nx_cdmap_lib.nx

nx_cdmap_lib.nx -- THE ONE centrality/distinctiveness ruler for every /compare board (2026-09-15). WHY. Operator, 2026-09-15 (the /goal): "a multi variable four quadrant visual thats emitted to properly show where we are and our competitors and where we are moving as time goes on daily". The field's instrument is the Centrality-Distinctiveness map (Dawar and Bagga, Harvard Business Review, June 2015, "A Better Way to Map Brand Strategy"): X = how representative of its category a brand is, Y = how far it stands apart, the bubble a third variable and its colour a fourth; the category's own averages cut four quadrants -- Aspirational (central AND distinctive), Mainstream (central, undistinctive), Peripheral (neither), Unconventional (distinctive, uncentral). Operator, same day: "extensible as we get more and more variables ... a 3 dimensional x y z axis cube with a 2d cut and a 3d view". So the AXES ARE A REGISTRY (cd_axis_*), every axis reads on one permil scale, a board picks any two as its 2D cut and any three as its cube through DATA (knowledge/compare/<dom>.cdmap), and the isometric projection lives HERE so the gate can pin it. Adding a variable is one axis id, one name, one value rule. HERE EVERY INPUT IS THE MATRIX THE BOARD ALREADY MEASURES. The map is a PROJECTION of the same cells the page grades (Nishi's cell measured on disk, the rivals' cells documented presence), re-derived on every publish, so it cannot say anything the cells do not; and the board's own history -- a per-domain day spine this lib writes once per calendar day -- is the time axis, so "where we are moving" is a path on the page, never a claim. THE ARITHMETIC (integer permil; nofloat; every constant named). players P = Nishi + the @cols rivals. pts(p,r) = cd_pts(code): Best 3, Yes 2, Part 1, No 0 -- the scale the page's pros/cons strip already uses (pc_pts). have(p,r) = pts > 0. hc(r) = players holding row r. CENTRALITY(p) = 1000 * sum_r have(p,r)*hc(r) / sum_r hc(r) the share of the category's feature mass the player covers, each feature weighted by how many hold it: a player holding everything the field holds reads 1000; one holding only what nobody else has reads low. DISTINCTIVENESS(p) = 1000 * sum_r lead(p,r) / (3 * (P-1) * sum_r have(p,r)), lead(p,r) = sum over rivals q of max(0, pts(p,r) - pts(q,r)): the average lead over each rival on the rows the player holds -- a Best where rivals hold Yes counts, a feature no rival holds counts most, a player whose every feature is matched reads 0. A player holding nothing reads 0 on both axes and quadrant ABSENT (never a division by zero). BREADTH(p) = 1000 * sum_r pts(p,r) / (3 * rows) -- depth-weighted share of the whole matrix (the bubble). DEPTH(p) = 1000 * sum_r pts(p,r) / (3 * held) -- how deeply the rows it holds are held (Best everywhere = 1000). MOMENTUM(p) = (C_today - C_prev) + (D_today - D_prev) over the spine -- signed; unknown until day two; plotted as (m + 1000) / 2 so a still player sits mid-axis. The quadrant dividers are the MEANS over the players -- the category's own centre, as the map's authors draw it. Ties: central iff C >= mean; distinctive iff D > mean (a field of identical players is Mainstream, never Aspirational). THE SPINE. <dir><dom>.spine, one row per player per calendar day (UTC), appended by the FIRST publish of the day; a re-publish the same day is a no-op by construction (the day column is the key): cd|<epoch>|<day>|<player>|<centrality>|<distinctiveness>|<breadth-points>|<rows>|<players>|<held> (held was appended 2026-09-15 for the depth axis; an older row without it reads held 0, never a crash.)