The theory tiers

Every scientific claim in SAGE carries a confidence tier, maintained in the claims ledger and stated in every relevant docstring:

Tier	Meaning	Examples
exact	Proved identities. Implemented as verified primitives, cited, never claimed as ours.	Gibbs variational principle; log-partition = CGF; Gibbs measure in potential games; the Hodge decomposition
derived	Proved in-house and/or numerically checked. Ours to claim, positioned honestly.	The resolvent transfer (χ^eq inherits B's symmetry exactly); ℛ as a λ-free observable
conjectured	Argued but not established. The ledger states what would count as each one being wrong.	Tightness of the cycling → dissipation chain
speculative	Exploratory framings, kept out of user-facing claims.	Sparse/entmax responses for 9-ending prices

Tiers move — in both directions — as evidence arrives. The prior-art history is part of the ledger: what we once thought new and turned out to be textbook is recorded, not erased.