t27t-savings and paper-claims widgets, two blog posts: int8 tensor cores cut training 16-24%; 8 of 45 paper numbers miss (Closes #1689)

apps/website/public/learn/goldenfloat.t27

@@ -181,7 +181,7 @@ pub const LESSON_WIDGETS : [27]str = [
     "golden-gft16", "golden-gft32", "golden-decode"
 ];
 pub const LESSON_ALSO : [27]str = [
-    "", "", "",
+    "paper-claims", "", "",
     "", "", "",
     "", "", "",
     "", "", "",

apps/website/public/learn/neural-networks.t27

@@ -171,7 +171,7 @@ pub const LESSON_ALSO : [27]str = [
     "nn-sgd,nn-rmsprop,nn-lamb",
     "nn-xor,nn-lamb,tc-tiny-layer",
     "nn-backprop,nn-lamb,tc-tiny-layer",
-    "nn-adam,nn-xor,nn-backprop",
+    "nn-adam,nn-xor,nn-backprop,t27t-savings",
     "nn-lstm,nn-attention",
     "nn-rnn,nn-attention,nn-sigmoid",
     "nn-rnn,nn-lstm,nn-encoder",

apps/website/public/widgets/paper-claims/index.html

@@ -0,0 +1,47 @@
+<!doctype html>
+<!-- Generated by scripts/widget-pages-from-spec.mjs from specs/widgets/paper-claims.t27 (sha256 9d5580455c28fbc9); do not edit. -->
+<html lang="en">
+<head>
+<meta charset="utf-8">
+<meta name="viewport" content="width=device-width,initial-scale=1">
+<title>Three format papers, 45 printed numbers, recomputed exactly &middot; Trinity S³AI</title>
+<meta name="description" content="Every number the GoldenFloat, Golden Ruler and TNF papers print that a rule can recompute, run through exact integer arithmetic in a t27 spec: 34 fit, 8 do not, 3 cannot be checked.">
+<meta name="t27:hook" content="45 numbers from three format papers, recomputed in exact integers. 34 fit. 8 do not.">
+<link rel="canonical" href="https://t27.ai/widgets/paper-claims/">
+<link rel="icon" href="../../favicon.svg" type="image/svg+xml">
+<meta property="og:type" content="website">
+<meta property="og:site_name" content="Trinity S³AI">
+<meta property="og:url" content="https://t27.ai/widgets/paper-claims/">
+<meta property="og:title" content="Three format papers, 45 printed numbers, recomputed exactly">
+<meta property="og:description" content="Every number the GoldenFloat, Golden Ruler and TNF papers print that a rule can recompute, run through exact integer arithmetic in a t27 spec: 34 fit, 8 do not, 3 cannot be checked.">
+<meta property="og:image" content="https://t27.ai/widgets/paper-claims/card.png?v=21be18ba1bba">
+<meta property="og:image:width" content="1200">
+<meta property="og:image:height" content="630">
+<meta property="og:image:alt" content="A table of 45 claims from three papers. GoldenFloat: 9 fit, 1 not checkable. Golden Ruler: 8 fit, 1 does not fit (12 clusters printed, the catalog has 13), 1 not checkable. TNF: 15 fit, 7 do not fit, 1 not checkable. Two sums over the t27 repo tables fit.">
+<meta name="twitter:card" content="summary_large_image">
+<meta name="twitter:site" content="@t27_dev">
+<meta name="twitter:title" content="Three format papers, 45 printed numbers, recomputed exactly">
+<meta name="twitter:description" content="Every number the GoldenFloat, Golden Ruler and TNF papers print that a rule can recompute, run through exact integer arithmetic in a t27 spec: 34 fit, 8 do not, 3 cannot be checked.">
+<meta name="twitter:image" content="https://t27.ai/widgets/paper-claims/card.png?v=21be18ba1bba">
+<meta name="twitter:image:alt" content="A table of 45 claims from three papers. GoldenFloat: 9 fit, 1 not checkable. Golden Ruler: 8 fit, 1 does not fit (12 clusters printed, the catalog has 13), 1 not checkable. TNF: 15 fit, 7 do not fit, 1 not checkable. Two sums over the t27 repo tables fit.">
+<link rel="stylesheet" href="../widget.css?v=5ed0683d6108">
+<script type="importmap">{"imports":{"../infographic.js":"../infographic.js?v=5ed0683d6108"}}</script>
+<script>if(/[?&]embed=1\b/.test(location.search))document.documentElement.classList.add('embed')</script>
+</head>
+<body class="t27-widget-page t27-widget-compiler">
+<header class="t27-widget-head">
+<a class="t27-widget-brand" href="../../" target="_top"><img src="../../favicon.svg" alt="" width="18" height="18">Trinity S³AI</a>
+<h1>Three format papers, 45 printed numbers, recomputed exactly</h1>
+<p>Every number the GoldenFloat, Golden Ruler and TNF papers print that a rule can recompute, run through exact integer arithmetic in a t27 spec: 34 fit, 8 do not, 3 cannot be checked.</p>
+</header>
+<main id="widget" class="t27-widget-main" aria-live="polite"></main>
+<noscript><p class="t27-widget-noscript">This widget runs in your browser and needs JavaScript.</p></noscript>
+<footer class="t27-widget-foot">
+<p>This page sets no cookie and sends nothing anywhere.</p>
+<details><summary>Where the numbers come from</summary><ul><li>gHashTag/t27 specs/numeric/paper_claims.t27 (gHashTag/t27#10392): t27c 0.5.2 test-report on the Railway lab, 10 of 10 tests pass, 0 vacuous; tri papers runs the same spec</li><li>The t27 MCP tool t27_paper_claims (gHashTag/t27-mcp#23), wasm generated from that spec with t27c gen-c and zig 0.16.0, called once on the lab with no filter; every row below is one row of its answer</li><li>The papers: arXiv:2606.05017v5 (GoldenFloat), arXiv:2606.09686v3 (Golden Ruler), and the TNF paper by Dmitrii Vasilev, 2026-08-11</li></ul></details>
+<p><a href="./paper-claims.t27" target="_blank" rel="noopener">This widget's .t27 source</a> &middot; <a href="../../#/queen?tab=widgets" target="_top">All widgets</a></p>
+</footer>
+<script>window.T27_WIDGET={"KIND":"widget-tool","ID":"paper-claims","TITLE":"Three format papers, 45 printed numbers, recomputed exactly","DESCRIPTION":"Every number the GoldenFloat, Golden Ruler and TNF papers print that a rule can recompute, run through exact integer arithmetic in a t27 spec: 34 fit, 8 do not, 3 cannot be checked.","IMAGE_ALT":"A table of 45 claims from three papers. GoldenFloat: 9 fit, 1 not checkable. Golden Ruler: 8 fit, 1 does not fit (12 clusters printed, the catalog has 13), 1 not checkable. TNF: 15 fit, 7 do not fit, 1 not checkable. Two sums over the t27 repo tables fit.","HOOK":"45 numbers from three format papers, recomputed in exact integers. 34 fit. 8 do not.","CATEGORY":"compiler","DATA_SOURCES":["gHashTag/t27 specs/numeric/paper_claims.t27 (gHashTag/t27#10392): t27c 0.5.2 test-report on the Railway lab, 10 of 10 tests pass, 0 vacuous; tri papers runs the same spec","The t27 MCP tool t27_paper_claims (gHashTag/t27-mcp#23), wasm generated from that spec with t27c gen-c and zig 0.16.0, called once on the lab with no filter; every row below is one row of its answer","The papers: arXiv:2606.05017v5 (GoldenFloat), arXiv:2606.09686v3 (Golden Ruler), and the TNF paper by Dmitrii Vasilev, 2026-08-11"],"READS_LOCAL_FILES":false,"SENDS_NOTHING":true,"SAY_TABLE_CAPTION":"45 printed numbers and what exact integer arithmetic gives","SAY_TABLE_HEAD":["Paper","Where","Claim","Printed","Recomputed","Verdict"],"SAY_TABLE_CELLS":["GoldenFloat","Table 1","e = round((N-1)/phi^2), f = N-1-e gives the printed (e, f) at all 17 widths","17","17","fits","GoldenFloat","Table 1","(N-1)/phi^2 to four decimals, as printed, at all 17 widths","17","17","fits","GoldenFloat","Table 1","GF16: e = 6","6","6","fits","GoldenFloat","Table 1","GF1024: e = 391","391","391","fits","GoldenFloat","Table 1","GF16: (N-1)/phi^2 = 5.7295","5.7295","5.7295","fits","GoldenFloat","Abstract","phi^(2n) + phi^(-2n) = L_(2n) for n = 1..45 (the paper claims 1..256 at 500 digits; u64 stops at 45)","45","45","fits","GoldenFloat","GF16 anchor","GF16 code 0x47C0 (e = 6, f = 9, bias 31) decodes to 30","30","30","fits","GoldenFloat","GF16 anchor","30 = 1^2 + 2^2 + 3^2 + 4^2, the dot4 anchor","30","30","fits","GoldenFloat","Look-elsewhere","p = K / N_s = 83 / 80000 = 1.04e-3","1.04e-3","1.04e-3","fits","GoldenFloat","Abstract","35 of 35 testbench vectors pass; the clock printed beside them is withdrawn (RESEARCH_CLAIMS.md, Retraction 2026-08-18)","35","-","not checkable","Golden Ruler","Abstract","the catalog holds 109 formats","109","109","fits","Golden Ruler","Abstract","the 109 formats span 12 clusters","12","13","does not fit","Golden Ruler","Packs","3.0 in BF16 is 0x4040","0x4040","0x4040","fits","Golden Ruler","Packs","3.0 in FP8 E4M3 is 0x44","0x44","0x44","fits","Golden Ruler","Packs","3.0 in FP8 E5M2 is 0x42","0x42","0x42","fits","Golden Ruler","Packs","3.0 in the MXFP4 element E2M1 is 0x5","0x5","0x5","fits","Golden Ruler","Packs","3.0 in GF16 is 0x4100","0x4100","0x4100","fits","Golden Ruler","Packs","3.0 has no E8M0 code: E8M0 holds powers of two only","none","none","fits","Golden Ruler","Anchor","phi^2 + phi^-2 = L_2 = 3","3","3","fits","Golden Ruler","Abstract","the packs are cross-validated against ml_dtypes 0.5.4","-","-","not checkable","TNF","Table 1","2^-(M+1) matches the printed M at all 8 rungs","8","8","fits","TNF","Table 1 vs Sec. 10","the printed M equals the adopted M = N - 1 - Et at all 8 rungs (Sec. 10: all rungs satisfy 1 + Et + M = N)","8","2","does not fit","TNF","Eq. (1)","TNF16 value = (1 + M/2^9) 2^e: a 9-bit mantissa, where 1 + 4 + M = 16 needs 11","9","11","does not fit","TNF","Sec. 2","four balanced trits give e in [-40, 40]","40","40","fits","TNF","Sec. 2","four balanced trits give 3^4 = 81 exponent steps","81","81","fits","TNF","Sec. 3","error constant (1/2) ln 2 = 0.3466 for a uniform significand","0.3466","0.3466","fits","TNF","Sec. 3","error constant 1/(4 ln 2) = 0.3607 for a logarithmic significand","0.3607","0.3607","fits","TNF","Table 10","bits = ceil(Et log2 3) at all 7 rows","7","7","fits","TNF","Table 10","efficiency 3^Et / 2^bits to 0.1% at all 7 rows","7","7","fits","TNF","Table 11","k = N - (1 + Et + M) at all 10 rows","10","10","fits","TNF","Table 11","reconciled M = N - 1 - Et at all 9 rows, equal to the repo tnf*.t27","9","9","fits","TNF","Sec. 17","ternary radix economy 3/ln 3 sits 0.46% above e/ln e","0.46%","0.46%","fits","TNF","Sec. 17","binary radix economy 2/ln 2 sits 6.15% above e/ln e","6.15%","6.15%","fits","TNF","Cor. 18","kappa(3)/kappa(2) = 1.683 with kappa(r) = (r-1)^2 / (r ln r)","1.683","1.682","does not fit","TNF","Sec. 17","kappa(3)/kappa(2) = 1.68","1.68","1.68","fits","TNF","Cor. 26","1 - log3 2 = 0.3691","0.3691","0.3691","fits","TNF","Table 22","E* = ceil(log2 b) at all 4 percentiles","4","4","fits","TNF","Sec. 17","the family F_N has N - 3 members (N = 16: 13)","13","13","fits","TNF","Table 24","the GF-T column follows Et = round((N-1)/phi^2) at all 9 rungs","9","1","does not fit","TNF","Table 24","GF-T and TNF give the same layout at 8 of 9 rungs (by their rules: golden GF-T against reconciled TNF)","8","1","does not fit","TNF","Table 24 vs Sec. 10","the TNF column obeys 1 + Et + M = N at all 9 rungs (Sec. 10)","9","3","does not fit","TNF","Table 23","BNF8 is E = 3, M = 4 (the repo bnf8.t27 is E = 5, M = 2)","3","5","does not fit","TNF","Table 23","magnitude counts 129 / 109 / 73 for GF8, GF-T8, TNF8","-","-","not checkable","t27 repo","gft*.t27","the repo GF-T rungs follow Et = round((N-1)/phi^2) at all 9 rungs","9","9","fits","t27 repo","tnf*.t27, bnf*.t27","every repo TNF and BNF rung obeys 1 + E + M = N (9 TNF, 8 BNF)","17","17","fits"],"K_TABLE_COLS":6,"K_TABLE_ROWS":45,"K_TABLE_CELLS":270,"K_FITS":[9,8,15,2],"K_MISFITS":[0,1,7,0],"K_UNCHECKED":[1,1,1,0],"K_ROWS_PER_PAPER":[10,10,23,2],"K_FITS_ALL":34,"K_MISFITS_ALL":8,"K_UNCHECKED_ALL":3,"SAY_FLOW_TITLE":"How each printed number is checked","SAY_FLOW_STEPS":["the number as printed","the rule the paper states","exact u64 arithmetic in paper_claims.t27","fits, does not fit, or not checkable"],"SAY_NOTE":"No floating point anywhere: square roots are integer square roots, constants are series sums at scale 1e12, and three-digit values are rounded half to even. A claim the paper gives no rule for is not checkable, never fits. Run it yourself: tri papers, or the MCP tool t27_paper_claims."}</script>
+<script type="module" src="./tool.js?v=5ed0683d6108"></script>
+</body>
+</html>