Research: prove sharp six source-XOR floor at seven queries (no new kappa)

[VictorLiwentao]

Change and scope

In the five-source common-B mutable-source alphabet of #1898, every restored straight-line word with exactly seven queries needs at least six source XORs. The bound is sharp: the path-lowered champion (0,1,2,6,12,24,16,0) attains 7 Q / 82 R / 6 X (abstract tariff 442 at (b,a,x)=(38,2,2)).

X length	Min interaction components	Query floor 5+c	Admits Q=7?
≤2	≥4	≥9	no
4 or 5	3	8	no
6	2	7	yes (sharp)

This closes the non-path XOR floor left open by the path-lowered mutable-source-789q-invoice OQ1: already X≤5 is impossible at Q=7, so X≤2 with R=82 is impossible. Graph digests for lengths 0–6 match open #2455's published census (that PR proves X≥8 at six queries).

Scoped obstruction with sharp attainment; no new kappa. No claim that seven-query words cannot undercut tariff 436 by lowering R while keeping X≥6. Leave-alone through #2593 and pending mutable-source-789q-invoice were not reopened.

Result

Package: research/seven-query-xor-floor/.
Tip: 14fd0c3177b51f8d17e6fa8ba7ed3ee81989285a.

Exact: Q=7 forces min_X=6; X≤5 blocked; champion attains sharpness.

Validation

python3.12 -I -B research/seven-query-xor-floor/verify.py
python3.12 -I -O -B research/seven-query-xor-floor/verify.py
python3.12 -I -B research/seven-query-xor-floor/independent.py
python3.12 -I -B research/seven-query-xor-floor/test_package.py
python3.12 -B scripts/research_package.py --package research/seven-query-xor-floor

Expected:

PASS_SEVEN_QUERY_XOR_FLOOR Q=7 min_X=6 sharp X<=5 blocked answers_789q_oq1 no_new_kappa
PASS_INDEPENDENT_SEVEN_QUERY_XOR_FLOOR min_X=6 floors_block_X_le_5 ... tariff=442 controls=2
PASS_SEVEN_QUERY_XOR_FLOOR_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/seven-query-xor-floor outcome=completed

Default verify is read-only. Admission uses need(); -O also passes.

Overlap and credit

Closest priors: #2455 (X≥8 at Q=6), #1898, path-lowered 789q invoice (OQ1). Freestanding package; no competing open PR on this claim at refresh.

Credit the mutable-source / PR1898 / PR2455 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.