Reduce sufficient uniform-rank exponent 18.28× with net taxes and log moments

research/fresh-helper-boundary/ARITHMETIC-RESULT.json

@@ -0,0 +1,219 @@
+{
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+      "actual_logarithmic_gamma_guard",
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+      "gaussian_above_main",
+      "new_semantic_guard_with_C1_one"
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+}

research/fresh-helper-boundary/ATTEMPTS.md

@@ -0,0 +1,44 @@
+# Scope of discovery
+
+The new contribution changes helper entrances and exits jointly with scalar
+contact frames. The old choice was optimized for a hosted owner fill. Once
+all helper fields are fresh independent inputs, that objective is different:
+price the paid moment minus the actual productive helper moment.
+
+Exploratory checks before this pivot (compiled C++ discovery, not registered
+proofs or global optimality certificates):
+
+- All 262,144 paired p7 masks: 256 modular candidates; none passes the numerical test C=.00268649.
+  The old rank profile and root were reproduced.
+- All 2,097,152 paired p8 masks: 576 modular candidates; none passes C=.00268649.
+- 2,391,496 masks within six individual-bank toggles of the selected p7 mask:
+  6,278 modular candidates; none passes the numerical test C=.00268649.
+- No untouched consecutive native transports fuse. Single common-frame
+  components, and alpha expansions over the 1,159 existing frame spaces with
+  all boundaries fixed, gave no improvement at C=.003.
+
+The rank-sum modular test is a discovery filter. If a polynomial matrix A has
+invertible A(1), a constant-basis diagonal monomial factorization implies that
+the sum of ranks of its nonzero coefficient matrices equals the dimension.
+A necessary mod-2 screen is particularly cheap here because A(1) stays
+invertible mod 2. Scientific acceptance of the selected word uses rational
+Laurent replay and full native replay, not this filter.
+
+Allowing helper boundary frames changes the result. A binary alpha-expansion
+cut changes a selected set of scalar contacts to one frame, while hard
+constraints preserve every nested chronological path and every warp contact.
+The energy is the complete paid moment minus productive helper moment. Entry
+and exit moves are optimized separately because their joint concave reward
+is not a submodular binary cost. The submitted finite choices are recorded
+explicitly in CHANGES.json; replay needs no optimizer or C++ compiler.
+
+The optimizer is a discovery aid. Passing every tested label does not prove
+global optimality. In particular, simultaneous different-label moves, changed
+scalar order, new operators, center sharing and new geometry remain open.
+
+A subsequent scan added all binary lines, all hyperplanes and all coordinate
+subspaces of F2^9: 1,264 new distinct labels, for 2,423 tested spaces. Separate
+entry and exit alpha-expansion sweeps from the submitted profile found no
+negative move at C=.003. The registered proof uses only the final finite
+choices and exact native/moment replay; no claim of global optimality or
+exact mathematical acceptance is drawn from floating discovery costs.