From 45323d210ebf6f4b201b1d2a27729d14d059f2e2 Mon Sep 17 00:00:00 2001 From: Jacob Sussman <95983206+jacobalansussman@users.noreply.github.com> Date: Tue, 20 Oct 2026 12:00:00 +0000 Subject: [PATCH] =?UTF-8?q?research/lever-mixed-targets-2979:=20the=20recu?= =?UTF-8?q?rsion=20lever;=20full=20cut=20on=20#2979's=20words,=20b=20=3D?= =?UTF-8?q?=201.7887046e-3=20(no=20new=20=CE=BA)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit On #2979's words, unchanged and read in place from main: 16,086 literal rank-48 heads per round (8,064 + 8,022) in my lowering and network; cutting each by 24 of its 48 axes lets its array take a job of 49 axes, and the mixed-target recursion (Theorem 1G, PROOF.md; separated since 48 < 49) prices the words at b = 1.7556473153e-3 for the DFT (uniform: 1.7290339826e-3). Registered check: verify.py --part main / --part controls (standard library). Replays of the other instances: #3945, 1.7501109246e-3 (README section 6), and #3945 with every head kept (its table of hosts re-solved by the community's allocation programs with one added condition, carried in fills/3945H/), 1.7581520168e-3 (README section 7), and on that table the full cut (heads removed, the other rank-48 blocks split 24 + 24), 1.7806935406e-3 (README section 8). The DFT bounds are proved in Lean outside this repository, the highest at 1.7806935e-3 (README section 5). Only research/lever-mixed-targets-2979 is added. Headline (registered: verify.py --instance 2979Fc, both parts): #2979's words with a table of hosts re-solved for the full cut (A-fc, fills/2979Fc/): 16,576 heads removed (job 25), no other rank-48 block, b = 1.7887045643e-3, certified at 17887045/10^10; checked by computer, not proved in Lean. Its own figure with no lever is 1.6897030e-3, so the community's admission rejects it at its strict-gain steps (README section 9). Co-Authored-By: Claude Opus 5.5 --- .../lever-mixed-targets-2979/.gitattributes | 2 + research/lever-mixed-targets-2979/NOTICE | 33 + research/lever-mixed-targets-2979/PROOF.md | 78 ++ research/lever-mixed-targets-2979/README.md | 342 +++++ research/lever-mixed-targets-2979/RESULT.json | 185 +++ .../lever-mixed-targets-2979/SOURCES.json | 108 ++ research/lever-mixed-targets-2979/TASK.json | 96 ++ research/lever-mixed-targets-2979/VERIFY.json | 68 + .../controls/t74/FILL.json.gz | Bin 0 -> 1575283 bytes .../controls/t74/PROFILE.json | 1 + .../controls/t74/extra.gcert1b.json.gz | Bin 0 -> 34661 bytes .../controls/t74/gauge44.gcert1b.json.gz | Bin 0 -> 34668 bytes .../controls/t74/inputs/DISPATCH.json | 1 + .../controls/t74/inputs/ORDER.json | 1 + .../controls/t74/inputs/PLAN.json.gz | Bin 0 -> 126 bytes .../fills/2979Fc/FILL.json.gz | Bin 0 -> 1325567 bytes .../fills/2979Fc/PROFILE.json | 14 + .../fills/3945H/FILL.json.gz | Bin 0 -> 6532322 bytes .../instances/2979.json | 133 ++ .../instances/2979Fc.json | 139 +++ .../instances/3945.json | 111 ++ .../instances/3945F.json | 114 ++ .../instances/3945H.json | 114 ++ .../network/Gates.lean | 174 +++ .../network/XHost/HCert.lean | 230 ++++ .../network/XHost/HStage.lean | 1103 +++++++++++++++++ .../network/XHost/HostK.lean | 95 ++ .../lever-mixed-targets-2979/tools/README.md | 18 + .../tools/g0_staged.py | 310 +++++ .../tools/lever_price.py | 103 ++ .../lever-mixed-targets-2979/tools/lower_w.py | 584 +++++++++ .../lever-mixed-targets-2979/tools/mixed.py | 24 + .../tools/price_ours.py | 34 + .../lever-mixed-targets-2979/tools/pricer.py | 202 +++ .../tools/rate_cert.py | 162 +++ .../tools/transport.py | 400 ++++++ research/lever-mixed-targets-2979/verify.py | 304 +++++ 37 files changed, 5283 insertions(+) create mode 100644 research/lever-mixed-targets-2979/.gitattributes create mode 100644 research/lever-mixed-targets-2979/NOTICE create mode 100644 research/lever-mixed-targets-2979/PROOF.md create mode 100644 research/lever-mixed-targets-2979/README.md create mode 100644 research/lever-mixed-targets-2979/RESULT.json create mode 100644 research/lever-mixed-targets-2979/SOURCES.json create mode 100644 research/lever-mixed-targets-2979/TASK.json create mode 100644 research/lever-mixed-targets-2979/VERIFY.json create mode 100644 research/lever-mixed-targets-2979/controls/t74/FILL.json.gz create mode 100644 research/lever-mixed-targets-2979/controls/t74/PROFILE.json create mode 100644 research/lever-mixed-targets-2979/controls/t74/extra.gcert1b.json.gz create mode 100644 research/lever-mixed-targets-2979/controls/t74/gauge44.gcert1b.json.gz create mode 100644 research/lever-mixed-targets-2979/controls/t74/inputs/DISPATCH.json create mode 100644 research/lever-mixed-targets-2979/controls/t74/inputs/ORDER.json create mode 100644 research/lever-mixed-targets-2979/controls/t74/inputs/PLAN.json.gz create mode 100644 research/lever-mixed-targets-2979/fills/2979Fc/FILL.json.gz create mode 100644 research/lever-mixed-targets-2979/fills/2979Fc/PROFILE.json create mode 100644 research/lever-mixed-targets-2979/fills/3945H/FILL.json.gz create mode 100644 research/lever-mixed-targets-2979/instances/2979.json create mode 100644 research/lever-mixed-targets-2979/instances/2979Fc.json create mode 100644 research/lever-mixed-targets-2979/instances/3945.json create mode 100644 research/lever-mixed-targets-2979/instances/3945F.json create mode 100644 research/lever-mixed-targets-2979/instances/3945H.json create mode 100644 research/lever-mixed-targets-2979/network/Gates.lean create mode 100644 research/lever-mixed-targets-2979/network/XHost/HCert.lean create mode 100644 research/lever-mixed-targets-2979/network/XHost/HStage.lean create mode 100644 research/lever-mixed-targets-2979/network/XHost/HostK.lean create mode 100644 research/lever-mixed-targets-2979/tools/README.md create mode 100644 research/lever-mixed-targets-2979/tools/g0_staged.py create mode 100644 research/lever-mixed-targets-2979/tools/lever_price.py create mode 100644 research/lever-mixed-targets-2979/tools/lower_w.py create mode 100644 research/lever-mixed-targets-2979/tools/mixed.py create mode 100644 research/lever-mixed-targets-2979/tools/price_ours.py create mode 100644 research/lever-mixed-targets-2979/tools/pricer.py create mode 100644 research/lever-mixed-targets-2979/tools/rate_cert.py create mode 100644 research/lever-mixed-targets-2979/tools/transport.py create mode 100644 research/lever-mixed-targets-2979/verify.py diff --git a/research/lever-mixed-targets-2979/.gitattributes b/research/lever-mixed-targets-2979/.gitattributes new file mode 100644 index 0000000000..382c511659 --- /dev/null +++ b/research/lever-mixed-targets-2979/.gitattributes @@ -0,0 +1,2 @@ +# Keep the package bytes exact: the repository default normalizes text, and verify.py and SOURCES.json record hashes. +* -text diff --git a/research/lever-mixed-targets-2979/NOTICE b/research/lever-mixed-targets-2979/NOTICE new file mode 100644 index 0000000000..3368fe125e --- /dev/null +++ b/research/lever-mixed-targets-2979/NOTICE @@ -0,0 +1,33 @@ +research/lever-mixed-targets-2979 +Copyright 2026 Jacob Sussman. Licensed under the Apache License, Version 2.0 (the repository's LICENSE). + +The new files were written by AI agents (Claude) under my direction. No person outside this project has +reviewed them. + +Read in place, not copied: the ten files of PR #2979 (Marius-Paul Dumitrean, research/rank7-joint-endframes, +Apache-2.0) listed in SOURCES.json. Their notices remain in force. + +Copied into this package: +- network/Gates.lean: unmodified copy of lean/complex588/Work/Bridge401/Gates.lean of Ryan Shea's repository + https://github.com/shea256/fourier-transform-below-nlogn, commit 52394849c7ecf3412d39b925d75fc7fdb98994d8, + Apache-2.0 (sha256 077bcf0362a06cdf222477ae8fb68a1c556aa740119df50520efaa6705715d3f). Its header credits + Dugongue (#401), Lydakis (#275), jacklightChen (#377), DaysSky (#363) and me. +- network/XHost/HStage.lean, HCert.lean, HostK.lean: my files, from my repository + https://github.com/jacobalansussman/wht-power-saving-lean (Apache-2.0). +- tools/*.py: my files, from the same repository (tools/README.md says what each one comes from and whose + work it implements). +- controls/t74/: data derived by my programs from the files of PR #1839 (Jeremy Kothe; its PLAN, DISPATCH and + owner table) and from my earlier lowering of #1839's two words; the same files are in my repository. + +The second instance (PR #3945, Dugongue, research/staged544-terminal-gap-fill) is not copied; instances/3945.json +records the sha256 of the files its replay reads. + +- fills/3945H/FILL.json.gz: a table of hosts for the words of PR #3945 (Dugongue, Apache-2.0), made from #3945's + own files by the allocation programs that #3945 uses (Erwan Secousses / ChaloupeMusic, PR #3815), run by me with + one added condition (every block that can be a head stays empty). The same file is in my repository + (package/leverB/fill/FILL.json.gz). instances/3945H.json records its sha256 and those of #3945's files. +- fills/2979Fc/FILL.json.gz and PROFILE.json: a table of hosts and its paid profile for the words of PR #2979 + (Marius-Paul Dumitrean, Apache-2.0), made by me from a class solution of my own mixed-integer program and a + placement with the construction of PR #3815 (Erwan Secousses / ChaloupeMusic) run on #2979's files in a + tolerant mode (README section 9). The same files are in my repository + (research/record-track/data/a-fc/design/). instances/2979Fc.json records their sha256. diff --git a/research/lever-mixed-targets-2979/PROOF.md b/research/lever-mixed-targets-2979/PROOF.md new file mode 100644 index 0000000000..a1475f7dde --- /dev/null +++ b/research/lever-mixed-targets-2979/PROOF.md @@ -0,0 +1,78 @@ +# Theorem 1G: a recursion with jobs of several sizes + +Status of each part, in words: +- the theorem below is **argued by hand** in a simple model of jobs (this file), and its numerical checks were run by + computer on small rules; +- the recursion that the DFT proof actually uses, with the two job sizes of this package, is **proved in Lean** inside + OpenAI's machine model, in the repository named in README section 5; +- whether the community's outer step for integer multiplication accepts such a recursion is **open**. + +## 1. The model of jobs + +A job of size s is a transform on s address bits of a register; its cost is counted in passes per entry. A *rule* +(a word, read as a recursion) has targets W_k for k in K: in one round a unit at column c consumes W_k jobs of size +k c for each k (W = sum W_k arrays, m = max K the full job, k_min = min K the smallest job). It pays P rounds j, in +word order, of ranks r_j >= 1 (n_r rounds of rank r, r_max = max r_j), each round being one job of size r_j c, plus F +free passes. A job a + b may be split into a and b, and a plain job of size s costs s. + +The balance τ in (0, 1) is the root of + + sum_j r_j^τ = sum_k W_k k^τ. + +With the single target {73: W} this is the community's moment equation, and b = 1 - τ is its complex root. For the +lever on #2979: K = {73, 49}, W_73 = 50,218, W_49 = 16,086, and the paid ranks are those of README section 2. + +**Separation hypothesis (S):** r_max < k_min, that is, every paid block is smaller than every job. On #2979 with the +half cut, r_max = 48 < 49 = k_min. With the full cut (job 25) the other rank-48 blocks would break (S) unless they are +split, which is why the half cut is the one used. + +## 2. The theorem + +**Theorem 1G.** Under (S), T(n) <= C n^τ (ln n)^κ for all n >= 3, with κ = ceil(ln(2/η) / ln(1/θ)), +θ = ln r_max / ln k_min < 1, η a constant of the rule, and C depending only on the rule. So T(n) = O(n^(τ+δ)) for every +δ > 0: every saving below 1 - τ is reached with a fixed constant. + +The proof builds a **dilated lockstep tree** of classes of units: + +- **Lemma B (exact balance).** Index classes by sequences of rounds. Round j of a class feeds exactly one child + class, and at every point the child's demand equals the parent's supply, both jobs of the same integer size (a + product of ranks; no rounding of sizes). This uses (S). +- **Lemma C (sources only at the top).** Every job that is not produced inside the tree is a source of size in + (L/m, L], cut from the top job. +- **Lemma D (exits).** Jobs leave the tree only at the last generation, with sizes at most r_max (L/m)^θ, so ln e <= + θ ln L; they are done by fresh top calls, which costs the (ln n)^κ factor. +- **Lemma E (number of units).** The number of units is at most a constant times the sources' weight, with no log + factor. +- **Lemma F (order).** Processing class by class, round by round, is a straight-line program with no deadlock: a + round j + 1 is issued only after every unit that consumed a round-j job has finished. + +The induction then closes with the top split (Lemma A: the exact condition for closing the induction with leftovers). +The numerical checks on three small separated rules and a rank-1 control found every class exactly fed, all sources +in (L/m, L], the exits' weight equal to the sources', and the largest exit within the bound of Lemma D, at L up to +10^7 (up to 1.6e10 classes counted with multiplicity). + +Exact O(n^τ) with no log factor is **not** proved for grouped paid blocks; rules that break (S) are **open**. + +## 3. What the mixed recursion needs that the community's uniform recursion does not have + +The community's recursion is one call per job: a call of size s slices its own batch into W arrays of rank m at +column s/m, and each paid block is an independent recursive call; no call ever needs a job of another size. Theorem +1G needs: + +1. **Several sizes at once.** A unit at column c takes rank-73 arrays of size 73c and rank-49 arrays of size 49c in a + fixed ratio (50,218 : 16,086 for #2979). They come from different producers' outputs, never from one call's batch. +2. **Fractional portions.** Classes are fractional portions of batches: a portion step in the cost model, and dyadic + rounding with enough batch bits (the number of classes is polynomial in n). +3. **A class tree in lockstep.** Round j of every unit in a class is issued together, and the child class consumes + exactly those outputs plus top sources; a careless order deadlocks. +4. **A top split.** The top job is cut into portions of sizes in (n/m, n] plus rests, done recursively. +5. **Exit calls.** Jobs of size at most r_max (n/m)^θ are completed by fresh top calls. So the Lean statement uses a + rational exponent strictly inside the root, with an existential constant: the figure N/10^10 sits below the root + (README section 2), and the Lean rate fact is stated two hundredths of a grid step further inside. +6. **Words for the smaller job.** The word with each head cut must be correct for the job of 49 axes on the head's + array and the full job everywhere else. In Lean this is the head lemma: removing half of a head leaves a program + that does exactly the smaller job on that array. +7. **Hypothesis (S).** #2979 with the half cut meets it: 48 < 49. +8. **The heads.** Each cut block must be a literal head: the first non-identity operation on its own array, acting on + that array alone, with nothing hosted there before. `verify.py` counts them in my lowering and my network; the Lean + proof checks the same property for the blocks it cuts. diff --git a/research/lever-mixed-targets-2979/README.md b/research/lever-mixed-targets-2979/README.md new file mode 100644 index 0000000000..13e51e0640 --- /dev/null +++ b/research/lever-mixed-targets-2979/README.md @@ -0,0 +1,342 @@ +# The recursion lever on the community's words: b = 1.7887046e-3 on #2979's words with the full cut (checked by computer), DFT bounds up to 1.7806935e-3 proved in Lean (complex side only, no new κ) + +Jacob Sussman. Apache-2.0 ([NOTICE](NOTICE)). Built with AI agents (Claude); see *Credit* below. + +## 1. What this is + +Marius-Paul Dumitrean's #2979 (`research/rank7-joint-endframes`, on main) prices its words at a complex-side root of +b = 1.7290339826e-3. This package changes nothing in those words or their packing, and in its registered +instance 2979 nothing in their allocation; the headline A-fc (section 9) carries a re-solved allocation (table of +hosts) for the same words. It changes the +**recursion** that turns a word into a running time, and with that change the same words give + +| | figure | status | +|---|---|---| +| #2979 as it is on main (one job size, 73 axes) | 1.7290339826e-3 | the community's own checks; reproduced here to 24 digits | +| **#2979 with the lever (jobs of 73 and 49 axes)** | **1.7556473153e-3** | the registered check: price, heads and rate inequality checked by computer here; the DFT bound at 1.7556473e-3 is proved in Lean (section 5) | +| the same lever on Dugongue's #3945 | 1.7501109246e-3 | checked by computer with the same programs (section 6); proved in Lean at 1.7501109e-3 | +| **the lever on #3945 with every head kept** (#3945's words and price, a re-solved table of hosts) | **1.7581520168e-3** | checked by computer with the same programs and the table this package carries (section 7); the DFT bound at **1.7581520e-3** is proved in Lean (section 5) | +| **the full cut on #3945 with every head kept** (the same table; heads removed, job 25 on their arrays; the other rank-48 blocks split 24 + 24) | **1.7806935406e-3** | checked by computer with the same programs (section 8); the DFT bound at **1.7806935e-3** is proved in Lean (section 5), the highest of the five | +| the lever on #2979 with every head kept | 1.7564708e-3 | proved in Lean at 1.7564707e-3 (section 7); not replayed in this package | +| **the full cut on #2979's words with a re-solved table (A-fc)** (#2979's words, order and dispatch unchanged; a new table of hosts carried here, with its own paid profile; heads removed, job 25 on their arrays) | **1.7887045643e-3** | **the headline of this package**: checked by computer here, as registered commands (section 9); **not proved in Lean**. Its own figure with no lever is 1.6897030e-3, below #2979's, so the community's admission rejects it at its strict-gain steps (section 9) | + +The highest figure here, A-fc's 1.7887046e-3, is checked by computer and not proved in Lean; the highest figure proved +in Lean is the full cut on #3945 with every head kept, 1.7806935e-3. The figure is a saving for the **discrete Fourier transform** in OpenAI's exact-arithmetic machine model, the model +of OpenAI's "Exact Fourier transforms below n log n" (openai/math, family 130): the program computes the DFT of every +length n in O(n (log n)^(1-s)) operations with s = 1.7806935e-3. It is the same kind of number as the community's +complex side b, so the comparison above is b against b. It is not a κ for integer multiplication: whether the outer +step accepts a recursion with two job sizes is open (section 4), and no κ is claimed. + +## 2. The idea in one paragraph, and the numbers + +The community's recursion gives every array of a unit a full job of 73 axes. In #2979's unit, 16,086 of the 28,190 +rank-48 blocks per round are **literal heads**: each is the first non-identity operation on its own array, acting on +that array alone, with no helper hosted there before it. On such an array the unit can take a smaller job instead. +I cut each head by 24 of its 48 axes, so that its array takes a job of 49 axes and the head pays a block of rank 24; +every other array keeps the full job of 73. The recursion must then feed the word with jobs of two sizes in a fixed +ratio (66,304 arrays per round: 50,218 full jobs and 16,086 cut jobs). Theorem 1G ([PROOF.md](PROOF.md)) shows that +such a *mixed-target recursion* runs at the speed its balance predicts, provided every paid block is smaller than every +job (here 48 < 49). Its balance is the root b of + + sum_r n_r (r/73)^(1-b) = 50,218 + 16,086 (49/73)^(1-b), + +with the paid blocks n_r = {1: 1,645,680, 2: 470,196, 3: 159,468, 4: 71,928, 5: 13,716, 8: 5,328, 24: 16,086, +48: 12,104} per round. Cutting only half of each head (not all of it) is what keeps every paid block below the +smaller job here. I call this step *the lever*. Cutting the whole head (a job of 25 axes) needs every other paid block +below 25 as well: on #3945 with every head kept, splitting each remaining rank-48 block into two blocks of 24 on the +same role does that, and that *full cut* is the highest figure proved in Lean here (section 8). On #2979's words a +table of hosts re-solved for the full cut (A-fc) has no rank-48 block other than its 16,576 heads, so nothing needs +to be split, and the full cut prices at 1.7887045643e-3 (section 9, checked by computer, not proved in Lean). + +## 3. The registered check + + python3 -B research/lever-mixed-targets-2979/verify.py --part main # about 50 s on a laptop + python3 -B research/lever-mixed-targets-2979/verify.py --part controls # about 5 s + python3 -B research/lever-mixed-targets-2979/verify.py --instance 2979Fc --part main # A-fc, section 9 + python3 -B research/lever-mixed-targets-2979/verify.py --instance 2979Fc --part controls + +The last two run the same checks on the headline A-fc (section 9). Standard library only; it reads #2979's ten files on main (pinned in `SOURCES.json`, declared in `VERIFY.json`) and +writes only to a temporary folder. What it checks, in order: + +1. **Pins.** Every input and every data file of this package equals its recorded sha256; the stated local profile, + widths, zero buffers and complex root are read from #2979's `CLAIM.json` and `allocation/PROVIDERS.json`. +2. **My conversion of both words** (gauge44 and extra). `tools/transport.py` rebuilds the community's native + canonical form from the borrowed word (the PR does not ship one) and replays it exactly on all 632 columns, in + both orientations. `tools/lower_w.py` lowers it to my certificate format: frames nested at every climb, warps + carried by their maps, residual widths equal to #2979's widths helper by helper, the block histogram equal to + the local profile, the whole program replayed to the community's endpoint (91 zero buffers back at zero), and + seven wrong versions of each word rejected. For #3945 the same transport reproduces the community's own native + canonical words exactly (equal content hashes), which is how it was validated. +3. **The head test** (`tools/g0_staged.py`) in my network: the step order of my nine-stage hosted network, read as + data from its Lean source (`network/`; nothing is compiled), run on #2979's ORDER, DISPATCH, PLAN, TEMPLATE and all + 271,728 FILL rows. Every role lies in a window of my network, no bin exceeds its rank, every role is used once + per call, and the global paid profile equals `allocation/PROFILE.json` digit for digit. It finds **16,086 literal + heads** (8,064 in child 8, 8,022 in child 10) and 12,104 other rank-48 blocks (children 12 and 13) that are + neither heads nor tails. Its controls: moving gate A4 before its climb leaves no heads; deleting gate C2 turns + the 12,104 other blocks into tails. +4. **The price** (`tools/price_ours.py`, with `pricer.py`, an exact re-implementation of the community's moment + engine, and `mixed.py`): the uniform root of my profile equals #2979's `complex_lower` to all 24 digits; the half + cut gives 1.7556473153e-3; the full cut is priced as a what-if only. +5. **The rate certificate** (`tools/rate_cert.py`): on the half-cut profile derived from the measured heads (not + typed in), exact rational enclosures prove the inequality of section 2 at the figure 17,556,473/10^10 and + refute it one grid step higher. The derived profile equals the histogram of the Lean rate module. +6. **Controls** (second command): the head test on the earlier T74 circuit (`controls/t74`, from Jeremy Kothe's + #1839) finds the 11,010 heads (6,150 + 4,860) of the first head test; the figure is refused with a single head, + with one head fewer (16,085), for a profile that is not separated, and one grid step above. + +## 4. What changes from the community's model, and what does not + +- **Changed: the recursion.** The community's recursion is one call per job, and every paid block is an independent + call of the same job size; the ceiling tool assumes this. The mixed-target recursion needs several job sizes at + once, fractional portions of batches, a tree of classes run in lockstep, a top split and exit calls + ([PROOF.md](PROOF.md) section 3). As the card `complex-new-helper-inventory` allows when the coverage law changes, + Theorem 1G is given as the replacement bound, and the incumbent ceiling is not applied. +- **Unchanged: the words, the packing, the endpoint.** No gate moves; no axis moves between children. The cut changes + the job taken by an array whose first operation is the head; the rest of the word is the same. The allocation is + #2979's own in the registered instance 2979 and #3945's own in instance 3945; the instances 3945H and 3945F and the + headline A-fc (2979Fc) each carry a re-solved table of hosts (sections 7 and 9), checked as a table by the + community's own programs. +- **Not checked here: the community's eight-stream operator model.** The heads and the cut are checked in my + lowering and my network (and, for the DFT, proved in Lean, section 5), not in the community's exact operator + replay. The idle-axis moves retracted on 18 and 19 October changed that operator; this package does not exchange + idle blocks, but the check in that model has not been run (open question 2). +- **κ.** None is claimed. For orientation only: b = 1.7556e-3 is above the selected bit side c = 1.7334270e-3 + (#589), so if the outer step accepted this supplier the bit side would bind, at κ = 1.7334270e-3 in the newer + convention or 1.7304275e-3 in the older one. The halving guard m^2 > 2R^2 of the outer recipe, read per array, holds + for the half cut (on a head array the remaining paid block has 24 axes and 49^2 > 2 * 24^2; argued, not checked) + but fails for the full cut, the headline included (25^2 = 625 < 2 * 23^2 = 1,058; < 1,152 on #3945), so the outer + recipe as written does not take the full cut; one more reason no κ is claimed. + +## 5. The Lean proofs (outside this repository) + +The DFT bounds are proved in Lean 4 in my public repository +[jacobalansussman/wht-power-saving-lean](https://github.com/jacobalansussman/wht-power-saving-lean), commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a`, one package per instance: `package/leverF` (the full cut on #3945 with every head kept, the +highest), `package/leverB` (#3945 with every head kept, 1.7581520e-3), `package/leverA` (#2979 with every head kept, +1.7564707e-3), `package/lever2979` (#2979, 1.7556473e-3) and `package/lever` (#3945, 1.7501109e-3). For the highest, +the statement is OpenAI's `UniformFourier` statement with only the exponent (1 - 17806935/10^10) and the names changed +(statement file sha256 `2e32984d9d6a269b19d2fabafc9085360284d352d4bdccf90e4dff5786061f35`); the theorems are +`OAI.PowerSaving.transform_mainL3945F` and `OAI.PowerSaving.convolution_mainL3945F`, with only the axioms `propext`, +`Classical.choice` and `Quot.sound`. The other four are the same statement at their own exponents. The same statement one +grid step stronger is refused. The official comparator, with the Lean kernel and nanoda, accepts it against OpenAI's statement at this exponent and rejects the statement one step stronger. It is prepared for the Lean leaderboard +bigospeedrun.com/exact-dft, whose robot re-checks it independently: a pull request with it is meant to be opened alongside this package, and I will add its link and the robot's receipt as a comment once it is open. + +This repository cannot pin bytes outside its own Git history, so the link is by content: every program in `tools/` +(`*.py`) and every file under `network/` of this package equals, byte for byte, a file of that commit (`SOURCES.json` lists the pairs of +paths), and the Lean rate modules `Rate2979`, `Rate3945H` and `Rate3945F` there state the inequality of section 2 for +the profiles recorded in `instances/2979.json`, `instances/3945H.json` and `instances/3945F.json`. Lean is not run by +this check. + +## 6. The second instance: #3945 + +The same programs on Dugongue's #3945 (`research/staged544-terminal-gap-fill`, head `91f81d13`, archived on main on 20 October 2026 with the same files): +57,312 literal heads (28,672 + 28,640), the global profile equal to #3945's, the uniform root equal to its stated +root to 24 digits, and a half-cut price of **1.7501109246e-3**, certified at 17,501,109/10^10. It is not a registered +check here: when this package was made, #3945's files were on an open pull request. Its folder on main is the +default source of the instance, so it replays from the repository root with + + python3 -B research/lever-mixed-targets-2979/verify.py --instance 3945 + +(about 3 minutes; every input is checked against `instances/3945.json`; on a checkout of #3945's head, add +`--source `). The DFT bound at 1.7501109e-3 on #3945 is +proved in Lean too, in the same repository (`package/lever`). On #3945's published table the lever gives less than +on #2979's, from a unit five times the size (360 replicas against 74); with every head kept it gives more than on either published table +(section 7), and the full cut on that table gives the most (section 8). + +## 7. Every head kept: #3945 with a re-solved table of hosts + +The community's programs that decide where helper storage goes (the table of hosts, `owner/FILL.json.gz`) put each +empty rank-48 block either where it is a head or where it never is, at the same price, as their solvers happened to: +on #3945, 57,312 of the 80,640 blocks of children 8 and 10 end up as heads. I re-ran the community's own allocation +programs (Erwan Secousses' / ChaloupeMusic's, from #3815, as #3945 uses them) with one added condition, that every +block that can be a head stays empty. The result, `fills/3945H/FILL.json.gz`, keeps #3945's words, order, dispatch, +plan, template and global profile (`PROFILE.json` is unchanged), so the circuit's own price stays #3945's +1.7306632365e-3; #3945's complete stated verification (`owner/verify.py` and `admission/full_replay.py`) passes on +it from scratch, with all 119 of its controls rejected (checked by computer, the community's own programs). Then +**80,640** blocks are heads (40,320 in child 8, 40,320 in child 10), and the half cut prices at **1.7581520168e-3**: + + python3 -B research/lever-mixed-targets-2979/verify.py --instance 3945H + +(about 6 minutes; the same checks as section 3 on #3945's files and this package's table: 80,640 literal heads, +57,312 other rank-48 blocks, the global profile equal to #3945's, the uniform root equal to its stated root to 24 +digits, and the rate certificate at 17,581,520/10^10, refused one step higher). The DFT bound at 1.7581520e-3 is +proved in Lean (section 5). The commands that made the table are in the Lean repository, `package/leverB/fill/`. +On #2979 the same condition gives 16,576 heads instead of 16,086 and 1.7564708e-3 (proved in Lean at 1.7564707e-3, +one grid step lower, because the Lean rate enclosure stops just short of the rounded price); its table and the +community's complete replay of #2979 on it are in `package/leverA/fill/` of the Lean repository. + +## 8. The full cut on #3945 with every head kept + +On the same table, each of the 80,640 heads can be removed entirely instead of halved: its array then takes a job of +73 - 48 = 25 axes. The recursion needs every paid block smaller than every job, so the other 57,312 rank-48 blocks of +the unit (children 12 and 13, whole idle bins that host no role) are each split into two blocks of rank 24 on the same +role. A block of rank 24 + 24 is the product of its first 24 and its last 24 directions, so the split changes no +output; it only makes the recursion pay two blocks of 24 where it paid one of 48. Every paid block then has rank at +most 24 < 25. The balance becomes + + sum_r n_r (r/73)^(1-b) = 241,920 + 80,640 (25/73)^(1-b), + +with n_r = {1: 8,041,680, 2: 2,306,880, 3: 729,648, 4: 353,160, 5: 69,120, 8: 25,920, 24: 114,624} per unit, and its +root is **1.7806935406e-3**, 1.28 % above the half cut on the same table and 2.89 % above #3945's own figure. On #3945's +published table the full cut does not pay (1.7307680e-3, break-even 57,262 heads against 57,312); with every head +kept it does. + + python3 -B research/lever-mixed-targets-2979/verify.py --instance 3945F + +(about 3 minutes; the same checks as section 7, then the full-cut price, the profile derived from +the measured heads equal to the Lean rate module `Rate3945F`, the rate certificate at 17,806,935/10^10, refused one +step higher, and as controls the figure refused with a single head, with one head fewer, and without the split.) The +DFT bound at 1.7806935e-3 is proved in Lean (section 5, `package/leverF`); in Lean the split is a general identity +(a block of rank a + b is the product of two blocks of ranks a and b), with no hypothesis on the block. + +## 9. The headline: the full cut on #2979's words with a re-solved table (A-fc) + +**Status: checked by computer, not proved in Lean.** #2979's words, order, dispatch, plan and template are unchanged +and read in place from main; only the table of hosts is new (`fills/2979Fc/FILL.json.gz`, with its paid profile +`fills/2979Fc/PROFILE.json`). I re-solved it for the full cut: a class solution of a mixed-integer program on +#3815's Hall model, then a literal placement with #3815's own reverse-time placement (Erwan Secousses' / +ChaloupeMusic's `construction/build_fill.py`) run in a tolerant mode: a role with no planned slot left at its call +goes to the cheapest spare place, a bin open at that call that is not a head bin, not yet used at that call, and has +room in its final capacity. **Nine roles were placed that way** (8 of width 6 at call 553 and 1 of width 4 at call 0), +and 8 planned width-6 slots stayed idle. These are exactly the window, same-call and capacity rules that the +community's owner engine enforces. However the table was made, it is checked as a table: it passes #2979's unmodified +owner engine (PR2839, `allocation/vendor/independent_owners.py`, 271,728 roles, T = 74), and that engine rejects all +seven of its corruption controls. + + python3 -B research/lever-mixed-targets-2979/verify.py --instance 2979Fc --part main + python3 -B research/lever-mixed-targets-2979/verify.py --instance 2979Fc --part controls + +(the same checks as section 3, on #2979's files and this package's table: **16,576 literal heads** (8,288 in child 8, +8,288 in child 10) and **no other rank-48 block**, the global profile equal to `fills/2979Fc/PROFILE.json`, the +uniform root equal to the community's own root for this table to 24 digits, then the full-cut price, the full-cut +profile derived from the measured heads, and the rate certificate at 17,887,045/10^10, refused one step higher; as +controls, the figure is refused with a single head, with one head fewer, and with the heads kept as blocks of 48 +while their arrays take the job of 25.) Every head is removed, its array takes a job of 73 - 48 = 25 axes, and every +paid block has rank at most 23 < 25, so the recursion is separated. The balance is + + sum_r n_r (r/73)^(1-b) = 49,728 + 16,576 (25/73)^(1-b), + +with n_r = {1: 1,630,639, 2: 470,196, 3: 154,512, 4: 71,928, 5: 11,988, 6: 5, 7: 3, 8: 5,328, 17: 8, 19: 1, 23: 25,905} +per round, and its root is **b = 1.7887045643e-3** (three routes, exact rational enclosures on a 1e-24 grid, 60-digit +arithmetic and an independent 70-digit interval program, agree to 3e-60). + +**Why the community's admission rejects it.** The table's own figure with no lever (the uniform root of its paid +profile, as the community's exact moment auditor computes it) is **1.6897030e-3**, below #2979's 1.7290340e-3: this +table pays off only with the full cut. The community's checks of #2979's line, run unmodified on a fresh clone at the +base, reject it at every step that compares that lower figure with a higher one, by design, and nowhere else: + +| check of #2979's line (unmodified) | A-fc | +|---|---| +| `verify.py` (three-stage local replay of the words, 86 controls) | pass | +| `check_allocation.py`: pins, words, PROVIDERS, the PR2839 owner engine, the physical count 66,813, its 5 rejection controls | pass | +| `check_allocation.py`: the exact moment auditor (`tools/audit_allocation_moment.py`): rank mass, root bracket, exact bisection | pass, root 1.6897030e-3 | +| `check_allocation.py`: the auditor's strict-gain step (`audit_allocation_moment.py` line 65) | **rejected**: `strict frontier improvement and lower endpoint` | +| `check_cap.py`: cap certificate, rank mass, local profile paid, root at most the cap | pass | +| `check_cap.py`: `recorded gap` (line 68) | **rejected**: this is a near-optimality bound on #2979's own claim (the root within 1e-6 of the cap 1.7290358e-3), not literally a strict-gain check; A-fc's gap is 3.93e-5, the same lower figure measured against the cap | +| complete replay (`reproduce.py`): exports, fresh retained bootstrap, the native stages, owners, parent lift, rebind, discovery (7 steps), outer ledger (63 positive checks), independent check | pass | +| complete admission (`admit_extension.py` line 388) | **rejected**: `candidate must strictly improve full exact pinned frontier headline before full release` | +| the release stage, run past that step by my own driver: its `verify.py` (139 strict controls rejected) and outer checks | pass; then **rejected** at its strict-gain list over earlier packages, at `ledger kappa does not exceed PR2269` | + +The same harness passed #2979's published table and design A completely (positive controls). + +**Why the community's moment engine cannot price this figure.** The community's moment engine asserts the halving +constraint m^2 > 2 r_max^2. For the uniform model of this table it holds (73^2 = 5,329 > 2 * 48^2 = 4,608; its largest rank is the +48 of the 16,576 heads), and that is the 1.6897030e-3 above. With the cut arrays' job of 25 it fails +(25^2 = 625 < 2 * 23^2 = 1,058; after the cut the largest paid rank is 23), so the community's engine +cannot price A-fc's model with two job sizes at all. The figure 1.7887046e-3 comes from my own pricing under +Theorem 1G (`tools/price_ours.py`, `tools/mixed.py`, `tools/rate_cert.py`), which has no such condition: the full cut on +#3945 with every head kept, with 25^2 = 625 < 2 * 24^2 = 1,152, is proved in Lean the same way (section 8). + +**What is proved in Lean and what is not.** Proved in Lean, in the Lean repository of section 5: Theorem 1G, the +recursion with jobs of two sizes (`Eng.engine_seam_final`), and the general theorem of the full cut +(`cut_heads_full` in `Work/Mixed/Bridge/CoreF`), as used for the full cut on #3945 with every head kept at +1.7806935e-3. **Not in Lean: A-fc's own instance**, that is, its heads-first certificate, the cut fact on +#2979's words, and the rate fact at 17,887,045/10^10. Its heads-first certificate and the rate fact are checked by +computer (this section's commands); the cut fact on #2979's words is argued by hand from the template it shares with +#3945's (where it is proved in Lean), not checked. + +**What is claimed.** b, the complex side only, for the DFT in OpenAI's model, checked by computer. No κ: even if the +outer step accepted this supplier, κ would be capped by the selected bit side, about 1.7334e-3 (#589). The figure is +above every complex-side construction claimed on the hub by others; some research notes there print higher ceilings, +targets or hypothetical ledgers, which are not constructions. + +## Open next questions + +The structured list with first steps is `open_questions` in [TASK.json](TASK.json); in short: + +1. **The outer step with two job sizes.** Does the outer theorem accept a complex supplier whose recursion uses jobs + of 73 and 49 axes (the half cut), or of 73 and 25 axes (the full cut, the headline)? First step: write the mixed recursion as a supplier interface in the outer theorem's terms and + list the changed hypotheses (PROOF.md section 3). +2. **The cut in the community's operator model.** First step: replay the cut of a sample of heads with #3187's exact + eight-stream operator replay, with a control that a wrong cut changes the operator. +3. **A-fc in Lean.** The full cut on #2979's words is checked by computer with the re-solved table A-fc (section 9, + 1.7887046e-3), and proved in Lean on #3945 with every head kept (section 8). First step: build A-fc's instance in + Lean the way the full cut on #3945 was built (its heads-first certificate, the cut fact on #2979's words, the rate + module at 17,887,045/10^10). +4. **More heads.** Keeping every head that the table of hosts allows is done (section 7). Still open: whether some + of the remaining 'neither' blocks (children 12 and 13) can become heads by moving the first touch of their array. + First step: for each, find that touch before its climb and test whether it can be moved after it. +5. **Newer words** (for example #4088). First step: write `instances/.json` and run the head test. +6. **The log factor of Theorem 1G.** First step: search small separated rules for a flow whose exits carry less + than the sources (PROOF.md, remark after Theorem 1G). + +## Credit + +- **The words, allocation and checks this package reads** are Marius-Paul Dumitrean's #2979 (with substantial AI + assistance, Anthropic Claude via Claude Code), on Jeremy Kothe's #2957 / #2948 / #2966 rewrites, Mason Hale's #2917, + Jeremy Diviney's #2908, Dugongue's #2969, #2863 and #2839, Yiyang Lu's #2857 / #2848, RossRichardson's #2918, + Jeremy Kothe's #2894 / #2833, Tekalign's owner checker, icekylinx's auditor, themilkman216's integrality + observation and Gareth Davidson's #1995 / #2013, as #2979's NOTICE and CREDITS.md name them. +- **The borrowed helpers and their warps** that #2979 uses are Cinna Davis's (1337isnot1337, #2226), with Jeremy + Kothe's width exchange (#2312); the T74 layout underneath grows from the work of Rohan Arun, Marius-Paul Dumitrean, + Jeremy Kothe, LeverRank, Thomas DiFiore, Jeremy Diviney, Chafik Boukhalfa (chafreaky) and Vlado Vojdanovski. + The T74 control data come from Jeremy Kothe's #1839. +- **The headline's table** (`fills/2979Fc/`) was placed with the construction of Erwan Secousses (ChaloupeMusic, + #3815), its Hall model and reverse-time placement, run in a tolerant mode of mine, on #2979's own files. +- **The second instance** is Dugongue's #3945 (with substantial OpenAI Codex assistance, as its NOTICE says) and the + line of circuits it ends, as its NOTICE names them: dataisfire's #3734, zxv's #3682 and #3638, Ross Richardson's + #3605, Erwan Secousses' (ChaloupeMusic's) #3815, hexapode's #3802 and #3875, Dugongue's #3857 and #3929, and the + earlier line under them. I read and re-ran the checks of #3945 by others, among them Chris R's (Clear1nsight's) + audits #3969, #3988, #3994 and #4016. The table + with every head kept (`fills/3945H/`) was made with the allocation programs of Erwan Secousses (ChaloupeMusic, + #3815) that #3945 uses, from #3945's own files. +- **The moment engine** that `tools/pricer.py` re-implements is the community's + (`research/native-complex-moment552`, `research/gauge44-frames-x`). +- **The Lean route** rests on Ryan Shea's conversion pipeline, generators and Lean tree, Nil Mamano's gauged Lean + extension and Fourier chain templates, and OpenAI's model and statement. `network/Gates.lean` is a file of Ryan + Shea's tree; its header credits Dugongue (#401), Lydakis (#275), jacklightChen (#377) and DaysSky (#363). +- **New here** (mine): the lever (the head test, the half cut, the full cut with the split, the mixed-target + recursion and Theorem 1G), the tables with every head kept (the added condition), the table A-fc (its class solution and the tolerant placement), + my transport and lowering of these words, the rate + certificate, and the Lean proofs of section 5. The new files were + written by AI agents (Claude) under my direction; the Lean proof is checked by Lean's kernel, and no person outside + this project has reviewed this package. + +## Files + +| path | what | +|---|---| +| `verify.py` | the registered check (both parts) and the replays of the other instances | +| `instances/2979.json`, `instances/3945.json`, `instances/3945H.json`, `instances/3945F.json` | each instance's input paths and sha256, the stated values, and the recorded results (`3945F`: the full cut on the table of `3945H`) | +| `fills/3945H/FILL.json.gz` | the table of hosts of #3945 with every head kept (section 7) | +| `instances/2979Fc.json`, `fills/2979Fc/FILL.json.gz`, `fills/2979Fc/PROFILE.json` | the headline A-fc: its instance, its table of hosts and that table's paid profile (section 9) | +| `tools/` | `transport.py`, `lower_w.py` (my conversion), `g0_staged.py` (head test), `pricer.py`, `mixed.py`, `lever_price.py`, `price_ours.py` (price), `rate_cert.py` (rate certificate); [tools/README.md](tools/README.md) says where each comes from | +| `network/` | the Lean source of my nine-stage hosted network, read as data by the head test | +| `controls/t74/` | the T74 regression data | +| `PROOF.md` | Theorem 1G and what the mixed recursion needs | +| `RESULT.json` | the result in machine-readable form (no κ field) | +| `TASK.json`, `SOURCES.json`, `VERIFY.json`, `NOTICE`, `.gitattributes` | package metadata | + +## Sources + +- #2979: `research/rank7-joint-endframes` on main, head be191346391661f4d35fc0d1508d0a6029572576; the ten inputs + with their Git blobs and sha256 in `SOURCES.json`. #3945: head 91f81d131252db704f945891da1ea54e29d46b8b. The + table with every head kept: `fills/3945H/FILL.json.gz`, sha256 + 9c06677d66b04436b02ec8d88036327bdc8fb12e6fd4f71a1b9c7e915c10c2d3. The headline's table (A-fc): + `fills/2979Fc/FILL.json.gz`, sha256 7fc766c6c3e1561cee60b258138a918020b96d85ea782a2b01ad0ee035fd082e; the programs + that made it are in the Lean repository, `research/record-track/programs/a-fc/`, with the class solution and the + re-create commands in `research/record-track/data/a-fc/`. The community's checks of section 9 were run on a fresh + clone at the base on 20 October 2026. +- The package's base commit is `SOURCES.json` `base_commit`. Hub figures as their authors state them, read on + 20 October 2026, 03:00 EDT. +- The Lean repository: commit `563b4e6e913625637f36ba7869bf5fcd0dd4975a`; leaderboard submission a pull request to bigospeedrun/verifier adding submissions/dft/jacobalansussman-lever-3945-full-cut. diff --git a/research/lever-mixed-targets-2979/RESULT.json b/research/lever-mixed-targets-2979/RESULT.json new file mode 100644 index 0000000000..b3a8b54f91 --- /dev/null +++ b/research/lever-mixed-targets-2979/RESULT.json @@ -0,0 +1,185 @@ +{ + "schema": "lever-mixed-targets/1", + "what": "The recursion lever on community words: the DFT saving of the half cut (each literal rank-48 head cut by 24 of its 48 axes, job 49 on its array, every other array the full job 73), in OpenAI's exact-arithmetic machine model for the DFT; registered on PR #2979's words (on main), replayed on PR #3945's words and on #3945 with every head kept, and, on that table, the FULL cut (each head removed, job 25 on its array, every other rank-48 block split 24 + 24). Complex side only; no kappa is claimed. Headline: on #2979's words with a table of hosts re-solved for the full cut (A-fc, instance 2979Fc), the full cut prices at b = 1.7887045643e-3, checked by computer, not proved in Lean.", + "headline": { + "instance": "2979Fc", + "what": "A-fc: #2979's words, order, dispatch, plan and template unchanged (the price changes with the table: its own uniform figure is 1.6897030e-3), with a table of hosts re-solved for the full cut (fills/2979Fc/FILL.json.gz, a class solution of a mixed-integer program on #3815's Hall model, placed with #3815's reverse-time placement in a tolerant mode: 9 roles placed in spare bins open at their call, 8 planned width-6 slots left idle); each of the 16,576 literal heads removed (job 73 - 48 = 25 on its array); no other rank-48 block, so nothing is split; every paid block has rank at most 23 < 25", + "figure": "1.7887045e-3", + "figure_rounded": "1.7887046e-3", + "dft_numerator": 17887045, + "dft_denominator": 10000000000, + "uniform_b_of_the_table": "1.6897030111e-03", + "uniform_b_note": "the table's own figure with no lever, as the community's exact moment auditor computes it; below #2979's 1.7290339826e-03, so the community's admission rejects this table at its strict-gain steps (README section 9)", + "half_cut_b": "1.7159005029e-03", + "full_cut_b": "1.7887045643e-03", + "heads": 16576, + "other_rank48": 0, + "full_cut_profile": { + "1": 1630639, + "2": 470196, + "3": 154512, + "4": 71928, + "5": 11988, + "6": 5, + "7": 3, + "8": 5328, + "17": 8, + "19": 1, + "23": 25905 + }, + "jobs": { + "73": 49728, + "25": 16576 + }, + "largest_paid_block": 23, + "table_of_hosts_sha256": "7fc766c6c3e1561cee60b258138a918020b96d85ea782a2b01ad0ee035fd082e", + "community_checks_on_this_table": "every check of #2979's line passes except the strict-gain steps (check_allocation.py moment auditor, admit_extension.py line 388, the release's strict-gain list at PR2269) and check_cap.py's recorded gap (a near-optimality bound on #2979's own claim); run unmodified on a fresh clone at the base (README section 9)", + "community_moment_engine": "cannot price this two-target model: its halving constraint m^2 > 2 r_max^2 holds for the uniform model (5,329 > 2 * 48^2 = 4,608) and fails for the job of 25 (625 < 2 * 23^2 = 1,058); the figure comes from this package's pricing under Theorem 1G", + "registered_here": true, + "lean_status": "not proved in Lean. Proved in Lean (Lean repository): Theorem 1G (Eng.engine_seam_final) and the general full-cut theorem (cut_heads_full, Work/Mixed/Bridge/CoreF). Not in Lean: this table's instance. Its heads-first certificate and the rate fact 17887045/10^10 are checked by computer; the cut fact on #2979's words is argued by hand from the template it shares with #3945 (where it is proved in Lean), not checked", + "half_cut_note": "the half cut (job 49) on this table is below #2979's own half cut 1.7556473153e-03; the table is made for the full cut" + }, + "first_instance": { + "instance": "2979", + "figure": "1.7556473e-3", + "dft_numerator": 17556473, + "dft_denominator": 10000000000, + "uniform_b_of_the_word": "1.7290339826e-03", + "half_cut_b": "1.7556473153e-03", + "heads": 16086, + "other_rank48": 12104, + "job_sizes": { + "full": 73, + "cut": 49 + }, + "largest_paid_block": 48, + "note": "the first registered instance (#2979's published table); the headline is A-fc (headline), the highest Lean-checked bound is highest_lean_bound" + }, + "highest_lean_bound": { + "instance": "3945F", + "figure": "1.7806935e-3", + "dft_numerator": 17806935, + "dft_denominator": 10000000000 + }, + "second_instance": { + "instance": "3945", + "author": "Dugongue", + "figure": "1.7501109e-3", + "dft_numerator": 17501109, + "uniform_b_of_the_word": "1.7306632365e-03", + "half_cut_b": "1.7501109246e-03", + "heads": 57312, + "registered_here": false, + "why": "its files were on an open pull request when this package was made (archived on main on 20 October 2026 with the same files); README section 6 gives the replay", + "lean_status": "proved in Lean (package/lever of the Lean repository)" + }, + "third_instance": { + "instance": "3945H", + "what": "#3945 with every head kept: #3945's words, order, dispatch, plan, template and price, with the table of hosts fills/3945H/FILL.json.gz (the community's allocation programs with one added condition)", + "figure": "1.7581520e-3", + "dft_numerator": 17581520, + "uniform_b_of_the_word": "1.7306632365e-03", + "half_cut_b": "1.7581520168e-03", + "heads": 80640, + "other_rank48": 57312, + "table_of_hosts_sha256": "9c06677d66b04436b02ec8d88036327bdc8fb12e6fd4f71a1b9c7e915c10c2d3", + "community_complete_verification_on_this_table": "passes (owner/verify.py, admission/full_replay.py; 119 of 119 controls rejected), checked by computer", + "registered_here": false, + "why": "its files were on an open pull request when this package was made (archived on main on 20 October 2026 with the same files); README section 7 gives the replay", + "lean_status": "proved in Lean (package/leverB of the Lean repository)" + }, + "fourth_instance": { + "instance": "3945F", + "what": "the full cut on #3945 with every head kept: the table of the third instance; each of the 80,640 literal heads removed (job 73 - 48 = 25 on its array) and each of the other 57,312 rank-48 blocks split into two blocks of rank 24 on the same role (an exact identity); every paid block then has rank at most 24 < 25", + "figure": "1.7806935e-3", + "dft_numerator": 17806935, + "uniform_b_of_the_word": "1.7306632365e-03", + "half_cut_b": "1.7581520168e-03", + "full_cut_b": "1.7806935406e-03", + "heads": 80640, + "other_rank48_split": 57312, + "full_cut_profile": { + "1": 8041680, + "2": 2306880, + "3": 729648, + "4": 353160, + "5": 69120, + "8": 25920, + "24": 114624 + }, + "jobs": { + "73": 241920, + "25": 80640 + }, + "table_of_hosts_sha256": "9c06677d66b04436b02ec8d88036327bdc8fb12e6fd4f71a1b9c7e915c10c2d3", + "registered_here": false, + "why": "its files were on an open pull request when this package was made (archived on main on 20 October 2026 with the same files); README section 8 gives the replay", + "lean_status": "proved in Lean (package/leverF of the Lean repository)" + }, + "other_lean_bounds": { + "3945 with every head kept (half cut)": "1.7581520e-3 (package/leverB)", + "2979": "1.7556473e-3 (package/lever2979)", + "2979 with every head kept": "1.7564707e-3 (package/leverA; its price 1.7564708e-3)", + "3945": "1.7501109e-3 (package/lever)" + }, + "what_if_not_claimed": { + "full_cut_b_2979": "1.7744822149e-03", + "full_cut_b_2979_every_head_kept": "1.7797095e-03", + "note": "the full cut on #2979 (heads cut fully, job 25; the other rank-48 blocks split 24 + 24), on #2979's table and on the table with every head kept; priced only, not built in Lean, not claimed. The full cut on #3945 with every head kept is built (fourth_instance). The full cut on #2979's words with a re-solved table (A-fc) is the headline (checked by computer, not proved in Lean)." + }, + "status": { + "headline_A-fc_price_heads_and_rate_certificate": "checked by computer (verify.py --instance 2979Fc, both parts); not proved in Lean", + "price_heads_and_rate_certificate_other_instances": "checked by computer (verify.py, both parts, and --instance 3945 / 3945H / 3945F)", + "dft_bound": "proved in Lean up to 1.7806935e-3 (instance 3945F; lean section below); the headline's 1.7887045e-3 is not proved in Lean", + "kappa": "not claimed", + "outer_step_with_two_job_sizes": "open" + }, + "lean": { + "repository": "https://github.com/jacobalansussman/wht-power-saving-lean", + "commit": "563b4e6e913625637f36ba7869bf5fcd0dd4975a", + "solution_module": "Work.FourierL3945F.Main", + "theorems": [ + "OAI.PowerSaving.transform_mainL3945F", + "OAI.PowerSaving.convolution_mainL3945F" + ], + "statement": "OpenAI's UniformFourier statement (openai/math, family 130, commit fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb), only the exponent and the names changed", + "statement_file_sha256": "2e32984d9d6a269b19d2fabafc9085360284d352d4bdccf90e4dff5786061f35", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "one_step_stronger_refused": "refused by Compare.lean and by the official comparator at 1 - 17806936/10^10", + "official_comparator": "accepted (Lean kernel and nanoda); one step stronger rejected", + "leaderboard": "prepared as a pull request to bigospeedrun/verifier, meant to be opened alongside this package; link and receipt to follow as a comment once it is open", + "rate_modules": { + "2979": "Work/Mixed/Rate2979.lean", + "3945": "Work/Mixed/Rate3945.lean", + "3945H": "Work/Mixed/Rate3945H.lean", + "3945F": "Work/Mixed/Rate3945F.lean" + } + }, + "instances": { + "2979": "instances/2979.json", + "3945": "instances/3945.json", + "3945H": "instances/3945H.json", + "3945F": "instances/3945F.json", + "2979Fc": "instances/2979Fc.json" + }, + "package_data_sha256": { + "network/Gates.lean": "077bcf0362a06cdf222477ae8fb68a1c556aa740119df50520efaa6705715d3f", + "network/XHost/HCert.lean": "68c0bee5f71a75869f5fabfa98ce5c5f22c2a09bfecf837b5a2688eefbd70a23", + "network/XHost/HStage.lean": "fb59e998e31b7fb5501ff79f98072dd09f8283f51e65f5c6b7d36a5365ab577a", + "network/XHost/HostK.lean": "595a84d2ca7c46e8f14c2481d602a0d1c07d6c918547d9fc65f8f041ab5b1eeb", + "controls/t74/FILL.json.gz": "3bdcbb685677bebb0c4e16c58888e4c7e31b145d525f589e63ed07906aed7085", + "controls/t74/PROFILE.json": "a77801295540df04326c701c3b1ed9198cd17343db4a2f6070932b664b8961c4", + "controls/t74/extra.gcert1b.json.gz": "6aa87f1513dab2581f9e8a211d935f44e2d585512426346fdd1182a9457a03a7", + "controls/t74/gauge44.gcert1b.json.gz": "3dd245e81edac391a143361c43e42023bd0b288a4bf2a91352913bdfabc55476", + "controls/t74/inputs/DISPATCH.json": "ff91d189be8ad2d083ef74e4d411e67d39c5fb0d15278dff126df39ae12baa0a", + "controls/t74/inputs/ORDER.json": "b98452454a86bb6ea61e65bf2079d534bd8487ce6b288d04f41528c566da203d", + "controls/t74/inputs/PLAN.json.gz": "bb18714735a2e239fc59d2d92ac3716e32c5046be6b708add33662fe2aa73aff", + "fills/3945H/FILL.json.gz": "9c06677d66b04436b02ec8d88036327bdc8fb12e6fd4f71a1b9c7e915c10c2d3", + "fills/2979Fc/FILL.json.gz": "7fc766c6c3e1561cee60b258138a918020b96d85ea782a2b01ad0ee035fd082e", + "fills/2979Fc/PROFILE.json": "5df7941120150492c64e62dc3362095eff3dfac9facff041ebb5c25b2e78f75e" + } +} diff --git a/research/lever-mixed-targets-2979/SOURCES.json b/research/lever-mixed-targets-2979/SOURCES.json new file mode 100644 index 0000000000..13cf6fc071 --- /dev/null +++ b/research/lever-mixed-targets-2979/SOURCES.json @@ -0,0 +1,108 @@ +{ + "schema_version": 1, + "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244", + "upstream_repository": "https://github.com/CrocSwap/integer-mult-bounds", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/rank7-joint-endframes/data/WORD-base.json.gz", + "usage": "input", + "git_blob": "d9aa96a93fea5f7395e7783aef0bc117c0a0ae89", + "sha256": "abaf67bfcb257528658c906b612f57025617592bd7889828f92b97a5f4f4300d" + }, + { + "path": "research/rank7-joint-endframes/data/WORD-extra.json.gz", + "usage": "input", + "git_blob": "74f6cb64595c21f7726ae77e69437868620bdcee", + "sha256": "e0eaf64c4d5d324693d43889bce1b9e53e8da00402105c8c978fd102f208bed7" + }, + { + "path": "research/rank7-joint-endframes/allocation/FILL.json.gz", + "usage": "input", + "git_blob": "8d4fd644d60ba2c98106dc770803b647afdf0963", + "sha256": "c2136be9434cda511a1a8a44d98f9f72ea5376830a8426674253b4ee351c4c39" + }, + { + "path": "research/rank7-joint-endframes/allocation/ORDER.json", + "usage": "input", + "git_blob": "7409c4df1092241729739596c7648bda504e6aad", + "sha256": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1" + }, + { + "path": "research/rank7-joint-endframes/allocation/DISPATCH.json", + "usage": "input", + "git_blob": "9544fee4e6ee1f202cee22bfaeaf229ee3b2515e", + "sha256": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c" + }, + { + "path": "research/rank7-joint-endframes/allocation/PROFILE.json", + "usage": "input", + "git_blob": "46a83eeda67ab67cccbffe8b7ad8e44368b40ea7", + "sha256": "94a819747f3ced41f1544ada0036c983fc0c92847b9644380f877a06cd7931cf" + }, + { + "path": "research/rank7-joint-endframes/allocation/PROVIDERS.json", + "usage": "input", + "git_blob": "e1d99e12cfa3ac8375984d85c0b040dc36ea1312", + "sha256": "f2edb7922f3029a5d607437e737775ff3371bca49ebab62e5e2495d16d3bf573" + }, + { + "path": "research/rank7-joint-endframes/allocation/vendor/PLAN.json.gz", + "usage": "input", + "git_blob": "7a1db55a4d53ee99280be4f3ab7d29f7b2033adf", + "sha256": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e" + }, + { + "path": "research/rank7-joint-endframes/allocation/vendor/TEMPLATE.json.gz", + "usage": "input", + "git_blob": "114808c32b1799da53524bdc25cea67efb60009e", + "sha256": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e" + }, + { + "path": "research/rank7-joint-endframes/CLAIM.json", + "usage": "input", + "git_blob": "8ec2ce4e440c0b584ee982c551e526a011c9324c", + "sha256": "436e0d297cbdf195445d3697d496ac675e95210b79e70ce602a6a6667a4c6ce9" + } + ], + "inputs_note": "The ten input rows are PR #2979's files (Marius-Paul Dumitrean, research/rank7-joint-endframes, merged on main at head be191346391661f4d35fc0d1508d0a6029572576). They are read in place; nothing of #2979 is copied into this package.", + "external_sources": [ + { + "what": "the Lean proofs of the DFT bounds and the published copies of this package's programs and network files", + "repository": "https://github.com/jacobalansussman/wht-power-saving-lean", + "commit": "563b4e6e913625637f36ba7869bf5fcd0dd4975a", + "byte_equality": "every program in tools/ (*.py), every file under network/ and both files under fills/2979Fc/ of this package equals, byte for byte, a file of that commit (the pairs of paths are listed in 'paths'); this cannot be pinned here because that commit is not a Git object of this repository", + "paths": "tools/transport.py = tools/lever-hub/transport.py; tools/lower_w.py = tools/lever-hub/lower_w.py; tools/rate_cert.py = tools/lever-hub/rate_cert.py; tools/g0_staged.py = tools/lever/g0_staged.py; tools/pricer.py = tools/lever/pricer.py; tools/mixed.py = tools/lever/mixed.py; tools/lever_price.py = tools/lever/lever_price.py; tools/price_ours.py = tools/lever/price_ours.py; network/Gates.lean = tools/lever-hub/network/Gates.lean; network/XHost/HCert.lean = tools/lever-hub/network/XHost/HCert.lean; network/XHost/HStage.lean = tools/lever-hub/network/XHost/HStage.lean; network/XHost/HostK.lean = tools/lever-hub/network/XHost/HostK.lean; fills/3945H/FILL.json.gz = package/leverB/fill/FILL.json.gz; fills/2979Fc/FILL.json.gz = research/record-track/data/a-fc/design/FILL.json.gz; fills/2979Fc/PROFILE.json = research/record-track/data/a-fc/design/PROFILE.json" + }, + { + "what": "network/Gates.lean", + "repository": "https://github.com/shea256/fourier-transform-below-nlogn", + "commit": "52394849c7ecf3412d39b925d75fc7fdb98994d8", + "path": "lean/complex588/Work/Bridge401/Gates.lean", + "sha256": "077bcf0362a06cdf222477ae8fb68a1c556aa740119df50520efaa6705715d3f" + }, + { + "what": "the second instance, PR #3945 (Dugongue, research/staged544-terminal-gap-fill), archived on main on 20 October 2026 with the same files as its head (merge commit 0a2d65f22afd532ce3d17cdf229d98fbed910d59)", + "head": "91f81d131252db704f945891da1ea54e29d46b8b", + "pinned_in": "instances/3945.json (sha256 of each input file)" + }, + { + "what": "the third instance, PR #3945 with every head kept: #3945's files (the head above) with this package's table of hosts fills/3945H/FILL.json.gz, made by the allocation programs that #3945 uses (Erwan Secousses / ChaloupeMusic, #3815) with one added condition; the commands that made it are in the Lean repository's package/leverB/fill/", + "head": "91f81d131252db704f945891da1ea54e29d46b8b", + "pinned_in": "instances/3945H.json (sha256 of each input file and of the table of hosts)", + "table_of_hosts_sha256": "9c06677d66b04436b02ec8d88036327bdc8fb12e6fd4f71a1b9c7e915c10c2d3" + }, + { + "what": "the fourth instance, the full cut on PR #3945 with every head kept: #3945's files (the head above) with the same table of hosts fills/3945H/FILL.json.gz; nothing new is read", + "head": "91f81d131252db704f945891da1ea54e29d46b8b", + "pinned_in": "instances/3945F.json (sha256 of each input file and of the table of hosts)", + "table_of_hosts_sha256": "9c06677d66b04436b02ec8d88036327bdc8fb12e6fd4f71a1b9c7e915c10c2d3" + } + ], + "source_boundary": "Only this new package is submitted. No file outside research/lever-mixed-targets-2979 changes." +} diff --git a/research/lever-mixed-targets-2979/TASK.json b/research/lever-mixed-targets-2979/TASK.json new file mode 100644 index 0000000000..b5e674393b --- /dev/null +++ b/research/lever-mixed-targets-2979/TASK.json @@ -0,0 +1,96 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "priority_revision": 7, + "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "scope_status": "changed", + "actual_scope": "On PR #2979's words (Marius-Paul Dumitrean; unchanged, read in place from main) and, in the registered instance 2979, its allocation: the recursion lever. In #2979's unit, 16,086 of the 28,190 rank-48 blocks (8,064 in child 8, 8,022 in child 10) are literal heads in my lowering and my network: each is the first non-identity operation on its own array, on that array alone, with nothing hosted there before. Cutting each head by 24 of its 48 axes lets its array take a job of 49 axes instead of 73, and a recursion that feeds a word with jobs of two sizes in a fixed ratio (the mixed-target recursion, Theorem 1G of PROOF.md) prices the word at b = 1.7556473153e-3 for the DFT, against #2979's uniform 1.7290339826e-3. The registered check re-derives the heads, the profile and the price from #2979's files and certifies the rate inequality exactly; the DFT bound itself is proved in Lean outside this repository (README section 5). The same check on PR #3945 (second instance, not registered here because its files were on an open pull request when this package was made; archived on main on 20 October 2026 with the same files) gives 57,312 heads and 1.7501109246e-3. On #3945's words with a table of hosts re-solved so that every head is kept (fills/3945H/FILL.json.gz, made by #3815's allocation programs with one added condition; #3945's own complete verification passes on it), instance 3945H gives 80,640 heads and a half-cut price of 1.7581520168e-3, and instance 3945F, the full cut on the same table (the heads removed, job 25 on their arrays; the other 57,312 rank-48 blocks split 24 + 24, so every paid block has rank at most 24 < 25), gives 1.7806935406e-3; the DFT bounds at 1.7581520e-3 and 1.7806935e-3 are proved in Lean outside this repository (README sections 5, 7 and 8). Neither is registered, for the same reason as the second instance. Headline (registered, verify.py --instance 2979Fc, both parts): #2979's words, order and dispatch with a table of hosts re-solved for the full cut (A-fc, fills/2979Fc/); removing its 16,576 literal heads (job 25 on their arrays; no other rank-48 block, so every paid block has rank at most 23 < 25) prices it at b = 1.7887045643e-3, certified at 17887045/10^10; checked by computer, not proved in Lean. Its own uniform figure, 1.6897030e-3, is below #2979's, so the hub's admission rejects it at its strict-gain steps (README section 9).", + "scope_change_reason": "The card asks whether a changed local cost interface beats the current packing within the hub's model. This package does not change the word, the inventory or the packing: it changes the recursion, which is the coverage law. The hub's recursion gives every array the same job; the mixed-target recursion gives the head arrays a job of 49 axes and every other array the full 73. The card's own allowed variation covers this case ('If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope'). The replacement bound is Theorem 1G (PROOF.md), whose hypothesis is that every paid block is smaller than every job (48 < 49); the incumbent ceiling tool assumes uniform jobs and is not applied. The figure is a complex-side b for the DFT in OpenAI's exact-arithmetic machine model; whether the hub's outer step for integer multiplication accepts a supplier with two job sizes is open, so no kappa is claimed.", + "bottleneck_link": "The complex side binds (current priorities); the lever adds +1.539 % to #2979's complex root without changing a single gate of its words, and its size grows with the number of literal heads (break-even 1 head for the half cut). On #2979 the half cut lifts b from 1.7290339826e-3 to 1.7556473153e-3, above the selected bit side c = 1.7334270e-3, so if the hub's outer step accepted it the bit side would bind. With a table of hosts re-solved for the full cut on the same words (the headline A-fc, checked by computer, not proved in Lean), b is 1.7887045643e-3, +3.451 % over #2979's root; the highest figure proved in Lean is the full cut on #3945 with every head kept, 1.7806935e-3.", + "budget_minutes": 300, + "stop_rule": "Publish only if the head count in my lowering equals the count from the community's own allocation, the global profile equals PROFILE.json digit for digit, the uniform root reproduces #2979's stated root to 24 digits, the half-cut figure is strictly above every complex-side construction claimed on the hub by others, and the DFT bound at that figure is proved in Lean with the standard axioms and refused one grid step higher. For the headline A-fc the same on its own table and paid profile (the head count from my lowering and from the table, the global profile equal to fills/2979Fc/PROFILE.json, the uniform root equal to the community's root for this table to 24 digits, the full-cut figure strictly above every complex-side construction claimed on the hub by others, its rate certificate at 17887045/10^10 refused one grid step higher), except that its DFT bound is not proved in Lean, which the package states.", + "outcome": "completed", + "evidence": "verify.py --part main (standard library): pins; my transport and lowering of both #2979 words (exact replays, residual widths helper by helper, 7 rejected mutants each, recorded content hashes); the head test in my network on all 271,728 FILL rows (16,086 heads, 12,104 other rank-48 blocks, global profile = PROFILE.json, two network controls); the price (uniform root = CLAIM.json complex_lower to 24 digits, half cut 1.7556473153e-3, full cut 1.7744822149e-3 as a what-if); the exact rational rate certificate at 17556473/10^10, refuted at 17556474/10^10. verify.py --part controls: the T74 regression (11,010 heads) and four price controls. Outside this repository (README section 5): the Lean proofs of OpenAI's DFT statement with the exponent 1 - 17556473/10^10 (this instance) and, for the instances below, 1 - 17581520/10^10 (3945H) and 1 - 17806935/10^10 (3945F); the leaderboard's own re-check is of the last one. Second instance: verify.py --instance 3945 on #3945's head files (57,312 heads, 1.7501109246e-3, all controls pass). Headline: verify.py --instance 2979Fc --part main and --part controls (registered): the table and its paid profile pinned by sha256 (fills/2979Fc/FILL.json.gz and PROFILE.json, recorded in instances/2979Fc.json), 16,576 literal heads (8,288 + 8,288) and no other rank-48 block, the global profile equal to fills/2979Fc/PROFILE.json, the uniform root equal to the community's root for this table (1.6897030111e-3) to 24 digits, the full-cut price 1.7887045643e-3, the full-cut profile derived from the measured heads, and the exact rational rate certificate at 17887045/10^10, refused at 17887046/10^10; controls: the figure refused with a single head, with one head fewer, and with the heads kept as blocks of 48 while their arrays take the job of 25. Not in Lean (README section 9). Third and fourth instances: verify.py --instance 3945H (the table pinned by sha256, 80,640 heads, 57,312 other rank-48 blocks, the global profile equal to #3945's, the uniform root equal to its stated root to 24 digits, half cut 1.7581520168e-3, the rate certificate at 17581520/10^10, refused one step higher) and verify.py --instance 3945F (the full cut on the same table, 1.7806935406e-3, the profile derived from the measured heads equal to the Lean rate module Rate3945F, the rate certificate at 17806935/10^10, refused one step higher; controls: the figure refused with a single head, with one head fewer and without the split).", + "author": "Jacob Sussman", + "ai_assistance": "Substantial AI assistance: the programs, checks, Lean files and texts were written by AI agents (Anthropic Claude) under my direction. The Lean proof is checked by Lean's kernel; no independent human review of this package is claimed.", + "open_questions": [ + { + "question": "Does the hub's outer step for integer multiplication accept a complex supplier whose recursion uses two job sizes (73 and 49 axes for the half cut, 73 and 25 for the full cut of the headline) in a fixed ratio?", + "why_it_matters": "Only then does the complex-side b of this package become a supplier for kappa; until then it is a DFT result in OpenAI's model, compared with the hub's complex side b against b.", + "first_step": "Write the mixed-target recursion as a supplier interface in the terms of the outer theorem the hub uses (its recursion, its halving guard m^2 > 2R^2, its portion and rounding steps) and list which hypotheses change; PROOF.md section 3 lists what the mixed recursion needs that the uniform one lacks.", + "blocked_by": "A precise statement of the outer theorem's supplier hypotheses for a uniform supplier." + }, + { + "question": "Is the half cut of the 16,086 heads correct in the hub's own exact eight-stream operator model, not only in my lowering?", + "why_it_matters": "The refuted idle-axis moves of 18-19 Oct changed the exact operator while keeping the profile; reviewers will want the cut checked in the hub's own operator model.", + "first_step": "Replay the cut of a sample of heads (one per child and replica class) with #3187's exact eight-stream operator replay, as #4046 did for the idle-axis moves, with a control that a wrong cut (24 axes taken from a non-head block) changes the operator.", + "blocked_by": "None." + }, + { + "question": "Can the full cut on #2979's words (the headline A-fc, checked by computer at 1.7887045643e-3) be proved in Lean?", + "why_it_matters": "A-fc is the highest figure here but rests on a computer check of its own instance; the full cut is proved in Lean only on #3945 with every head kept (instance 3945F, 1.7806935e-3). Theorem 1G and the general full-cut theorem are in Lean already.", + "first_step": "Build A-fc's instance in Lean the way instance 3945F was built: its heads-first certificate on fills/2979Fc/FILL.json.gz, the cut fact on #2979's words, and a rate module at 17887045/10^10 with the profile of instances/2979Fc.json.", + "blocked_by": "None." + }, + { + "question": "Beyond keeping every head that the table of hosts allows (done: #3945 with every head kept, README section 7), can more of the rank-48 blocks become literal heads?", + "why_it_matters": "The half-cut price rises with every head; on #2979, 12,104 rank-48 blocks (children 12 and 13) are neither heads nor tails, and on #3945 with every head kept 57,312 are.", + "first_step": "From the head test's examples (g0 output, 'neither' class), list for each such block the first non-identity touch of its array before its climb, and test whether that touch can be moved after the climb without changing the word's operator.", + "blocked_by": "None." + }, + { + "question": "Does the lever carry over to the newest staged words (for example #4088 at 1.7309791e-3)?", + "why_it_matters": "The lever is independent of the word; a word with a higher uniform b and as many heads would give a higher DFT figure.", + "first_step": "Write instances/.json for the word (its file paths and sha256) and run verify.py --instance ; the expected head count is not known in advance, so start with the head test alone.", + "blocked_by": "none: #4088 and the other staged words of that line were archived on main on 20 October 2026; their files can be read there." + }, + { + "question": "Is the factor (log n)^kappa of Theorem 1G real for grouped paid blocks, or does the mixed recursion reach O(n^tau) exactly?", + "why_it_matters": "The DFT figure is unaffected (any saving below the root is reached), but an exact bound would simplify the supplier interface.", + "first_step": "Search small separated rules for a flow with Phi(exits) <= (eta - beta) Phi(sources) (PROOF.md, remark after Theorem 1G).", + "blocked_by": "None." + } + ] +} diff --git a/research/lever-mixed-targets-2979/VERIFY.json b/research/lever-mixed-targets-2979/VERIFY.json new file mode 100644 index 0000000000..9239c2ab15 --- /dev/null +++ b/research/lever-mixed-targets-2979/VERIFY.json @@ -0,0 +1,68 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/rank7-joint-endframes/data/WORD-base.json.gz", + "research/rank7-joint-endframes/data/WORD-extra.json.gz", + "research/rank7-joint-endframes/allocation/FILL.json.gz", + "research/rank7-joint-endframes/allocation/ORDER.json", + "research/rank7-joint-endframes/allocation/DISPATCH.json", + "research/rank7-joint-endframes/allocation/PROFILE.json", + "research/rank7-joint-endframes/allocation/PROVIDERS.json", + "research/rank7-joint-endframes/allocation/vendor/PLAN.json.gz", + "research/rank7-joint-endframes/allocation/vendor/TEMPLATE.json.gz", + "research/rank7-joint-endframes/CLAIM.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "main" + ], + "timeout_seconds": 360, + "checks": "Pins of the ten #2979 inputs and of this package's data; my conversion of both #2979 words (transport to the native canonical form with exact replay on all 632 columns in both orientations, lowering to gcert/1w and 1b with frames, warps, residual widths helper by helper, local profile, full replay to the endpoint, 7 rejected mutants per word, recorded content hashes; stated local profile, widths and zero buffers from CLAIM.json and PROVIDERS.json); the head test in my nine-stage network on #2979's ORDER, DISPATCH, PLAN, TEMPLATE and 271,728 FILL rows (windows, bin ranks, one use per role, global profile = PROFILE.json, 16,086 literal rank-48 heads = 8,064 + 8,022, 12,104 other rank-48 blocks, and its two network controls); the price (uniform root = CLAIM.json complex_lower to 24 digits; half cut 1.7556473153e-3; full cut as a what-if); the exact rational rate certificate of the mixed-target recursion on the half-cut profile derived from the measured heads, at 17556473/10^10 and refuted at 17556474/10^10, with the derived profile equal to the Lean rate module's." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "controls" + ], + "timeout_seconds": 120, + "checks": "Regression of the head test on the earlier T74 circuit (11,010 heads = 6,150 + 4,860, remainders {48: 22,748}, global profile); price controls: the figure is refused with a single head and with one head fewer (16,085), a profile that is not separated is refused, and one grid step above the figure is refused." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--instance", + "2979Fc", + "--part", + "main" + ], + "timeout_seconds": 480, + "checks": "The headline A-fc: the same checks as --part main on #2979's ten inputs, with this package's table of hosts fills/2979Fc/FILL.json.gz and its paid profile (pinned): 16,576 literal rank-48 heads = 8,288 + 8,288, no other rank-48 block, global profile = fills/2979Fc/PROFILE.json, uniform root = the community's root for this table (1.6897030111e-3) to 24 digits, the full-cut price 1.7887045643e-3 (heads removed, job 25, every paid block of rank <= 23), the full-cut profile derived from the measured heads, and the exact rational rate certificate at 17887045/10^10, refuted at 17887046/10^10." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--instance", + "2979Fc", + "--part", + "controls" + ], + "timeout_seconds": 180, + "checks": "The headline A-fc, controls: the T74 regression; the figure is refused with a single head, with one head fewer (16,575), with the heads kept as blocks of 48 while their arrays take the job of 25 (not separated), and one grid step above." + } + ] +} diff --git a/research/lever-mixed-targets-2979/controls/t74/FILL.json.gz 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