Tool contract 3.16.0

The control next to every number (docs/reviews/2026-09-19-INTERFACE-REVIEW.md Part 4, Phase 3): every tool that serves a rate, trend, rank or sum carries the control the 3.13.0 principle names, and a note fires only on a detected confound.

• players_summary: last_30_days.modes (the window's battles by mode group); top_deck and best_deck carry modes and dominant_mode; trophy_floor when the window holds ladder battles; the deck comparability note and the floor note.
• clans_standings members carry modes, ladder_battles, mean_level_gap and level_gap_battles, log_recorded and recorded_since; the response carries comparable (false when two ranked members' dominant modes differ or their gaps are half a level apart, the note naming them) and basis (recorded | roster_and_war_only). trophy_net reads null when ladder_battles is 0, where it read an ambiguous 0 before (a field the docs never defined as a sum-or-zero).
• battles_trends weeks carry modes (the week's battles by mode group) and, when the window clips a week, partial: true with covers {from, to} and a note; a pooled-modes note fires when mode was omitted and a week holds more than one group.
• battles_meta_decks and battles_meta_cards rows carry modes and mean_level_gap (deck rows level_gap_battles and dominant_mode too); the response carries comparable, modes_in_window when mode was omitted, the pooled-modes note, and on a segment read a note when every returned row is one player's.
• The three meta tools take trophy_band (under_5000, 5000_8000, 8000_11000, 11000_13000, 13000_plus: the observation's own player's starting trophies), answered from a banded season rollup once the nightly rebuild has filled it and from the raw rows with a note before; cards_synergy's anchor carries modes.
• clans_pilot_scores members carry mean_starting_trophies, modal_arena {id, name} (the population they were scored in) and current_arena, with a note naming the members whose modal arena inside the window differs from their current one.
• clans_participation members carry log_recorded, recorded_since, last_battle_time_in_clan and war_days_battled (per war week, null without coverage); the response carries basis (recorded | roster_and_war_only) and the activity-scope note.
• clans_timeline gains the members_with_profile aggregate (the denominator of the profile-derived ones); war_rivals rows carry colosseum_races with a note when any; rankings_timeline notes when rated_players is 0 at every point (an empty field, not a flat one); rankings_clans carries field_size (the placed players the counts were taken over).
• The population is named (product call 5): on the six segment tools (battles_meta_decks, battles_meta_cards, battles_trends, cards_synergy, badges_rarity, badges_holders) segment also accepts the strings 'mine' (the caller's clan; no_subject when there is none) and 'corpus' (the whole recorded corpus, explicitly). The corpus is one population among the others, never a default: a read that omits segment still answers it, carries a note saying so (that note only), and a corpus read carries population {recorded_clans, recorded_players, players_in_window}. 4.0.0 makes segment required.

Additive; migration 0135 adds the band tables and the level-gap columns, empty, filled nightly.