# Core Notes notation register

Version: v0.3-draft working control layer  
Research cutoff: 2026-08-24  

This register prevents the same symbol from silently changing meaning across
the 12 chapters. A symbol marked **latent/proxy-sensitive** may be measured
directly only in a controlled system; a closed-surface study must name its
observable proxy.

| Symbol | Domain / unit | Meaning | Observability | First use |
|---|---|---|---|---|
| $q$ | text / structured request | user query or task request | observed | Ch. 1 |
| $u$ | versioned state record | user, account, locale, and conversation state | partly observed | Ch. 1 |
| $t$ / $T$ | timestamp / time window | observation time or declared analysis window | observed | Ch. 1 |
| $\mathcal W_t$ | set of source representations | information environment accessible to the system at time $t$ | latent/proxy-sensitive | Ch. 1 |
| $\theta$ | version/configuration record | identifiable generative-search system state | partly observed | Ch. 1 |
| $\mathcal G_\theta$ | stochastic kernel | conditional generative-search system | conceptual or controlled | Ch. 1 |
| $Y,y$ | random variable / realized text object | generated response | observed at the surface | Ch. 1 |
| $\mathcal A,\mathcal a$ | set of citation objects | displayed attributions or citations | observed after resolution | Ch. 1 |
| $L,\ell$ | event trace | observable interaction or action trace | surface/consent dependent | Ch. 1 |
| $s$ | source ID | governed source artifact and version | observed | Ch. 1 |
| $c$ | claim ID | minimal scoped proposition | constructed and reviewed | Ch. 2 |
| $e$ | evidence ID or evaluation cell, context disambiguates | evidence record in Ch. 2; versioned evaluation cell in Ch. 6 | constructed | Chs. 2, 6 |
| $\Pi(d)$ | ordered/set-valued transformation | versioned passages or representations derived from document $d$ | observed in controlled stack | Ch. 4 |
| $\widehat q$ | text / query object | retrieval query emitted by a query plan | observed only when traced | Ch. 3 |
| $\mathcal D_t$ | corpus snapshot | frozen candidate corpus at time $t$ | observed in controlled stack | Ch. 4 |
| $R_k(q)$ | ordered list | top-$k$ retrieved representations for $q$ | controlled or exposed trace | Ch. 4 |
| $g_{qi}$ | integer grade, usually 0–3 | preregistered relevance label for candidate $i$ | human/judge measurement | Ch. 4 |
| $C$ | ordered context | effective passages/representations presented to generation | latent/proxy-sensitive | Ch. 4 |
| $A(y)$ | set of atomic answer claims | smallest material claims in answer $y$ that retain quantity, scope, condition, time, and attribution | constructed and reviewed | Ch. 5 |
| $R(y)$ | set of resolved citation objects | displayed anchors resolved with canonical identity, version, access time, and exact passage when available | observed plus governed resolution | Ch. 5 |
| $E_y$ | set of ordered claim--citation pairs | visible or rule-declared attachment edges for answer $y$; attachment does not imply support | constructed from interface scope or a declared resolver | Ch. 5 |
| $w_j$ | nonnegative claim-weight units | preregistered materiality weight for atomic claim $a_j$ | declared and sensitivity-audited | Ch. 5 |
| $C^{-s}$ | ordered context | counterfactual context formed by removing source $s$ while logging every collateral order, budget, position, replacement, and truncation change | controlled construction | Ch. 5 |
| $U$ / $U_i$ | declared answer-utility units / binary fixture outcome | preregistered utility for a context contrast; in the Orchid Bay fixture, whether all three source-distinctive claims appear faithfully | constructed measurement | Ch. 5 |
| $\Delta_s(C)$ | declared utility units | bounded contribution contrast between $C$ and $C^{-s}$ under the stated intervention and assumptions | estimated only in a controlled design | Ch. 5 |
| $B$ | tokens, cost, or capability units, context disambiguates | context/edit/attacker budget | declared protocol parameter | Chs. 4, 9, 11 |
| $Z_{\mathrm{ctx}}(s)$ | binary/graded | source $s$ is selected into effective context | latent/proxy-sensitive | Ch. 5 |
| $Z_{\mathrm{use}}(s)$ | binary/graded | bounded method attributes material answer influence to $s$ | inferred by stated method | Ch. 5 |
| $Z_{\mathrm{abs}}(s)$ | binary/graded | preregistered source-specific claims appear faithfully | measured | Ch. 5 |
| $Z_{\mathrm{cite}}(s)$ | binary/graded | displayed citation resolves to $s$ | observed | Ch. 5 |
| $S_{jk}$ | binary/graded support label | source passage $k$ supports answer claim $j$ under a labeling guide | human/judge measurement | Ch. 5 |
| $Q,M$ | distributions or finite weighted panels | target query and system distributions | declared | Ch. 6 |
| $w_q,w_m$ | nonnegative normalized weights | query and system target weights | declared/estimated | Ch. 6 |
| $D_i$ | binary or multivalued assignment | assigned treatment version for experimental unit $i$ | observed | Ch. 7 |
| $Y_i(d,S_t)$ | potential outcome | outcome for unit $i$ under treatment $d$ and system state $S_t$ | counterfactual; one state observed | Ch. 7 |
| $\tau$ | outcome units | explicitly defined treatment estimand | estimated under assumptions | Ch. 7 |
| $x,x'$ | versioned source states | baseline and candidate source/release states | observed | Ch. 8 |
| $\delta$ | typed change record | permitted intervention from one source state to another | observed and governed | Ch. 8 |
| $\mathcal X_{\mathrm{perm}}(x)$ | set of source states | revisions allowed by claim, policy, safety, and release constraints | constructed | Ch. 9 |
| $\mathbf J(x')$ | vector with declared component units | retrieval, citation, absorption, fidelity, utility, risk, and cost objectives | estimated | Ch. 9 |
| $a$ | asset ID in Ch. 10; account state elsewhere | multimodal asset when inside $\Pi(a)$ | context-dependent; avoid unqualified reuse | Ch. 10 |
| $\Pi(a)$ | set of versioned representations | controlled text, pixel, caption, metadata, and page representations derived from governed asset $a$ | observed in a controlled stack; otherwise subset/transform may be latent | Ch. 10 |
| $B(y)$ | set of governed entity IDs | brand entities resolved from mentions in answer $y$ | constructed through a versioned resolver | Ch. 10 |
| $C_b(y)$ | set of scoped claims | answer claims attached to resolved brand $b$ | constructed and reviewed | Ch. 10 |
| $\mathbf V_b$ | seven-component outcome vector | mention, correctness, citation, absorption, prominence, action, and separately defined risk for brand $b$ | measured with component-specific units; no implicit composite | Ch. 10 |
| $G=(V,E)$ | directed graph | claim/source/publisher/version provenance dependency graph | observed to audit coverage | Ch. 10 |
| $o(s)$ | origin-cluster mapping | earliest verified provenance-origin cluster for source $s$ | constructed from an auditable provenance trace | Ch. 10 |
| $N_{\mathrm{origin}}(S)$ | count of verified origin clusters | number of distinct mapped origins represented in source set $S$ | descriptive and trace-completeness dependent | Ch. 10 |
| $D(\delta)$ | detector score | declared manipulation or safety detector output | measured, calibration required | Ch. 11 |
| $\Gamma(r)$ | structured release record | identity, claims, evidence, risks, controls, approvals, monitoring, rollback | observed/project-controlled | Ch. 12 |

## Notation gates

1. Every estimator adds a hat; every realized value is distinguished from its
   random variable when the distinction matters.
2. Every probability states its conditioning set or points to the frozen
   evaluation cell.
3. Every vector lists component units and cannot be averaged without declared
   scaling and weights.
4. Every use of $e$, $B$, or $a$ must be locally disambiguated because the
   manuscript retains explicitly registered legacy meanings.
5. A hidden closed-platform state is never presented as observed; proxies and
   reconstructed hypotheses are labeled.
6. Any remaining overloaded symbol must be listed in Appendix E with its local
   domain, first-use definition, and forbidden substitution before release.