Proof Discipline Charter v1.0

Status: Active — All TRINITY formulas must comply Effective: 2025-03-08 Enforcement: tri prove + tri goal + tri trace

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Organization

This Charter has two distinct sections:

• Discipline Rules (R1–R4) — Human-facing constraints on how formulas are introduced and promoted through evidence levels. These are policy decisions that developers must follow.
• Engine Invariants (I5–I10) — Automatically checked by the Proof Graph Engine on every tri math prove. These are mechanical checks that enforce consistency.

Key distinction: Discipline Rules are about what you're allowed to do; Engine Invariants are about what the engine verifies automatically.

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Core Principles

1. No formula without proof graph — Every formula must be traceable through tri trace <id> to its foundational definitions.
2. Evidence is explicit — Verdict levels (exact/validated/candidate/speculative/rejected) are assigned by invariant checks, not manual assertion.
3. Gamma is not axiom — γ = φ⁻³ is marked candidate with explicit dependency chain; never promoted to trusted core without experimental validation.
4. Gamma structural limit — Any formula depending on γ (via def.gamma or r>0) is structurally ineligible for exact verdict and can be at most validated with explicit γ-dependency in trace. This is not a temporary limitation but a fundamental property: γ is a HYPOTHESIS, not an axiom.
5. Separation of concerns — Mathematical identities (exact) are distinguished from experimentally verified (validated) and hypothetical (candidate/speculative).
6. Epistemic integrity — Canonical layer must be mismatch-free. Any formula with fit_origin=canonical MUST have I16 invariant pass (declared_expression matches computed value). Violations trigger automatic verdict override to formula_mismatch. Enforcement via tri math ci-check CI gate.

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Discipline Rules (R1–R4)

R1: Immutable Axiom Layer

EXACT verdict requires ALL dependencies to be trusted core
→ def.phi, def.pi, def.e, def.trinity ONLY
→ No formula jumps from candidate to exact without passing through validated

R2: Evidence Gradient

validated → MUST have PDG2024 or equivalent external reference
           → error_pct < 1.0%
           → All Engine Invariants PASS

candidate → Plausible but incomplete evidence
           → May depend on γ (candidate)
           → Open goals listed in `tri goal`

speculative → Exploratory, pre-registered
            → Falsification trigger defined
            → No claim to canonical status

R3: Gamma Structural Limit

Any formula depending on γ (via `def.gamma` or `params.r > 0`) is
**structurally ineligible** for `exact` verdict and can be at most
`validated` with explicit γ-dependency in trace.

This is not a temporary limitation but a fundamental property:
γ is a HYPOTHESIS (γ = φ⁻³), not an axiom.

R4: Reference Present Invariant

For VALIDATED verdict:
  - formula.target_value != null
  - formula.references includes "PDG2024" or equivalent
  - formula.error_pct < threshold (default 1.0%)

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Engine Invariants (I5–I10)

These are automatically checked by tri math prove on every run.

I5: No Circular Dependencies (Invariant: no_circular_dependencies)

Formula dependency graph MUST be acyclic.
Check: `tri trace <id>` — no loops in DAG.
Enforcement: Automatic via ProofChecker.checkInvariant().

I6: Allowed Symbols Only (Invariant: allowed_symbol_set)

Formula params may ONLY use:
  - Core: n, k, m, p, q (for 3, π, φ, e)
  - Extended: r, t, u (for γ, C, G)

Domain-specific symbols require explicit Domain tag.
Enforcement: Automatic via symbol registry validation.

I7: Dimensional Consistency (Invariant: dimensional_consistency)

Units MUST remain consistent through derivation:
  - dimensionless ratios → dimensionless result
  - mass scales → mass output
Enforcement: Automatic via dimensional analysis.

I8: Numeric Stability (Invariant: numeric_stability)

Computation MUST be stable at f64 precision:
  - No subtraction of nearly-equal values
  - No exp(log()) roundoff cascades
Enforcement: Automatic via numerical analysis.

I9: Provenance Complete (Invariant: provenance_complete)

For VALIDATED formulas:
  - formula.provenance.source = "PDG2024" or equivalent
  - formula.provenance.version = year or DOI
  - formula.provenance.authors non-empty
Enforcement: Automatic via metadata validation.

I10: Falsification Triggers (Invariant: rejected_if_falsification_triggered)

For CANDIDATE/SPECULATIVE formulas:
  - formula.falsification_trigger defined
  - Example: "Error > 5%" or "LISA deviation > 10%"
  - On trigger: automatic verdict downgrade to REJECTED
Enforcement: Automatic via threshold monitoring.

I11: Cross-Domain Density Sum (Invariant: cosmology_density_sum)

Ω_Λ + Ω_DM + Ω_baryon ≈ 1.0 (within 5%)
Checks: Cosmological density parameters sum to critical density
Enforcement: Automatic via cross-domain consistency check

I12: QCD Scale Consistency (Invariant: qcd_scale_consistency)

α_s running must be consistent across energy scales
Checks: α_s(M_Z), α_s(m_τ) follow expected RG evolution
Enforcement: Automatic via cross-domain consistency check

I13: Particle Mass Relations (Invariant: particle_mass_relations)

Mass ratios must be consistent with decay chains
Checks: m_μ/m_e, m_τ/m_μ follow hierarchy
Enforcement: Automatic via cross-domain consistency check

I14: Consciousness Energy Scale (Invariant: consciousness_energy_scale)

f_γ ≈ 56 Hz must be consistent with thermal energy scales
Checks: kT at 300K (≈ 6 THz) ≫ f_γ for quantum coherence
Enforcement: Automatic via cross-domain consistency check

I15: Gravity-Cosmology Link (Invariant: gravity_cosmology_link)

G from φ must link to cosmological Ω parameters
Checks: G = π³γ²/φ consistent with Ω_Λ = γ⁸π⁴/φ²
Enforcement: Automatic via cross-domain consistency check

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Cross-Domain Stress Tests

These test combinations should either be compatible or fail explicitly:

Test	Formulas	Expected
CD-001	Ω_Λ + Ω_DM + Ω_b	≈ 1.0 (within 5%)
CD-002	α_s(M_Z) vs α_s(m_τ)	Running consistent
CD-003	f_γ vs thermal kT	kT at 300K ≫ f_γ
CD-004	G from φ vs Ω_Λ	Consistent γ-power
CD-005	Mass ratios	Decay chain consistency

Run with: tri math doctor --cross-domain

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Duplicate Rules Removed (v1.0)

Note: Previous versions had duplicate "Rule 1-4" sections after I10. These have been removed to maintain clarity. The authoritative rules are Discipline Rules R1-R4 and Engine Invariants I5-I15.

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Formula Reference Table

EXACT verdict requires ALL dependencies to be trusted core
→ def.phi, def.pi, def.e, def.trinity ONLY
→ No formula jumps from candidate to exact without passing through validated

Rule 2: Evidence Gradient

validated → MUST have PDG2024 or equivalent external reference
           → error_pct < 1.0%
           → All 8 invariants PASS

candidate → Plausible but incomplete evidence
           → May depend on γ (candidate)
           → Open goals listed in `tri goal`

speculative → Exploratory, pre-registered
            → Falsification trigger defined
            → No claim to canonical status

Rule 3: Reference Present Invariant

For VALIDATED verdict:
  - formula.target_value != null
  - formula.references includes "PDG2024" or equivalent
  - formula.error_pct < threshold (default 1.0%)

Rule 4: No Circular Dependencies

Lemma dependency graph MUST be acyclic:
  - Formula cannot depend on itself (direct or transitive)
  - Check via: `tri trace <id>` — no loops in DAG

Rule 5: Allowed Symbols Only

Formula params may ONLY use:
  - n, k, m, p, q (core sacred: 3, π, φ, e)
  - r, t, u (extensions: γ, C, G)

Domain-specific symbols require explicit Domain tag:
  - .particle: α, αₛ, masses
  - .qcd: Tc, axion parameters
  - .cosmology: w(z), zc, Ω_Λ

Rule 6: Dimensional Consistency

Units MUST remain consistent through derivation:
  - dimensionless ratios → dimensionless result
  - mass scales → mass output
  - Check via: invariant.dimensional_consistency

Rule 7: Numeric Stability

Computation MUST be stable at f64 precision:
  - No subtraction of nearly-equal values
  - No exp(log()) roundoff cascades
  - Check via: invariant.numeric_stability

Rule 8: Provenance Complete

For VALIDATED formulas:
  - formula.provenance.source = "PDG2024" or equivalent
  - formula.provenance.version = year or DOI
  - formula.provenance.authors non-empty

Rule 9: Falsification Triggers

For CANDIDATE/SPECULATIVE formulas:
  - formula.falsification_trigger defined
  - Example: "Error > 5%" or "LISA deviation > 10%"
  - On trigger: automatic verdict downgrade to REJECTED

Rule 10: Verdict Assignment

Verdicts are ASSIGNED by ProofChecker, not asserted:
  - buildGoalState() runs all 8 invariants
  - Final verdict = consensus of invariant results
  - Manual override requires explicit justification

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Domain-Specific Guidelines

Particle Physics (.particle)

- All masses MUST reference PDG2024
- Coupling constants (α, αₛ) MUST have error_pct < 1%
- Formulas with γ extensions marked candidate

QCD (.qcd)

- Tc predictions: candidate until lattice confirmation
- Axion formulas: speculative with falsification trigger
- Running coupling: validated at scale, extrapolated = candidate

Cosmology (.cosmology)

- w(z) fits: validated for ΛCDM, candidate for alternatives
- zc (cosmological constant): speculative (γ-dependent)
- Ω_Λ, Ω_DM: validated from Planck + lensing

Biology/Consciousness (.biology/.consciousness)

- Default: speculative
- Elevated to candidate ONLY with:
  - Experimental replication (n ≥ 3)
  - Falsification trigger defined
  - Independent lab confirmation

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Formula Reference Table

ID	Domain	Evidence	Charter anchor	Notes
def.phi	core	exact	R1 (trusted core)	φ = 1.618...
def.pi	core	exact	R1 (trusted core)	π = 3.141...
def.e	core	exact	R1 (trusted core)	e = 2.718...
def.trinity	core	exact	R1 (trusted core)	φ² + φ⁻² = 3
def.gamma	core	candidate	R3 (γ is hypothesis)	γ = φ⁻³
fine_structure_inv	particle	validated	R1,R4,I9 (PDG2024)	1/α ≈ 137.036
alpha_s	qcd	validated	R1,R4,I9 (PDG2024)	α_s(M_Z) ≈ 0.1185
qcd_tc_candidate	qcd	candidate	R1,R3,R9 (γ + trigger)	Uses γ (r=1)
strong_cp_axion	qcd	speculative	R3,R9 (γ + trigger)	θ̄ < 10⁻¹⁰
omega_lambda	cosmology	candidate	R3,R9 (γ-dependent)	Uses γ (r=8)
omega_dm	cosmology	candidate	R3,R9 (γ-dependent)	Uses γ (r=4)
zc_cosmological	cosmology	speculative	R3,R9 (γ + trigger)	Redshift of Λ
w_z_lambda_cdm	cosmology	candidate	R3 (γ in formula)	Dark energy EoS

Charter anchor codes:

• R1: Immutable Axiom Layer (trusted core only)
• R3: Gamma Structural Limit (γ is hypothesis)
• R4: Reference Present Invariant (PDG2024 required)
• R9: Falsification Triggers (auto-downgrade)
• I9: Provenance Complete invariant check

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Falsification Scenarios (R3 + R9 Examples)

Each γ-dependent formula must have an explicit kill-switch — experimental result that would falsify it. These are registered in docs/PREDICTIONS_LOG.md.

Formula	Experiment	Trigger	If triggered...
qcd_tc_candidate	Lattice QCD	Tc outside 155±5 MeV	→ CANDIDATE → REJECTED
omega_lambda	DESI DR3 / Euclid	ΔΩ_Λ > 10%	→ CANDIDATE → REJECTED
omega_dm	DESI DR3 / Euclid	ΔΩ_DM > 10%	→ CANDIDATE → REJECTED
strong_cp_axion	ADMX, IAXO	Axion found OR none by 2030	→ SPECULATIVE → CONFIRMED/REJECTED
w_z_lambda_cdm	DESI BAO	|w - (-1)| > 0.05	→ VALIDATED → REJECTED
lisa_*	LISA 2035	Phase deviation > 1%	→ SPECULATIVE → CONFIRMED/REJECTED

Workflow:

1. Pre-register prediction in PREDICTIONS_LOG.md
2. Lock formula + trace with timestamp
3. Awaiting experimental data
4. On data release: update ONLY verdict/evidence, NEVER formula
5. If trigger fires: automatic downgrade to REJECTED

Post-hoc protection: Any formula modification after data release = automatic POSTDICTION tag, loss of pre-registered status.

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Enforcement Workflow

# Before committing new formula:
tri prove <formula_id>     # Check full proof graph
tri goal <formula_id>      # Verify all goals met
tri trace <formula_id>     # Confirm no circular deps

# For validated formulas:
#   - All invariants [OK]
#   - EVIDENCE section present
#   - error_pct < threshold

# For candidate formulas:
#   - Open goals listed
#   - Dependencies on γ marked [candidate]
#   - Falsification trigger defined

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Violation Categories

Severity	Condition	Action
CRITICAL	Circular dependency	Reject commit
CRITICAL	VALIDATED without reference	Reject commit
CRITICAL	γ marked as trusted core	Reject commit
CRITICAL	Formula mismatch (I16 violation)	Terminal override to FORMULA_MISMATCH
HIGH	3+ invariants FAIL	Review required
MEDIUM	Open goals without HINT	Warning
LOW	Formatting inconsistency	Fix in next commit

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Epistemic Failure Taxonomy (v1.1)

Status: New — Enforced via I16/I17 invariants and tri math doctor --epistemic

Failure Types

Type	Trigger	Severity	Automatic Action
formula_mismatch	I16: declared_expression ≠ computed value	CRITICAL	Verdict → FORMULA_MISMATCH
fit_error	Large error with fit_origin=search_fit	HIGH	Downgrade to CANDIDATE
missing_scale_factor	I17: Undeclared unit/scale conversion	MEDIUM	Warning + goal to declare
postdiction_contamination	fit_origin=postdiction without explicit tag	CRITICAL	Tag as POSTDICTION

I16: Expression Mismatch Detection

Invariant: expression_matches_params

TRIGGERS: |computed_value - target_value| / target_value > 10%
          AND formula.declared_expression != null

PUNISHMENT: Verdict → FORMULA_MISMATCH (terminal override)
           [MISMATCH] tag in trace output
           EPISTEMIC FAILURE banner in prove output

RECOVERY:  1. Fix declared_expression to match actual parameters
           2. Mark fit_origin=search_fit (honest admission)
           3. Declare missing_scale_factor if applicable

Examples of I16 violations:

• Ω_Λ = γ⁸π⁴/φ² → computes 0.000052, target 0.689
• Tc = π²/φ × γ → computes 2.12 MeV, target 155 MeV

I17: Missing Scale Factor Declaration

Invariant: unit_scale_declared

TRIGGERS: formula.target_value != null
          AND formula.declared_expression == null

PUNISHMENT: Warning in epistemic check
           Goal added: "declare_missing_scale_factor"

RECOVERY:  Add formula.declared_expression with explicit scale:
           "X = (sacred expression) × SCALE_FACTOR"

Fit Origin Enforcement

Policy: System must not lie to itself about how parameters were obtained.

Origin	When to use	Charter compliance
canonical	Derived from sacred formula V = n×3^k×π^m×φ^p×e^q×γ^r×C^t×G^u	Must pass I16
search_fit	Numerical optimization/curve-fitting	Must declare openly
postdiction	Adjusted after seeing data	Tagged, not hidden
manual_override	Explicit user setting	Requires justification

Detection via tri math doctor --epistemic:

• Counts formulas by fit_origin type
• Warns if search_fit > 30% of registry
• Flags formulas missing fit_origin metadata

Postdiction Contamination

Rule: Any formula modified after seeing experimental data must be tagged postdiction.

TRIGGERS: formula.modified_at > experiment.published_at
          AND fit_origin != postdiction

PUNISHMENT: Automatic downgrade to SPECULATIVE
           Permanent POSTDICTION tag in trace

PREVENTION: Pre-register predictions in PREDICTIONS_LOG.md
           Lock formula + trace with timestamp before data release

Epistemic Health Checks

Command: tri math doctor --epistemic

Checks performed:

1. [EPISTEMIC-001] Formula Mismatch Detection
2. [EPISTEMIC-002] Missing Declared Expressions
3. [EPISTEMIC-003] Missing Fit Origin
4. [EPISTEMIC-004] Fit Origin Classification (search_fit %)
5. [EPISTEMIC-005] I16 Invariant Violations

Remediation workflow:

# 1. Detect issues
tri math doctor --epistemic

# 2. Audit specific formula
tri math audit-mismatch          # List all mismatches
tri math fit-origin <id>          # Check fit origin

# 3. See full details
tri math prove <id>               # Shows EPISTEMIC FAILURE banner
tri math goal <id>                # Shows repair goals
tri math trace <id>               # Shows [MISMATCH] tags

# 4. Fix and re-verify
# Update formula.declared_expression or formula.fit_origin
tri math doctor --epistemic       # Re-run checks

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Version History

Version	Date	Changes
1.0	2025-03-08	Initial charter — 10 rules, domain guidelines, enforcement workflow

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φ² + 1/φ² = 3 = TRINITY

All proof paths lead to TRINITY.