hodge_structure
plain-language theorem explainer
The declaration equates the Recognition Science Hodge conjecture scaffold to the Birch-Swinnerton-Dyer structural input. Researchers examining algebraic geometry links inside the RS framework would reference this equivalence. The proof is a direct term assignment of the BSD theorem, which rests on the irrationality of phi.
Claim. The structural placeholder for the Recognition Science Hodge conjecture program holds, as it is identical to the Birch-Swinnerton-Dyer ledger condition established by the irrationality of $phi$.
background
Module M-006 formalizes a structural RS scaffold for Hodge-type algebraicity statements. The definition hodge_from_ledger is the Prop bsd_from_ledger and serves as placeholder for the RS Hodge-conjecture program. The upstream bsd_structure theorem proves bsd_from_ledger via phi_irrational, with the explicit comment that BSD structure implies irrationality of phi.
proof idea
The proof is a one-line term wrapper that directly applies bsd_structure to discharge hodge_from_ledger.
why it matters
This theorem bridges the Hodge scaffold to the BSD structure inside the Recognition Science framework and fills a slot in the M-006 program. It inherits the irrationality of phi from the upstream BSD result. With no recorded downstream uses, its role in larger chain steps remains open for further integration.
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