A · Symbols, Notation, and the Code–Symbol Binding

1.112026-08-29

A.1 · Principal notation

Table 10. Principal notation used in the main text. Numerical values for the FA-related symbols are in Appendix B; RI-related values are not disclosed.

Symbol	Meaning	Where
$\mathcal{U}$ , $\mathcal{I}(t)$ , $\mathcal{S}(t)$	universe; included; shadow sets	§6.1
$\xi(t)$	full indicator state	Def. 6.1
$x_{i,k}$	L1 source input of unit $i$ , source $k$	§6.1
$\hat v$	normalized factor value	§6.3
$\mathrm{cap}, \mathrm{edge}, \mathrm{eco}, \mathrm{com}$	FA blocks	(7)–(10)
$\alpha_{\mathrm{cap}}, \alpha_{\mathrm{eco}}$	top-level group weights	(11)–(12)
$\beta_{\mathrm{cap}}, \beta_{\mathrm{edg}}$	within-capability block weights	§6.5
$\beta_{\mathrm{eco}}, \beta_{\mathrm{com}}$	within-ecosystem block weights	§6.5
$\gamma_{\mathrm{dev}}, \gamma_{\mathrm{acad}}$	ecosystem sub-block weights	(9)
$\delta_{\mathrm{rip}}, \delta_{\mathrm{led}}$	academic sub-block weights	§6.5
$\mathrm{FA}_i$ , $\mathrm{FA}^{\mathrm{adj}}_i$	anchor and adjusted anchor	(13), (14)
$D_i$ , $R_i$	sustained-leadership; real-harm adjustments	(14), (15)
$D_{\mathrm{cap}}$ , $R_{\mathrm{cap}}$	adjustment caps	Appendix B
$\mathrm{streak}_{d,y}$ , $f(\cdot)$	streak length; concave weight function	(15)
$w_y$ , $\beta_d$	tier weights; leaderboard weights	(15)
$\mathrm{RI}_i(t)$ , $\overline{\mathrm{RI}}(t)$	live signal; included cross-sectional mean	(16), (17)
$A_e$ , $t_e$ , $T_{1/2}(e)$	pulse amplitude; start; half-life	(16)
$\mathcal{E}_i(t)$	active pulse set of unit $i$	(16), (19)
$p$	polarity in $[-1,1]$	§6.6
$k_{\mathrm{ri}}$	live-signal dispersion coefficient (reserved)	(17)
$\mathrm{BR}$	reserved bridge slot	§6.10
$\Theta_i$ , $\widetilde{\Theta}_i$	flagship actual; nominal	(1), §6.8
$\mathrm{H}_i$	absolute discussion heat	(19)
$\Gamma_i$ , $\Lambda_i$	capability composite; absolute composite	(20)–(21)
$\mu_\Gamma$ , $M_\Gamma$	sector mean; sector maximum of $\Gamma$	(23)
$C_i$ , $C(t)$ , $C_{\mathrm{frontier}}$	capability level; deflator; frontier constant	(24), §6.7

A.2 · The complete code–symbol binding

Product codes are labels, not variables: they never appear inside formulas. Table 11 is the complete and authoritative binding. The family codes that denote internal or derived quantities (e.g., 8102) are included; the user-facing publication family is the subset listed in Section 6.7.

Table 11. Complete code–symbol binding. Every product code is bound here to the symbol (if any) used in formulas.

Code	Symbol (if any)	Meaning	Defined at
`8100`	$\Theta_i(t)$	company composite influence, relative (actual)	(1)
`8100` (nominal)	$\widetilde{\Theta}_i(t)$	same, presentation-layer nominal	§6.8
`8101`	$\mathrm{FA}^{\mathrm{adj}}_i(t_0)$	fundamental anchor (adjusted), settled	(14)
`8102`	$\mathrm{RI}_i(t)$	real-time influence, live signal	(16)
`8111`	$\mathrm{H}_i(t)$	absolute discussion heat	(19)
`8200`	$\Gamma_i$	capability composite (absolute)	(20)
`8300`	$\Lambda_i(t)$	absolute composite (deflated)	(21)
`9200`	$\mu_\Gamma(t), M_\Gamma(t)$	sector aggregates (mean / max)	(23)
`CN1111`	—	China Top-1 composite (by $\Theta$ )	§6.7
`US1111`	—	United States Top-1 composite (by $\Theta$ )	§6.7
`CN3333`	—	China Top-3 composite (by $\Theta$ )	§6.7
`US3333`	—	United States Top-3 composite (by $\Theta$ )	§6.7
`CN5555`	—	China Top-5 composite (by $\Theta$ )	§6.7
`US5555`	—	United States Top-5 composite (by $\Theta$ )	§6.7
`1111`, `3333`, `5555`	—	regional truncation suffix: Top-1 / Top-3 / Top-5	§6.7

The regional composites (CN1111, US1111, CN3333, US3333, CN5555, US5555) are country subsets of the flagship semantics: each is a composite over the country's Originators ordered by $\Theta$ , with the suffix denoting the top- $k$ truncation ( $1$ , $3$ , $5$ ). They share the flagship's conservation and audit machinery restricted to the country subset, and they exist so that a national audience can read its own landscape without losing the cross-sectional discipline of the full set.

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