discriminatorMatrixCert
plain-language theorem explainer
A master certificate that packages three independent theorem-grade distinctions between Recognition Science and rival quantum-gravity programs (LQG, string theory, uniform discreteness, no-echo semiclassical). Track 6 closure arguments and the RS-vs-LQG/string QNM separation cite it. The body is pure structure assembly: it wires the three already-proved sub-discriminator certificates into one record.
Claim. There is an inhabited master discriminator certificate whose three fields are: (i) a leading-log entropy coefficient discriminator with proved margins $c_{\mathrm{RS}}-c_{\mathrm{LQG}}>1/4$ and $c_{\mathrm{RS}}-c_{\mathrm{string}}>5/4$; (ii) an echo-damping ratio discriminator with $1/\varphi\in(1/2,1)$; (iii) a rung-phase delay discriminator with delay in $(0,1/2)$. Together they separate RS from LQG, string theory, and no-echo alternatives on named observational channels.
background
Gravity Track 6 closes the master-plan binding criterion that three or more discriminators be theorem-grade derivations from $\varphi$ with named observational channels. The ambient module aggregates three such inequalities, already proved from RS-internal $\varphi$-rational predictions, into one certificate and records the numerical margins needed for observational falsification.
The leading-log cell uses the RS entropy coefficient $c_{\mathrm{RS}}=-\log\varphi/2\approx-0.241$, set against $c_{\mathrm{LQG}}=-1/2$ and $c_{\mathrm{string}}=-3/2$, with Session-90 margins $c_{\mathrm{RS}}-c_{\mathrm{LQG}}>1/4$ and $c_{\mathrm{RS}}-c_{\mathrm{string}}>5/4$. The echo-damping cell uses the RS bounce ratio $1/\varphi\in(0.617,0.622)$, strictly above $1/2$ and below $1$, against classical Hawking (no echoes). The rung-phase cell bounds a $\varphi$-ladder phase delay strictly below $1/2$.
The master structure simply records one certificate of each kind: leading-log, echo-damping, and rung-phase. Upstream, each field is already inhabited by a dedicated holds-definition that packages the corresponding inequalities.
proof idea
Definitional structure construction, not a tactic proof. The three fields of the master certificate are filled by the three upstream holds-definitions: the leading-log holds-def (Session-90 margins against LQG and string), the echo-damping holds-def (ratio above $1/2$, below $1$, positive, and unequal to $1/2$), and the rung-phase holds-def (delay below $1/2$, positive, and unequal to $1/2$). No new inequalities are derived here; the cert is the product of those three prior certificates.
why it matters
This is the aggregation step that turns three separate discriminators into the single Track-6 matrix certificate demanded by the master plan. Downstream, discriminatorMatrixCert_inhabited is the one-line Nonempty witness built from this value, and the MasterTheorem result rs_qnm_distinct_LQG_string_proven packages it with the QNM and echo distinctness statements to discharge the RS-vs-LQG/string separation claim.
In framework terms it is the gravity-side counterpart of the forcing-chain uniqueness story: once $\varphi$ is fixed (T6) and the ledger/echo/rung predictions are in hand, the observational channels (BH ringdown spectroscopy, echo trains, rung-phase delays) become theorem-grade separators rather than numerical fits. It does not invent new physics; it certifies that the three $\varphi$-rational margins already proved are simultaneously available as one inhabited cert.
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