# Operator Saturation Curves — per-operator completeness table

Per runbook §6: track accepted-new-primes per 100 applications (Stage-5 acceptances, not Stage-2
NEWs). Retire an operator when trailing rate < ~2% over two consecutive batches. This table IS the
completeness claim.

| Operator | Batch | Apps | Stage-2 NEW | Stage-3 survivors | Stage-4 accept+hold | Stage-5 accepted | Notes |
|---|---|---|---|---|---|---|---|
| 01 dualization | PILOT v1 (50+3, 2026-07-02) | 159 | 44 (27.7%) — 1a 16/53, 1b 6/53, 1c 22/53 | 43 (27.0% of apps) | 1 + 4 | pending owner | gate NOT met; template v2 fixes applied |
| 01 dualization | RE-PILOT v2 (frozen sample, 2026-07-02) | 159 | 68 (42.8%) — 1a 29, 1b 20, 1c 19 | 70 (44.0% of apps) | 1 + 2 new holds (+3 reconfirmed) | pending owner | gate i PASS (0 silent deaths; ex.3 3/3, ex.4 3/3); gate ii FAIL (44%); v3 = NOT_A_PRIME label in retrieval check + 1a absence instruction — see manifest_dualization_v2.yaml |
| 01 dualization | v3 VALIDATION (frozen sample, 2026-07-02) | 159 | 60 (37.7%) — 1a 20, 1b 28, 1c 12 | 24 (15.1% of apps) | no new finds | — | **GATE FAIL — precision**: `restatement` label silently killed negative_transfer, heterarchy, multiple_realizability on ALL routes; `absence` label (5 kills) + funnel narrowing (44%→15%) validated; v4 spec below |
| **01 dualization — 1a FULL SWEEP** (v4, 2026-07-02) | 1,325 | 333 (25.1%) | 210 (15.8%) | 2 accepts + 5 new holds (+2 merges) | pending owner | **zero-silent-deaths PASS** (gap noted: Stage-2 self-collapses bypass protection — fix before 1b/1c); cost ≈ 2.2M subagent tokens ≈ 0.31M per accept+new-hold; details `manifest_sweep_1a.yaml` |
| **01 dualization — 1b FULL SWEEP** (v4.1, 2026-07-03) | 1,325 | 703 (53.1%) | 437 (33.0%) | 1 accept-rec + 6 new holds (+ reconfirmations) | pending owner | zero-silent-deaths PASS; protection 8×; details `manifest_sweep_1bc.yaml` |
| **01 dualization — 1c FULL SWEEP** (v4.1, 2026-07-03) | 1,323 (2 unrecovered) | 549 (41.5%) | 618 (46.6%) | 3 accept-recs + 12 new holds (+ reconfirmations) | pending owner | zero-silent-deaths PASS; protection 3× + 2 Stage-2 rescues; 1c cheap-check kills weakest (failure-modes read structure-like) — sonnet absorbed; details `manifest_sweep_1bc.yaml` |

| **13 cluster-without-parent** | FULL RUN (2026-07-03, frozen corpus) | 82 coherent parentless clusters | — | — | 0 accepted-new | **SATURATED/RETIRED** — 0 new primes, 12 DAG-gap edge proposals (byproduct worklist in `manifest_op13.yaml`); confirms companion-doc §3 prediction that ops 12/13 were exhausted reactively in project-06 |
| **08 threshold/phase** | PILOT-ONLY → RETIRED (frozen 53-sample × 2 flavors, sonnet, 2026-07-03) | 106 | 8a 2 / 8b 0 (both non-genuine) | 1 (domain-specific) | 2 gaps captured: catastrophe, order_parameter | **SATURATED/RETIRED** — threshold/phase region already complete (tipping_points, threshold, percolation_threshold, critical_mass, nucleation, hysteresis, symmetry_breaking, regime_change, ...); 8b = pure op-04 4b redundancy. NO full sweep (saved ~4M sonnet). 2 stubs + bifurcation-split note. `manifest_op08_threshold.yaml` |
| **07 perspective inversion** | PILOT-ONLY → RETIRED (frozen 53-sample, single pass, sonnet, 2026-07-03) | 53 | 1 (framed) | 1 | 1 gap captured: interpellation (framed) | **SATURATED/RETIRED** — relational/perspective core nearly counted (both seats of canonical pairs already named: signaling+screening, principal+agent, ...; + perspective/frame_of_reference/figure_ground/duality/complementarity). Single pass (not sub-flavors); overlaps dualization 1b. 8 alias confirmations + 7 symmetric fixed points. NO full sweep. haiku 12/15. 1 stub. `manifest_op07_perspective.yaml` |
| **12 interpolation** (n-ary) | FULL PRE-FILTERED RUN → RETIRED (61 large-gap subsumption edges, sonnet, 2026-07-03) | 61 | 4 → 0 genuine | — | **0 new primes**; 13 missing-edge flags + 13 mis-parent flags | **SATURATED/RETIRED** — DAG already tight (0 edges cos<0.5, 12<0.6); all 4 "NEW" were child-restatements or existing (habituation). Confirms project-06/op-13 reactive exhaustion. Byproduct = DAG densification. ~1.24K tok/app. `manifest_op12_interpolation.yaml` |
| **11 analogy completion** (n-ary) | FULL 1,325 SWEEP (sonnet, 2026-07-04) | 1,325 | 12 → 7 genuine | 7 | **7 domain-general: ergodicity + allostasis STRONG; coherentism, generativity, boundary_object(×2), construal_level + envy_freeness→backlog** | **NON-SATURATED — the ONLY n-ary with real yield.** Cross-relational analogy reaches diagonal/composite primes the axis-sweeps structurally cannot. Full-rate 0.9% (<< sample's 6% — corpus more saturated than sample implied) but high-quality finds. Regress lattice gap (infinitism absent → op-14). 7 stubs. ~1.0K tok/app, ≈1.4M total. `manifest_op11_analogy.yaml` |
| **10 tension-resolution** (n-ary) | PILOT-ONLY → RETIRED (frozen 53-sample, sonnet, 2026-07-04) | 53 | 0 | — | 0 new primes | **SATURATED/RETIRED** — 0/53. Corpus already names its tensions/dilemmas/tradeoffs + resolutions (risk_return_tradeoff, collingridge_dilemma, social_dilemma, ambidexterity, jevons_paradox, dialectics, ...); "resolutions" are generic balance (not a prime) or dualization re-runs (already swept). Overlaps op-1b. NO full run. `manifest_op10_tension.yaml` |
| **09 composition** (n-ary) — THE LAST OPERATOR | PILOT-ONLY → RETIRED (diverse 88-pair sample, sonnet, 2026-07-04) | 88 | 0 | — | 0 new primes; 23 subsumption→edge-harvest | **SATURATED/RETIRED** — 0/88. Tight co-occurring pairs are mere conjunctions or already-named composites (natural_selection etc.). Composition RECOMBINES existing primes → same category as op-10/12/13, all saturated. NO full run. `manifest_op09_composition.yaml`. **FULL 14-OPERATOR SET NOW EXHAUSTED.** |
| **14 lattice/symmetry completion** (catalog) | FRONTIER PASS (opus, 2026-07-04) | 15 candidate gaps | — | 5 | **5 genuine cells: infinitism + cheap_talk STRONG; common_pool_resource, positional_good, type_iii_error** | **2nd n-ary with yield.** Mendeleev-style: k-1-of-k gaps in near-complete families. Both STRONG = exact duals of present primes (regress trilemma; costly/costless signaling). Finds cluster in FRAMED families (governance/welfare/epistemology). impossibility→alethic family, heterarchy already stubbed (convergence). Frontier self-rejected present/vacuous cells. 5 stubs. ≈0.04M. `manifest_op14_lattice.yaml` |
| **05 generalization** | PILOT v1 (frozen 53-sample, 2026-07-03) | 53 | 32 (60%) | 25 (47%) | 0 — every survivor a same-level restatement | **GATE FAIL — capability floor**: haiku cannot perform the lift (0 genuine genera in 53; G3 holdout not reproduced); v2 spec = sibling-evidence requirement + SONNET Stage 2 + framed-stratum-first budget; see template §Status |
| **05 generalization** | FRAMED-STRATUM SWEEP (v2, 2026-07-03) | 236 | 60 (25.4%) | 35 | 8 new holds (exploration_exploitation + consilience STRONG) | pending owner | + 9 alias confirmations, 34 missing-edge flags, stigmergy side-spot; sonnet Stage-4 blanket-zero overridden (retrieval-proximity fallacy — §D amendment in template); ≈49K tokens/new-hold; `manifest_op05_framed.yaml` |
| **05 generalization** | REMAINING-STRATA SWEEP (v2, 2026-07-03) | 1,037 | 155 (15.0%) | 174 | 33 holds (Tier A: partial_order, LLN/inevitability, information_discarding_projection, nested_epistemic_depth STRONG; +common_mode_failure route#3) | pending owner | §D-amended Stage-4 did NOT blanket-zero; structural holds skew to sonnet coinages (Tier B, low keep-rate expected); **213 missing-edge flags — largest edge harvest**; ≈4.1K tokens/app; `manifest_op05_rest.yaml` |

| **02 self-application** | PILOT v1 (frozen 53-sample + 2 holdouts, sonnet, 2026-07-03) | 55 | 0 (0%) — sonnet over-collapses | 15 (27%) via step-0 + articulated-candidate rescue | 6 holds (2 STRONG: evolvability, second_order_preference; 4 mod/weak) + 4 alias confirmations | pending owner | **GATE PASS with v1.1 articulated-candidate rescue rule** (load-bearing; without it second_order_preference dies silently). 15 fixed-point audit rows. Haiku probe (15) = mirror failure (6 vacuous NEW). `manifest_op02_pilot.yaml` |

| **02 self-application** | FULL SWEEP (v1.1, sonnet, 2026-07-03) | 1,325 | 207 (16%) | 526 (40%) survivors | ~10 STRONG canonically-named holds + ~5 moderate + 95 alias confirmations | pending owner | Kurt authorized after pilot gate pass. **536 fixed points (41%) → audit census** (op-02 = highest-fixed-point operator per companion §6). Yield concentrated by CROSS-INPUT CONVERGENCE (second_order_preference ×5, metanorm ×4, others ×2). ~490 Tier-B coinage holds bulk-listed. 8 stubs. `manifest_op02_sweep.yaml` |

| **03 temporalization** | PILOT (frozen 53-sample, sonnet + haiku probe, 2026-07-03) | 159 | 50 (31%) — 3a 17 / 3b 22 / 3c 11 | 50 survivors | fixed-point calib correct; healthy NEW | GATE PASS | tier decision: **haiku** (12/15 pilot agreement w/ sonnet); 3b = discovery engine, 3a = rate-of-X coinage. 17-row already-temporal audit. `crank/op03_pilot.jsonl` |
| **03 temporalization** | FULL 3-FLAVOR SWEEP (haiku, 2026-07-03) | 3,971 (3a/3b/3c × 1,325) | 3a 420 / 3b 493 / 3c 255 | 1,258 survivors → 660 prioritized | **1 STRONG (transient_response, ×12 convergence) + 4 moderate** + 357 alias confirmations | pending owner | Kurt authorized full 3-flavor sweep. **1,450 fixed points → 788-prime already-temporal census** (59% of corpus is inherently dynamic — strong audit result). ~600 Tier-B coinage bulk. 5 stubs. `manifest_op03_sweep.yaml`, `op03/s4/shortlist.md` |

| **04 spatialization** | PILOT (frozen 53-sample, sonnet + haiku probe, 2026-07-03) | 159 | 4a 23 / 4b 17 / 4c 17 | 57 survivors | fixed-point calib correct; discreteness→continuity alias | GATE PASS | tier decision: **SONNET** (haiku only 5/15 vs op-03's 12/15 — spatialization needs judgment). |
| **04 spatialization** | FULL 3-FLAVOR SWEEP (sonnet, 2026-07-03) | 3,975 (4a/4b/4c × 1,325) | 4a 243 / 4b 423 / 4c 342 | 1,016 survivors → 591 prioritized | **3 STRONG (field [genus convergence], mean_field, continuous_relaxation) + 3 moderate** + 200 alias confirmations | pending owner | Kurt authorized full sonnet sweep (Option 1). **716 fixed points → 495-prime already-spatial census** (37% — less saturated than op-03's temporal 59%). ~1,000 Tier-B coinage bulk. 6 stubs. Most expensive unary op (~4.5M sonnet). `manifest_op04_sweep.yaml`, `op04/s4/shortlist.md` |

| **06 modalization** | PILOT (frozen 53-sample, sonnet + haiku probe, 2026-07-03) | 159 | 6a 20 / 6b 17 / 6c 6 | 86 survivors | fixed-point calib correct; markov→FP, decision→optionality | GATE PASS | tier: **SONNET** (haiku 7/15 — marginal, between op-03 12/15 and op-04 5/15). 6c low-yield. |
| **06 modalization** | FULL 3-FLAVOR SWEEP (sonnet, Option 2, 2026-07-03) | 3,975 (6a/6b/6c × 1,325) | 6a 374 / 6b 350 / 6c 70 | 882 survivors → 633 prioritized | **possibility [genus] STRONG + defeasibility + deontic_modality + expected_value (fold-flagged)** + 407 alias confirmations | pending owner | Kurt authorized full sonnet sweep. **350 fixed points → 297-prime already-modal census (22% — LEAST-saturated axis)** but 407 aliases (modal layer well-covered by fewer powerful primes). 4 domain-general stubs + ~9 domain-specific → backlog. ~800 Tier-B bulk. `manifest_op06_sweep.yaml`, `op06/s4/shortlist.md` |

**OPERATOR 02 (self-application) — FULL-CORPUS SWEEP COMPLETE / RETIRED 2026-07-03.** Kurt
authorized the full 1,325 sweep after the pilot passed the gate. Sonnet Stage 2 (v1.1) → **207 NEW
(16%) / 582 COLLAPSE / 536 FIXED_POINT (41%)** → funnel (step-0 alias verification +
articulated-candidate rescue) → 526 survivors → 12 sonnet Stage-4 batches → frontier shortlist.
**Yield:** ~10 STRONG canonically-named second-order primes, all verified absent, ranked by
cross-input convergence — `second_order_preference` (×5: preference, expected_utility,
time_preference, other_regarding_preferences, indifference_curves), `metanorm` (×4: normativity,
informal_enforcement, tolerance_paradox, accountability), `meta_learning` (×2), `structural_stability`
(×2), `evolvability` (×2), `meta_optimization`, `second_order_uncertainty`, `second_order_probability`,
`recursive_theory_of_mind`, `kompetenz_kompetenz` + ~5 moderate (metacognitive_load,
meta_stereotype_threat, model_risk, model_uncertainty, meta_decision). **8 stubbed** in
v2_density_pilot/ (evolvability, second_order_preference, metanorm, meta_learning,
structural_stability, meta_optimization, second_order_uncertainty + prior); the rest are manifest
holds. **536-row fixed-point audit census** → `audit_self_duals.jsonl` (op-02 = highest-fixed-point
operator, as companion §6 predicted). **95 balanced-granularity alias confirmations.** ~490 Tier-B
mechanical "X-of-X" coinage holds bulk-listed in `survivors/op02_sweep.jsonl` (op-05 Tier-B
precedent; low keep-rate; many are latent DAG-composition signals). **Keystone method findings:**
(1) Stage-2 verdict untrustworthy from both tiers in opposite directions — funnel gates on step-0 +
articulated-candidate rescue + Stage-4, never Stage-2 NEW; (2) at Stage-4 the §D amendment makes
sonnet OVER-HOLD, so the real discriminator is **cross-input convergence + canonical-name presence**
(rank Stage-4 survivors by these; auto-Tier-B the single-route un-named coinages). Cost ≈ 1.9M
sonnet tokens ≈ 0.19M per strong hold + census & confirmations as bycatch. **Operator 02 RETIRED
for this corpus state** (pending owner Stage-5 curation counts). `manifest_op02_sweep.yaml`,
`op02/s4/shortlist.md`. Fixed points → `audit_self_duals.jsonl` (560 rows: 24 op-01 + 536 op-02).

**OPERATOR 05 (generalization) — FULL-CORPUS SWEEP COMPLETE 2026-07-03.** 1,326 applications
across pilot + framed + structural strata. Cumulative pending-owner: ~47 op-05 holds (a handful
Tier-A strong: exploration_exploitation, consilience, inductive_bias, partial_order, LLN;
the rest framed-lift holds + structural coinages needing keep/kill) + **259 missing-edge
proposals** (op05 247 + op13 12) — the DAG-densification byproduct rivals the prime yield in
value. Cost ≈ 9.4M subagent tokens. Saturation note: framed stratum is the yield engine (staircase
confirmed — 34/hold framed vs coinage-heavy structural); a second op-05 pass would be low-EV.
**Operator 05 RETIRED for this corpus state.**
| **05 generalization** | PILOT v2 (sonnet + sibling-evidence, 2026-07-03) | 53 | 8 (15.1%) | — | 6 new holds + 2 alias confirmations | **GATE PASS** — capability floor cleared (8 genuine lifts vs v1's 0); alias-claim precision 13/14 (sonnet ~eliminates hallucinated aliases); G3 lift performed (resolves onto existing cue_outcome_decoupling — correct corpus-state-aware outcome; broader maladaptation genus still an open sweep target); cost 3.6K tokens/app; framed-stratum sweep (~260 primes ≈ 1M sonnet) authorized-pending-owner; `manifest_op05_pilot.yaml` |

**OPERATOR 03 (temporalization) — FULL-CORPUS 3-FLAVOR SWEEP COMPLETE / RETIRED 2026-07-03.** Kurt
authorized the full sweep after the pilot passed the gate. **HAIKU Stage 2** (tier decision: 12/15
pilot agreement with sonnet; mechanical axis-add like dualization; funnel gates downstream). 3,971
applications (3a/3b/3c). Funnel → **1,450 fixed points / 1,258 survivors / 357 alias confirmations /
906 rejects**. **The primary deliverable is AUDIT: an 788-prime already-temporal census** (59% of
the corpus is inherently dynamic — feedback, half_life, markov_process, diffusion, oscillation,
random_walk, hysteresis, tipping_points, ...; 192 flagged in all 3 flavors) **+ 357
balanced-granularity alias confirmations** — together a strong statement that the corpus's dynamic
layer is near-complete. **Discovery yield is small (as companion §6 predicts): 1 STRONG genuinely
convergent find — `transient_response`/relaxation_dynamics (×12 inputs: equilibrium, feedback,
impedance_mismatch, fail_safe, ...)** — plus 4 moderate dynamic primes (`critical_slowing_down`,
`overshoot`, `predictability_horizon`, `phase_synchronization`). **5 stubbed** in v2_density_pilot/.
~600 Tier-B "rate-of-X" coinages bulk-listed in `survivors/op03_sweep.jsonl`. Cost ≈ 2.8M haiku
(Stage 2, cheap) + 0.5M sonnet (Stage 4) — far cheaper per token than op-02/05 thanks to the haiku
tier. Fixed points → `audit_temporalization.jsonl` (788 rows). **Operator 03 RETIRED for this corpus
state** (pending owner Stage-5 curation). `manifest_op03_pilot`-in-crank + `manifest_op03_sweep.yaml`
+ `op03/s4/shortlist.md`. Next per §5: ops 4 (spatialization) / 6 (modalization) / 8 (threshold).

**OPERATOR 07 (perspective inversion) — PILOT-ONLY, RETIRED AS SATURATED 2026-07-03.** Single pass
(the move is always "swap to the complementary seat" — not sub-flavors). Verified at build that the
corpus already names BOTH seats of every canonical relational pair (signaling+screening,
principal/agent, moral_hazard, adverse_selection, information_asymmetry, coercion=compellence+deterrence,
reciprocity, exchange, theory_of_mind) plus the perspective meta-primes (perspective, frame_of_reference,
figure_ground, duality, complementarity, top/bottom_up_perspectives). Pilot (53 apps, sonnet, haiku
probe 12/15) = **1 NEW / 53 (a FRAMED critical-theory construct), 8 alias confirmations, 7 symmetric
fixed points, 37 non-relational rejects** → **RETIRED without a full sweep** (§8), like op-08/op-13.
The lone find captured as a stub: **`interpellation`** (the subject/addressee seat of
grand_narrative — the party constituted-as-subject by a structure's address; flagged framed/
domain-specific, screen vs performativity). Cost ≈ 0.14M sonnet. `manifest_op07_perspective.yaml`,
`audit_perspective.jsonl` (7 fixed points). **This completes ALL UNARY OPERATORS (1,2,3,4,5,6,7,8) +
op-13; only the n-ary/combinatorial operators 9/10/11/12/14 remain (pre-filtered pair sets, not
full-corpus sweeps).**

**OPERATOR 08 (threshold/phase) — PILOT-ONLY, RETIRED AS SATURATED 2026-07-03.** The threshold/phase
region is one of the most-covered areas of the corpus, and flavor 8b (continuity→discreteness)
duplicates op-04's already-run flavor 4b. The pilot doubled as a saturation check (like op-13's full
run) and confirmed near-zero yield: **8a 2 NEW / 53 (both non-genuine on inspection — one a
domain-specific Shannon-limit coinage, one an alias to the op-03 `phase_synchronization` stub); 8b
0 NEW / 53 (pure redundancy — 9/9 sampled aliases → discrete_vs_continuous_quantization).** So op-08
is **RETIRED without a full sweep** (runbook §8: stop early on saturation), saving ~4M sonnet. The 2
genuine domain-general gaps it surfaced/confirmed are captured as stubs: **`catastrophe`** (Thom/Zeeman
— control-surface geometry beyond a bare tipping point; close refinement of tipping_points) and
**`order_parameter`** (Landau — the emergent observable that measures symmetry breaking; complements
symmetry_breaking). Owner notes: `bifurcation` is absent-but-aliased-to-tipping_points (possible split);
`critical_exponent` → domain-specific backlog. 19 already-critical pilot fixed points →
`audit_threshold.jsonl`. Cost ≈ 0.16M sonnet (pilot only). `manifest_op08_threshold.yaml`. **This
completes all 8 unary operators (1,2,3,4,6,8) + generalization(5) + cluster(13); next are op 7
(perspective inversion) and the n-ary/combinatorial ops 9/10/11/12/14.**

**OPERATOR 06 (modalization) — FULL-CORPUS 3-FLAVOR SWEEP COMPLETE / RETIRED 2026-07-03.** Kurt
authorized the full 3-flavor sweep (Option 2). **TIER: SONNET** (pilot haiku probe 7/15 — too
marginal; between op-03's 12/15 and op-04's 5/15). 3,975 applications. Funnel → **350 fixed points /
882 survivors / 407 alias confirmations / 2,336 rejects.** **The modal axis is the LEAST-saturated at
the fixed-point level — only 297 unique already-modal primes (22%, vs op-03's 59% temporal / op-04's
37% spatial / op-02's 41%) — BUT the corpus's existing modal primes absorb an unusually high 407
modalizations as aliases**, so the modal layer is well-covered by a smaller set of powerful primes
(probability, optionality, counterfactual_reasoning, modal_reasoning, uncertainty, risk,
expected_utility, mixed_strategy). **Genuine domain-general yield is the SMALLEST of the operators: 4
holds — `possibility` (STRONG genus convergence: hundreds of "possibility space of P" 6a inputs →
the absent alethic-modality prime), `defeasibility` (×6, the 6c find), `deontic_modality`,
`expected_value` (fold-flagged: expected_utility is present, so genus-vs-fold).** 4 stubbed. ~9
domain-specific finds (genetic_drift, first_passage_time, hazard_rate, sampling_distribution,
stationary_distribution, random_utility_model, quenched_disorder, reference_class_forecasting,
posterior_predictive) → deferred backlog (task #19). ~800 Tier-B coinages bulk-listed. Cost ≈ 4.0M
sonnet Stage 2 + 0.5M Stage 4. Fixed points → `audit_modalization.jsonl` (297 rows). **Operator 06
RETIRED for this corpus state.** `manifest_op06_sweep.yaml`, `op06/s4/shortlist.md`. Next per §5:
op 8 (threshold/phase) — the last cheap unary sweep.

**OPERATOR 04 (spatialization/scaling) — FULL-CORPUS 3-FLAVOR SWEEP COMPLETE / RETIRED 2026-07-03.**
Kurt authorized the full 3-flavor sweep (Option 1). **TIER: SONNET** — the pilot haiku probe agreed
with sonnet only 5/15 (vs op-03's 12/15), so spatialization needs judgment (is P already spatial?
does a genuine field/aggregate emerge?), closer to op-05's lift than a mechanical flip. 3,975
applications. Funnel → **716 fixed points / 1,016 survivors / 200 alias confirmations / 2,043
rejects** (sonnet stricter than op-03's haiku). **Primary deliverable is AUDIT: a 495-prime
already-spatial census** (37% of corpus — LESS saturated than op-03's temporal 59%) **+ 200
balanced-granularity alias confirmations.** **Discovery: 3 STRONG — `field` (the genus convergence:
hundreds of "field of P" inputs → the missing general field prime; corpus has gradient/diffusion
which act ON fields but no field), `mean_field` (×3: mean-field theory/game/self-consistent field),
`continuous_relaxation` (×2: LP/convex relaxation)** — plus 3 moderate (`spatial_random_field`,
`continuum_limit`, `density`-as-field-facet). **5 stubbed** in v2_density_pilot/. ~1,000 Tier-B
"field-of-P" coinages bulk-listed. Notable corpus-state finds: `wave` present (oscillation→wave =
confirmation), `power_law` now aliased to `allometry_and_scaling_law` (op-05 memory said absent).
Cost ≈ 4.0M sonnet Stage 2 + 0.5M Stage 4 = most expensive unary operator. Fixed points →
`audit_spatialization.jsonl` (495 rows). **Operator 04 RETIRED for this corpus state.**
`manifest_op04_sweep.yaml`, `op04/s4/shortlist.md`. Next per §5: ops 6 (modalization) / 8 (threshold).

**Operator 01 (dualization) — SWEEP COMPLETE 2026-07-03.** 3,973 applications across three
flavors. Cumulative yield pending owner curation: **6 accept-recommendations** (eager_evaluation,
risk_seeking, confabulation, pareidolia, hold_up_problem, consequentialism) **+ ~25 holds**, plus
convergence-strengthened manifest holds (heterarchy ×3 routes, foundationalism ×3,
common_mode_failure ×2, negative_transfer ×3, brittleness ×2), a double lattice gap
(consequentialism + deontology both absent beside virtue_ethics), 9 balanced-granularity
confirmations at sweep scale, and ~1,250 retained negatives. Total cost ≈ 6.9M subagent tokens
≈ 0.22M per accept-or-new-hold. **Saturation assessment:** 1a/1b/1c have each been run once to
completion; the §6 stop-rule (trailing accepted-new rate over two consecutive batches) is not yet
measurable — it requires owner Stage-5 acceptance counts. Next per §5 sequencing: ops 13+5
(cluster-without-parent + generalization lift) after curation of the operator-01 queue.

## Pilot findings (2026-07-02) — dualization, 50-prime stratified + 3 injected holdouts

**Yield.** 1 accept (`eager_evaluation` — holdout exemplar 3, reproduced end-to-end) + 4 holds
(`heterarchy`, `sloppy_parameters`, `expansion_unpacking`, `multiple_realizability`) from 159
applications. Even at pilot scale the operator found four genuine gap-candidates that were not
planted. Details: `manifest_dualization.yaml`.

**Calibration gate: NOT MET** (template §D.5 requires all injected exemplars reproduced). Ex.3
partial-pass, Ex.4 pass-against-current-corpus, Ex.5 fail (it is really an op-5 generalization
exemplar). Required template fixes before the full sweep:

1. **Stage-3 must verify Stage-2 alias claims.** The cheap model hallucinates "already in corpus"
   (54 of 74 claimed NEAREST slugs do not exist). Rule: a COLLAPSE-alias whose NEAREST fails both
   slug/alias-map lookup and the embedding screen is routed onward as a *clean-gap* candidate.
   This rule is what the ex.3 recovery needs to be deterministic instead of lucky (only 1c said NEW).
2. **Alias-screen threshold does not transfer.** Candidate-sentences vs full-signature embeddings
   run cool (~0.60–0.83); true aliases (omission_bias 0.71, bottom_up_perspectives 0.69,
   continuity ~0.71) sit in the same band as non-aliases, so the 0.80 screen killed only 1/44 and
   passed 43 to Stage 4 (27% — design target is 1–5%). Fix: screen against one_liner embeddings
   (register-matched short texts) + a lexical name check against slug+alias map; retune on the
   pilot data. Fixed-point 0.90 never fired (max cos-to-input 0.86); drop to ~0.80 for
   candidate-vs-input or rely on Stage-2 self-declarations (which worked: 17 self-dual audit rows).
3. **1c needs its own solved few-shot and a "failure-mode ≠ absence" instruction.** 1c batch 2
   drifted to opposing-force and emitted 19/26 NEW (vs batch 1's 3/27) — prompt-adherence variance
   between identical batches is the single biggest false-NEW source.
4. **Move exemplar 5 (maladaptation) to op-5's calibration set.**

**Sub-flavor profile.** 1b is the consistency-checker (47/53 collapse, mostly correct existing-dual
identifications); 1a and 1c carry the discovery signal. Framed stratum produced framed-antonym
noise as predicted (template §E) — 6 of the framed inputs' survivors were value-laden opposites,
0 accepted.

**Audit byproducts.** 12 balanced-granularity confirmations (e.g. action_bias↔omission_bias,
discreteness↔continuity, coupling↔modularity, markov_process↔path_dependence); 17 candidate
self-duals in `audit_self_duals.jsonl`; 116 retained negatives in `negatives/dualization.jsonl`.

**Cost proxy.** 7 haiku subagent calls (~180K tokens) for 159 applications ≈ 1.1K tokens/application;
embedding screen near-free (local onnx); Stage-4 the dominant cost *because the funnel is too fat* —
fixing (2) is the cost lever. Cached corpus embeddings for all 1,325 primes now at
/tmp (regenerate: `dist/derived/embeddings/` latest is stale at 654 primes — worth refreshing as a
side task).

## Re-pilot findings (2026-07-02, template v2) — see `manifest_dualization_v2.yaml`

**Holdouts: clean sweep.** Ex.3 recovered 3/3 flavors (step-0 clean-gap route fired
deterministically on both hallucinated-alias claims); ex.4 resolved correctly 3/3 (retrieval
check mapped both `inaction_bias` hallucinations onto `omission_bias`). Zero silent deaths.

**Two NEW verified-gap holds:** `negative_transfer` (buried by an unverified alias claim in
pilot #1 — step-0's poster child) and `decision_paralysis` (1c breakdown-framing upgraded what
pilot #1 rejected as privative). Plus `common_mode_failure` adjudicated (recommend accept), and
reconfirmed convergence on heterarchy / sloppy_parameters / expansion_unpacking.

**Embedding alias-screen: retired.** Calibration on pilot-#1 ground truth showed NO separating
threshold in either signature or one_liner space (true aliases 0.60–0.83 overlap spurious NEWs
0.71–0.81; bge signal weak — consistent with workflow-00). Replaced by the **retrieval-grounded
cheap-model check**: candidate + top-6 one_liner-space neighbors as a menu, haiku says
ALIAS_OF/NONE, answer verified against the menu. Killed 39 with good precision (known over-kill
risk: mapped medium-independence onto `invariance`).

**Funnel width regressed for an honest reason** (27% → 44% to Stage 4): stopping silent
alias-deaths reroutes that stream to Stage 4, and nothing cheap kills *privative not-primes*.
**v3 fix is two lines:** add `NOT_A_PRIME: <absence|restatement|domain_instance|NONE>` to the
retrieval-check output (same call, same packet) + restore a 1a instruction "the mere
absence/complement of P, with no structure of its own, is COLLAPSE" (v2's verification warning
overcorrected 1a: 29/53 NEW vs v1's 16/53). 1c batch variance persists (5/27 vs 14/26) — watch.

## v3 validation run (2026-07-02, frozen sample) — GATE FAIL, v4 specified

**What validated.** Funnel narrowed 44% → 15% (24/159 survivors). The `absence` NOT_A_PRIME
label works (5 kills, all defensible — including correctly labeling the 1a/1b privative
phrasings of non-transfer). The `domain_instance` label was quiet (4 kills). eager_evaluation,
decision_paralysis, expansion_unpacking, sloppy_parameters all still reach Stage 4 via ≥1 route.

**What failed — the `restatement` label (34 of 43 NAP kills).** A dual necessarily references
its input's structure, so the cheap model labels genuine duals "restatement of the input":
it killed **negative_transfer, heterarchy, and multiple_realizability on ALL their routes** —
three known holds dead silently. Precision criterion FAIL. (Aggravating: 1b lazy_evaluation's
correct eager candidate was also restatement-killed; only the 1a route saved it.)

**Also observed.** Stage-2 batch variance is the persistent instability: 1a NEW split 18/2
across identical batches (v2: 19/10), 1b 11/17, 1c 4/8. Single-sample haiku judgments are
noisy at every stage; kills that gate a known-good candidate's LAST route matter dispropor-
tionately, which argues for convergence-aware routing rather than per-route thresholds alone.

**v4 spec (not applied):**
1. **Drop or defang `restatement`** — for dualization it is structurally unusable as a kill
   label. Either remove it (kills flow to Stage 4) or reword to "restates the INPUT ITSELF as
   though it were new; an opposite pole or failure-mode of the input is NEVER a restatement"
   and re-measure.
2. **Convergence-aware safety net:** a candidate proposed by ≥2 flavors (or matching a
   known manifest hold) may not be killed by NOT_A_PRIME alone — route its best-phrased
   variant to Stage 4.
3. Optional stability fix for batch variance: run the retrieval check twice (same packet,
   independent calls) and only kill on agreement — doubles a cheap cost to protect the
   expensive error.

### Defang trial (2026-07-02, same v3 packet, retrieval check only — ~58K haiku tokens)

Reworded `restatement` to "same pole as the input, re-phrased; an opposite pole or failure-mode
is NEVER a restatement." Results vs the v3 run (same 90 items):

- **Restatement kills 34 → 12**, and the 12 remaining are mostly defensible (ZPD-negation,
  blocking-negation are genuinely privative). The four strongest candidates — eager_evaluation,
  negative_transfer, decision_paralysis, heterarchy — **all survive at candidate level on label
  semantics alone.**
- **But the leak moved rather than closed:** sloppy_parameters, expansion_unpacking, and
  multiple_realizability still die at candidate level — now via bad ALIAS kills (two
  "explicit-redundancy" candidates mapped onto `injectivity`, which is wrong) and a still-
  misapplied restatement on a last-route item ("diffusion of effect is leverage's negation" —
  exactly what the defang wording forbids).
- Survivor rate: **30%** (47/159) vs 36% for plain drop vs 15% for v3-as-was.

**Conclusion: single-haiku label reliability is the binding constraint — no wording fixes it.**
The convergence/manifest protection rule (v4 spec #2) is load-bearing under EVERY variant: with
it, all 7 known candidates survive under defang. Recommended v4 = defang wording + protection
rule; expected full-sweep Stage-4 volume ~1,150–1,300 items (vs ~1,430 for drop+protection).
The bigger cost lever is Stage-4 strategy: batch pre-adjudication by sonnet subagents with
frontier review only of their accept/hold shortlist would cut the expensive stage ~10× (est.
full sweep ≈ 4M haiku + 1.5M haiku + ~1.6M sonnet + small frontier pass; can be run one flavor
at a time to spread across budget weeks).

**v4 ADOPTED (owner, 2026-07-02):** defang + protection rule + sonnet-batched Stage 4, gate
re-based to zero-silent-deaths + Stage-4 cost-per-accepted-prime (≤5% survivor target retired).
Template updated (§A/§B/§D). **Standing next action:** owner curation of the 1 accept + 7 holds
(drafting deferred; corpus 1,325), then owner authorization of the full sweep — recommended
one flavor at a time (1a → 1b → 1c), curating between flavors, since incorporations change the
alias ground truth. Cost-per-accepted-prime is now the number this table must report per batch.
