Natural Math authority

Natural Math v5 is the governing frozen integer baseline.

Natural Math is a bounded local-process model for exact integer state, deterministic replay, and controlled morphology experiments. Higher version numbers do not establish authority by themselves.

Authority note: Natural Math v5 is the governing frozen integer baseline. Later-numbered diagnostic and experimental branches remain separate unless a versioned, hash-bound qualification record explicitly promotes them.

Version hierarchy

Do not infer authority from numbering.

Verified / Frozen

v5

Frozen integer/reference baseline with exact specification hashes, frozen operators, bounded fixtures, and deterministic replay evidence.

Extension line

v5.1

Extension line only. It does not silently replace v5.

Research branch

v6, v6.18, Stage 10

Later diagnostic or research branches, separately qualified where applicable, not the governing frozen base.

Candidates

v10.3.2, v12, higher

Active or historical research candidates. They do not supersede v5 without an explicit frozen compatibility decision.

Natural Math authority ladder showing v5 as the frozen baseline and later branches as separate candidates or diagnostic branches. — Authority flows from frozen qualification, not from the largest version number.

Frozen v5 evidence

What v5 establishes.

Operators

Integer division, squared grid distance, energy deficit, exact-rational gradient, pressure projection, action selection, movement conflict resolution, bifurcation, bonding, cluster stepping, seeded randomness, serialization, and default parameters are bound to CLAIM-0001 through CLAIM-0013.

Rerun result

Natural Math v5 passed 40/40 frozen oracle fixtures and 210/210 replay configurations in the 2026-07-23 read-only rerun. Claim: CLAIM-0014.

Boundary

The result is deterministic software behavior under declared integer parameters and fixtures. It is not a general law of biology, physics, intelligence, or morphology.

Applied experiments

Playable systems that make local rules easier to inspect.

Playable Applied Experiment

Eracii Arena: Duel

Playable applied development · Led by Melissa Ellen Clow

Eracii Arena translates selected Natural Math design principles into a playable deterministic strategy system. Two legends act within a finite grid, bounded rounds, explicit resources, local movement constraints, persistent positional consequences, and exact action resolution.

Once the combatants and player decisions are fixed, match outcomes arise from declared rules rather than random rolls or hidden outcome modifiers. The game also exposes the rival's current planned action and records a chained match history, making decisions and consequences inspectable rather than opaque.

Eracii is an independent applied-development lane. It is informed by Natural Math but is not part of the frozen Natural Math v5 conformance or qualification record.

Play Eracii Duel →

Namespace discipline

Natural Math actions are not Basin actions.

Namespace	States	Boundary
Natural Math action	EXTEND, SENSE, RESTRICT_DIE	Local process operators in the frozen integer baseline.
Cognitive Basin action	EXTEND, HOLD, RETRACT	Governed memory/action posture, not a rewrite of source events.
Cognitive Basin evidence	SUPPORTED, UNRESOLVED, CONTRADICTED	Evidence status layer.
Specificity posture	OPERATIONAL, CAUTION, CONSTRAINED, CRITICAL, EXCEEDED	Target-contract response, not truth itself.

A source event may lead to a separate interpretation or governance request, but the original source state is never rewritten into a different namespace.