IndisputableMonolith.Foundation.RS_AdSCFT_RS
Module packaging a Recognition Science certificate for an AdS/CFT-style bulk/boundary cost match. It defines a domain cost from the RS J-cost, a positive canonical threshold, and an inhabited certificate structure RSAdSCFTRS. Foundation and holography readers cite it when wiring RS units into a bulk-boundary comparison. Content is mostly definitions and elementary positivity/equality lemmas over Cost and Constants.
claimIn RS-native units, assign to each domain a nonnegative cost $C(\Omega)$ built from the $J$-cost, fix a canonical threshold $\theta>0$, and package the bulk/boundary cost comparison as an inhabited certificate $\mathsf{RSAdSCFT\text{-}RS}$ asserting the AdS/CFT-style match under those data.
background
Recognition Science derives dynamics from a unique cost $J$ fixed by the Recognition Composition Law, with native units $c=1$ and time quantum $\tau_0=1$ tick from Constants. The Cost import supplies that $J$-cost and its elementary calculus (nonnegativity, normalization at the identity).
This module sits in Foundation and treats AdS/CFT as a cost-matching statement rather than a full string dual: a domain cost is evaluated on bulk and boundary data, then compared against a canonical positive threshold. The sibling definitions domainCost, canonicalThreshold, and the structure RSAdSCFTRS are the vocabulary for that comparison; equality and nonnegativity lemmas pin the arithmetic.
No forcing-chain step (T0–T8) is re-proved here. The module only specializes existing cost infrastructure to a holography-shaped certificate interface.
proof idea
Definition-heavy module. Domain cost is introduced as a thin wrapper around the imported $J$-cost; domainCost_at_eq and domainCost_nonneg are direct transfers of Cost identities. The canonical threshold is a positive RS-native constant (canonicalThreshold_pos). The main object RSAdSCFTRS bundles those data into a certificate type, with cert / cert_inhabited supplying a trivial inhabitant so downstream code can assume the interface is live. No deep tactic proof; structure is definitions plus one-line positivity and equality facts.
why it matters in Recognition Science
Gives Foundation a named place to hang an RS reading of AdS/CFT: bulk/boundary agreement is a cost inequality against a fixed threshold, not a separate dynamical principle. Downstream graph currently lists no consumers, so the module is an interface seed rather than a proved link in the forcing chain. It does not claim the Maldacena duality, a concrete bulk metric, or a CFT operator dictionary; it only standardizes cost-side hypotheses that a later holography or ledger theorem could discharge. Landmarks touched only indirectly: $J$-uniqueness (T5) via Cost, and RS units via Constants.
scope and limits
- Does not prove AdS/CFT or any bulk reconstruction theorem.
- Does not derive a bulk metric, Einstein equation, or boundary CFT spectrum.
- Does not fix numerical values for domain costs beyond nonnegativity and threshold positivity.
- Does not connect to the T0–T8 forcing chain or mass ladder.
- Does not supply downstream consumers; used_by is empty.