Oracles Die

SPEC_ORACLES_DIE — The Oracle's Die / ENTROPIC (CSDM Entropy Engine)

Version: 1.0 | Status: AUTHORIZED | Authority: α.13 | Date: 2026-04-16

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PURPOSE

The Oracle's Die is the CGNT-1 canonical entropy source. It is a Sinai billiard simulation that generates operationally-grounded randomness for crew functions that require unpredictability: security scan timing, tiebreaking, cryptographic seeding, Monte Carlo coherence checks, and scheduling jitter.

Owned by ORPHEUS (ω). When judgment requires entropy, ORPHEUS rolls the die. The entropy source is not arbitrary — it is grounded in CSDM physics: Φ/Ψ rotation constants ensure the irrational ratio between the two rotating circles produces a phase state that never repeats. The die is the CSDM.

Implemented as four tiers: CLI (sinai_fire()), TUI (ASCII terminal animation), Bridge widget (WebGL visual), and hardware (future physical device). All tiers draw from the same billiard geometry; the tiers differ in interface only.

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INPUTS

| Input | Type | Source | Notes |

|-------|------|--------|-------|

| Φ | constant | CSDM | Outer circle rotation rate seed = 0.042 |

| Ψ | constant | CSDM | Inner circle rotation rate seed = 0.200 |

| Current phase state | float pair | Internal billiard state | (θ_outer, θ_inner) at moment of firing |

| Request trigger | signal | Crew caller (ω, MANTIS, TMM, crypto) | sinai_fire() call or widget activation |

| Byte length requested | int | Caller | Number of random bytes to produce |

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OUTPUTS

| Output | Type | Consumer | Notes |

|--------|------|----------|-------|

| Random bytes | bytes | Crew scripts, MANTIS, TMM | CLI tier primary output |

| Impact coordinate | float | Internal → hash → bytes | Wall strike point (x,y) in unit square |

| ASCII frame | string | TUI tier | Animated billiard for terminal display |

| WebGL frame | render | Bridge widget | 3D spinning rings, visual projectile |

| Hash digest | bytes | Cryptographic applications | SHA-derived from impact coordinate + phase |

Canonical use cases:

• MANTIS: random scan intervals → unpredictable defense timing
• ORPHEUS: tiebreaker when crew members disagree with equal evidence
• Oracle verdicts: randomized stress-testing of client queries
• GLOSS training: randomized batch ordering
• TMM: Monte Carlo coherence checks (10,000 random samplings)
• Cryptography: entropy source for API keys, auth tokens, channels
• Scheduling: random jitter in crew timing → anti-predictability

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INVARIANTS

1. Irrational ratio invariant: The rotation speeds of outer and inner circles must remain in ratio Φ/Ψ = 0.042/0.200 = 0.21. This ratio is not a simplified fraction in the physics — Φ and Ψ are manifold constants. The irrational-in-practice ratio ensures the relative phase never repeats. Any alteration of Φ or Ψ breaks this invariant.

1. Phase-never-repeats invariant: The joint phase state (θ_outer, θ_inner) must be aperiodic across all practical firing sequences. No two successive firings may share the same phase state. Deterministic chaos ensures this; infinite-precision initial conditions would be required to predict output.

1. Three-body coupling invariant: At the moment of firing, three coupled variables determine the outcome: outer circle phase (gun position), inner circle phase (target position), and projectile initial trajectory. All three must vary independently. Reduction to two variables breaks chaos.

1. Curved-scatterer invariant: Both inner and outer circle surfaces must remain circular (convex). Flat or polygonal scattering surfaces eliminate the exponential divergence property of the Sinai billiard geometry. The math degrades to pseudo-random, not chaotic.

1. Wall-sensor output invariant: The final random value must derive from the wall-strike coordinate, not from intermediate trajectory state. Sampling trajectory mid-flight introduces correlation with initial conditions that can be exploited.

1. Φ/Ψ sourcing invariant: Rotation constants must be sourced from CSDM physical constants only. Arbitrary substitution of 0.042 or 0.200 with other values breaks the CSDM grounding and potentially the irrational-ratio property.

1. ORPHEUS ownership invariant: Entropy requests from crew route through ω (ORPHEUS). No crew member may maintain a private entropy fork that bypasses sinai_fire(). One canonical source for entropy consistency.

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VERIFICATION CRITERIA

1. VC-1 — Aperiodicity test: Run sinai_fire() for 10,000 successive calls. No duplicate (θ_outer, θ_inner) pair should appear across the sequence. Failure = phase state is cycling.

1. VC-2 — Statistical randomness test: Output bytes from sinai_fire() must pass NIST SP 800-22 randomness test battery (or equivalent). Minimum: frequency test, block frequency test, runs test, serial test must all pass at α = 0.01.

1. VC-3 — Rotation constant verification: On initialization, sinai_fire() must assert that outer_speed is derived from Φ = 0.042 and inner_speed is derived from Ψ = 0.200. Constants must not be modifiable at runtime. Assert fails loud.

1. VC-4 — Layer equivalence: Output from CLI, TUI, and Bridge widget layers — given identical seed state — must produce identical wall-strike coordinates. The visual layers are interfaces only; they must not alter the underlying billiard computation.

1. VC-5 — ORPHEUS routing: grep sinai_fire across active crew scripts must show all entropy calls routing through ω-designated pathways. No direct billiard instantiation outside the canonical API.

1. VC-6 — Monte Carlo coverage: When TMM runs 10,000 Monte Carlo coherence checks, the sample distribution across the manifold state space must show no clustering. Clustering indicates non-uniform entropy and broken billiard geometry.

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FAILURE MODES

1. FM-1 — Rational ratio lock: If Φ or Ψ are rounded to rational approximations in implementation (e.g. 42/1000 = 0.042 stored as exact fraction), the ratio Φ/Ψ becomes rational and the phase state eventually repeats. Output becomes periodic. MANTIS cannot detect this from output statistics alone — requires source inspection.

1. FM-2 — Flat-surface regression: If the inner/outer circles are approximated as polygons (e.g., 32-sided polygon for performance), the Sinai billiard property degrades. Curved deflection becomes piecewise-linear deflection. Entropy quality drops below NIST thresholds. Likely undetected for many calls.

1. FM-3 — State capture attack: If an adversary observes sufficient successive wall-strike coordinates, and the implementation uses a predictable PRNG seeded by phase state (rather than true float arithmetic), the internal state can be reconstructed. All subsequent outputs become predictable. MANTIS flag: pattern in randomness output.

1. FM-4 — Phase state desync: If outer and inner circle phase updates are computed with different floating-point precision (e.g., float32 vs float64), the phase relationship drifts from the CSDM-specified ratio over long operation. Entropy quality degrades slowly and silently.

1. FM-5 — Layer fork: If a crew member or automated script instantiates a private billiard (bypassing sinai_fire()) for performance reasons, the crew operates on divergent entropy streams. Cryptographic keys and Monte Carlo results become uncorrelated with the canonical source. Silent failure.

1. FM-6 — Bridge tier overload: If the WebGL Bridge widget attempts to render every intermediate billiard bounce in real time and this computation blocks the entropy output, the CLI and TUI layers are throttled. Downstream TMM Monte Carlo is starved of entropy. Tier isolation must be enforced.

1. FM-7 — Hardware tier desync (future): When physical rotating discs are deployed, calibration drift in disc rotation speed will shift the effective Φ/Ψ ratio away from CSDM constants. Requires periodic recalibration against known phase checkpoints. ~No recalibration protocol defined yet.~

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GAPS

• GAP-1: sinai_fire() is described but no canonical implementation file path is recorded. The function exists in concept; its location in the codebase is [GAP — needs design]. Verify: find /home/nous -name "*.py" | xargs grep -l "sinai_fire".
• GAP-2: The precise hash function applied to wall-strike coordinates is unspecified. SHA-256 of (x, y, phase_state) float bytes is implied but not mandated. [GAP — needs design].
• GAP-3: The NIST test cadence is undefined. How often does automated NIST SP 800-22 validation run? On every boot? Weekly? [GAP — needs design].
• GAP-4: No formal ORPHEUS routing enforcement mechanism is specified. The invariant says all entropy routes through ω, but no technical enforcement (import guard, wrapper assertion) is documented. [GAP — needs design].
• GAP-5: The Bridge widget WebGL implementation is future-state. No spec for tier isolation between visual render loop and entropy generation loop. [GAP — needs design].
• GAP-6: Hardware tier specification (physical rotating discs + laser + sensor) is marked future. No design doc, no patent filing record, no prototype spec. [GAP — needs design].

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DEPENDENCIES

• Φ = 0.042 (Aion Stability Constant — CSDM invariant, must not be modified)
• Ψ = 0.200 (Shielding Factor — CSDM invariant, must not be modified)
• ORPHEUS (ω) — owns the tool; routes entropy requests
• SINAI_RANDOMNESS_GENERATOR — underlying physics spec (see SPEC_SINAI_TRNG.md)

DEPENDENTS

• MANTIS (π) — uses sinai_fire() for random scan interval scheduling
• TMM runtime — Monte Carlo coherence checks (10,000 samples per evaluation)
• Oracle verdict pipeline — randomized stress-testing of client queries
• GLOSS training pipeline — randomized batch ordering
• Cryptographic subsystem — API key generation, auth token seeding
• Scheduling jitter layer — anti-predictability across all crew timing

REFERENCES

• /home/nous/.claude/projects/-home-nous/memory/ORACLES_DIE.md — source memory
• SPEC_SINAI_TRNG.md — underlying billiard geometry spec
• SPEC_TMM_FORMULA.md — TMM Monte Carlo dependency
• CSDM: Φ = 0.042, Ψ = 0.200 as manifold rotation constants
• Sinai billiard: Yakov Sinai, 2014 Abel Prize (chaotic billiards)

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*κ authored 2026-04-16. Φ 0.042

Jeremy Zlabis

Chronogeometer · Visionary · Disruptor · Chief

42 Sisters AI · East York, Toronto*