diff --git a/research/bit589-recipe-floor/EXPECTED.json b/research/bit589-recipe-floor/EXPECTED.json new file mode 100644 index 0000000000..71878e5ab1 --- /dev/null +++ b/research/bit589-recipe-floor/EXPECTED.json @@ -0,0 +1,408 @@ +{ + "pins": { + "research/e8-bit-carrier-skeleton/code/hub/e8-r740-replica32/code/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482", + "research/e8-bit-p111-tuned/tune/EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4", + "research/e8-bit-p111-tuned/data/selection9-p111.json": "4ab1ed4529683cd184987f8bc3031fb7408b9cd22c25ab9cf541a8aaf896eaf1", + "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/global_k.py": "6368196a393ac25bb2918880e4c4bd31ed733b762c27b6873ab391cbc0c5c3c8", + "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/hosting_k.py": "081c3b95b18d900d97ce82af64fb428f085b6adc6d8ca93ea920797dad7eb81e", + "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/idle-axis-hosting/hosting_core.py": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3" + }, + "positive_control": { + "windows": { + "0": [ + 1, + 14, + [ + 0, + 1 + ] + ], + "1": [ + 1, + 7, + [ + 2 + ] + ], + "2": [ + 2, + 28, + [ + 0, + 1, + 2, + 3 + ] + ], + "3": [ + 2, + 7, + [ + 4 + ] + ], + "4": [ + 3, + 42, + [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + ], + "5": [ + 3, + 7, + [ + 6 + ] + ], + "6": [ + 0, + 42, + [ + 3, + 4, + 5, + 6, + 7, + 8 + ] + ], + "7": [ + 1, + 28, + [ + 5, + 6, + 7, + 8 + ] + ], + "8": [ + 2, + 14, + [ + 7, + 8 + ] + ] + }, + "remainder": { + "2": 435, + "4": 444, + "6": 444, + "7": 666, + "42": 9 + }, + "c": "1733427039589844234749/1000000000000000000000000", + "frozen_selection_remainder_equal": true, + "official_saving": 13174.7497998684 + }, + "negative_controls": { + "drop_bridge_before_stage_2": "rejected", + "drop_bridge_before_stage_3": "rejected", + "drop_bridge_before_stage_4": "rejected", + "drop_bridge_before_stage_5": "rejected", + "drop_bridge_before_stage_6": "rejected", + "drop_bridge_before_stage_7": "rejected", + "drop_local_0": "rejected", + "drop_local_1": "rejected", + "drop_local_2": "rejected", + "drop_local_3": "rejected", + "drop_local_4": "rejected", + "drop_local_5": "rejected", + "drop_local_6": "rejected", + "drop_local_7": "rejected", + "drop_local_8": "rejected", + "stage0_removed_from_all_windows": "hosting infeasible", + "flip_local_type_stage4": "rejected", + "invariants_at_identity": [ + 4, + 0, + 0, + 4 + ], + "invariants_at_template_product": [ + 0, + 4, + 4, + 0 + ] + }, + "search_K3": { + "valid_recipes": 28464, + "distinct_window_structures": 135 + }, + "search_K4": { + "valid_recipes": 2070720, + "distinct_window_structures": 1064 + }, + "search_K4_sha256": "42ec9e70fe11573dd1e19042f1b897965855d536f3563f369c44a9f1fe0f7b50", + "priced_K4": { + "structures": 1064, + "hosting_feasible": 46, + "hosting_infeasible": 1018, + "template": { + "windows": [ + [ + 7, + [ + 2 + ] + ], + [ + 7, + [ + 4 + ] + ], + [ + 7, + [ + 6 + ] + ], + [ + 14, + [ + 0, + 1 + ] + ], + [ + 14, + [ + 7, + 8 + ] + ], + [ + 28, + [ + 0, + 1, + 2, + 3 + ] + ], + [ + 28, + [ + 5, + 6, + 7, + 8 + ] + ], + [ + 42, + [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + ], + [ + 42, + [ + 3, + 4, + 5, + 6, + 7, + 8 + ] + ] + ], + "c": "1733427039589844234749/1000000000000000000000000", + "position": 1 + }, + "best": { + "windows": [ + [ + 7, + [ + 0 + ] + ], + [ + 7, + [ + 4 + ] + ], + [ + 7, + [ + 6 + ] + ], + [ + 14, + [ + 1, + 2 + ] + ], + [ + 14, + [ + 7, + 8 + ] + ], + [ + 28, + [ + 0, + 1, + 2, + 3 + ] + ], + [ + 28, + [ + 5, + 6, + 7, + 8 + ] + ], + [ + 42, + [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + ], + [ + 42, + [ + 3, + 4, + 5, + 6, + 7, + 8 + ] + ] + ], + "witness": [ + [ + null, + 0, + "F" + ], + [ + [ + 0, + 1, + -1 + ], + 0, + "R" + ], + [ + null, + 0, + "F" + ], + [ + [ + 0, + 1, + 1 + ], + 1, + "R" + ], + [ + [ + 1, + 2, + 1 + ], + 1, + "F" + ], + [ + [ + 1, + 2, + -1 + ], + 2, + "R" + ], + [ + [ + 2, + 3, + 1 + ], + 2, + "F" + ], + [ + [ + 2, + 3, + -1 + ], + 3, + "R" + ], + [ + null, + 3, + "F" + ] + ], + "remainder": { + "2": 435, + "4": 444, + "6": 444, + "7": 666, + "42": 9 + }, + "c": "1733427039589844234749/1000000000000000000000000", + "c_decimal": "0.001733427039589844234749", + "gain_over_pr589": "0", + "relative_gain": "0.000000%" + }, + "structures_strictly_above_pr589": 0, + "structures_equal_to_pr589": 8, + "distinct_hostable_prices": [ + "1733427039589844234749/1000000000000000000000000", + "866330643502981582543/500000000000000000000000", + "1731431510116874317849/1000000000000000000000000", + "1730667518959605464817/1000000000000000000000000", + "1729727562234116433443/1000000000000000000000000" + ], + "max_total_capacity": 3996, + "residuals_needed": 3951, + "outcome": { + "a stage lacks spanning capacity": 27, + "hostable": 46, + "joint stage transport or remainder cap": 2, + "total capacity below 3951": 989 + }, + "idle_segments": { + "9": 75, + "10": 513, + "11": 476 + } + } +} diff --git a/research/bit589-recipe-floor/PROOF.md b/research/bit589-recipe-floor/PROOF.md new file mode 100644 index 0000000000..c213c1ee91 --- /dev/null +++ b/research/bit589-recipe-floor/PROOF.md @@ -0,0 +1,123 @@ +# Local-count floor for the stage recipe + +This note shows that the stage recipe of the nine-stage bit template uses the +fewest possible local invocations for its number of data pairs. The recipe is +in `global_k.py` (`recipe(K)`), from the PR #386/#436/#443/#463 lineage as +generalised by PR #510. + +**Priority.** The bound is not new. The archived campaign report M states that +exchanging P bank pairs needs at least 2P+1 stages. Open PR #743 (Johnny +Franks) proves it uniformly with the potential `rank(A) + rank(D)` of the +diagonal blocks. That potential equals `2K − ν − μ'` below, so the two proofs +are the same argument. This independent formulation is kept because its four +invariants also drive the pruning of `recipe_search.py`. No priority is +claimed. + +## Scalar model of a recipe + +The template's own integer replay (`small()` in `global_k.py`) abstracts a +recipe to an integer matrix on `2K` banks. Bank `2p` is side 0 of pair `p`, and +bank `2p+1` is side 1. Order the coordinates as `V = V0 ⊕ V1`, where +`V0 = span(side 0 of every pair)` and `V1 = span(side 1 of every pair)`. Write +`L0 = V0 ⊕ 0` and `L1 = 0 ⊕ V1`. The events act as follows: + +| event | effect | form | +|---|---|---| +| forward local on pair `p` | `side1_p += side0_p` | lower unipotent `[[I,0],[S,I]]`, `S = e_p e_pᵀ`, rank 1 | +| reverse local on pair `p` | `side0_p -= side1_p` | upper unipotent `[[I,T],[0,I]]`, `T = -e_p e_pᵀ`, rank 1 | +| bridge `(d,s,c)` | `side0_d += c side0_s`, `side1_s -= c side1_d` | block diagonal `diag(A, A⁻ᵀ)` | +| final exchange | `(side0_p, side1_p) -> (side1_p, -side0_p)` | block anti-diagonal `X` | + +The template asserts that the whole recipe composes to the identity. Let `P` be +the product of all locals and bridges, so that `X P = I` (and bridges after the +last local are part of `P`). Then `P = X⁻¹` is block anti-diagonal: +`P(L0) = L1` and `P(L1) = L0`. + +## Theorem + +Work over any field. Let + +`P = Λ_n τ_n Λ_{n-1} ... Λ_1 τ_1 Λ_0`, + +where: + +- every `Λ_i` maps `L0` to `L0` and `L1` to `L1`; +- every `τ_i` is lower (`[[I,0],[S_i,I]]`) or upper (`[[I,T_i],[0,I]]`), with + `r_i = rank(τ_i - I)`. + +The matrices `S_i` and `T_i` may be arbitrary; they need not be symmetric or +integral. If `P(L0) = L1` and `P(L1) = L0`, then + +`Σ_i r_i ≥ 2K + 1`. + +**Corollary.** Every local of the bit template has rank 1, and every bridge +sequence is block diagonal. So any recipe that ends in the exchange of all `K` +pairs needs at least `2K + 1` locals, which is `2K + 1` stages. `recipe(K)` +uses exactly `2K + 1`, so it is optimal in this respect. Equivalently, at +`L = 9` stages there are at most `K = 4` exchanged pairs. The rank-mass +deficit `T(2Kv - L·cst)` therefore cannot be raised by re-designing the stage +recipe in this model: at fixed `L`, `K` cannot increase, and at fixed `K`, `L` +cannot decrease. + +## Proof + +For a linear map `g`, define + +- `μ(g) = dim(g L0 ∩ L0)` and `μ'(g) = dim(g L1 ∩ L0)`; +- `ν(g) = dim(g L0 ∩ L1)` and `ν'(g) = dim(g L1 ∩ L1)`. + +At `g = I` these are `(μ, μ', ν, ν') = (K, 0, 0, K)`. At `g = P` they must be +`(0, K, K, 0)`. Build `P` from the right, one factor at a time. + +**(a) Block-diagonal factors change nothing.** On the left, `Λ` preserves both +`L0` and `L1`, so `dim(ΛU ∩ L_j) = dim(Λ(U ∩ L_j)) = dim(U ∩ L_j)`. On the +right, `gΛL_j = gL_j`. + +**(b) A lower factor fixes ν and ν'; an upper factor fixes μ and μ'.** A lower +`τ` maps `L1` onto itself, so `dim(τU ∩ L1) = dim(U ∩ τ⁻¹L1) = dim(U ∩ L1)`. +The same argument applies to an upper `τ` with `L0`. + +**(c) A factor of rank r changes each quantity by at most r.** Let `U` and `W` +be subspaces and `x ∈ U ∩ W ∩ ker(τ - I)`. Then `x = τx ∈ τU ∩ W`, so +`dim(τU ∩ W) ≥ dim(U ∩ W) - r`. Applying the same bound to `τ⁻¹`, which also +has `rank(τ⁻¹ - I) = r`, gives the reverse inequality. + +By (a)–(c), only lower factors move `μ` and `μ'`, and only upper factors move +`ν` and `ν'`. Each moves them by at most its rank. So `Σ_lower r_i ≥ K` and +`Σ_upper r_i ≥ K`. + +Now look at the first factor `τ_1`; `Λ_0` does not matter by (a). + +- **`τ_1` is lower.** It fixes `L1` pointwise, so `τ_1 Λ_0 L1 = L1` and + `μ' = dim(L1 ∩ L0) = 0` stays 0. The later lower factors alone must raise + `μ'` from 0 to `K`. Hence `Σ_lower r_i ≥ K + r_1 ≥ K + 1`. +- **`τ_1` is upper.** It fixes `L0` pointwise, so `ν` stays 0 after it, and + symmetrically `Σ_upper r_i ≥ K + 1`. + +In both cases `Σ r_i ≥ 2K + 1`. ∎ + +## Tightness and checks + +- **Tightness.** `recipe(K)` attains the bound: `F_0` followed by + `(R_j B+ F_j B−)` for `j = 0..K-1`, which is `2K + 1` rank-1 locals. +- **Brute force.** `floor_check.py` independently confirms `K = 1` and `K = 2`. + For `K = 1` it uses vectors in `[-3,3]`; for `K = 2` it uses all primitive + vectors in `[-2,2]²` and entries up to 50. No product of `2K` rank-1 shears is + block anti-diagonal, while products of `2K + 1` shears are. This is a finite + check of the bounded class only; the theorem above is the general statement. + +## Scope + +- **What the theorem covers.** The theorem is about the template's scalar + abstraction: each local is a rank-1 shear on one pair. Its conclusion does + not depend on the coefficients, on the field (it holds over F2, where the + template also replays its columns), or on which block-diagonal maps sit + between locals. +- **What it does not cover.** It does not cover templates in which a local + acts on several pairs at once, or in which free data movement is + off-block-diagonal, for example a cheap `side1 += side0` addition that is not + a paid local. Nor does it cover architectures where the exchange is not + required on every data pair. +- **Hosting, words and κ.** It says nothing about how idle children are + hosted, which is the subject of the search in `README.md`. It says nothing + about the local word either. It changes no κ. diff --git a/research/bit589-recipe-floor/README.md b/research/bit589-recipe-floor/README.md new file mode 100644 index 0000000000..efb4604ec6 --- /dev/null +++ b/research/bit589-recipe-floor/README.md @@ -0,0 +1,190 @@ +# Nine-stage stage recipes cannot improve PR #589's idle hosting + +**Status: scoped negative result (bit supplier). No new κ.** + +The question is whether any nine-stage stage recipe can improve PR #589's idle hosting. The domain searched is every +recipe with four exchanged pairs, one rank-1 local per stage and at most one ±1 bridge per gap: 2,070,720 valid +recipes, 1,064 distinct idle-window structures. **None raises PR #589's bit c.** The template recipe attains the +maximum, tied by seven other structures that leave the identical remainder. The width-8 hosting wall `R ≤ 4v = 444` +holds for every recipe in the class. + +The selected #1094 assembly is complex-bound: complex b is 0.0016755 and bit c is 0.0017334. No bit-side result +changes κ (0.001672660197076918). + +## Question and predecessors + +PR #589's nine-stage bit c is fixed by two inputs. The first is the word's local paid profile, which PR #886 and #933 +showed is locally optimal. The second is the **idle remainder** `{2:435, 4:444, 6:444, 7:666, 42:9}` per replica that +PR #442 hosting leaves behind. + +- **Fixed windows (bit589-width-packing).** The merged `research/bit589-width-packing` (Sagar Thakrar) proved that, + with the template's idle windows held fixed, no width-8 re-hosting improves c. It identified helper width 7 as the + lever. +- **Geometric audit (#1307).** Open #1307 (commdata2338) audits the geometric disjointness of the same hosting. +- **This note: vary the windows.** Here the windows themselves vary. They are produced by the *stage recipe* + (`recipe(K)` in `global_k.py`, PR #463/#510 lineage). Per data-coordinate copy, the template advances idle pairs + by Δ = {6,6,4,4,2,2,1,1,1} levels. A Δ-level advance is a rank-7Δ child, which can host ⌊7Δ/8⌋ width-8 residuals + from the stages it spans. +- **What was open.** Could another valid recipe produce fewer or longer advances, and so more capacity and a + cheaper remainder? + +## Results + +| question | answer | +|---|---| +| Fewer locals per exchanged pair? | **No: 2K+1 locals are necessary.** First proved uniformly by open #743 (Johnny Franks; archived report M). `PROOF.md` gives an equivalent formulation whose invariants drive the search's pruning. `floor_check.py` confirms K = 1, 2. At nine stages K ≤ 4, so the deficit `T(2Kv − L·cst)` cannot be raised by a recipe. | +| PR #589 from the recipe alone? | **Exact.** The template recipe, read unchanged from the vendored `global_k.py`, gives windows equal to the frozen official selection index by index. It gives the same remainder and c = `1733427039589844234749/10^24`. | +| Optimistic ceiling: any split of the 27 idle level-steps, pooled residuals, no recipe validity | c ≤ 0.001927 (+11.2%), but only with 4–5 segments such as Δ = 8+8+6+5. | +| The same ceiling with ≥ 9 segments | c ≤ 0.0017515 (+1.04%), which needs advances of 8 levels. | +| Exhaustive K = 4 class | **2,070,720** recipes form **1,064** window structures with 9 / 10 / 11 idle segments (75 / 513 / 476 structures). Σ Δ = 27 and max Δ ≤ 6 throughout. | +| Hosting (count/window programme, 0 banks, paid remainder ≤ 45) | Capacity is `27 − #segments ≤ 18` slots per copy set, at most **3,996** against 3,951 needed. 989 structures fail total capacity, 27 lack capacity at some stage, 2 fail the joint transport or remainder cap, and **46 are hostable**. | +| Best exact c | **PR #589's c exactly**, attained by 8 structures with the same remainder. The other hostable structures sit at four lower values, 0.044% to 0.213% lower. **None is higher.** | + +### Why the remainder is pinned + +- **Capacity equals Δ − 1.** For 1 ≤ Δ ≤ 8, `⌊7Δ/8⌋ = Δ − 1`. A fully hosted advance therefore leaves exactly + `8 − Δ`, and capacity per copy set is `Σ(Δ_i − 1) = 27 − #segments`. +- **The template already has the fewest segments.** The smallest segment count in the class grows as 3(K−1): 3, 6 + and 9 for K = 2, 3, 4. The longest advance grows as 2(K−1): 2, 4 and 6. Hence, at K = 4: + - capacity is at most 18 slots, so `R ≤ 18·2v/9 = 4v` for every recipe; + - no advance reaches the 7–8 levels that the optimistic layouts need. +- **The same conclusion as with fixed windows.** With 9 segments and Σ Δ = 27, the remainders `8 − Δ` total 45 per + copy set. The 45 spare slots are best left as whole rank-42 copies, as bit589-width-packing proved for the fixed + windows. +- **Where a gain must come from instead.** Any further bit gain must come from outside this class: + - wider gaps (open question 1); + - other stage counts (eleven stages is already worse for this word: 0.0017110); + - banks or split residuals (#448/#480, not established); + - **helper width**, which is bit589-width-packing's lever. + +## Method + +1. **Scalar model.** The model is the template's own integer replay. A forward local is `side1_p += side0_p`, a + reverse local is `side0_p −= side1_p`, and a bridge is `diag(A, A⁻ᵀ)`. A recipe is valid iff the product is block + anti-diagonal, so that a final bridge sequence plus the exchange gives the identity. + - A Levi before the first local, or after the last, cannot change validity, because it preserves L0 and L1. + - So the search omits both and, by pair symmetry, puts the first local on pair 0. +2. **Search.** Depth-first search with exact integer ranks. + - It prunes with `max(μ, K−μ') + max(K−ν, ν') ≤ remaining stages` from `PROOF.md`. + - Completability of (stage, product) is memoised. + - Entries are capped at |8|. At K = 3, a cap of 64 gives the identical 28,464 recipes. +3. **Idle children and windows.** Idle children are inserted exactly as `global_k` does: before a local, before a + bridge, and finally in pair order. Windows follow PR #442 `hosting_core.windows`. +4. **Hosting.** Hosting is an exact integer programme with PR #442's objective. + - Every residual is hosted (0 banks, as PR #589). + - A residual of stage s is hosted only in a window spanning s. + - Every paid remainder is ≤ 45, which keeps halving depth 2 and row 18,355 < 20,161. + - The template and the best five structures are re-solved with the **vendored official** `hosting_k.solve` + (`host_all=True, max_remainder=45`). It must give the same objective and the same c. +5. **Price.** The price is the pinned rational moment engine of the selected assembly (sha256 `81cbc864…`), with the + inherited bad-branch surcharge. The global profile is `288 ×` local + `32 ×` remainder. The rank-mass identity + `T(2Kv − L·cst) = 10,272` and halving depth 2 are asserted for every structure. + +## Reproduce + +```sh +python3.12 -m pip install numpy==2.5.4 scipy==1.18.1 +python3.12 -B research/bit589-recipe-floor/verify.py --reuse --jobs 2 # registered generic replay, about 2 minutes +python3.12 -B research/bit589-recipe-floor/verify.py --jobs 12 # also reruns the K=4 search, about 25 minutes +python3.12 scripts/research_package.py --package research/bit589-recipe-floor +``` + +- **`--reuse`** re-prices the committed search `data/search-K4.json`, which is hash-pinned in `EXPECTED.json`. +- **Without `--reuse`**, the search is rerun and must equal the committed file in content. +- **Measured.** `--reuse --jobs 2` takes 24 s through `scripts/research_package.py` (Python 3.12.15). The full run + takes 26 min 55 s with `--jobs 12` and 165 MB RSS. Both used numpy 2.5.4 and scipy 1.18.1 on Linux x86-64. + +Expected last line: + +```text +PASS_BIT589_RECIPE_FLOOR floor=2K+1 K3_recipes=28464 K4_recipes=2070720 K4_structures=1064 max_capacity=3996 hostable=46 best_c=1733427039589844234749/1000000000000000000000000 equal=8 above_pr589=0 no_new_kappa (…s) +``` + +## Controls + +- **Positive.** The template recipe composes with the exchange to the identity. Its windows equal the frozen + `selection9-p111.json` index by index. The own programme, the frozen selection and the official programme agree, + and the price is PR #589's c exactly. +- **Negative (19).** These all fail as they should: + - dropping any of the six internal bridges; + - dropping any of the nine locals; + - flipping one local's type; + - removing stage 0 from every window (hosting becomes infeasible). + + The invariants are `(4,0,0,4)` at the identity and `(0,4,4,0)` at the template product. +- **Agreement between implementations.** + - The numpy and pure-Python floor checks agree (K = 2: 180,092 states at length 5, 12 hits, none shorter). + - A separate prototype search found the same 2,070,720 recipes and the same 1,064 structures at K = 4. + - The prototype and package also agree on all 135 K = 3 structures. + +## Scope + +- **Searched class.** Nine-stage recipes with K = 4, one local per stage, at most one bridge (coefficient ±1) per + gap, and entries |≤ 8|. Priced with PR #589's word under PR #442 width-8 whole-residual hosting, 32 replicas and + 0 banks. +- **Hosting relaxes geometry.** "Hostable" means admissible in PR #442's count/window programme. Open #1307 shows that + this does not imply disjoint physical axes. The search is therefore a relaxation, and a stricter geometric check could + only remove candidates. It cannot weaken the negative result. +- **Not searched.** + - Gaps with two or more bridges: a K = 3 probe did not finish in 20 minutes. + - Banks, and cross-copy or split residuals. + - Other stage counts, words or replica schemes. + - Locals that are not single-pair rank-1 shears. + - Width-7 helpers. + + "No better structure" is a statement about this class only. +- **Proof status.** The 2K+1 floor has written proofs here and in #743. The K = 4 result is an exhaustive finite + enumeration, not a formal proof. Hosting is optimal only within the stated integer programme. +- **κ and inherited assumptions.** κ is unchanged. All inherited bit assumptions remain: mutable-source realization, + whole-call hosting, all-size compiler, precision and tape, and H1–H5. +- **Files.** Only this directory is added. The selected record, PR #589's package and `upstream/` are unchanged. + +## Open next questions + +The same three questions, with their fields, are in `TASK.json`. + +1. **Wider gaps.** + - *Question:* can a gap holding several bridges give a K = 4 recipe with fewer than 9 idle segments, or with an + advance of 7–8 levels? + - *Why it matters:* it is the only lever left inside this template. + - *First step:* rerun `recipe_search.py 3 --bridges-per-gap 2` with stronger pruning. + - *Blocked by:* search cost. +2. **A segment theorem.** + - *Question:* is "at least 3(K−1) idle segments" a theorem for every bridge recipe? + - *Why it matters:* it would make `R ≤ 4v` recipe-independent at width 8, at every K. + - *First step:* generalise the observed 3/6/9 into entry, final and borrowing synchronisation counts. + - *Blocked by:* a written proof; the rank invariants bound locals, not syncs. +3. **The width-7 interaction.** + - *Question:* once width-7 helpers exist, which recipe is best? + - *Why it matters:* 7 divides every 7Δ window, so capacity becomes 27 slots for every recipe. + - *First step:* re-price `data/search-K4.json` at width 7 under bit589-width-packing's bracket. + - *Blocked by:* no width-7 bit helper exists yet. + +## Provenance + +- **Base.** `410026dc5513b87db92ae98571d1d5984c69a983`. The work was started on `8bddbee3`; every pinned input is + byte-identical on both bases. +- **Assignment and card.** OS-random assignment seed **18** (bit supplier track). Catalogue card `selected-packing`, + with scope declared `refined` in `TASK.json`. +- **Pins.** All inputs are hash-pinned in `SOURCES.json` and `recipe_lib.py` and checked by `verify.py`: + - the moment engine and PR #589's `EXPECTED.json`, which match the selected assembly's own input pins; + - the vendored `global_k.py`, `hosting_k.py` and `hosting_core.py`; + - the frozen selection. +- **Claim.** [Discussion #1427](https://github.com/CrocSwap/integer-mult-bounds/discussions/1427). +- **Overlap.** `scripts/find_overlap.py --refresh` was run on 2026-10-14 over 785 open PRs and 145 discussions, + searching recipe, hosting, idle and stage terms. It found no recipe-variation search. The adjacent work is credited: + bit589-width-packing, #1307, #743, #886 and #933. + +## Credit + +- **Template and recipe lineage.** Zhihao Chen and eumemic (PR #386/#436), chafreaky (#439/#443), and + DreamingOfClouds (#463 generalisation, #510 nine-stage chain, #589). +- **Hosting.** DaysSky (PR #442 idle-axis hosting). +- **The word.** eumemic (#543/#555), DreamingOfClouds (#545/#589), and Jacob Sussman (the E8 unit and the borrowing + chain). +- **The 2K+1 floor.** Archived report M and Johnny Franks (#743). +- **Fixed-window hosting bound.** Sagar Thakrar (bit589-width-packing). +- **Geometric audit.** commdata2338 (open #1307). +- **Paid-profile predecessors.** SethBurkart123 (#886) and #933. + +Prepared by Ian Libânio with substantial AI assistance (Claude Opus 5.5, Anthropic, via Claude Code). Apache-2.0. diff --git a/research/bit589-recipe-floor/SOURCES.json b/research/bit589-recipe-floor/SOURCES.json new file mode 100644 index 0000000000..23317954b3 --- /dev/null +++ b/research/bit589-recipe-floor/SOURCES.json @@ -0,0 +1,54 @@ +{ + "schema_version": 1, + "base_commit": "410026dc5513b87db92ae98571d1d5984c69a983", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "c05fafaa25ba95b2d5af86b1800427198e3d20eb", + "sha256": "89b5928bc92c81e2647b6d702a7ad85a6795b8f44e2eb267b2ff3145d8f2b2ce" + }, + { + "path": "research/e8-bit-carrier-skeleton/code/hub/e8-r740-replica32/code/engines/moment.py", + "usage": "input", + "git_blob": "7d697cb45203fe72d97037403d6da41f71f3b7fd", + "sha256": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482" + }, + { + "path": "research/e8-bit-p111-tuned/data/selection9-p111.json", + "usage": "input", + "git_blob": "e69ea66a3add357f570fc5552ab6368b3c8f9bb2", + "sha256": "4ab1ed4529683cd184987f8bc3031fb7408b9cd22c25ab9cf541a8aaf896eaf1" + }, + { + "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json", + "usage": "input", + "git_blob": "e293ddc557742637f9f679f083a1a282d87b1b13", + "sha256": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4" + }, + { + "path": "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/global_k.py", + "usage": "input", + "git_blob": "3df12bd632f1fdba825ced57110a1fee82eb2857", + "sha256": "6368196a393ac25bb2918880e4c4bd31ed733b762c27b6873ab391cbc0c5c3c8" + }, + { + "path": "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/hosting_k.py", + "usage": "input", + "git_blob": "02fea8320b676e14f8ffa242c3ddfa85fa829e31", + "sha256": "081c3b95b18d900d97ce82af64fb428f085b6adc6d8ca93ea920797dad7eb81e" + }, + { + "path": "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/idle-axis-hosting/hosting_core.py", + "usage": "input", + "git_blob": "68b536daa9e6546c0aa046934bf840aaa3c3fde3", + "sha256": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3" + } + ] +} diff --git a/research/bit589-recipe-floor/TASK.json b/research/bit589-recipe-floor/TASK.json new file mode 100644 index 0000000000..53f1c4ba65 --- /dev/null +++ b/research/bit589-recipe-floor/TASK.json @@ -0,0 +1,72 @@ +{ + "schema_version": 1, + "task_id": "selected-packing", + "priority_revision": 2, + "base_commit": "410026dc5513b87db92ae98571d1d5984c69a983", + "original_card": { + "id": "selected-packing", + "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?", + "starting_points": [ + "certificates/selected-result.json", + "research/heterogeneous-owner-assembly/README.md" + ], + "methods": [ + "Search a named unclaimed canonical candidate domain with a reproducible partition.", + "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem." + ], + "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.", + "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.", + "allowed_variations": [ + "One bounded residual packing instance or exact relaxation." + ], + "scope_change_triggers": [ + "Rerunning an existing search with only a different seed as a separate mathematical contribution." + ], + "overlap_terms": [ + "T16", + "owner exchange", + "packing" + ] + }, + "scope_status": "refined", + "actual_scope": "Bit-side selected packing: can any nine-stage stage recipe (K = 4 exchanged pairs, one rank-1 local per stage, at most one +-1 bridge before each local, entries |<= 8|) change PR #589's idle windows so that PR #442 whole-residual hosting (width 8, 0 banks, paid remainder <= 45) raises the exact nine-stage bit c above 1733427039589844234749/10^24?", + "scope_change_reason": "The card's starting points are complex-side packings. Here the packing is the selected bit supplier's: 3,951 width-8 residuals per replica in the idle windows of the nine-stage template. research/bit589-width-packing proved that re-hosting cannot help with the template recipe's windows held fixed; this search varies the recipe that generates those windows. The canonical domain is every valid recipe of the stated class, enumerated exhaustively (not a seeded heuristic).", + "bottleneck_link": "Side result for the non-binding supplier: the selected #1094 assembly is complex-bound (complex b 0.0016755 < bit c 0.0017334), so a bit gain only raises the bit cap. It closes the recipe/hosting lever for PR #589's word in this class and leaves helper width (bit589-width-packing) as the identified bit-side lever.", + "budget_minutes": 240, + "stop_rule": "Price the optimistic bound over all idle-segment partitions first; then enumerate the class exhaustively and price every distinct window structure exactly; stop at the first structure above PR #589's c or at completion of the enumeration.", + "outcome": "negative-result", + "evidence": "2,070,720 valid recipes (1,064 window structures, 9-11 idle segments, max advance 6 levels). Capacity is 27 - #segments <= 18 slots per copy set (3,996 vs 3,951 needed) for every structure; 46 are hostable with 0 banks; the best c equals PR #589's exactly (8 tied structures, identical remainder), none is higher. Template recipe reproduces PR #589's c and frozen selection from the recipe alone; official hosting_k.solve agrees on the top and template structures. The 2K+1 local-count floor (duplicating open #743) is re-proved in PROOF.md. See README.md and EXPECTED.json.", + "author": "Ian Libânio", + "ai_assistance": "Substantial: search, proofs, code and text prepared with Claude Opus 5.5 (Anthropic) via Claude Code; assignment seed 18 from Python secrets on the first base 8bddbee3, rebased onto 410026dc with unchanged inputs.", + "open_questions": [ + { + "question": "Can a gap holding several bridges (a Levi element with support larger than two pairs) give a K = 4 recipe with fewer than 9 idle segments or an advance of 7-8 levels?", + "why_it_matters": "It is the only route left inside the nine-stage, width-8 template that could raise hosting capacity above 18 slots (the R <= 4v wall) or reach the optimistic +1.04% layouts.", + "first_step": "Run recipe_search.py 3 --bridges-per-gap 2 with stronger pruning (the plain run did not finish in 20 minutes on 12 cores) and compare its idle-partition set with the single-bridge one.", + "blocked_by": "Search cost; a segment-count proof (next question) would replace it." + }, + { + "question": "Is 'at least 3(K-1) idle segments' a theorem for every bridge recipe that exchanges K pairs with 2K+1 rank-1 locals?", + "why_it_matters": "With floor(7D/8) = D-1 it would make the width-8 hosting wall R <= 4v recipe-independent at every K, closing the recipe lever without enumeration.", + "first_step": "Generalise the observed minima (3, 6, 9 segments for K = 2, 3, 4): K-1 entry advances, K-1 final advances, and one level-synchronising advance per borrowing step between pairs.", + "blocked_by": "A written proof of the synchronisation count; the rank invariants of PROOF.md bound locals, not level syncs." + }, + { + "question": "Once width-7 bit helpers exist, which recipe minimises the idle remainder?", + "why_it_matters": "Width 7 divides every 7D window, so capacity becomes 27 slots per copy set for every recipe and the recipe ranking may change; bit589-width-packing prices up to +23% for the template alone.", + "first_step": "Re-price data/search-K4.json with width-7 residuals (generalise recipe_lib.host to width w) under bit589-width-packing's local-profile bracket.", + "blocked_by": "No width-7 bit helper exists yet (H4 literal cleanup retiming, per bit589-width-packing)." + } + ] +} diff --git a/research/bit589-recipe-floor/VERIFY.json b/research/bit589-recipe-floor/VERIFY.json new file mode 100644 index 0000000000..4a30b578f6 --- /dev/null +++ b/research/bit589-recipe-floor/VERIFY.json @@ -0,0 +1,31 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [ + "numpy==2.5.4", + "scipy==1.18.1" + ], + "inputs": [ + "research/e8-bit-carrier-skeleton/code/hub/e8-r740-replica32/code/engines/moment.py", + "research/e8-bit-p111-tuned/data/selection9-p111.json", + "research/e8-bit-p111-tuned/tune/EXPECTED.json", + "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/global_k.py", + "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/hosting_k.py", + "research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/idle-axis-hosting/hosting_core.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--reuse", + "--jobs", + "2" + ], + "timeout_seconds": 600, + "checks": "pins; template-recipe positive control (frozen selection windows, remainder, exact PR589 c, official hosting_k objective); 19 negative controls; K=1,2 floor check; full K=3 search (28,464 recipes); hash-pinned K=4 search re-priced over all 1,064 structures with official-programme cross-checks; comparison with EXPECTED.json" + } + ] +} diff --git a/research/bit589-recipe-floor/data/search-K4.json b/research/bit589-recipe-floor/data/search-K4.json new file mode 100644 index 0000000000..70f770f458 --- /dev/null +++ b/research/bit589-recipe-floor/data/search-K4.json @@ -0,0 +1 @@ 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diff --git a/research/bit589-recipe-floor/floor_check.py b/research/bit589-recipe-floor/floor_check.py new file mode 100644 index 0000000000..238d08b341 --- /dev/null +++ b/research/bit589-recipe-floor/floor_check.py @@ -0,0 +1,69 @@ +#!/usr/bin/env python3 +"""Finite confirmation of the local-count floor (PROOF.md) for K = 1, 2. + +Breadth-first over products of rank-1 shears: lower u uᵀ (forward local conjugated by any bridge sequence) and upper +-w wᵀ (reverse local), u, w primitive integer vectors with entries in [-B, B], matrix entries bounded by E. A product +that maps L0 -> L1 and L1 -> L0 (block anti-diagonal) is what a recipe with a free final Levi and the exchange needs. +Expected: none at length 2K, some at 2K + 1. Standard library only. This is a bounded finite check, not the proof. +Prepared by Ian Libânio with substantial AI assistance (Claude Opus 5.5, Anthropic, via Claude Code). Apache-2.0.""" +import itertools, json, math, sys + + +def primitive_vectors(K, B): + out = [] + for v in itertools.product(range(-B, B + 1), repeat=K): + if any(v) and next(x for x in v if x) > 0 and math.gcd(*map(abs, v)) == 1: + out.append(v) + return out + + +def generators(K, B): + gens = [] + for u in primitive_vectors(K, B): + S = [[u[i] * u[j] for j in range(K)] for i in range(K)] + low = [[int(i == j) for j in range(2 * K)] for i in range(2 * K)] + up = [[int(i == j) for j in range(2 * K)] for i in range(2 * K)] + for i in range(K): + for j in range(K): + low[K + i][j] = S[i][j] + up[i][K + j] = -S[i][j] + gens += [tuple(map(tuple, low)), tuple(map(tuple, up))] + return gens + + +def mul(A, B): + n = len(A) + return tuple(tuple(sum(A[i][k] * B[k][j] for k in range(n) if A[i][k]) for j in range(n)) for i in range(n)) + + +def anti(P, K): + return all(P[i][j] == 0 for i in range(K) for j in range(K)) and \ + all(P[i][j] == 0 for i in range(K, 2 * K) for j in range(K, 2 * K)) + + +def run(K, B, E): + gens = generators(K, B) + ident = tuple(tuple(int(i == j) for j in range(2 * K)) for i in range(2 * K)) + layer = {ident}; rows = [] + for length in range(1, 2 * K + 2): + new = set() + for M in layer: + for g in gens: + P = mul(g, M) + if max(abs(x) for r in P for x in r) <= E: + new.add(P) + layer = new + hits = sum(1 for P in layer if anti(P, K)) + rows.append(dict(length=length, states=len(layer), block_antidiagonal=hits)) + return dict(K=K, vector_bound=B, entry_bound=E, generators=len(gens), layers=rows, + floor_holds=all(r['block_antidiagonal'] == 0 for r in rows if r['length'] <= 2 * K), + attained_at_2K_plus_1=rows[2 * K]['block_antidiagonal'] > 0) + + +if __name__ == '__main__': + res = [run(1, 3, 50), run(2, 2, 50)] + for r in res: + print(' K=%d: %s' % (r['K'], ', '.join('L%d:%d/%d' % (x['length'], x['block_antidiagonal'], x['states']) for x in r['layers']))) + assert r['floor_holds'] and r['attained_at_2K_plus_1'], r + json.dump(res, sys.stdout if len(sys.argv) < 2 else open(sys.argv[1], 'w'), indent=1) + if len(sys.argv) < 2: print() diff --git a/research/bit589-recipe-floor/price_structures.py b/research/bit589-recipe-floor/price_structures.py new file mode 100644 index 0000000000..fa3545700c --- /dev/null +++ b/research/bit589-recipe-floor/price_structures.py @@ -0,0 +1,100 @@ +#!/usr/bin/env python3 +"""Price every idle-window structure of a K = 4 recipe search with PR #589's word at nine stages. + +For each structure: the stage-compatible hosting programme (recipe_lib.host: every residual hosted, 0 banks, every paid +remainder <= 45) and the exact rational nine-stage c of the pinned moment engine. The best structures and the template +structure are re-solved with the vendored official PR #442 programme (hosting_k.solve, host_all=True, max_remainder=45) +and must give the same objective. +usage: price_structures.py SEARCH.json OUT.json [--jobs N] +Prepared by Ian Libânio with substantial AI assistance (Claude Opus 5.5, Anthropic, via Claude Code). Apache-2.0.""" +import argparse, json, sys, time +from collections import Counter +from fractions import Fraction as Q +from multiprocessing import Pool +from pathlib import Path +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import recipe_lib as RL + +L = 9 + + +def solve_one(row): + w = RL.pr589() + win = {i: (None, r, frozenset(st)) for i, (r, st) in enumerate(row['windows'])} + out = RL.host(win, L, 2 * w['v'], w['R']) + if out is None: return dict(row, hosting='infeasible') + rem, proxy = out + return dict(row, hosting='feasible', remainder={str(r): n for r, n in sorted(rem.items())}, proxy=proxy) + + +def official(row, HK): + w = RL.pr589() + win = {i: (None, r, frozenset(st)) for i, (r, st) in enumerate(row['windows']) if st} + ys, zs, val = HK.solve(win, 2 * w['v'], {(s, 8): w['R'] for s in range(L)}, RL.M9, host_all=True, max_remainder=45) + rem = Counter() + for (i, pat), n in ys.items(): + if win[i][1] - sum(pat): rem[win[i][1] - sum(pat)] += n + for i, (r, st) in enumerate(row['windows']): + if not st: rem[r] += 2 * w['v'] # a window with no stage cannot host (dropped by emit_k too) + return val, rem + + +if __name__ == '__main__': + ap = argparse.ArgumentParser(); ap.add_argument('search', type=Path); ap.add_argument('out', type=Path) + ap.add_argument('--jobs', type=int, default=1); ap.add_argument('--official-top', type=int, default=5) + a = ap.parse_args(); t0 = time.time() + RL.check_pins(); E = RL.moment_engine(); w = RL.pr589() + S = json.loads(a.search.read_text()); assert S['K'] == 4 and S['stages'] == L + rows = S['structures'] + with Pool(a.jobs) as pool: res = pool.map(solve_one, rows, chunksize=4) + feas = sorted((r for r in res if r['hosting'] == 'feasible'), key=lambda r: r['proxy']) + # template structure + st, fin = RL.from_template(RL.template_recipe(4), 4) + tkey = [[r, list(s)] for r, s in RL.structure_key(RL.windows(RL.schedule(st, 4)))] + for r in feas: + rem = Counter({int(k): n for k, n in r['remainder'].items()}) + c, up = RL.price(E, RL.global_profile(w['local'], rem, L), 4, L, w['v'], w['cst']) + r['c'] = str(c); r['c_decimal'] = E.decimal(c) + feas.sort(key=lambda r: (-Q(r['c']), r['proxy'])) + template = next(r for r in feas if r['windows'] == tkey) + assert Q(template['c']) == w['c'], 'template structure does not reproduce PR589 c' + HK = RL.official_hosting(); checks = [] + for r in feas[:a.official_top] + [template]: + val, rem = official(r, HK) + own = {int(k): n for k, n in r['remainder'].items()} + saving_own = sum(RL.f(rr) * 2 * w['v'] for rr, _ in r['windows']) - r['proxy'] + assert abs(val - saving_own) < 1e-6, ('official objective differs', val, saving_own) + cc, _ = RL.price(E, RL.global_profile(w['local'], rem, L), 4, L, w['v'], w['cst']) + assert cc == Q(r['c']), ('official selection prices differently', cc, r['c']) + checks.append(dict(windows=r['windows'], official_saving=val, own_saving=saving_own, same_c=True)) + best = feas[0]; rank = [Q(r['c']) for r in feas] + need = L * w['R']; reasons = {} + for r in res: + cap = sum((rk // 8) * 2 * w['v'] for rk, st in r['windows'] if st) + r['capacity'] = cap + if r['hosting'] == 'feasible': why = 'hostable' + elif cap < need: why = 'total capacity below %d' % need + elif any(sum((rk // 8) * 2 * w['v'] for rk, st in r['windows'] if s in st) < w['R'] for s in range(L)): why = 'a stage lacks spanning capacity' + else: why = 'joint stage transport or remainder cap' + reasons[why] = reasons.get(why, 0) + 1 + segs = {} + for r in res: segs[len(r['windows'])] = segs.get(len(r['windows']), 0) + 1 + out = dict(status='PASS_RECIPE_STRUCTURES_PRICED', search=dict((k, S[k]) for k in S if k != 'structures'), + structures=len(rows), hosting_feasible=len(feas), hosting_infeasible=len(rows) - len(feas), + template=dict(windows=tkey, c=template['c'], position=1 + sum(1 for x in rank if x > Q(template['c']))), + best=dict(windows=best['windows'], witness=best['witness'], remainder=best['remainder'], c=best['c'], c_decimal=best['c_decimal'], + gain_over_pr589=str(Q(best['c']) - w['c']), relative_gain='%.6f%%' % (100 * float(Q(best['c']) / w['c'] - 1))), + structures_strictly_above_pr589=sum(1 for x in rank if x > w['c']), + structures_equal_to_pr589=sum(1 for x in rank if x == w['c']), + distinct_hostable_prices=sorted({str(x) for x in rank}, key=Q, reverse=True), + max_total_capacity=max(r['capacity'] for r in res), residuals_needed=need, + outcome=dict(sorted(reasons.items())), idle_segments={str(k): segs[k] for k in sorted(segs)}, + top=[dict(c=r['c'], windows=r['windows'], remainder=r['remainder'], witness=r['witness']) for r in feas[:10]], + official_crosscheck=checks, all=[dict(c=r.get('c'), hosting=r['hosting'], capacity=r['capacity'], windows=r['windows']) for r in sorted(res, key=lambda r: r['windows'])], + seconds=round(time.time() - t0, 1)) + a.out.write_text(json.dumps(out, indent=1) + '\n') + print(' %d structures (idle segments %s): %d hostable with 0 banks; outcome %s; max capacity %d for %d residuals' + % (len(rows), out['idle_segments'], len(feas), out['outcome'], out['max_total_capacity'], need)) + print(' template c = PR589 c (rank %d); best c = %s (%s); %d equal, %d above PR589; official programme agrees on %d' + % (out['template']['position'], best['c_decimal'][:28], out['best']['relative_gain'], out['structures_equal_to_pr589'], + out['structures_strictly_above_pr589'], len(checks))) diff --git a/research/bit589-recipe-floor/recipe_lib.py b/research/bit589-recipe-floor/recipe_lib.py new file mode 100644 index 0000000000..893203ab6c --- /dev/null +++ b/research/bit589-recipe-floor/recipe_lib.py @@ -0,0 +1,247 @@ +"""Shared code: scalar model of a nine-stage stage recipe, idle insertion, hosting windows, hosting programme and price. + +A recipe is a list of stages; stage s carries (gap, pair, type): `gap` is None or one bridge (d, src, c) applied just +before the local, `type` is 'F' (forward local, side1 += side0) or 'R' (reverse local, side0 -= side1). Stage 0 has no +gap (a Levi before every local is a global basis change). Bridges after the last local are a free final Levi: they act +when every pair is already at level L-1 and touch no window. Idle children are inserted exactly when a level must rise +(before a local, before a bridge, and at the end in pair order), as in PR #463/#510 global_k.py; windows follow PR #442 +hosting_core.windows (a bridge or local touching the pair closes its window). +Prepared by Ian Libânio with substantial AI assistance (Claude Opus 5.5, Anthropic, via Claude Code). Apache-2.0.""" +import gzip, hashlib, importlib.util, json, math +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +PINS = { + # selected assembly input pin (research/community-frontier942-audit/ASSEMBLY.json input_sha256["engines/moment.py"]) + 'research/e8-bit-carrier-skeleton/code/hub/e8-r740-replica32/code/engines/moment.py': + '81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482', + # PR #589 supplier record (local paid profile, c, frozen nine-stage remainder source) + # (= the selected assembly input pin "package:inputs/PR589-EXPECTED.json") + 'research/e8-bit-p111-tuned/tune/EXPECTED.json': 'b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4', + 'research/e8-bit-p111-tuned/data/selection9-p111.json': '4ab1ed4529683cd184987f8bc3031fb7408b9cd22c25ab9cf541a8aaf896eaf1', + 'research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/global_k.py': + '6368196a393ac25bb2918880e4c4bd31ed733b762c27b6873ab391cbc0c5c3c8', + 'research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/hosting_k.py': + '081c3b95b18d900d97ce82af64fb428f085b6adc6d8ca93ea920797dad7eb81e', + 'research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/idle-axis-hosting/hosting_core.py': + 'd8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3', +} +H, M9, T = 8, 64, 32 + + +def sha(rel): + return hashlib.sha256((ROOT / rel).read_bytes()).hexdigest() + + +def load(rel, name): + sp = importlib.util.spec_from_file_location(name, ROOT / rel) + mod = importlib.util.module_from_spec(sp); sp.loader.exec_module(mod); return mod + + +def moment_engine(): + rel = 'research/e8-bit-carrier-skeleton/code/hub/e8-r740-replica32/code/engines/moment.py' + assert sha(rel) == PINS[rel], 'moment engine differs from the selected assembly pin' + return load(rel, 'pinned_moment') + + +def check_pins(): + bad = {rel: sha(rel) for rel, want in PINS.items() if sha(rel) != want} + assert not bad, ('pinned inputs differ', bad) + return dict(PINS) + + +def official_hosting(): + """the vendored PR #510/#545 hosting_k (PR #442 programme with host_all / max_remainder), imported unchanged""" + return load('research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/hosting_k.py', + 'official_hosting_k') + + +def pr589(): + e = json.loads((ROOT / 'research/e8-bit-p111-tuned/tune/EXPECTED.json').read_text()) + w = e['word'] + return dict(v=w['v'], R=w['R'], cst=w['decoder_constant'], local={int(r): n for r, n in w['local_histogram'].items()}, + c=Q(e['nine']['bit_lower']), profile={int(r): n for r, n in e['nine']['profile'].items()}, + rank_mass=w['legality']['rank_mass']) + + +def template_recipe(K): + """recipe(K) of the vendored global_k.py, extracted by AST and executed alone (the module needs the parent tree).""" + import ast + rel = 'research/e8-bit-p111-tuned/vendor/pr510/e8-r480-nine-stage/vendor/e8-r715-eleven-stage-whole/code/global_k.py' + src = (ROOT / rel).read_text(); tree = ast.parse(src) + fn = next(n for n in tree.body if isinstance(n, ast.FunctionDef) and n.name == 'recipe') + ns = {}; exec(compile(ast.Module(body=[fn], type_ignores=[]), rel, 'exec'), ns) + return ns['recipe'](K) + + +def from_template(events, K): + """global_k recipe events -> (stages, final_bridges) in this module's format; asserts the template has one bridge per gap.""" + stages = []; pending = []; final = [] + for e in events: + if e['kind'] == 'local': + assert e['stage'] == len(stages) and len(pending) <= 1 + stages.append((pending[0] if pending else None, e['pair'], 'R' if e['reverse'] else 'F')); pending = [] + elif e['kind'] == 'bridge': + pending.append((e['dst'], e['src'], e['coefficient'])) + final = pending + assert stages[0][0] is None + return stages, final + + +# ---------- scalar model (exact integers, row operations) ---------- +def ident(K): + return tuple(tuple(int(i == j) for j in range(2 * K)) for i in range(2 * K)) + + +def addrow(P, i, j, c): + P = list(P); P[i] = tuple(a + c * b for a, b in zip(P[i], P[j])); return tuple(P) + + +def local(P, K, p, ty): + return addrow(P, K + p, p, 1) if ty == 'F' else addrow(P, p, K + p, -1) + + +def bridge(P, K, d, s, c): + P = list(P) + rd = tuple(a + c * b for a, b in zip(P[d], P[s])); rs = tuple(a - c * b for a, b in zip(P[K + s], P[K + d])) + P[d] = rd; P[K + s] = rs; return tuple(P) + + +def exchange(P, K): + P = list(P) + for j in range(K): + P[j], P[K + j] = P[K + j], tuple(-x for x in P[j]) + return tuple(P) + + +def antidiagonal(P, K): + return all(P[i][j] == 0 for i in range(K) for j in range(K)) and \ + all(P[i][j] == 0 for i in range(K, 2 * K) for j in range(K, 2 * K)) + + +def gap_bridges(g): + """a gap is None, one bridge (d, src, c), or a list of bridges""" + if g is None: return [] + return [tuple(g)] if isinstance(g[0], int) else [tuple(b) for b in g] + + +def product(stages, K, final=()): + P = ident(K) + for g, p, ty in stages: + for b in gap_bridges(g): P = bridge(P, K, *b) + P = local(P, K, p, ty) + for g in final: P = bridge(P, K, *g) + return P + + +def rank(rows): + """exact integer rank (fraction-free elimination)""" + A = [list(r) for r in rows]; n = len(A); m = len(A[0]); r = 0; prev = 1 + for c in range(m): + piv = next((i for i in range(r, n) if A[i][c]), None) + if piv is None: continue + A[r], A[piv] = A[piv], A[r] + for i in range(r + 1, n): + A[i] = [(A[r][c] * A[i][j] - A[i][c] * A[r][j]) // prev for j in range(m)] + prev = A[r][c]; r += 1 + if r == n: break + return r + + +def invariants(P, K): + """(mu, mu', nu, nu') of PROOF.md for the current product P""" + P00 = [P[i][:K] for i in range(K)]; P01 = [P[i][K:] for i in range(K)] + P10 = [P[i][:K] for i in range(K, 2 * K)]; P11 = [P[i][K:] for i in range(K, 2 * K)] + return K - rank(P10), K - rank(P11), K - rank(P00), K - rank(P01) + + +# ---------- idle insertion and windows ---------- +def schedule(stages, K): + """events with idle children inserted when a level must rise; final idle in pair order (global_k's s == 2K branch)""" + L = 2 * K + 1; lev = [-1] * K; out = []; idx = 0 + def adv(p, to): + nonlocal idx + if lev[p] < to: + out.append(dict(kind='idle', pair=p, rank=7 * (to - lev[p]), idx=idx)); idx += 1; lev[p] = to + for s, (g, p, ty) in enumerate(stages): + for d, src, _ in gap_bridges(g): # several bridges in one gap: synchronised one by one, in order + t = max(lev[d], lev[src]); adv(d, t); adv(src, t) + out.append(dict(kind='bridge', dst=d, src=src)) + assert lev[p] <= s - 1, 'a pair cannot be above the level its local needs' + adv(p, s - 1); out.append(dict(kind='local', stage=s, pair=p)); lev[p] = s + for p in range(K): adv(p, L - 1) + return out + + +def windows(sched): + """PR #442 hosting_core.windows, reimplemented: stages of other-pair locals strictly between the pair's last touch and + the idle child""" + last = {}; out = {}; locs = [] + for pos, e in enumerate(sched): + k = e['kind'] + if k == 'local': locs.append((pos, e['stage'], e['pair'])); last[e['pair']] = pos + elif k == 'bridge': last[e['dst']] = pos; last[e['src']] = pos + else: + p = e['pair']; lo = last.get(p, -1) + out[e['idx']] = (p, e['rank'], frozenset(s for q, s, pp in locs if lo < q < pos and pp != p)) + return out + + +def structure_key(win): + return tuple(sorted((r, tuple(sorted(st))) for (_, r, st) in win.values())) + + +# ---------- hosting programme and price ---------- +def f(r, m=M9): + return r * math.log(m / r) if r else 0.0 + + +def host(win, L, copies, R, m=M9, maxrem=45, time_limit=120): + """Exact integer programme, PR #442 objective with every residual hosted (0 banks, as PR #589) and every paid + remainder <= maxrem (halving depth 2, row 18,355 < 20,161). Width 8 for every helper (PR #589 has entrance total 0). + Returns (remainder Counter per replica, proxy cost) or None if infeasible.""" + import numpy as np + from scipy.optimize import milp, LinearConstraint, Bounds + var = [] + for i, (p, r, st) in win.items(): + for k in range(r // 8 + 1): + if r - 8 * k <= maxrem: var.append(('y', i, k)) + for s in st: var.append(('z', i, s)) + if not var: return None + n = len(var) + c = np.array([f(win[v[1]][1] - 8 * v[2], m) if v[0] == 'y' else 0.0 for v in var]) + A = []; lo = []; hi = [] + for i in win: + A.append([1.0 if v[0] == 'y' and v[1] == i else 0.0 for v in var]); lo.append(copies); hi.append(copies) + A.append([float(v[2]) if v[0] == 'y' and v[1] == i else (-1.0 if v[0] == 'z' and v[1] == i else 0.0) for v in var]) + lo.append(0); hi.append(0) + for s in range(L): + A.append([1.0 if v[0] == 'z' and v[2] == s else 0.0 for v in var]); lo.append(R); hi.append(R) + res = milp(c, constraints=LinearConstraint(np.array(A), lo, hi), integrality=np.ones(n), + bounds=Bounds(np.zeros(n), np.full(n, np.inf)), options=dict(time_limit=time_limit)) + if res.x is None or res.status != 0: return None + rem = Counter(); hosted = 0 + for v, x in zip(var, res.x): + x = int(round(x)) + if v[0] == 'y' and x: + hosted += v[2] * x + if win[v[1]][1] - 8 * v[2]: rem[win[v[1]][1] - 8 * v[2]] += x + assert hosted == L * R + return rem, sum(f(r, m) * k for r, k in rem.items()) + + +def global_profile(local_hist, rem, L, T=T): + P = Counter({r: L * T * n for r, n in local_hist.items()}) + for r, n in rem.items(): P[r] += T * n + return dict(sorted(P.items())) + + +def price(engine, P, K, L, v, cst, T=T): + m = 1 + 7 * L; W = T * 2 * K * v + mass = sum(r * n for r, n in P.items()) + assert m * W - mass == T * (2 * K * v - L * cst), 'rank-mass identity T(2Kv - L cst) fails' + assert 2 * max(P) ** 2 < m ** 2, 'halving depth 2 fails' + out = engine.certify(P, m, W, True) + return Q(out['lower']), Q(out['upper']) diff --git a/research/bit589-recipe-floor/recipe_search.py b/research/bit589-recipe-floor/recipe_search.py new file mode 100644 index 0000000000..36dd6cf5af --- /dev/null +++ b/research/bit589-recipe-floor/recipe_search.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +"""Exhaustive search of K-pair stage recipes with one local per stage, L = 2K+1 stages (the floor of PROOF.md). + +Class (stated in README.md): stage s >= 1 may be preceded by no bridge or by exactly ONE bridge (d, src, c), c = +-1, +d != src; stage 0 has none; any final Levi (bridges after the last local) is free. A recipe is valid iff its scalar +product maps L0 -> L1 and L1 -> L0, i.e. a final bridge sequence plus the exchange restores the identity. Products with +an entry above BOUND in absolute value are pruned (BOUND = 8; at K = 3, BOUND = 64 gives the same recipes). +Pruning uses the invariants of PROOF.md: max(mu, K-mu') + max(K-nu, nu') <= remaining stages (a necessary condition). +Completability of (stage, product) is memoised, so only completable branches are walked. + +Output (JSON): counts and every distinct idle-window structure with one witness recipe each. +usage: recipe_search.py K OUT.json [--jobs N] [--bound B] [--depth D] +Prepared by Ian Libânio with substantial AI assistance (Claude Opus 5.5, Anthropic, via Claude Code). Apache-2.0.""" +import argparse, json, sys, time +from functools import lru_cache +from multiprocessing import Pool +from pathlib import Path +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import recipe_lib as RL + +K = L = BOUND = BPG = None +BR = [] + + +def setup(k, bound, bpg=1): + global K, L, BOUND, BR, GAPS, BPG + K, L, BOUND, BPG = k, 2 * k + 1, bound, bpg + BR = [(d, s, c) for d in range(K) for s in range(K) if d != s for c in (1, -1)] + GAPS = gap_options(bpg) + + +def feasible(P, t): + mu, mup, nu, nup = RL.invariants(P, K) + return max(mu, K - mup) + max(K - nu, nup) <= L - t + + +GAPS = None + + +def gap_options(bpg): + opts = [None] + BR + if bpg >= 2: opts += [[b1, b2] for b1 in BR for b2 in BR if b1[:2] != b2[:2]] + return opts + + +def children(t, P): + for g in ([None] if t == 0 else GAPS): + Q = P + for b in RL.gap_bridges(g): Q = RL.bridge(Q, K, *b) + if g is not None and Q == P: continue + for p in range(K): + if t == 0 and p: continue # relabel pairs: the first local acts on pair 0 + for ty in 'FR': + R = RL.local(Q, K, p, ty) + if max(abs(x) for r in R for x in r) <= BOUND and feasible(R, t + 1): + yield (g, p, ty), R + + +@lru_cache(maxsize=None) +def can(t, P): + if t == L: return RL.antidiagonal(P, K) + return any(can(t + 1, R) for _, R in children(t, P)) + + +def walk(item): + k, bound, bpg, t0, P0, hist0 = item + if (K, BOUND, BPG) != (k, bound, bpg): setup(k, bound, bpg) + out = {}; count = 0 + def rec(t, P, hist): + nonlocal count + if t == L: + count += 1 + key = RL.structure_key(RL.windows(RL.schedule(hist, K))) + out.setdefault(key, list(hist)); return + for step, R in children(t, P): + if can(t + 1, R): rec(t + 1, R, hist + [step]) + rec(t0, P0, hist0) + return count, out + + +def canon(h): + return [(tuple(RL.gap_bridges(g)), p, ty) for g, p, ty in h] + + +def run(k, jobs=1, bound=8, depth=3, log=True, bpg=1): + setup(k, bound, bpg); t0 = time.time() + front = [(0, RL.ident(K), [])] + for _ in range(min(depth, L - 1)): + front = [(t + 1, R, h + [step]) for t, P, h in front for step, R in children(t, P)] + items = [(k, bound, bpg, t, P, h) for t, P, h in front] + total = 0; structures = {} + pool = Pool(jobs) if jobs > 1 else None + it = pool.imap_unordered(walk, items, chunksize=1) if pool else map(walk, items) + for i, (cnt, out) in enumerate(it): + total += cnt + for key, h in out.items(): + if key not in structures or canon(h) < canon(structures[key]): structures[key] = h # deterministic witness + if log and (i + 1) % max(1, len(items) // 10) == 0: + print(' %d/%d branches, %d recipes, %d structures, %.0fs' % (i + 1, len(items), total, len(structures), time.time() - t0), flush=True) + if pool: pool.close(); pool.join() + rows = [dict(windows=[[r, list(st)] for r, st in key], witness=[[[list(b) for b in RL.gap_bridges(g)] if bpg > 1 and g else (list(g) if g else None), p, ty] for g, p, ty in h]) + for key, h in sorted(structures.items())] + return dict(K=k, stages=2 * k + 1, bridges_per_gap=bpg, entry_bound=bound, valid_recipes=total, + distinct_window_structures=len(rows), structures=rows, seconds=round(time.time() - t0, 1)) + + +if __name__ == '__main__': + ap = argparse.ArgumentParser(); ap.add_argument('K', type=int); ap.add_argument('out', type=Path) + ap.add_argument('--jobs', type=int, default=1); ap.add_argument('--bound', type=int, default=8) + ap.add_argument('--depth', type=int, default=3); ap.add_argument('--bridges-per-gap', type=int, default=1, choices=(1, 2)) + a = ap.parse_args() + res = run(a.K, a.jobs, a.bound, a.depth, bpg=a.bridges_per_gap) + a.out.write_text(json.dumps(res, separators=(',', ':')) + '\n') + print(' K=%d: %d valid recipes, %d distinct window structures (%.0fs)' % (a.K, res['valid_recipes'], res['distinct_window_structures'], res['seconds'])) diff --git a/research/bit589-recipe-floor/verify.py b/research/bit589-recipe-floor/verify.py new file mode 100644 index 0000000000..bf275d6f75 --- /dev/null +++ b/research/bit589-recipe-floor/verify.py @@ -0,0 +1,123 @@ +#!/usr/bin/env python3 +"""Replay of research/bit589-recipe-floor (see README.md). + +usage: python3 -B research/bit589-recipe-floor/verify.py [OUTDIR] [--jobs N] [--reuse] + OUTDIR fresh output directory (default: a new temporary directory) + --reuse re-price the committed K = 4 search (data/search-K4.json, hash-checked) instead of re-running the search + (the full search takes about 25 minutes with 12 jobs; this is the registered generic replay). +Needs numpy and scipy (hosting programme), as research/e8-bit-p111/requirements.txt. +Prepared by Ian Libânio with substantial AI assistance (Claude Opus 5.5, Anthropic, via Claude Code). Apache-2.0.""" +import argparse, hashlib, json, subprocess, sys, tempfile, time +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import recipe_lib as RL +import recipe_search as RS + + +def step(msg): print(msg, flush=True) + + +def main(): + ap = argparse.ArgumentParser(); ap.add_argument('out', type=Path, nargs='?') + ap.add_argument('--jobs', type=int, default=4); ap.add_argument('--reuse', action='store_true') + ap.add_argument('--record', action='store_true', help='maintainer use: write EXPECTED.json from this run instead of comparing') + a = ap.parse_args(); t0 = time.time() + a.out = a.out or Path(tempfile.mkdtemp(prefix='bit589-recipe-floor-')); a.out.mkdir(parents=True, exist_ok=True) + exp = {} if a.record else json.loads((HERE / 'EXPECTED.json').read_text()); got = {} + + step('0. pinned inputs (moment engine and PR589 EXPECTED.json = the selected assembly pins; global_k, hosting code, frozen selection)') + got['pins'] = RL.check_pins(); E = RL.moment_engine(); w = RL.pr589() + + step('1. positive control: the template recipe(4) reproduces PR589 nine-stage hosting and c from the recipe alone') + st, fin = RL.from_template(RL.template_recipe(4), 4) + assert RL.exchange(RL.product(st, 4, fin), 4) == RL.ident(4) + assert RL.antidiagonal(RL.product(st, 4), 4) # its final bridges are a free Levi + win = RL.windows(RL.schedule(st, 4)) + sel = json.loads((RL.ROOT / 'research/e8-bit-p111-tuned/data/selection9-p111.json').read_text())['bit'] + assert all(s in win[i][2] and wd == 8 for i, wd, s, n in sel['stages']) + frozen = Counter() + for i, pat, n in sel['patterns']: + if win[i][1] - sum(pat): frozen[win[i][1] - sum(pat)] += n + rem, proxy = RL.host(win, 9, 2 * w['v'], w['R']) + assert rem == frozen, (rem, frozen) + P = RL.global_profile(w['local'], rem, 9); assert P == w['profile'] + c, _ = RL.price(E, P, 4, 9, w['v'], w['cst']); assert c == w['c'] + HK = RL.official_hosting() + ys, zs, val = HK.solve({i: x for i, x in win.items() if x[2]}, 2 * w['v'], {(s, 8): w['R'] for s in range(9)}, RL.M9, + host_all=True, max_remainder=45) + assert abs(val - sel['proxy_saving']) < 1e-6 + got['positive_control'] = dict(windows={str(i): [p, r, sorted(s)] for i, (p, r, s) in win.items()}, remainder={str(k): v for k, v in sorted(rem.items())}, + c=str(c), frozen_selection_remainder_equal=True, official_saving=val) + step(' template windows = frozen PR589 selection windows; remainder %s; c = %s (PR589 exactly); official programme saving %.4f' + % (dict(sorted(rem.items())), c, val)) + + step('2. negative controls') + ctl = {} + for j in range(len(st)): # drop each internal bridge + if st[j][0] is None: continue + bad = list(st); bad[j] = (None,) + tuple(st[j][1:]) + assert RL.exchange(RL.product(bad, 4, fin), 4) != RL.ident(4) and not RL.antidiagonal(RL.product(bad, 4), 4) + ctl['drop_bridge_before_stage_%d' % j] = 'rejected' + for j in range(len(st)): # drop each local (2K locals): no recipe with 8 stages exists + bad = st[:j] + st[j + 1:] + assert not RL.antidiagonal(RL.product([(None if (k == 0) else g, p, ty) for k, (g, p, ty) in enumerate(bad)], 4), 4) + ctl['drop_local_%d' % j] = 'rejected' + nowin = {i: (p, r, s - {0}) for i, (p, r, s) in win.items()} + assert RL.host(nowin, 9, 2 * w['v'], w['R']) is None; ctl['stage0_removed_from_all_windows'] = 'hosting infeasible' + flip = list(st); flip[4] = (flip[4][0], flip[4][1], 'R') + assert not RL.antidiagonal(RL.product(flip, 4), 4); ctl['flip_local_type_stage4'] = 'rejected' + assert RL.invariants(RL.ident(4), 4) == (4, 0, 0, 4); ctl['invariants_at_identity'] = [4, 0, 0, 4] + assert RL.invariants(RL.product(st, 4), 4) == (0, 4, 4, 0); ctl['invariants_at_template_product'] = [0, 4, 4, 0] + got['negative_controls'] = ctl; step(' %d controls rejected as expected' % len(ctl)) + + step('3. local-count floor, finite confirmation (K = 1, 2; PROOF.md has the general proof)') + r = subprocess.run([sys.executable, '-B', str(HERE / 'floor_check.py'), str(a.out / 'floor.json')], check=True, capture_output=True, text=True) + print(r.stdout, end=''); got['floor'] = json.loads((a.out / 'floor.json').read_text()) + + step('4. exhaustive recipe search, K = 3 (28,464 recipes expected)') + k3 = RS.run(3, a.jobs, 8, 2, log=False) + got['search_K3'] = dict(valid_recipes=k3['valid_recipes'], distinct_window_structures=k3['distinct_window_structures']) + step(' K=3: %d valid recipes, %d window structures' % (k3['valid_recipes'], k3['distinct_window_structures'])) + + step('5. exhaustive recipe search, K = 4 (nine stages)') + committed = HERE / 'data/search-K4.json' + if a.reuse: + h = hashlib.sha256(committed.read_bytes()).hexdigest(); assert a.record or h == exp['search_K4_sha256'], h + search = committed; step(' reusing committed search, sha256 %s' % h) + else: + k4 = RS.run(4, a.jobs, 8, 3); search = a.out / 'search-K4.json' + search.write_text(json.dumps(k4, separators=(',', ':')) + '\n') + if a.record: + committed.parent.mkdir(exist_ok=True); committed.write_text(json.dumps(dict(k4, seconds=None), separators=(',', ':')) + '\n') + same = json.loads(committed.read_text()) + assert {k: v for k, v in k4.items() if k != 'seconds'} == {k: v for k, v in same.items() if k != 'seconds'}, 'fresh search differs from the committed one' + step(' fresh K=4 search equals the committed data/search-K4.json') + got['search_K4_sha256'] = hashlib.sha256(committed.read_bytes()).hexdigest() + s4 = json.loads(search.read_text()) + got['search_K4'] = dict(valid_recipes=s4['valid_recipes'], distinct_window_structures=s4['distinct_window_structures']) + + step('6. price every K = 4 structure (stage-compatible hosting, 0 banks, remainder <= 45, exact rational c)') + subprocess.run([sys.executable, '-B', str(HERE / 'price_structures.py'), str(search), str(a.out / 'PRICED-K4.json'), '--jobs', str(a.jobs)], check=True) + pr = json.loads((a.out / 'PRICED-K4.json').read_text()) + got['priced_K4'] = {k: pr[k] for k in ('structures', 'hosting_feasible', 'hosting_infeasible', 'template', 'best', 'structures_strictly_above_pr589', + 'structures_equal_to_pr589', 'distinct_hostable_prices', 'max_total_capacity', 'residuals_needed', 'outcome', 'idle_segments')} + + step('7. compare with EXPECTED.json') + keys = ('pins', 'positive_control', 'negative_controls', 'search_K3', 'search_K4', 'search_K4_sha256', 'priced_K4') + if a.record: + (HERE / 'EXPECTED.json').write_text(json.dumps({k: got[k] for k in keys}, indent=1) + '\n'); exp = json.loads((HERE / 'EXPECTED.json').read_text()) + for k in keys: + assert got[k] == exp[k], (k, got[k], exp[k]) + assert [x['floor_holds'] and x['attained_at_2K_plus_1'] for x in got['floor']] == [True, True] + (a.out / 'RESULT.json').write_text(json.dumps(got, indent=1) + '\n') + b = pr['best'] + print('PASS_BIT589_RECIPE_FLOOR floor=2K+1 K3_recipes=%d K4_recipes=%d K4_structures=%d max_capacity=%d hostable=%d best_c=%s equal=%d above_pr589=%d no_new_kappa (%.0fs)' + % (got['search_K3']['valid_recipes'], s4['valid_recipes'], s4['distinct_window_structures'], pr['max_total_capacity'], pr['hosting_feasible'], + b['c'], pr['structures_equal_to_pr589'], pr['structures_strictly_above_pr589'], time.time() - t0)) + + +if __name__ == '__main__': + main()