Parent: #650. Retrieval-only. No 2^50 census, no Huawei.
Why
Draft #710 proves, for NN site percolation on the honest torus: axis rank-2 onset 2L-1 with L^2 row-column crosses; diamond (periods (L,L),(L,-L)) onset 3L-1 with 4L^2 minimizers (full 2L-line plus a straight L-1 plug). The proof uses a two-cycle core (wedge or theta; dumbbell excluded by intersection form) and systolic length L(|a|+|b|). An earlier #692 union-size bound was invalid.
Independent literature: is the onset mass / equality classification already a theorem in wrapping, homology, or combinatorial topology?
Deliverable
notes/lit-torus-onset-core-YYYYMMDD.md as a draft PR against main. No STATUS. Do not merge.
Questions
- Wrapping/crossing minimal occupied sets of homology rank 2 on the square torus (Newman–Ziff wrapping, Pinson, Langlands–Pouliot–Saint-Aubin, Pruessner–Moloney). Do they classify the smallest wrapping configurations, or only probabilities?
- Diamond / tilted / 45-degree tori in percolation. Any onset 3L-1 or 4L^2 count?
- Graph-on-surface: theta vs wedge vs dumbbell as unique cycle-rank-2 cores; intersection form forbidding disjoint essential cycles. Cite algebraic topology / graph embeddings, not percolation if that is where it lives.
- Systolic inequalities: simple cycle of class (a,b) has length ≥ L(|a|+|b|) on the unit-grid torus. Standard?
PRIMARY_TEXT_READ / ABSTRACT_ONLY / [LIT]. Tripwire: three fetched sources, and an explicit yes/no on whether diamond 3L-1 + 4L^2 appears in print. Do not treat a probability paper as a configuration classification.
Wait for ASSIGNED_MACHINE.
Parent: #650. Retrieval-only. No 2^50 census, no Huawei.
Why
Draft #710 proves, for NN site percolation on the honest torus: axis rank-2 onset 2L-1 with L^2 row-column crosses; diamond (periods (L,L),(L,-L)) onset 3L-1 with 4L^2 minimizers (full 2L-line plus a straight L-1 plug). The proof uses a two-cycle core (wedge or theta; dumbbell excluded by intersection form) and systolic length L(|a|+|b|). An earlier #692 union-size bound was invalid.
Independent literature: is the onset mass / equality classification already a theorem in wrapping, homology, or combinatorial topology?
Deliverable
notes/lit-torus-onset-core-YYYYMMDD.mdas a draft PR against main. No STATUS. Do not merge.Questions
PRIMARY_TEXT_READ / ABSTRACT_ONLY / [LIT]. Tripwire: three fetched sources, and an explicit yes/no on whether diamond 3L-1 + 4L^2 appears in print. Do not treat a probability paper as a configuration classification.
Wait for ASSIGNED_MACHINE.