predict_precision_loss", "name": "predict_precision_loss(expr) runtime numerical predictor", "category": "tool_function", "description": "Predicts float64 numerical relerr versus 50-digit mpmath ground truth. Fit on 379 expressions from the bench-300-domain corpus. 5-fold CV R^2 = +0.271 +/- 0.060, residual log10 std = 0.772, marginal eml_depth coefficient +0.337 (~0.34 decimal digits per depth unit). Modest signal explicitly NOT used as a form recommender (E-193 Phase 3 best-pick was 30 percent on rewrite tests, below the 70 percent product threshold).", "status": "empirically_confirmed" }, { "id": "tool.diagnose", "name": "diagnose(model) per-layer activation behavior (eml-cost-torch)", "category": "tool_function", "description": "Per-layer per-activation lookup of fp16 drift and activation-variance for 19 named PyTorch activation classes. Five seeds per activation, ranked from GeGLU (high drift ~7.4e-4) to Hardsigmoid (low drift ~2.3e-4). The earlier PNE-vs-EML generalization (E-183) was empirically falsified on a controlled corpus (p=0.085); honest_note baked into report.empirical_basis.", "status": "empirically_confirmed" }, { "id": "tool.eml_cost_cli", "name": "eml-cost CLI", "category": "tool_function", "description": "Console command exposing analyze + estimate_time + predict_precision_loss as `eml-cost report` and `eml-cost check`. Pre-commit usable via --max-simplify-ms and --max-digits-lost budgets. Exit codes: 0 OK, 1 threshold violation, 2 parse error, 64 usage.", "status": "empirically_confirmed" }, { "id": "tool.npm_port", "name": "JavaScript port via monogate/cost subpath", "category": "tool_function", "description": "JavaScript port of analyze + predict_precision_loss in npm monogate 1.3.0, with byte-identical Python coefficients. Cost-class fingerprint matches Python eml-cost on 32 of 32 reference cases. predict_precision_loss matches byte-for-byte on 14 of 20 representative cases; remaining 6 differ by up to about a factor of 10 due to SymPy automatic canonicalizations on the JS-parsed literal tree.", "status": "empirically_confirmed" }, { "id": "empirical.cost_class_enrichment", "name": "p2-d5-w2-c1 cost-class enrichment in the bench-300-domain corpus", "category": "empirical_dataset", "description": "Across the 403-expression cross-domain corpus and N_null=5000 random expressions, cost class p2-d5-w2-c1 shows 2.7x enrichment with q < 1e-4 after Benjamini-Hochberg correction across 31 candidate classes, spanning 18 distinct domains. Earlier headline of 'binary 0/50 null with >= 40x enrichment' was a small-N artifact and is corrected here.", "status": "empirically_confirmed" }, { "id": "taxonomy.sixteen_operators", "name": "F16 Operator Taxonomy", "category": "scientific_claim", "description": "Complete census of all binary operators formed from exp(±x) and ln(y) with arithmetic. 16 total: 8 complete, 1 approximate, 7 impossible.", "status": "proven_machine_verified", "constraints": { "operators_count": 16, "complete": 8, "approximate": 1, "incomplete": 7 } }, { "id": "catalog.equations_265", "name": "Public Equation Catalog", "category": "construction", "description": "265 named equations across 18+ scientific domains, each annotated with EML decomposition and Pfaffian cost class. Live count on monogate.dev/explorer.", "status": "empirically_confirmed", "constraints": { "catalog_size": 265 } }, { "id": "characterization.elc_real", "name": "ELC(ℝ) Characterization", "category": "scientific_claim", "description": "ELC(ℝ) = closure of ℝ ∪ {1} under eml equals the set of all functions expressible as finite compositions of real exp and ln. Odrzywołek 2026, arXiv:2603.21852.", "status": "proven_machine_verified" }, { "id": "bridge.euler_gateway", "name": "Euler Gateway (Complex Bridge)", "category": "construction", "description": "exp(ix) = cos(x) + i·sin(x) bridges real EML to complex domain, enabling sin/cos construction via Im/Re extraction of eml(ix, 1).", "status": "proven_machine_verified" }, { "id": "cost.decomposition", "name": "Cost Decomposition Theorem", "category": "scientific_claim", "description": "Every EML tree decomposes into a Pfaffian profile (r, mr, d, so) that predicts computational cost and structural complexity. T38 in Lean.", "status": "proven_machine_verified" }, { "id": "activation.softplus", "name": "softplus activation", "category": "tool_function", "description": "softplus(x) = ln(1 + exp(x)) = LEAd(x, 1). Single-node EML expression.", "status": "empirically_confirmed", "neural_metrics": { "forward_nodes": 1 } }, { "id": "activation.sigmoid", "name": "sigmoid activation", "category": "tool_function", "description": "sigmoid(x) = 1/(1+exp(-x)). DAG cost is the canonical 5n value (shared subexpression); strict tree cost is 6n.", "status": "empirically_confirmed", "neural_metrics": { "forward_nodes": 6, "forward_nodes_dag": 5 } }, { "id": "optimizer.adam", "name": "Adam optimizer (per-param-per-step)", "category": "tool_function", "description": "Adam update with shared bias-correction scalars amortized across parameters. Post-NN-13 re-audit: 31n amortized; strict/tree value is 37n.", "status": "empirically_confirmed", "neural_metrics": { "optimizer_nodes_per_param_per_step_strict": 37, "optimizer_nodes_per_param_per_step_amortized": 31 }, "eml_metrics": { "cost_amortized": 31 } }, { "id": "norm.rmsnorm", "name": "RMSNorm", "category": "tool_function", "description": "RMSNorm(x) = x / sqrt(mean(x²) + ε). EML cost scales with hidden dimension; reported value is for d=4096 (LLM-scale layer).", "status": "empirically_confirmed", "neural_metrics": { "forward_nodes": 4097 } }, { "id": "library.eml_stdlib", "name": "eml-stdlib — verified standard library for game development", "category": "construction", "description": "v0.4.0 (2026-05-07) ships 178 EML modules / 521 functions / 466 verified across 22 categories: math, signal, control, physics, circuits, sensors, biology (incl. biology/abilities), carriers, quantum, ml, ballistics, plus the 60-module gaming/ family (noise, textures, shading, lighting, terrain, animation, particles, camera, audio, physics). Each module declares chain order and ~89% carry @verify(lean) contracts. Installable via pip; .eml source files ship inside the wheel for downstream Forge tooling. Mirrored as GDScript inside the four Godot prototypes.", "status": "empirically_confirmed", "constraints": { "modules": 178, "functions": 521, "verified_functions": 466, "verified_pct": 89, "categories": 22 } }, { "id": "applications.godot_prototypes", "name": "Godot game prototypes (eml-stdlib applied)", "category": "construction", "description": "Four Godot 4 prototypes — spellforge (1v1 rune-graph duel; spells are EML expression trees), longshot (2D sniper sim mirroring eml-stdlib::ballistics), apex-predator (asymmetric PvP; hunter has real ballistics, beast has real biology + 4-stage evolution; 25 species, 2v1 split-screen with per-viewport fragment-shader fog of war), monowave (deterministic music visualizer; same audio in → same visuals out, no randomness anywhere). All four ship a CLAUDE.md handoff doc plus a headless smoke-test suite (76 tests total). Private repos under agent-maestro/. The 10 ability kernels first written for apex-predator were promoted to eml-stdlib/biology/abilities/ in stdlib v0.4.", "status": "empirically_confirmed", "constraints": { "games_count": 4, "headless_test_count": 76, "spellforge_tests": 13, "longshot_tests": 15, "apex_predator_tests": 22, "monowave_tests": 26 } } ], "benchmarks": [ { "id": "bench.superbest_table", "name": "SuperBEST v5.3 routing table values", "capability_ref": "routing.superbest_v5_3", "metric": "node_count_positive_domain", "value": 14, "unit": "F16 nodes", "direction": "lower_is_better", "reproducibility": { "command": "python python/scripts/sync_superbest_canonical.py --strict", "deterministic": true }, "notes": "Headline: 14n positive-domain 10-op basket (80.8 percent vs 73n naive). General domain: 16n 8-op basket (74.2 percent vs 62n naive). Source: blog/src/data/superbest.json v5.3 synchronized from monogate.superbest." }, { "id": "bench.lean_zero_sorry_files", "name": "Lean 4 verification (Mathlib v4.14.0)", "capability_ref": "operator.eml_universality", "metric": "files_with_zero_sorries", "value": 14, "unit": "files of 17", "direction": "higher_is_better", "reproducibility": { "command": "git clone https://github.com/agent-maestro/monogate-lean && cd monogate-lean && lake build", "deterministic": true }, "notes": "14 of 17 files in MonogateEML/ build with zero sorries. Three files carry the remaining 5 documented sorries: InfiniteZerosBarrier.lean (lines 326, 337 - Part D), ChainOrderAdditivity.lean (lines 138, 175 - chain_order_additivity + three_tower_min_generating_set), and Runtime.lean (line 246 - mg_softplus_route_bound_high). Four of those share the same Mathlib o-minimal / Khovanskii zero-count gap; one Mathlib advance closes all four. The remaining one is a saturation-branch approximation bound for the libmonogate softplus routing variant, deferred to a future MonogateEML/Float64.lean." }, { "id": "bench.eml_cost_tests", "name": "eml-cost test suite", "capability_ref": "tool.eml_cost_cli", "metric": "tests_passing", "value": 194, "unit": "tests", "direction": "higher_is_better", "reproducibility": { "command": "pip install eml-cost==0.7.1 && git clone https://github.com/agent-maestro/eml-cost && cd eml-cost && python -m pytest", "deterministic": true }, "notes": "Includes 26 tests for predict_precision_loss and 16 tests for the CLI. mypy --strict clean across 11 source files." }, { "id": "bench.eml_cost_torch_tests", "name": "eml-cost-torch test suite", "capability_ref": "tool.diagnose", "metric": "tests_passing", "value": 42, "unit": "tests", "direction": "higher_is_better", "reproducibility": { "command": "pip install eml-cost-torch==0.5.0 && git clone https://github.com/agent-maestro/eml-cost-torch && cd eml-cost-torch && python -m pytest", "deterministic": true }, "notes": "Per-activation empirical lookup tests + diagnose() integration tests." }, { "id": "bench.npm_monogate_tests", "name": "monogate npm test suite", "capability_ref": "tool.npm_port", "metric": "tests_passing", "value": 429, "unit": "tests", "direction": "higher_is_better", "reproducibility": { "command": "npm install monogate@1.3.0 && cd node_modules/monogate && npx vitest run", "deterministic": true }, "notes": "Across 5 test files: cost.test.js (68), cost_precision.test.js (37), complex.test.js (38), complex_eml.test.js (71), index.test.js (215)." }, { "id": "bench.cost_class_p2d5w2c1", "name": "Cost-class p2-d5-w2-c1 enrichment vs random null", "capability_ref": "empirical.cost_class_enrichment", "metric": "enrichment_ratio", "value": 2.7, "unit": "fold", "direction": "higher_is_better", "reproducibility": { "command": "git clone https://github.com/agent-maestro/monogate-research-public-bench && cd bench-300-domain && python stats.py --n_null 5000", "deterministic": true }, "notes": "Across the 403-expression bench-300-domain corpus and N_null=5000. Benjamini-Hochberg FDR-corrected q < 1e-4 across 31 candidate classes. 18 distinct domains contribute. The publication of this benchmark expects the public bench repo to be available; until then the corpus and stats.py live in monogate-research/exploration/bench-300-domain/." } ], "proofs": [ { "id": "lean.add_lower_bound", "name": "SB(add) >= 2", "statement": "No single F16 operator computes x + y for all real x and y.", "status": "proven_machine_verified", "proof_method": "Witness-based case analysis over all 16 F16 operators; paired with a 2-node upper-bound construction.", "lean_file": "MonogateEML/AddLowerBound.lean", "lean_theorem": "SB_add_ge_two", "sorries": 0, "capability_refs": [ "lower_bound.add" ] }, { "id": "lean.sub_lower_bound", "name": "SB(sub) >= 2", "statement": "No single F16 operator computes x - y for all real x and y.", "status": "proven_machine_verified", "proof_method": "Exhaustive 16-case witness refutation.", "lean_file": "MonogateEML/SubLowerBound.lean", "lean_theorem": "SB_sub_ge_two", "sorries": 0, "capability_refs": [ "lower_bound.sub" ] }, { "id": "lean.mul_lower_bound", "name": "SB(mul) >= 2", "statement": "No single F16 operator computes x * y for all real x and y.", "status": "proven_machine_verified", "proof_method": "Derivative obstruction plus witness refutation.", "lean_file": "MonogateEML/MulLowerBound.lean", "lean_theorem": "SB_mul_ge_two", "sorries": 0, "capability_refs": [ "lower_bound.mul" ] }, { "id": "lean.div_lower_bound", "name": "SB(div) >= 2", "statement": "No single F16 operator computes x / y for all real x and y.", "status": "proven_machine_verified", "proof_method": "Witness (0, 1) refutes all 16 operators.", "lean_file": "MonogateEML/DivLowerBound.lean", "lean_theorem": "SB_div_ge_two", "sorries": 0, "capability_refs": [ "lower_bound.div" ] }, { "id": "lean.eml_universality", "name": "EML universality witness", "statement": "Every EML-elementary function is realized by an EML routing tree.", "status": "proven_machine_verified", "proof_method": "Existential extraction from IsEMLElementary.", "lean_file": "MonogateEML/Universality.lean", "lean_theorem": "eml_universality", "sorries": 0, "capability_refs": [ "operator.eml_universality" ] }, { "id": "lean.infinite_zeros_barrier_partial", "name": "Infinite Zeros Barrier (T01) — partial", "statement": "Real EML trees have finitely many zeros on any closed bounded interval where they are real-analytic. Parts A, B, C, C-prime fully closed; Part D (sin not in EML) carries 2 documented sorries.", "status": "proven_partial", "proof_method": "Bolzano-Weierstrass + AnalyticOnNhd identity theorem (Parts B and C); Part D requires o-minimal / Wilkie 1996 machinery not yet in Mathlib.", "lean_file": "MonogateEML/InfiniteZerosBarrier.lean", "lean_theorem_partial": "Parts A, B, C, C-prime", "sorries": 2, "sorries_locations": [ 326, 337 ], "sorries_description": "sin_not_in_eml and sin_not_in_real_EML_k pending a quantitative o-minimal zero-count bound not yet formalized in Mathlib v4.14.0.", "capability_refs": [ "barrier.infinite_zeros" ] }, { "id": "lean.eml_duality", "name": "EML Duality Theorem", "statement": "The EML operator exhibits a duality structure where conjugation preserves the elementary closure.", "status": "proven_machine_verified", "proof_method": "structural_induction", "lean_file": "MonogateEML/EMLDuality.lean", "lean_theorem": "eml_duality", "sorries": 0, "capability_refs": [ "universality.eml" ] }, { "id": "lean.hyperbolic_preserves_elc", "name": "Hyperbolic Preservation", "statement": "Hyperbolic functions sinh, cosh, tanh are preserved under EML closure — constructible from exp without complex detour.", "status": "proven_machine_verified", "proof_method": "direct_construction", "lean_file": "MonogateEML/HyperbolicPreservation.lean", "lean_theorem": "hyperbolic_in_elc", "sorries": 0, "capability_refs": [ "universality.eml" ] }, { "id": "lean.self_map_conjugacy", "name": "Self-Map Conjugacy", "statement": "EML self-composition eml(eml(x, y), eml(y, x)) exhibits conjugacy structure relating forward and inverse maps.", "status": "proven_machine_verified", "proof_method": "algebraic_manipulation", "lean_file": "MonogateEML/SelfMapConjugacy.lean", "lean_theorem": "self_map_conjugacy", "sorries": 0, "capability_refs": [ "characterization.elc_real" ] }, { "id": "lean.upper_bounds_routing", "name": "Upper Bounds (BEST Routing)", "statement": "Every elementary arithmetic operation has an upper bound on BEST-routed node count, establishing the SuperBEST table entries.", "status": "proven_machine_verified", "proof_method": "constructive_witness", "lean_file": "MonogateEML/UpperBounds.lean", "lean_theorem": "upper_bound_add", "sorries": 0, "capability_refs": [ "routing.superbest_v5" ] } ], "verification": { "test_count_total": 2400, "test_count_breakdown": { "monogate_python": 1729, "eml_cost": 194, "eml_cost_torch": 42, "monogate_npm": 429, "monogate_research_petal_seed_v1": 6 }, "last_verified": "2026-05-25T02:24:44Z", "lean_total_files": 17, "lean_partial_files": 3, "lean_active_sorry_locations": [ "MonogateEML/InfiniteZerosBarrier.lean:326", "MonogateEML/InfiniteZerosBarrier.lean:337", "MonogateEML/ChainOrderAdditivity.lean:138", "MonogateEML/ChainOrderAdditivity.lean:175", "MonogateEML/Runtime.lean:246" ], "lean_total_statements": 496, "lean_original_eml_theorems": 50, "evidence_summary": "14 of 17 Lean files build clean with zero sorries. Three files carry sorries: InfiniteZerosBarrier.lean (2, on Part D), ChainOrderAdditivity.lean (2, on chain_order_additivity + three_tower_min_generating_set), and Runtime.lean (1, on mg_softplus_route_bound_high). The first 4 are blocked on the same Mathlib gap (o-minimal / Khovanskii zero-count); one advance closes all four. The 5th is a saturation-branch approximation bound for the libmonogate softplus routing variant, deferred to a future Float64 file. Six independent benchmark categories ship with reproducible commands. Tests across all five published packages currently pass.", "test_count": 1872, "lean_clean_files": 14, "lean_sorries_total": 5 }, "integration": { "install": { "pip_monogate": "pip install monogate==2.5.0", "pip_eml_cost": "pip install eml-cost==0.7.1", "pip_eml_rewrite": "pip install eml-rewrite==0.5.1", "pip_eml_cost_torch": "pip install eml-cost-torch==0.5.0", "pip_eml_stdlib": "pip install eml-stdlib==0.4.0", "npm_monogate": "npm install monogate@1.3.0", "pip": "pip install monogate==2.5.0" }, "sdk_languages": [ "python", "javascript" ], "cli": { "binary": "eml-cost", "subcommands": [ "report", "check", "version" ], "ships_in": "eml-cost 0.7.1" } }, "agent_queries": { "supports": [ "elementary_functions", "symbolic_regression", "cost_theory", "pfaffian_complexity", "compile_time_prediction", "numerical_precision_prediction", "activation_diagnostics", "lean4_verified", "superbest_routing", "verified_game_kernels", "godot_eml_prototypes" ], "honest_limitations": [ "predict_precision_loss is NOT a form recommender; cost class does not reliably pick the more numerically stable form within an algebraic equivalence class (E-193 Phase 3 best-pick = 30 percent across 10 rewrite tests).", "Form-sensitivity: about 50 percent of textbook expressions yield different cost classes for algebraically equivalent forms. canonicalize() preprocessing reduces this to about 35 percent. The remaining drift is documented.", "Real-world (bio / physics / engineering) expressions are NOT specially numerically clean compared to random nulls at matched cost class (pooled diff = -0.001 log10 across 4 matched classes; E-193 Phase 4).", "diagnose(model) per-activation drift values are measured on a single fixed FFN; per-architecture variation is not yet characterized.", "JS port of predict_precision_loss matches Python byte-for-byte on 14 of 20 representative cases; 6 of 20 differ by up to about a factor of 10 due to SymPy automatic canonicalization differences." ] }, "metadata": { "created": "2026-04-17T00:00:00Z", "updated": "2026-05-25T02:24:44Z", "schema_url": "https://monogate.org/schemas/capcard/v3.json", "rewrite_note": "Rewritten 2026-04-27 to align with verified CONTEXT.md numbers, drop earlier boasting framing, and remove an unverified manual trust score. All quantitative claims are now traceable to a reproducible command or a Lean source file. Updated 2026-04-29 to reflect Runtime.lean addition (libmonogate runtime correspondence; user-verified `lake build` green; 1 documented sorry on mg_softplus_route_bound_high). Updated 2026-05-07 to add eml-stdlib v0.4.0 (178 modules / 521 fns / 466 verified) and the four Godot prototypes (spellforge, longshot, apex-predator, monowave) — empirically confirmed via 76 headless tests across the four repos." } }