Tooling: 1.54× faster production data_corners.cpp via cached update columns with identical receipts

research/copied-fixed/certificate.json

@@ -17769,7 +17769,7 @@
     "research/copied-fixed/comparison-pr46.json": "f7a34054403075c51289e58b583c05ff42c43e72d286b9c3ff4fc5ae7f4bca44",
     "research/copied-fixed/comparison-pr47.json": "d15ecc820d540a2bfea10bc7d72688240aea89245ff27de263b1de0e74e4273a",
     "research/copied-fixed/data-corners.json": "82dc2d3e116fc003348d6e9ff0cce90fd70d3d6c156580b769ff3d38b3399e17",
-    "research/copied-fixed/data_corners.cpp": "d134f43d31b896daf504511991be8608c6ba9d20a6606c57e2e12d4b203b7d44",
+    "research/copied-fixed/data_corners.cpp": "406a850d496589cd1216eb709baa84fdd8633048b648f05022ae184d1f279448",
     "research/copied-fixed/data_recovery.py": "0de7e0fc4f38b066ec319e4dde43bce8f20edd207be9f9736610babf95030253",
     "research/copied-fixed/links-23.uses": "b215350929d15711b502cdcf5878aeedb2cc7dc81dc764977a28d37ece17f86f",
     "research/copied-fixed/links-25.uses": "80dd63ea393931211bece7a44329a9da4e2936575cdc3f48c27690bedc2ad0ae",

research/copied-fixed/data_corners.cpp

@@ -50,9 +50,12 @@ int main(){
     for(int j=c+1;j<d;j++)if(available[j]){assert(!M[i][j]);zeros++;}
     determinant=mul(determinant,value);checked++;available[c]=false;
     int inv=power(value,prime-2);
+    int columns[d],length=0;
+    for(int j=0;j<d;j++)if(available[j]&&M[i][j])columns[length++]=j;
     for(int r=i+1;r<d;r++)if(M[r][c]){
      int ratio=mul(M[r][c],inv);
-     for(int j=0;j<d;j++)if(available[j]&&M[i][j]){
+     for(int k=0;k<length;k++){
+      int j=columns[k];
       int z=M[r][j]-mul(ratio,M[i][j]);M[r][j]=z<0?z+prime:z;
      }
      M[r][c]=0;

research/data-corner-performance/README.md

@@ -1,10 +1,14 @@
 # Exact data-corner replay with cached update columns
 
 **Tooling improvement; no new κ or construction claim.** This optional runner
-accelerates the historical `research/copied-fixed/data_corners.cpp` checker.
-It preserves the complete domain of 4,073,300 pairs of triples, every existing
-assertion, and the complete output receipt, including all ten modular failures.
-At the recorded base, the selected #626/#543 conditional result was
+proved a per-pivot cached update-column loop for the historical
+`research/copied-fixed/data_corners.cpp` checker. After
+`research/data-corner-production/`, that loop is the **production** default;
+this package vendors the pairwise-era source as `baseline.cpp` and differential
+replays baseline versus production. It preserves the complete domain of
+4,073,300 pairs of triples, every existing assertion, and the complete output
+receipt, including all ten modular failures. At the recorded base, the selected
+#626/#543 conditional result was
 κ = 51110230636731/31250000000000000 = 0.001635527380375392.
 
 ## Reproduce

research/data-corner-performance/SOURCE.json

@@ -1,11 +1,17 @@
 {
   "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
   "sha256": {
-    "research/copied-fixed/data_corners.cpp": "d134f43d31b896daf504511991be8608c6ba9d20a6606c57e2e12d4b203b7d44",
-    "research/copied-fixed/data-corners.json": "82dc2d3e116fc003348d6e9ff0cce90fd70d3d6c156580b769ff3d38b3399e17"
+    "research/data-corner-performance/baseline.cpp": "d134f43d31b896daf504511991be8608c6ba9d20a6606c57e2e12d4b203b7d44",
+    "research/copied-fixed/data-corners.json": "82dc2d3e116fc003348d6e9ff0cce90fd70d3d6c156580b769ff3d38b3399e17",
+    "research/copied-fixed/data_corners.cpp": "406a850d496589cd1216eb709baa84fdd8633048b648f05022ae184d1f279448"
   },
   "git_blob": {
-    "research/copied-fixed/data_corners.cpp": "251f6c87cca42619a0c1b6d83705df5cad0e9c33",
-    "research/copied-fixed/data-corners.json": "4cb7a2b26fc48afd020b7966c43fd30cf2321514"
-  }
+    "research/data-corner-performance/baseline.cpp": "251f6c87cca42619a0c1b6d83705df5cad0e9c33",
+    "research/copied-fixed/data-corners.json": "4cb7a2b26fc48afd020b7966c43fd30cf2321514",
+    "research/copied-fixed/data_corners.cpp": "51cef05c6ebfd86a5c3784c644492dcc9ae1ce3c"
+  },
+  "provenance_sha256": {
+    "research/copied-fixed/data_corners.cpp@pre-production": "d134f43d31b896daf504511991be8608c6ba9d20a6606c57e2e12d4b203b7d44"
+  },
+  "note": "After research/data-corner-production/, working data_corners.cpp is the cached-column production source. baseline.cpp vendors the pairwise-era bytes; replay compares baseline vs production without re-transforming production."
 }

research/data-corner-performance/baseline.cpp

@@ -0,0 +1,77 @@
+// Exhaustive rational nonvanishing certificates via a proved finite prime.
+// Adapted from Rohan Arun PR39 geometry.cpp, with James Chang PR34's pivots.
+// Both factors are now fixed I+J; every one of the 4,073,300 triple pairs is
+// checked. A failed residue test gets a charged 47-singleton fallback.
+// Zero identities are proved separately by the inherited exact rank cuts.
+// Apache-2.0. Prepared with OpenAI Codex assistance.
+#include <cstdint>
+#include <iostream>
+#include <vector>
+#include <array>
+#include <cassert>
+using namespace std;
+constexpr int prime=1000003,a=23,b=25,d=47;
+int mul(int x,int y){return int(int64_t(x)*y%prime);}
+int power(int x,int n){int z=1;for(;n;n>>=1,x=mul(x,x))if(n&1)z=mul(z,x);return z;}
+int main(){
+ for(int i=2;i*i<=prime;++i)assert(prime%i);
+ vector<int> R,C,piv;
+ for(int i=0;i<a;i++)R.push_back(i),C.push_back(i);
+ R.push_back(a-1);C.push_back(0);
+ for(int i=0;i<a;i++)R.push_back(i),C.push_back(i);
+ piv.push_back(2*a);
+ for(int i=1;i<a-1;i++)piv.push_back(i+a+1);
+ for(int i=a-1;i<a+5;i++)piv.push_back(2*a-i);
+ for(int i=a+5;i<2*a-1;i++)piv.push_back(i-a-3);
+ piv.push_back(1);piv.push_back(0);
+ assert(piv.size()==d);
+ const int xin=mul(3*(a+1),power(2*(3*(a+1)-10),prime-2));
+ const int xout=prime-mul(a+1,power(5,prime-2));
+ const int yin=mul(3*(b+1),power(2*(3*(b+1)-10),prime-2));
+ const int yout=prime-mul(b+1,power(5,prime-2));
+ int count=0,good=0;int64_t checked=0,zeros=0;
+ vector<array<int,7>> rejected;
+ cout<<"{\"prime\":"<<prime<<",\"dimensions\":[23,25],\"records\":[\n";
+ int records=0;
+ for(int aa=0;aa<a;aa++)for(int bb=aa+1;bb<a;bb++)for(int cc=bb+1;cc<a;cc++){
+  int xs[a];for(int i=0;i<a;i++)xs[i]=(i==aa||i==bb||i==cc)?xin:xout;
+  int rowgood=0,product=1;
+  for(int u=0;u<b;u++)for(int v=u+1;v<b;v++)for(int w=v+1;w<b;w++){
+   int ys[b],M[d][d];bool available[d];
+   for(int i=0;i<b;i++)ys[i]=(i==u||i==v||i==w)?yin:yout;
+   for(int i=0;i<d;i++){available[i]=true;for(int j=0;j<d;j++){
+    int z=prime-1;if(R[i]==C[j])z+=xs[R[i]];
+    if(i%b==(a*b-d+j)%b)z+=ys[i%b];M[i][j]=z%prime;
+   }}
+   bool ok=true;int determinant=1;
+   for(int i=0;i<d;i++){
+    int c=piv[i],value=M[i][c];assert(available[c]);
+    if(!value){rejected.push_back({aa,bb,cc,u,v,w,i});ok=false;break;}
+    for(int j=c+1;j<d;j++)if(available[j]){assert(!M[i][j]);zeros++;}
+    determinant=mul(determinant,value);checked++;available[c]=false;
+    int inv=power(value,prime-2);
+    for(int r=i+1;r<d;r++)if(M[r][c]){
+     int ratio=mul(M[r][c],inv);
+     for(int j=0;j<d;j++)if(available[j]&&M[i][j]){
+      int z=M[r][j]-mul(ratio,M[i][j]);M[r][j]=z<0?z+prime:z;
+     }
+     M[r][c]=0;
+    }
+   }
+   count++;
+   if(ok){good++;rowgood++;product=mul(product,determinant);}
+  }
+  assert(product);
+  if(records++)cout<<",\n";
+  cout<<"["<<aa<<","<<bb<<","<<cc<<","<<rowgood<<","<<product<<"]";
+  if(records%250==0)cerr<<"checked first triples "<<records<<" of 1771\n";
+ }
+ assert(count==4073300 && records==1771);
+ cout<<"\n],\"pairs\":"<<count<<",\"good\":"<<good<<",\"fallback\":"<<rejected.size()
+     <<",\"nonzero_pivots\":"<<checked<<",\"ordered_zero_checks\":"<<zeros<<",\"fallback_pairs\":[";
+ for(size_t i=0;i<rejected.size();i++){
+  if(i)cout<<",";cout<<"[";
+  for(int j=0;j<7;j++){if(j)cout<<",";cout<<rejected[i][j];}cout<<"]";
+ }
+ cout<<"]}\n";
+}

research/data-corner-performance/replay.py

@@ -1,5 +1,11 @@
 #!/usr/bin/env python3
-"""Source-pinned, opt-in replay of the complete historical data-corner check."""
+"""Source-pinned replay of the historical data-corner check.
+
+After research/data-corner-production/, working
+research/copied-fixed/data_corners.cpp already carries the cached-column loop.
+This runner vendors the pairwise-era source as baseline.cpp and compares it to
+production without re-applying the transform to the working tree.
+"""
 import argparse
 from hashlib import sha256
 import json
@@ -79,16 +85,19 @@ def main():
     require(args.benchmark >= 0, 'Negative benchmark pair count')
     require(not args.output or not args.output.exists(), 'Output already exists')
     manifest, blobs = admitted_inputs()
-    source = blobs['research/copied-fixed/data_corners.cpp'].decode()
+    baseline = blobs['research/data-corner-performance/baseline.cpp'].decode()
+    production = blobs['research/copied-fixed/data_corners.cpp'].decode()
+    require(production == transform(baseline),
+            'production data_corners.cpp must equal transform(baseline.cpp)')
     expected = json.loads(blobs['research/copied-fixed/data-corners.json'])
     compiler = shlex.split(os.environ.get('CXX', 'c++'))
     version = subprocess.check_output([*compiler, '--version'], text=True)
     samples = []
     with tempfile.TemporaryDirectory(prefix='data-corner-') as directory:
         work = Path(directory)
-        compile_program(transform(source), work / 'optimized', compiler)
+        compile_program(production, work / 'optimized', compiler)
         if args.benchmark:
-            compile_program(source, work / 'original', compiler)
+            compile_program(baseline, work / 'original', compiler)
         common_stdout = None
         for pair in range(args.benchmark or 1):
             modes = (['original', 'optimized'] if pair % 2 == 0 else
@@ -102,7 +111,7 @@ def main():
                 print(f'PASS pair={pair} {mode} wall={sample["wall_seconds"]:.3f}s', flush=True)
     evidence = dict(status='PASS_DATA_CORNER_REPLAY', base_commit=manifest['base_commit'],
         source_sha256=manifest['sha256'], implementation_sha256=sha256(Path(__file__).read_bytes()).hexdigest(),
-        generated_source_sha256=sha256((GUARD + transform(source)).encode()).hexdigest(),
+        generated_source_sha256=sha256((GUARD + production).encode()).hexdigest(),
         platform=platform.platform(), python=platform.python_version(), compiler=compiler,
         compiler_version=version, flags=['-O3', '-std=c++17'],
         coverage={k: expected[k] for k in ('pairs', 'good', 'fallback', 'nonzero_pivots', 'ordered_zero_checks')},

research/data-corner-performance/test_replay.py

@@ -67,9 +67,11 @@ def setUpClass(cls):
         cls.directory = tempfile.TemporaryDirectory(prefix='corner-controls-')
         cls.work = Path(cls.directory.name)
         _, cls.blobs = replay.admitted_inputs()
-        cls.source = cls.blobs['research/copied-fixed/data_corners.cpp'].decode()
+        cls.source = cls.blobs['research/data-corner-performance/baseline.cpp'].decode()
+        cls.production = cls.blobs['research/copied-fixed/data_corners.cpp'].decode()
         cls.expected = json.loads(cls.blobs['research/copied-fixed/data-corners.json'])
-        optimized = replay.transform(cls.source)
+        assert cls.production == replay.transform(cls.source)
+        optimized = cls.production
         variants = dict(original=cls.source, optimized=optimized,
             reversed=optimized.replace('for(int k=0;k<length;k++)', 'for(int k=length-1;k>=0;k--)'),
             missing_left=optimized.replace('columns[length++]=j;', 'if(j>c)columns[length++]=j;'))

research/data-corner-production/NOTICE.md

@@ -0,0 +1,18 @@
+# Attribution and license
+
+Prepared by Wentao Li ([VictorLiwentao](https://github.com/VictorLiwentao),
+[@Is__Victor](https://x.com/Is__Victor), wentaol4@illinois.edu) with substantial
+AI assistance for orientation, overlap search, profiling, production wiring,
+packaging, benchmarking and writing. Not independent human peer review.
+Apache-2.0; see the repository root `LICENSE`.
+
+The cached update-column algorithm and its equivalence argument were introduced
+in the opt-in adapter `research/data-corner-performance/` (see that package's
+NOTICE.md). This package wires an equivalent loop into the production
+`research/copied-fixed/data_corners.cpp` path used by
+`make copied-fixed-verify`.
+
+The historical copied-fixed data-corner checker, receipt and certificate lineage
+retain their original author credits in `research/copied-fixed/SOURCE.json` and
+`research/copied-fixed/PROOF.md`. Upstream material retains its own source
+notices and license.

research/data-corner-production/README.md

@@ -0,0 +1,108 @@
+# Production cached update columns for the historical data-corner checker
+
+**Tooling improvement; no new kappa.** At base
+`0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`,
+`research/copied-fixed/data_corners.cpp` still rescanned all 47 columns for
+every lower-row update. The opt-in adapter `research/data-corner-performance/`
+already proved an exact per-pivot cached-column list with identical receipts.
+This package wires that equivalent loop into the **production** checker used by
+`research/copied-fixed/producer.py` / `make copied-fixed-verify`.
+
+Only the `local_sha256` entry for `research/copied-fixed/data_corners.cpp`
+changes inside `research/copied-fixed/certificate.json`. The complete domain of
+4,073,300 pairs, every assertion, modular fallback recovery and the pinned
+`data-corners.json` receipt stay identical. Selected frontier untouched.
+
+The pairwise-era digest in `research/data-corner-performance/SOURCE.json` is
+demoted: that package now vendors `baseline.cpp` and treats working
+`data_corners.cpp` as the optimized production source, so research-packages /
+local replay do not fail working-source drift.
+
+## Reproduce
+
+Python **3.12**, a C++17 compiler (`CXX`, default `c++`), standard library only,
+from the repository root:
+
+```sh
+python3.12 -I -B research/data-corner-production/verify.py
+python3.12 -I -O -B research/data-corner-production/verify.py
+python3.12 -B scripts/research_package.py --package research/data-corner-production
+python3.12 -I -B research/data-corner-production/benchmark.py --rounds 5 --out /tmp/data-corner-production-result.json
+```
+
+Expected:
+
+```text
+PASS_DATA_CORNER_PRODUCTION pairs=4073300 good=4073290 fallback=10 corruption=… certs=1 no_new_kappa
+PASS_REGISTERED_RESEARCH_PACKAGE research/data-corner-production outcome=completed
+PASS_IDENTICAL_DATA_CORNER_PRODUCTION_RECEIPTS
+```
+
+Default verify is read-only. Temp-copy column-fill foil rejects via receipt
+mismatch or subprocess failure. Package gates under `-O` still launch
+assertion-enabled C++ children (`NDEBUG` is rejected at compile time). Full
+`make verify`, selected cold replay, Lean, and multiplication-theorem
+obligations were not rerun for this isolated historical-checker change.
+
+## Result
+
+On Linux / CPython 3.12.3 with g++ (taskset CPU 0), five alternating
+fresh-process pairs gave median wall time **170.101 → 110.463 seconds
+(1.54×)**. Timing is host-descriptive and is not a correctness gate; all
+samples and environment pins are in [`RESULT.json`](RESULT.json). Every stdout
+receipt matches the pinned `data-corners.json` fieldwise. An unpinned multi-core
+screen on the same host was noisier (~1.38×); the reported figure is the pinned
+five-pair series.
+
+## Why the cached columns are equivalent
+
+After accepting pivot `(i,c)`, neither `available` nor pivot row `M[i]` changes
+during the lower-row update loop. Collecting
+
+```text
+columns = [j | available[j] && M[i][j]]
+```
+
+once per pivot, then iterating that list for every lower row `r` with
+`M[r][c] != 0`, performs the same modular updates in the same column order as
+the historical nested scan. See `research/data-corner-performance/README.md`.
+
+## Overlap and credit
+
+Closest priors (different delivery):
+
+- `research/data-corner-performance/` — opt-in cached-column adapter; this is
+  the production wiring.
+- [CrocSwap/integer-mult-bounds#756](https://github.com/CrocSwap/integer-mult-bounds/pull/756)
+  — identical-receipt tooling quality bar.
+- Open leave-alone tooling on other objects (#1922 joint frames, #2039/#2054
+  shared-point, #2100 ternary, #2117 DisjointTensor, #2150 mixed-point,
+  #2194/#2210/#2231/#2239/#2257/#2263/#2276 production rewrites; #1076
+  quadratic-affine) was not reopened. Soft note: #2263/#2276 touch
+  `e8-bit-r420/MANIFEST.sha256`; this tip does not.
+
+Credit the authors of `research/data-corner-performance/` and the copied-fixed
+lineage. Prepared by Wentao Li
+([VictorLiwentao](https://github.com/VictorLiwentao),
+[@Is__Victor](https://x.com/Is__Victor)) with substantial AI assistance, under
+Apache-2.0.
+
+## Open next questions
+
+1. **Question:** Should adjacent historical copies under `research/pair-assembly/`,
+   `research/skip-strips/`, and `research/split-skip/` adopt the same cached
+   columns in a follow-up tip?
+   **Why it matters:** Those trees still pin pairwise-era digests without a
+   registered VERIFY matrix; a coordinated refresh would remove stale inventory
+   digests without changing receipts.
+   **First step:** Diff each `data_corners.cpp` against the production transform
+   site and list which SOURCE inventories would need provenance demotion.
+   **Blocked by:** Out of this session’s one-object stop rule.
+
+2. **Question:** Should `make copied-fixed-verify` grow a microbenchmark gate
+   for the full 4,073,300-pair replay?
+   **Why it matters:** A future edit could restore the nested scan without
+   failing equivalence tests.
+   **First step:** Decide whether RESULT.json medians belong in CI or remain
+   descriptive.
+   **Blocked by:** Maintainer CI-budget preference.