A registered result in its source context

QGEO.DICT.01

Original ledger classification: Exact [E] entries + quantified negatives (numeric prefilter, symbolic confirmation)

Original claim text

The cover dictionary, round 2 -- THREE compiler objects located as canonical cusp-Gram combinations on the mu3-cover (one module, 4 checks, <1 s; discovery probe cover_dictionary_probe.py 4/4, verdict DICT-THREE-ENTRIES): with T_1..T_4 the D4-conjugate cusp twists and G_k their Grams -- U ~ G_2 (char x^2(x-3), the winding operator as a single-cusp Gram; v597 entry); Q_- ~ G_1 - G_3 (char x(x^2-3)): THE MU4 SHEET COUPLING IS THE DIFFERENCE OF THE OPPOSITE CUSP GRAMS -- the diamond diagonal; ladder ~ 1 + G_1 + G_3 (char (x-1)(x-2)(x-4)): the binary AnchorLadder (1,2,4) = (2^0,2^1,2^2) of v568 is identity plus the diagonal sum. Supporting exact structure: opposite-twist products (1-T_1)(1-T_3) are nilpotent (cube zero), Q_-^2 has char x(x-3)^2. THE NEGATIVES QUANTIFIED: Q_+ ({1,2,3}), V ({0,1,2}), H ({1,1,2}) and Q itself are NOT contained in 7296 scanned canonical combinations (the integer Gram lattice a + bG_1 + cG_2 + dG_3 + eG_4 and its non-hermitian (1-T_i)(1-T_j) extension; numeric prefilter, exact confirmation; 0 matches) -- the grading half needs a generator outside the finite-cusp twist algebra, with the anti-holomorphic D4 reflections (the real structure) as the named suspect. The Strategy-I kill criterion is NOT triggered (the canonical space is not exhausted). GATE.QGEO does not move; no marker changes. [2026-08-01 XV: the named suspect is CONSTRUCTED -- v599: the real structure exists and is unique up to scale (R^2 = +1); its grading functor closes all three gaps at char level (V, H with the anchor spectrum, Q_+); the joint algebra embedding stays open (quantified negative); see QGEO.REAL.01.] [2026-08-01 XVI: the dictionary completes at algebra level -- v600: a Gamma-even degree-2 pair realizes (U, V) jointly (conjugation exact, index 81); canonicity open; see QGEO.EMBED.01.] [2026-08-01 XXVIII: retroactive typing confirmed -- v610's census shows single integer spectra are common on the cover; this module's char-level entries were correctly typed candidates, upgraded to the joint embedding only by v600; see QGEO.LANDSCAPE.01.]

Original classification detail

DICT-THREE-ENTRIES: U ~ G2, Q_- ~ G1-G3 (diamond diagonal), ladder ~ 1+G1+G3 -- all exact; grading half absent from 7296 canonical combinations (kill not triggered; real structure the named suspect); 4/4 checks

Dependencies as recorded

QGEO.COVER.01; QGEO.INVOL.01; DIAMOND.PARA.SELFCODE.01; v566; v568; v597