lattice-system

Deleted proof routes

Historical record moved losslessly from the former monolithic index.

Deleted routes: what this index used to document

Three abandoned proof routes had one index row per declaration. Their modules were deleted, so the rows described declarations and files that no longer exist; the 590 affected rows were removed (PR #5143, issue #5140). What was there, and how it went away:

Route the rows described Heading they sat under Removed by
Later γ-4 layers: predicted ground-state subspace and minimum energy of the bipartite toy model (bipartiteToyGroundStateSubspacePredicted*, bipartiteToyMinEnergyPredicted*, bipartiteImbalanceWeight*), Néel-state toy-Hamiltonian expectations (neelStateOfS*, heisenbergToyHamiltonianS*) and their spin-1/2 mirrors (neelStateOf*) Total spin operator (Tasaki §2.2 eq. (2.2.7), (2.2.8)) — 540 rows PR #3919 (7b65d59e, “delete 525 orphan modules, 35,002 lines”): 480 of the 482 modules those rows named; the other 2 paths are files that still exist
Callback-threaded Theorem23* chain toward tasaki_2_5_theorem_2_3 (energy-interval chains, lowering/raising predecessor coefficients, joint cross-ladder wrappers) Spin-S Marshall–Lieb–Mattis on the magnetization sector (Tasaki §2.5 Theorem 2.2 generic S, sector form) — 25 rows PR #3645 (f7947dfc, “delete unsound saturated-ladder Theorem 2.3 route”, 40 wrapper modules) for 8 modules; PR #3919 for the other 14
Saturated ferromagnetic ladder-iterate state (ladderIterateUp_*, allAlignedStateS / totalSpinSOp{Plus,Minus} expectation variants, saturatedFerromagnetJointEigenspace*) Spin-S saturated ferromagnetic state (Tasaki §2.4 generalised) — 25 rows PR #3919, all 25 modules

The surviving parts keep their rows: the earlier γ-4 steps (sublattice operators, sublattice Casimir, SU(2) commutation) and the sound per-sector Perron–Frobenius route to tasaki_2_5_theorem_2_3. The globs in the table above name the deleted variant families, not the stems they are built on: every one of those stems (bipartiteToyGroundStateSubspacePredicted, bipartiteToyMinEnergyPredicted, bipartiteImbalanceWeight, neelStateOf, neelStateOfS, heisenbergToyHamiltonianS, ladderIterateUp, allAlignedStateS, totalSpinSOpPlus/totalSpinSOpMinus, saturatedFerromagnetJointEigenspace) is still a live declaration prefix with surviving variants, and the Theorem23* module family is still 56 live modules under Quantum/SpinS/ (no declaration name carries that prefix). Most of those survivors keep their own rows in this index, but not all: of the 201 live public declarations under the declaration stems just listed, 158 are named verbatim in some row’s first column, two only inside another row’s prose, one only inside the stem list just given, and 40 are named verbatim nowhere in this file, though some of that last group are still named indirectly inside this file’s own abbreviated forms (brace families such as _totalSpinSOp{1,2,3} and suffix elisions such as / _sq). For ladderIterateUp_* the survivors are even the majority of the stem’s variants: of the 17 declarations with that prefix that the tree held before these deletions, 11 are still present. Only the variants enumerated above are gone. Likewise, deleted names of the form tasaki_2_5_theorem_2_3_of_..._threaded_... belonged to the abandoned route and are not the live capstone tasaki_2_5_theorem_2_3.