canon/tiers/01_Tier_1_Foundation/T1_RNG_Sigma_Constraint_System [ACTIVE v1.0].md
Humanity Project Canonical RNG Constraint Mechanic
Joshua Alexander Milks. CONFIDENTIAL.
Last updated: May 17, 2026\.
This doc owns: the canonical Sigma Constraint mechanic governing all probability-driven drop and event rolls across Tier A Solo Base, Tier B Solo DLC, and Tier C MMO scope; the sigma boundary rules (sigma \-1 floor, sigma \+1 ceiling); the reset semantics on drop events; the constraint scope across combat drops, trade yields, familiar bond events, tameable spawns, inscription discovery, and ambient world events; the downstream pipeline consumer interface for RNG-bound rows.
This doc does not own: per-row drop probability values or sigma calculation formulas (T0\_RNG\_Drop\_Table); deterministic gating events that bypass RNG entirely (T1\_Story\_Spine, T2 ChapterDesign, T1\_Integrity\_Paths\_Worldstates\_Master); combat damage variance and weapon proficiency rolls (T1\_Combat\_System\_Spec); trade-specific yield mechanics or per-ingredient probability windows (T1\_Trades\_Master); per-creature spawn weighting (T0\_Creature\_Roster when populated).
Tier 1 Foundation. Always-loaded by every Claude Project. Authored as substantive v1.0 at Phase 5M-5 close from the canonical Sigma Constraint lock dated May 2, 2026\. Prior to v1.0 the doc existed as a title-only placeholder in /01\_Tier\_1\_Foundation/ — Phase 5M-5 populate brings the body to canonical state matching the title stamp.
Drive placement: /Humanity/01\_Tier\_1\_Foundation/T1\_RNG\_Sigma\_Constraint\_System.
Estimated stable size: 5 to 8 pages at v1.0. Update cadence: refines when T0\_RNG\_Drop\_Table moves from scope-locked to active populate during Phase 4 Quest Writing or earlier if drop-table-dependent build work surfaces tuning needs. Future revisions surface through CVD §19 drift protocol.
All RNG-based drops and probability events in Humanity operate under the Sigma Constraint. The constraint binds raw probability rolls to a bounded window around the cumulative bell curve of expected drop frequency, eliminating outlier streaks and stabilizing player experience around configured drop rates without removing the perceived randomness of individual rolls.
The mechanic preserves what players want from RNG — surprise, anticipation, the satisfaction of a long-awaited drop — while removing what frustrates them — back-to-back streak floods that trivialize farming, or extended droughts that exceed reasonable expectation and break trust in the drop rate itself.
The constraint operates through three rules applied to every RNG-bound event.
Together the rules confine actual drop frequency to a tight band around the configured probability. Players experience drops as variable but bounded, not random in the unconstrained sense.
The Sigma Constraint applies to every RNG-bounded event in canonical scope.
The constraint does not apply to deterministic gating events. Story-locked chapter progression, hard-line scene triggers per CVD §17, integrity-band routing decisions, antagonist family encounter beats, and any event that operates on canonical worldstate rather than probability bypass the Sigma Constraint entirely. Those events fire on state conditions, not roll outcomes.
Per-event sigma calculation derives from the configured drop probability for that event class. The canonical formulation treats each drop event as a discrete trial against a configured base probability, with sigma tracking the cumulative deviation between observed drops and expected drops across the rolling window since last reset.
The specific per-event sigma formula and rolling window length live in T0\_RNG\_Drop\_Table per-row configuration. Drop classes with high base rates (above 50 percent) use shorter windows and tighter sigma bounds. Drop classes with low base rates (below 5 percent) use longer windows and looser sigma bounds calibrated to keep the expected variance within player-perception tolerance.
T0\_RNG\_Drop\_Table is currently scope-locked. The exact per-row formulation locks during T0\_RNG\_Drop\_Table population work in Phase 4 Quest Writing or earlier as build-side tuning requires.
The constraint surfaces to downstream pipelines as substrate fields on every RNG-bound row in T0\_RNG\_Drop\_Table and analogous registry consumers.
UE5 pipeline contract §1, Quest Writing pipeline contract §6, and Cinematic Scene Build pipeline contract §5 all read these fields at runtime and apply the constraint mechanic per T1\_Build\_Pipeline\_Contracts canonical pipeline integration.
T0\_RNG\_Drop\_Table is the canonical T0 registry that holds per-event drop probability configuration. T1\_RNG\_Sigma\_Constraint\_System owns the mechanic; T0\_RNG\_Drop\_Table owns the per-row data. The two docs evolve together — mechanic refinements surface here, per-event tuning surfaces in the registry.
T0\_RNG\_Drop\_Table sits at scope-locked state at Phase 5M close. Population happens during Phase 4 Quest Writing alongside the quest content build, or earlier if specific drop-table-dependent build work requires individual rows to land first. T1\_RNG\_Sigma\_Constraint\_System v1.0 holds the mechanic locked regardless of registry population state — downstream pipelines can read the spec and design against it ahead of registry population.
The Sigma Constraint targets a specific design feel. RNG should reward patience but never punish exhaustively. A 10 percent drop rate should average roughly ten drops per hundred attempts with variance bounded to feel fair, not five drops or twenty. A long-awaited drop should land within a window that respects player time investment. A streak of drops should still surprise but not break the pacing of farming or progression loops.
The constraint also serves the canonical design pillar that quality of player experience surpasses Zelda OoT and Wind Waker plus Mario 64 — drop systems in those references avoided streak frustration through careful tuning. Humanity formalizes the same instinct as a canonical mechanic enforced across all RNG-bound systems rather than tuned ad hoc per drop class.
Edge cases reserved for future revision.