FILE: EMERGENT_CANON_AUDIT.md

EMERGENT_CANON_AUDIT.md

Emergent Canon Audit — consolidating the post-φ/γ/e TNFR base

Status: COMPLETE — superseded by EMERGENT_DERIVATION_PLAN.md, which carried the φ/γ/e re-derivation through Stages 0–5 and now enforces it with a regression guard (tests/core_physics/test_emergent_constants_guard.py) · Started: 2026-06-27 · Completed: 2026-06-28 · Owner: TNFR refactor

0. Why this exists

The obsolete constants φ (golden ratio), γ (Euler–Mascheroni), e (Napier) were removed from the engine: only π is a genuine structural scale. But the prior purge only removed the φ/γ/e formulas from the code/comments — it left the numeric values frozen (e.g. K_TOP_FALLBACK = 2.803171 was φ/γ; MATH_DELTA_NFR_THRESHOLD = 0.067592 was γ/(eπ)). These frozen decimals are now magic numbers with no emergent meaning, and a few are outright non-physical (see below). Since all prior TNFR results depended on these constants and their interactions, the entire numeric base must be re-derived and reinterpreted so that every value either:

emerges from TNFR structure/dynamics (π, the spectral gap λ₂, the nodal coherence C(t) = 1/(1+mean|ΔNFR|+mean|dEPI|), the operator contracts, the grammar U1–U6, the derivative-tower tetrad), or
is an honest free parameter (a clean structural default — unit, π-fraction, 0, or a simple rational — explicitly labeled tunable), or
is an operational engine knob (cache/speedup/scoring; not nodal physics) set to a plain round value, explicitly labeled, or
is eliminated (meaningless / dead / redundant).

This file tracks what is done and what remains. Hold commit/push until a green milestone is confirmed by the user. Test command:

powershell

$env:PYTHONIOENCODING="utf-8"; $env:PYTHONPATH=(Resolve-Path -Path ./src).Path; & ".\.venv312\Scripts\python.exe" -m pytest -q --no-header -p no:cacheprovider

Baseline before this audit: 2201 passed, 12 skipped, 0 failed.

1. Decoder — the frozen φ/γ/e decimals (the "tell")

These recurring decimals across constants/canonical.py reveal a φ/γ/e origin and must be replaced. (Non-exhaustive; any 6-decimal value tied to these is suspect.)

Frozen decimal	Was (φ/γ/e)	Frozen decimal	Was (φ/γ/e)
`0.041774`	γ/(π·e·φ)	`0.737061`	φ/(φ+γ)
`0.067592`	γ/(e·π)	`0.750575`	(e·φ)/(π+e)
`0.098503`	γ/(π+e)	`0.618034`	1/φ
`0.135184`	2γ/(eπ)	`0.381966`	1/φ² (= 2−φ)
`0.155215`	γ/(π+γ)	`1.618034`	φ
`0.183733`	γ/π	`2.718282`	e
`0.463881`	e/(π+e)	`2.803171`	φ/γ
`0.490983`	~γ·φ/…	`3.025733`	(φ+1)·π/e
`0.933955`	~π·e/…	`5.083204`	φ·π
`0.330365`	~1/(e+γ)	`8539.734223`	large φ/γ/e artifact

2. Categories (counts approximate)

A — Emergent / clean (KEEP, ~40): π-derived (π/2, π/4, 0.9π, 1/(π+1), π/(π+1), 1/(2π), 1/(4π), 1/(8π), 2π, sin/cos of π-multiples, exp(LN_2)=2), unit/integer free params (0.9, 1.05, 0.10, 0.5, ±1, 1.0, 2, 6, 50, 100, 256), honest tolerances (1e-10, 1e-8, 1e-6).
B — Frozen φ/γ/e PHYSICS values (RE-DERIVE, ~25): enter the nodal eq / operators / grammar / fields / telemetry. Top priority — these define the paradigm. (Table in §4.)
C — Frozen φ/γ/e ENGINE knobs (CLEAN VALUES, ~200): scoring weights, cache sizes, speedups, prediction horizons, domain (medical/business/viz/example/cli) thresholds. Not nodal physics → plain round values or relocation/elimination.
D — Inline magic numbers in physics/, dynamics/, operators/, metrics/ modules (not named constants): audit separately.

3. Staged plan

Stage 0 — Full inventory + categorization + this tracking file.
Stage 1 — Tier-1 canonical physics re-derivation (§4). DONE (suite green 2201). All Tier-1 rows re-derived or eliminated; the PHYSICS_*_DEPENDENCY empirical-fit coefficients were reclassified to Tier-2 (Stage 2). The canonical physics base is now emergent.
Stage 2 — Tier-2 engine-knob clean-up (§5): DONE. 180 frozen φ/γ/e decimals rounded to clean operational values; all dead domain constants (MEDICAL_/BUSINESS_/VIZ_/EXAMPLE_/BENCH_/THERAP_/CLI_/SCRIPT_/TOOL_/UTILS_) and the dead CANONICAL_CONSTANTS registry + PHASE_8/9 dicts ELIMINATED; engine-used SDK_* relocated into sdk/builders.py. canonical.py ~770 → ~565 lines. Suite green 2201.
Stage 3 — Inline magic-number audit in modules (Category D). DONE (core modules were ~95% clean). Fixed the residual φ/γ/e artifacts + operator-gain inconsistencies; suite green 2201.
Stage 4 — Reinterpretation: updated theory/TNFR_NUMBER_THEORY.md §7.5 (the stale arith-trio "recalibration" table → the canonical π-derived tetrad thresholds) and added a CHANGELOG [Unreleased] consolidation entry. DONE.

4. Tier-1 PHYSICS constants — derivation table (Stage 1)

Legend: ☐ pending · ☑ done. "Derivation" = the emergent/honest replacement.

Constant	Was	→ Derivation (emergent / honest)	Status
`K_PHI_THRESHOLD` (arith)	3.227450	NON-PHYSICAL (>π, unreachable) → π (or eliminate the arith-recalibrated trio)	☐
`PHI_S_THRESHOLD` (arith)	0.745219	π/4 (canonical) or eliminate	☐
`GRAD_PHI_THRESHOLD` (arith)	0.259117	eliminate / canonical heuristic	☐
`MAX_STRUCTURAL_FREQUENCY`	5.083204 (φπ)	2π (one phase cycle, = VF_MAX)	☐
`MIN_STRUCTURAL_FREQUENCY`	0.183733 (γ/π)	0.0 floor (νf=0 death) or 1/(2π) tunable	☐
`MATH_DELTA_NFR_THRESHOLD`	0.067592 (γ/(eπ))	0.5 separator (prime ⟺ ΔNFR=0 exact)	☐
`MATH_DELTA_NFR_THRESHOLD_2X`	0.135184	1.0 (= 2×0.5) or eliminate	☐
`K_TOP_FALLBACK_CANONICAL`	2.803171 (φ/γ)	clean spectral fallback (π-fraction or 1.0)	☐
`K_TOP_MIN_CANONICAL`	0.041774	1/(8π) (= KL_MIN floor)	☐
`K_TOP_MAX_CANONICAL`	0.933955	π-fraction near 1 (tunable)	☐
`GLYPH_SELECTOR_MARGIN_CANONICAL`	0.041774	= KL_MIN (1/(8π)) (comment already claims this)	☐
`AU_CURVATURE_PERMISSIVE_THRESHOLD`	3.025733 ((φ+1)π/e)	0.96·π (permissive	K_φ
`CRITICAL_EXPONENT`	0.183733 (γ/π)	honest heuristic regime scale (decouple from GRAD_PHI)	☐
`GRAD_PHI_CANONICAL_THRESHOLD`	0.183733 (γ/π)	heuristic	∇φ
`INTEGRATORS_EPI_MARGIN_CANONICAL`

Each row: verify consumers + run the suite for the affected group before moving on. Some thresholds are consumed in tests that pin the old value — update those tests to the new emergent value (documenting the structural rationale).

5. Tier-2 engine knobs — bulk rule (Stage 2)

For every Category-C constant (OPT_ORCH_, PATTERN_, FFT_, PATTERNS_, SELF_OPT_, MULTIMODAL_, CACHE_OPT_, INTEGRATION_, NODAL_OPT_, STRUCT_CACHE_, CYCLE_* frozen, ALGEBRA_, EMERGENT_, OPERATORS_PATTERN_, SDK_, MEDICAL_, BUSINESS_, VIZ_, UTILS_ frozen, EXAMPLE_, BENCH_, THERAP_, CLI_, SCRIPT_, TOOL_, MIN_BUSINESS_COHERENCE):

Replace the frozen φ/γ/e decimal with a plain round operational value that preserves the intended magnitude (e.g. 2.803171 → 2.8, 0.737061 → 0.75, 0.618034 → 0.6, 8.539734 → 8.5), keeping the # operational tuning (not TNFR physics) label. Drop the false precision.
Where a knob is already = π or = UM_COMPAT_THRESHOLD etc., keep it.
Eliminate dead/duplicate aliases and empty registry plumbing.
Consider relocating domain-application constants (MEDICAL_/BUSINESS_/ EXAMPLE_/THERAP_/CLI_/SCRIPT_/TOOL_/VIZ_) out of constants/canonical.py into their own modules — they are not TNFR canon. (Decide with user.)

6. Status log

2026-06-27 — Stage 0 complete: full canonical.py inventory (~300 constants), categorized; this tracker created. Beginning Stage 1 (Tier-1 physics).
2026-06-27 — Stage 1 COMPLETE (suite green 2201 passed / 0 failed, twice):
- π-derived: MAX_STRUCTURAL_FREQUENCY=2π, MIN_STRUCTURAL_FREQUENCY=1/(2π), AU_CURVATURE_PERMISSIVE=0.96π, GLYPH_SELECTOR_MARGIN=1/(8π), CRITICAL_EXPONENT=π/16, GRAD_PHI_CANONICAL_THRESHOLD=π/16, DYNAMICS_SI_HI=π/(π+1), K_TOP_MIN=1/(8π), K_TOP_MAX=1.0, K_TOP_FALLBACK=π.
- Genuine emergent derivation: MATH_DELTA_NFR_THRESHOLD=0.5 (the unit-gap midpoint — prime ⟺ ΔNFR=0 exactly, every composite ΔNFR>1, from the unit-coeff arithmetic ΔNFR formula ζ(ω−1)+η(τ−2)+θ(σ/n−(1+1/n))); _2X=2×base=1.0.
- Clean free-params (tunable): INTEGRATORS_* (0.1/0.1/−0.15/0.75/0.5), FEEDBACK_* (0.15/0.1/1/3; DNFR auto), DYNAMICS_ADELIC_* (0.1, 1/16), MATH_COHERENCE_MIN=0.1, MATH_TOLERANCE=1e4 (→PRECISION=100), PHYSICS_HOTSPOT_FRACTION=0.1, CONFIG_* (0.5/0.15/0.5/0.5/0.1).
- Eliminated vestigial arith trio (PHI_S_THRESHOLD/GRAD_PHI_THRESHOLD/ K_PHI_THRESHOLD; the last was 3.2275 > π — non-physical/unreachable).
- No tests pinned values (verified via consumer map); CRITICAL_EXPONENT's zeta-bridge test is self-consistent. Stale theory/TNFR_NUMBER_THEORY.md table (lines ~311-313) referencing the removed arith trio → fix in Stage 4.
Beginning Stage 2 (Tier-2 engine knobs, ~200 frozen φ/γ/e decimals).
2026-06-27 — Stage 2 value-cleanup COMPLETE (suite green 2201 / 0 failed): 180 frozen φ/γ/e engine-knob decimals rounded to clean ≤2-decimal operational values (e.g. 2.803171→2.8, 0.737061→0.74, 0.618034→0.62, 0.098503→0.1, −0.155215→−0.16, 8.539734→8.5). 3 tiny measured values (1.8e-05, 0.00147, 0.001352) correctly left. Aliases auto-followed their rounded bases. ZERO test changes needed. Remaining: Stage 2b relocation (domain constants — needs user decision), Stage 3 (inline magic numbers in modules), Stage 4 (doc reinterpretation incl. the stale TNFR_NUMBER_THEORY arith-trio table).
2026-06-27 — Stage 2b COMPLETE (suite green 2201 / 0 failed): domain constants were all DEAD (no imports anywhere) → eliminated MEDICAL_/BUSINESS_/ VIZ_/EXAMPLE_/BENCH_/THERAP_/CLI_/SCRIPT_/TOOL_/UTILS_ (~45 constants) + the dead registry and PHASE_8/9 dicts. (used only by sdk/builders.py) relocated into that module as plain locals; 4 unused SDK_ dropped. canonical.py ~770 → ~565 lines. Beginning Stage 3 (inline magic numbers in physics/dynamics/operators/metrics modules).

FILE: EMERGENT_CANON_AUDIT.md

EMERGENT_CANON_AUDIT.md

Emergent Canon Audit — consolidating the post-φ/γ/e TNFR base

0. Why this exists

emerges from TNFR structure/dynamics (π, the spectral gap λ₂, the nodal coherence C(t) = 1/(1+mean|ΔNFR|+mean|dEPI|), the operator contracts, the grammar U1–U6, the derivative-tower tetrad), or
is an honest free parameter (a clean structural default — unit, π-fraction, 0, or a simple rational — explicitly labeled tunable), or
is an operational engine knob (cache/speedup/scoring; not nodal physics) set to a plain round value, explicitly labeled, or
is eliminated (meaningless / dead / redundant).

This file tracks what is done and what remains. Hold commit/push until a green milestone is confirmed by the user. Test command:

powershell

$env:PYTHONIOENCODING="utf-8"; $env:PYTHONPATH=(Resolve-Path -Path ./src).Path; & ".\.venv312\Scripts\python.exe" -m pytest -q --no-header -p no:cacheprovider

Baseline before this audit: 2201 passed, 12 skipped, 0 failed.

1. Decoder — the frozen φ/γ/e decimals (the "tell")

These recurring decimals across constants/canonical.py reveal a φ/γ/e origin and must be replaced. (Non-exhaustive; any 6-decimal value tied to these is suspect.)

Frozen decimal	Was (φ/γ/e)	Frozen decimal	Was (φ/γ/e)
`0.041774`	γ/(π·e·φ)	`0.737061`	φ/(φ+γ)
`0.067592`	γ/(e·π)	`0.750575`	(e·φ)/(π+e)
`0.098503`	γ/(π+e)	`0.618034`	1/φ
`0.135184`	2γ/(eπ)	`0.381966`	1/φ² (= 2−φ)
`0.155215`	γ/(π+γ)	`1.618034`	φ
`0.183733`	γ/π	`2.718282`	e
`0.463881`	e/(π+e)	`2.803171`	φ/γ
`0.490983`	~γ·φ/…	`3.025733`	(φ+1)·π/e
`0.933955`	~π·e/…	`5.083204`	φ·π
`0.330365`	~1/(e+γ)	`8539.734223`	large φ/γ/e artifact

2. Categories (counts approximate)

A — Emergent / clean (KEEP, ~40): π-derived (π/2, π/4, 0.9π, 1/(π+1), π/(π+1), 1/(2π), 1/(4π), 1/(8π), 2π, sin/cos of π-multiples, exp(LN_2)=2), unit/integer free params (0.9, 1.05, 0.10, 0.5, ±1, 1.0, 2, 6, 50, 100, 256), honest tolerances (1e-10, 1e-8, 1e-6).
B — Frozen φ/γ/e PHYSICS values (RE-DERIVE, ~25): enter the nodal eq / operators / grammar / fields / telemetry. Top priority — these define the paradigm. (Table in §4.)
C — Frozen φ/γ/e ENGINE knobs (CLEAN VALUES, ~200): scoring weights, cache sizes, speedups, prediction horizons, domain (medical/business/viz/example/cli) thresholds. Not nodal physics → plain round values or relocation/elimination.
D — Inline magic numbers in physics/, dynamics/, operators/, metrics/ modules (not named constants): audit separately.

3. Staged plan

Stage 0 — Full inventory + categorization + this tracking file.
Stage 1 — Tier-1 canonical physics re-derivation (§4). DONE (suite green 2201). All Tier-1 rows re-derived or eliminated; the PHYSICS_*_DEPENDENCY empirical-fit coefficients were reclassified to Tier-2 (Stage 2). The canonical physics base is now emergent.
Stage 2 — Tier-2 engine-knob clean-up (§5): DONE. 180 frozen φ/γ/e decimals rounded to clean operational values; all dead domain constants (MEDICAL_/BUSINESS_/VIZ_/EXAMPLE_/BENCH_/THERAP_/CLI_/SCRIPT_/TOOL_/UTILS_) and the dead CANONICAL_CONSTANTS registry + PHASE_8/9 dicts ELIMINATED; engine-used SDK_* relocated into sdk/builders.py. canonical.py ~770 → ~565 lines. Suite green 2201.
Stage 3 — Inline magic-number audit in modules (Category D). DONE (core modules were ~95% clean). Fixed the residual φ/γ/e artifacts + operator-gain inconsistencies; suite green 2201.
Stage 4 — Reinterpretation: updated theory/TNFR_NUMBER_THEORY.md §7.5 (the stale arith-trio "recalibration" table → the canonical π-derived tetrad thresholds) and added a CHANGELOG [Unreleased] consolidation entry. DONE.

4. Tier-1 PHYSICS constants — derivation table (Stage 1)

Legend: ☐ pending · ☑ done. "Derivation" = the emergent/honest replacement.

Constant	Was	→ Derivation (emergent / honest)	Status
`K_PHI_THRESHOLD` (arith)	3.227450	NON-PHYSICAL (>π, unreachable) → π (or eliminate the arith-recalibrated trio)	☐
`PHI_S_THRESHOLD` (arith)	0.745219	π/4 (canonical) or eliminate	☐
`GRAD_PHI_THRESHOLD` (arith)	0.259117	eliminate / canonical heuristic	☐
`MAX_STRUCTURAL_FREQUENCY`	5.083204 (φπ)	2π (one phase cycle, = VF_MAX)	☐
`MIN_STRUCTURAL_FREQUENCY`	0.183733 (γ/π)	0.0 floor (νf=0 death) or 1/(2π) tunable	☐
`MATH_DELTA_NFR_THRESHOLD`	0.067592 (γ/(eπ))	0.5 separator (prime ⟺ ΔNFR=0 exact)	☐
`MATH_DELTA_NFR_THRESHOLD_2X`	0.135184	1.0 (= 2×0.5) or eliminate	☐
`K_TOP_FALLBACK_CANONICAL`	2.803171 (φ/γ)	clean spectral fallback (π-fraction or 1.0)	☐
`K_TOP_MIN_CANONICAL`	0.041774	1/(8π) (= KL_MIN floor)	☐
`K_TOP_MAX_CANONICAL`	0.933955	π-fraction near 1 (tunable)	☐
`GLYPH_SELECTOR_MARGIN_CANONICAL`	0.041774	= KL_MIN (1/(8π)) (comment already claims this)	☐
`AU_CURVATURE_PERMISSIVE_THRESHOLD`	3.025733 ((φ+1)π/e)	0.96·π (permissive	K_φ
`CRITICAL_EXPONENT`	0.183733 (γ/π)	honest heuristic regime scale (decouple from GRAD_PHI)	☐
`GRAD_PHI_CANONICAL_THRESHOLD`	0.183733 (γ/π)	heuristic	∇φ
`INTEGRATORS_EPI_MARGIN_CANONICAL`

5. Tier-2 engine knobs — bulk rule (Stage 2)

Replace the frozen φ/γ/e decimal with a plain round operational value that preserves the intended magnitude (e.g. 2.803171 → 2.8, 0.737061 → 0.75, 0.618034 → 0.6, 8.539734 → 8.5), keeping the # operational tuning (not TNFR physics) label. Drop the false precision.
Where a knob is already = π or = UM_COMPAT_THRESHOLD etc., keep it.
Eliminate dead/duplicate aliases and empty registry plumbing.
Consider relocating domain-application constants (MEDICAL_/BUSINESS_/ EXAMPLE_/THERAP_/CLI_/SCRIPT_/TOOL_/VIZ_) out of constants/canonical.py into their own modules — they are not TNFR canon. (Decide with user.)

6. Status log

2026-06-27 — Stage 0 complete: full canonical.py inventory (~300 constants), categorized; this tracker created. Beginning Stage 1 (Tier-1 physics).
2026-06-27 — Stage 1 COMPLETE (suite green 2201 passed / 0 failed, twice):
- π-derived: MAX_STRUCTURAL_FREQUENCY=2π, MIN_STRUCTURAL_FREQUENCY=1/(2π), AU_CURVATURE_PERMISSIVE=0.96π, GLYPH_SELECTOR_MARGIN=1/(8π), CRITICAL_EXPONENT=π/16, GRAD_PHI_CANONICAL_THRESHOLD=π/16, DYNAMICS_SI_HI=π/(π+1), K_TOP_MIN=1/(8π), K_TOP_MAX=1.0, K_TOP_FALLBACK=π.
- Genuine emergent derivation: MATH_DELTA_NFR_THRESHOLD=0.5 (the unit-gap midpoint — prime ⟺ ΔNFR=0 exactly, every composite ΔNFR>1, from the unit-coeff arithmetic ΔNFR formula ζ(ω−1)+η(τ−2)+θ(σ/n−(1+1/n))); _2X=2×base=1.0.
- Clean free-params (tunable): INTEGRATORS_* (0.1/0.1/−0.15/0.75/0.5), FEEDBACK_* (0.15/0.1/1/3; DNFR auto), DYNAMICS_ADELIC_* (0.1, 1/16), MATH_COHERENCE_MIN=0.1, MATH_TOLERANCE=1e4 (→PRECISION=100), PHYSICS_HOTSPOT_FRACTION=0.1, CONFIG_* (0.5/0.15/0.5/0.5/0.1).
- Eliminated vestigial arith trio (PHI_S_THRESHOLD/GRAD_PHI_THRESHOLD/ K_PHI_THRESHOLD; the last was 3.2275 > π — non-physical/unreachable).
- No tests pinned values (verified via consumer map); CRITICAL_EXPONENT's zeta-bridge test is self-consistent. Stale theory/TNFR_NUMBER_THEORY.md table (lines ~311-313) referencing the removed arith trio → fix in Stage 4.
Beginning Stage 2 (Tier-2 engine knobs, ~200 frozen φ/γ/e decimals).
2026-06-27 — Stage 2 value-cleanup COMPLETE (suite green 2201 / 0 failed): 180 frozen φ/γ/e engine-knob decimals rounded to clean ≤2-decimal operational values (e.g. 2.803171→2.8, 0.737061→0.74, 0.618034→0.62, 0.098503→0.1, −0.155215→−0.16, 8.539734→8.5). 3 tiny measured values (1.8e-05, 0.00147, 0.001352) correctly left. Aliases auto-followed their rounded bases. ZERO test changes needed. Remaining: Stage 2b relocation (domain constants — needs user decision), Stage 3 (inline magic numbers in modules), Stage 4 (doc reinterpretation incl. the stale TNFR_NUMBER_THEORY arith-trio table).
2026-06-27 — Stage 2b COMPLETE (suite green 2201 / 0 failed): domain constants were all DEAD (no imports anywhere) → eliminated MEDICAL_/BUSINESS_/ VIZ_/EXAMPLE_/BENCH_/THERAP_/CLI_/SCRIPT_/TOOL_/UTILS_ (~45 constants) + the dead registry and PHASE_8/9 dicts. (used only by sdk/builders.py) relocated into that module as plain locals; 4 unused SDK_ dropped. canonical.py ~770 → ~565 lines. Beginning Stage 3 (inline magic numbers in physics/dynamics/operators/metrics modules).

CANONICAL_CONSTANTS

SDK_*

2026-06-27 — Stage 7: THIRD DEEP AUDIT (frozen φ/γ/e residue + internal coherence; suite green 2201 / 0 failed). Method: diffed the committed pre-purge HEAD canonical.py (still φ/γ/e) against current to find values the purge froze (replaced a φ/γ/e expression with its evaluated decimal, mislabeled "tunable") and stale comments citing the old value. Findings + fixes:

Coherence violation (load-bearing) — NUL densification: canonical.py states NUL_DENSIFICATION_FACTOR = 1/λ ≈ 1.111 ("DERIVED, conserves the nodal-equation product νf·ΔNFR"), but operators/__init__.py hardcoded densification_default = 1.35 ("extra amplification beyond 1/λ") citing the stale 0.9015. Reconciled the operator to the canonical 1/λ and fixed the contradictory comment.
Frozen transcendentals → clean free values: FEEDBACK_LEARNING_RATE 0.043 (=e^(−π)) → 0.05; FEEDBACK_TAU_ADAPTIVE 0.155 (=γ/(π+γ)) → 0.15; AU_CURVATURE_PERMISSIVE 0.96·π (0.96=(φ+1)/e) → 0.95·π; STRESS_NORM 0.0985 (=γ/(π+e)) → 0.1; unified_numerical MIN_BUSINESS_COHERENCE 0.750575 (=(e·φ)/(π+e)) → 0.75 and PHASE_GRADIENT_STABILITY 0.183733 (=γ/π) → π/16; six RemeshDefaults/GLYPH_THRESHOLDS/SELECTOR_WEIGHTS round(0.92.., 3) frozen round-of-literal artifacts → plain decimals; the misleading _EXP_NEG_PI alias → _FEEDBACK_LR; the (e*phi)/(pi+e) strong-coherence formula in SDK docstrings removed.
De-obfuscation: STRUCTURAL_ESCAPE = math.exp(LN_2) → plain 2.0 (= EPI span).
VAL_MIN_EPI precondition fallback 0.2 → the canonical 1/(2π).
~55 stale comments citing old φ/γ/e values updated to the current value across defaults_core, bifurcation (code/doc contradiction: docstring still said "νf/e", "EPI/0.922", old %), patterns, physics (interactions, signatures, phase_transition, canonical, integrity, calibration), riemann/zeta_bridge, telemetry, grammar, and the FFT/cache operational modules; the most pervasive was ≈ 0.1837 (γ/π) → ≈ 0.196 (π/16, ×~16).
Confirmed NOT used as an exponent: CRITICAL_EXPONENT (π/16) is a heuristic reference scale (function arg / spectral buffer), never x ** CRITICAL_EXPONENT.
Legitimately kept: the riemann/ golden-ratio / Euler-Mascheroni / Napier values are explicitly labeled non-resonant probe frequencies ("NOT TNFR structural scales"), the correct use of those numbers as negative controls.
Flagged (user decision): AGENTS.md §7 cites strong-coherence cut C > 0.7506 (= frozen (e·φ)/(π+e)); code now uses the clean operational 0.75. Recommend updating AGENTS.md to 0.75, or promoting the cut to the canonical band gate π/(π+1) ≈ 0.7616. Also PHI_S_GOLDEN_THRESHOLD (riemann alias for π/2) is a misnomer (no longer "golden").

2026-06-27 — Stage 8: DOCUMENTATION → EMERGENT CANONICITY (suite green 2201 / 0 failed). Resolved the Stage-7 flag by promoting the documented values to the genuinely-emergent π-derived ones across AGENTS.md + the .github/agents/my-agent.md mirror + theory/docs/examples + code docstrings:

Arithmetic error fixed: π/(π+1) is 0.7585, not 0.7616 (the latter does not complement 1/(π+1)=0.2415 to 1). Corrected the comment value in canonical.py (×5) and defaults_core.py, and everywhere in the docs.
Strong-coherence cut → emergent band gate: 0.7506 (frozen (e·φ)/(π+e)) → π/(π+1) ≈ 0.7585. The SDK COHERENCE_STRONG was re-aliased from the operational MIN_BUSINESS_COHERENCE (0.75) to the emergent HIGH_COHERENCE_THRESHOLD = π/(π+1); MIN_BUSINESS_COHERENCE (0.75) stays the separate operational business-health knob. Fixed the now-self-contradictory CONTRIBUTING.md "correct vs arbitrary" example (it had MIN_BUSINESS_COHERENCE = the "correct" value but it now equals the "arbitrary" 0.75) → uses the emergent gate.
Φ_s confinement → π-derived (was φ-framed): drift Δ Φ_s < π/2 ≈ 1.571 (half phase-wrap, was φ ≈ 1.618), per-node |Φ_s| < π/4 ≈ 0.785 (quarter phase-wrap, was empirical 0.7711) — in AGENTS.md §3/§6/§7, GLOSSARY, PHYSICS_VERIFICATION (canonicity MODERATE→HIGH), physics/__init__ (+ its doctest), conservation, variational, grammar_u6, telemetry/constants, and the two physics-regime examples.
SPIRAL_ATTRACTORS_AND_LOGARITHMIC_DYNAMICS.md — DELETED (with its broken demo examples/02_physics_regimes/32_spiral_attractors_demo.py). It was a pre-purge φ/γ/e "four constants" thesis whose distinctive claims were false: the "golden ratio as dynamical attractor" check was circular (set b = 2·ln(φ)/π by hand, then "verified" ratios = φ), the demo imported the purged φ/γ/e constants (could not run — so §6.3 "Status: Validated" was false), and §7 ("the fourth constant γ") is pure pre-purge paradigm. The only true content (log spirals from rotation + growth, free b = νf·k/ω) is trivial and non-distinctive. References removed from theory/README.md, FUNDAMENTAL_THEORY.md, examples/README.md.
Verified-correct (left as-is): the website brief and several theory files (FUNDAMENTAL_THEORY, MINIMAL_STRUCTURAL_DEGREES, GLOSSARY §VON_KOCH) already document the π/2–π/4 supersession; the riemann/ probes stay.

2026-06-27 — Stage 9: FULL theory/ DOC AUDIT (every theory/*.md checked for residual φ/γ/e false claims; yang_mills tests green 18/18; no engine code changed except cosmetic docstrings). Verdict: no further deletions needed — SPIRAL_ATTRACTORS (Stage 8) was the only doc whose thesis was false; all 26 remaining docs are genuinely emergent and only carried scattered stale φ/γ/e refs. Fixes applied (the code was already clean — these were doc-only, except 2 yang_mills docstrings):

FUNDAMENTAL_THEORY / EXTENDED_FIELDS / GAUGE_SYMMETRY / PHYSICAL_REGIME: Δ Φ_s < φ → π/2; Si < 1.5/(π+γ) → Si < 0.4; AU permissive curvature (φ+1)π/e → 0.95π; V < ½φ²·N → ½(π/2)²·N; heuristic γ/π → π/16.
STRUCTURAL_OPERATORS (≈23 refs): all operator-gain tables/formulas → the operational defaults_core.py values — IL φ/(φ+γ)≈0.737→0.75; OZ/NUL-dens φ/γ≈2.803→ OZ 2.0, NUL densification 1/λ≈1.111 (was wrongly 2.803); VAL 1+γ/(π·e)≈1.067→1.05; SHA/NUL scale 1−γ/(π+e)≈0.902→0.9; RA e^{−φ}≈0.198 and ZHIR φ/(e+γ)≈0.489 → labeled operational/free.
STRUCTURAL_CONSERVATION: IL/OZ Lyapunov proof ρ_IL 0.737→0.75, ρ_OZ 2.803→2.0 (product 1.5>1, argument preserved); |Φ_s|<φ→π/2; the full 13-operator energy table (VAL 1.05, AL 0.10, SHA 0.9, NUL-dens 1.111) + the sequence-contractiveness example (1+3.0)(1−0.438)⁴≈0.40<1.
STRUCTURAL_STABILITY / TNFR_VARIATIONAL_PRINCIPLE / TNFR_NUMBER_THEORY: IL/OZ rows → operational; Mutation ΔNFR φ×π≈5.083→5.0; γ_c=γ/π, noise floor, chirality → operational calibrated; |Φ_s|<φ→π/2; |∇φ| threshold γ/π→π/16; "Tetrahedral confinement" label → "U6 structural-potential confinement".
TNFR_YANG_MILLS (+ src/tnfr/yang_mills/structural_gap.py 2 docstrings): V_U6 "normalised by φ²" / "Φ_s²/φ²" / ρ_U6 = max|Φ_s|/φ → (π/2)² / U6_STRUCTURAL_POTENTIAL_LIMIT (the code already computed /(π/2)²; only the docstrings + note were stale).
CATALOG_TYPE_HYGIENE_PROGRAMME: removed the false "Universal Tetrahedral Correspondence γ ↔ |∇φ|" claim and the FUNDAMENTAL_THEORY — Universal Tetrahedral Correspondence cross-ref; stale canonical.py:506→:289.
TNFR_RIEMANN_RESEARCH_NOTES (20 refs — the subagent missed these): the refuted "Universal Tetrahedral Correspondence" (φ↔Φ_s, γ↔|∇φ|, π↔K_φ, e↔ξ_C) purged throughout — the explicit mapping → the minimal structural-field tetrad (only π structural); the three inter-prime kernels relabeled exploratory, not canonical; δ_coh derived from UTC → exploratory γ/π prefactor; U6 ΔΦ_s<φ→π/2; DNFR/SI weights (φ/γ/π/e-derived) → operational tunable (+ stale :57/:65/:150 line anchors → :85/:93/:186); SELECTOR_WEIGHTS {π/(π+e),1/(π+1),γ/(π+1)} → the operational {0.536, 1/(π+1)≈0.241, 0.139}; 8 narrative "nor from the Universal Tetrahedral Correspondence" tool-lists → "structural-field tetrad".
Confirmed clean (no changes): MINIMAL_STRUCTURAL_DEGREES, MATHEMATICAL_DYNAMICS_BASIS, GLOSSARY (§VON_KOCH deprecation honest), UNIFIED_GRAMMAR_RULES, DISSIPATIVE_AND_OPEN_SYSTEMS, EMERGENT_ONTOLOGY, REMESH_INFINITY_DERIVATION, APPLIED_STRUCTURAL_ANALYSIS, NUCLEUS_A/B, TNFR_BSD/HODGE/P_VS_NP/NAVIER_STOKES research notes (NAVIER_STOKES 2.803702 is simulation data; Riemann sin(γ_em·T) is an explicit non-resonant Euler-Mascheroni control — both legitimate). defaults_core.py/canonical.py already fully purged (weights labeled "tunable"; GAMMA/PHI/E intentionally absent).