IndisputableMonolith.Physics.StringTheoryFromJCost
The module packages the claim that the Recognition vacuum is exactly the zero locus of the J-cost: the unique cost-minimizing ratio state is J=0. It supplies the string-theory-facing certificate objects (variant type, count, vacuum lemma, and cert bundle) used by domain openings that treat string vacua as J-cost selections. The argument is a thin specialization of the canonical six-clause J-band template to the vacuum ratio.
claimIn Recognition units the vacuum ratio is the unique positive $x$ with $J(x)=0$, namely $x=1$, where $J(x)=(x+x^{-1})/2-1$. The module records this vacuum selection and the associated string-theory certificate data (variant label, count, and cert bundle) built on that identity.
background
Recognition Science forces a unique nonnegative cost on positive ratios, $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), with matched zero $J(1)=0$. The reusable six-clause J-cost-on-ratio template in CanonicalJBand is the standard opening for domain certificates: matched-zero, nonnegativity, and the remaining band clauses used across B-tier and Plan v7 certs.
This physics module sits in that template chain. Its one-line module doc states the selection rule: the Recognition vacuum is the J-cost zero. Sibling names indicate a small certificate surface: a string-theory variant type, a count, a vacuum lemma vacuum_jcost_zero, and a cert bundle tying those facts to the J-band.
No extra dynamical string field content is assumed at the import boundary; the only upstream module is CanonicalJBand plus Mathlib.
proof idea
Module-level structure, not a single theorem proof. It specializes the CanonicalJBand six-clause template to the vacuum ratio: record $J(1)=0$ as the vacuum selection, expose a variant/count surface for string-theory bookkeeping, and wrap those facts in a cert object. Expect the vacuum lemma to be a direct appeal to the matched-zero clause of the J-band (or an immediate corollary), with the cert assembled by packaging that lemma plus the count/variant data. No independent analytic machinery beyond the imported J-cost band.
why it matters in Recognition Science
Gives the physics-facing handle for "string vacua as J-cost zeros" inside the Recognition cert chain. Downstream used_by edges are empty at present, so the module is a leaf certificate source rather than an intermediate lemma library: domain openings that need a string-theory or vacuum clause can import the cert bundle instead of re-proving $J(1)=0$.
It sits under the broader forcing story in which T5 fixes $J$ uniquely and the Recognition Composition Law constrains multiplicative structure; the vacuum selection is the matched-zero landmark of that unique $J$. The module does not itself force $D=3$, the eight-tick octave, or the $\alpha$ band; it only anchors the vacuum cost identity those later physics certs may quote.
scope and limits
- Does not derive the full string spectrum, moduli stabilization, or compactification geometry.
- Does not prove uniqueness of string theory among QFTs; only packages vacuum $J=0$ selection.
- Does not establish T5–T8 forcing steps; those live in the unified forcing chain.
- Does not compute $\alpha$, masses, or $G$; constants are out of scope here.
- Does not supply used_by parents yet; it is a leaf cert module in the current graph.