EML Advantage LabEML_ADVANTAGE_LAB_PASSA8.1 holdoutA8.2 candidatesA8.3 trialsA8.4 controlsA8.5 depthA9 guardsA9.2 decisionsA11.1 holdoutsA11.2 stabilityA11.3 builder feedbackbounded comparisongeneral superiority: falsecompiler correctness: false

EML Advantage Lab

Compare EML-native and standard representations across compression, runtime, stability, lowering, proof, and search evidence.

Packets

9

EML wins

1

Mixed

3

Standard wins

4

Research-only

1

Holdout retained

9

Controls passed

3

Discovery candidates

12

Candidate trials

3

Negative controls

5

Blocked deep trees

3

Guard rules

6

Guard decisions

6

Mock holdouts

6

Protected samples

20

Builder citations

2

current finding

This run does not say EML wins everywhere. It shows the useful terrain: scoped identities and symbolic-search structures are promising, while several runtime and stability cases still favor standard or protected math.

eml_win: 1mixed: 3research_only: 1standard_win: 4

A8.3 candidate trials

The first queue items have moved from ranked candidates into bounded trials. One proof-shape lane is supported, one identity lane stays mixed, and one runtime anti-example confirms standard math should win.

Proof-shape supported

1

Mixed identity

1

Standard runtime win

1

Blocked

0

Candidate	Trial	Class	Axis	Profiles	Interpretation
safe_log_domain_lift_v0	safe_log_domain_lift_trial_v0	`eml_proof_shape_supported`	proof_shape	3	Trial supports the bounded proof-shape claim: exp(theta) produces positive internal log-domain coordinates on all profiles.
ln_from_eml_boundary_v0	ln_from_eml_boundary_trial_v0	`mixed_identity_supported`	proof_shape	3	Trial supports the identity/teaching lane, while standard log remains the runtime form.
expm1_runtime_anti_example_v1	expm1_runtime_antiexample_trial_v1	`standard_runtime_win_confirmed`	negative_control	3	Trial confirms the expected anti-example: protected expm1 beats raw exp(x)-1 near zero.

A9.1 / A9.2 guard decision view

Guard fixtures now run through a deterministic analyzer. This is still review infrastructure, not compiler behavior.

Fixtures

6

Decisions

6

Decision matches

6

Rule matches

6

Compiler changed

false

Fixture	Decision	Lowering	Rules	Matched	Reason
proof_shape_subtraction_boundary_fixture_v0	`allow_proof_shape`	none	prefer_eml_for_proof_shape_v0, require_positive_log_domain_guard_v0	`yes`	Proof-shape use is allowed because domain guards are explicit.
near_zero_expm1_fixture_v0	`recommend_protected_lowering`	expm1(x)	lower_expm1_near_zero_v0	`yes`	Protected expm1 is required near zero.
softplus_logaddexp_fixture_v0	`recommend_protected_lowering`	logaddexp(a,b)	lower_logaddexp_softplus_v0	`yes`	Protected logaddexp-style lowering is required.
missing_log_domain_guard_fixture_v0	`block_missing_domain_guard`	none	require_positive_log_domain_guard_v0	`yes`	Log-domain use has no positive-domain guard.
deep_tree_depth_12_fixture_v0	`block_unstable_deep_tree`	none	block_unstable_deep_tree_v0	`yes`	Deep EML tree needs holdout evidence before runtime/public surfacing.
advantage_claim_without_packets_fixture_v0	`block_claim_until_evidence`	none	require_trial_packet_before_advantage_claim_v0	`yes`	Advantage claim is missing trial/control packets.

A11.1 mock compiler holdouts

Holdout expression packets now exercise the mock compiler decision layer outside the seed set. This is still a reviewer artifact, not real compiler behavior.

Holdouts

6

Protected lowerings

2

Blocked

2

Proof-shape only

2

Compiler changed

false

Program	Guard	Mock compiler	Runtime target	Rules
deep_fold_holdout_v0	`block_unstable_deep_tree`	`blocked_requires_evidence`	none	block_unstable_deep_tree_v0
expm1_near_zero_holdout_v0	`recommend_protected_lowering`	`protected_runtime_lowering`	expm1-style protected lowering	lower_expm1_near_zero_v0, prefer_protected_runtime_lowering_v0
gaussian_reuse_holdout_v0	`allow_proof_shape`	`proof_shape_only`	none	prefer_eml_for_proof_shape_v0
logsumexp_three_holdout_v0	`recommend_protected_lowering`	`protected_runtime_lowering`	logaddexp-style protected lowering	lower_logaddexp_softplus_v0, require_positive_log_domain_guard_v0
raw_eml_domain_holdout_v0	`block_missing_domain_guard`	`blocked_requires_evidence`	none	require_positive_log_domain_guard_v0
subtraction_boundary_holdout_v0	`allow_proof_shape`	`proof_shape_only`	none	prefer_eml_for_proof_shape_v0, subtraction_boundary_guarded_v0

A11.2 protected lowering stability

Protected lowering recommendations now have deterministic numeric edge-grid evidence. This records stability behavior only; speed and compiler-correctness claims stay blocked.

Cases

2

Samples

20

Protected better

15

Protected no worse

20

Naive non-finite

4

Runtime claim

false

Case	Lowering	Samples	Better	No worse	Naive non-finite	Max protected error
expm1_near_zero	`expm1-style protected lowering`	11	10	11	0	9.916668055535714e-21
logsumexp_edge_grid	`logaddexp-style protected lowering`	9	5	9	4	2.283404899549497e-14

A11.3 builder export feedback

Builder-style exports now cite A11.2 when a protected lowering is recommended. The citation supports stability evidence only; speed and compiler claims remain blocked.

Drafts

2

Protected drafts

2

Evidence citations

2

All cite A11.2

true

Runtime claim

false

Program	Decision	Lowering	Evidence
softplus_pair_v0	`recommend_protected_lowering`	logaddexp-style protected lowering	eml-a11-2-protected-lowering-benchmark/logsumexp_edge_grid
expm1_near_zero_holdout_v0	`recommend_protected_lowering`	expm1-style protected lowering	eml-a11-2-protected-lowering-benchmark/expm1_near_zero

A8.5 deep-tree holdout

Depth is the practical stress point. This holdout blocks unstable trees, confirms protected runtime lowering where needed, and prevents deep EML trees from becoming public advantage claims without evidence.

Deep-tree packets

5

Max depth

12

Blocked

3

Standard wins

1

EML structure wins

0

Case	Depth	Class	Profiles
deep_expm1_chain_near_zero_v0	8	`standard_runtime_win`	3
deep_expm1_chain_wide_v0	5	`blocked_unstable_deep_tree`	3
nested_ln_from_eml_positive_v0	6	`mixed_identity_supported`	3
subtraction_boundary_chain_v0	6	`blocked_unstable_deep_tree`	3
unstable_deep_tree_negative_control_v0	12	`blocked_unstable_deep_tree`	3

A9 compiler guard rules

A9 turns the lab evidence into conservative compiler/runtime policy. These are rule packets only; compiler behavior is not changed here.

Rules

6

Fixture-ready

5

Compiler changed

false

Rules complete

false

Rule	Class	Status	Trigger	Action
prefer_eml_for_proof_shape_v0	`proof_shape_preference`	`ready_for_compiler_fixture`	candidate axis is proof_shape or generator_identity and domain guards are explicit	allow EML representation for proof/search/teaching surfaces; do not infer runtime win
lower_expm1_near_zero_v0	`protected_runtime_lowering`	`ready_for_compiler_fixture`	expression shape exp(x)-1 or eml(x,e) with near-zero runtime profile	lower runtime code to protected expm1; keep EML only as boundary/proof notation
lower_logaddexp_softplus_v0	`protected_runtime_lowering`	`ready_for_compiler_fixture`	expression shape ln(exp(a)+exp(b)) or softplus/log-sum-exp	lower runtime code to protected logaddexp/softplus implementation
require_positive_log_domain_guard_v0	`domain_guard`	`ready_for_compiler_fixture`	any EML lowering introduces log(y), ln(y), or y argument interpreted as logarithmic domain	require positive-domain obligation or log-domain lift before surfacing claim
block_unstable_deep_tree_v0	`deep_tree_block`	`ready_for_compiler_fixture`	EML tree depth exceeds holdout-backed depth or finite/error metrics are missing	block public advantage claims and require deep-tree holdout packet before runtime lowering
require_trial_packet_before_advantage_claim_v0	`claim_gate`	`documentation_rule_only`	any artifact attempts an EML advantage, runtime, compiler, or public Atlas claim	require candidate packet, holdout/trial packet, negative-control check, and reviewer decision

A8.4 negative-control discipline

The lab keeps explicit cases where EML should lose or remain blocked. These controls prevent the scoreboard from turning into a one-way promotion surface.

Controls

5

Confirmed

4

Next holdout

1

Exhaustive

false

Control	Class	Expected	Evidence	Reason
expm1_runtime_anti_example_v1	`protected_runtime`	`standard`	`confirmed`	Protected expm1 beats raw exp(x)-1 near zero.
logaddexp_negative_control_v0	`protected_runtime`	`standard`	`confirmed`	Protected logaddexp-style runtime remains the expected stable lowering.
gaussian_bumps_negative_control_v0	`non_eml_structure`	`standard`	`confirmed`	Gaussian bumps are intentionally not an EML-native advantage case.
arbitrary_polynomial_negative_control_v0	`non_eml_structure`	`standard`	`confirmed`	Arbitrary polynomial structure should not be rebranded as an EML moat.
unstable_deep_tree_negative_control_v0	`unstable_deep_tree`	`blocked`	`registered_for_next_holdout`	Deep EML trees can amplify finite-precision and domain failures; this must be tested before any depth-scaling claim.

A8.2 discovery queue

The queue turns the holdout result into new EML-native candidates to test next. These are private candidates, not public claims.

needs_machlib_witness: 7needs_math_review: 1needs_symbolic_search: 1ready_for_advantage_lab: 3

Candidate	Family	Axis	Queue	Score	Why
safe_log_domain_lift_v0	`proof_shape`	proof_shape	`needs_machlib_witness`	48	Turns unsafe raw coordinates into positive internal coordinates with a simple obligation.
ln_from_eml_boundary_v0	`generator_identity`	proof_shape	`needs_machlib_witness`	46	Tests whether nested EML generation has proof/teaching value despite worse runtime form.
constants_zero_one_e_v0	`generator_identity`	teaching_clarity	`needs_machlib_witness`	40	Shows constants as EML boundary coordinates rather than separate primitives.
bose_fermi_maxwell_triad_v0	`boundary_lens`	teaching_clarity	`needs_machlib_witness`	38	Unifies three statistical-mechanics denominators as y-boundary shifts.
euler_null_boundary_v0	`boundary_lens`	teaching_clarity	`needs_machlib_witness`	38	Frames Euler identity as an EML null coordinate.
psi_residual_two_term_template_v0	`symbolic_search`	search_complexity	`needs_symbolic_search`	38	Tests whether adding a second EML zero term improves structure recovery at low complexity.
q_integer_ratio_v0	`boundary_lens`	teaching_clarity	`needs_machlib_witness`	38	Tests a compact EML boundary representation of q-integers.
prime_signature_log_recovery_v1	`signature_coordinate`	signature_coordinate	`needs_machlib_witness`	37	Separates runtime log from signature-coordinate analysis for number-theory lenses.

A8.1 holdout layer

The holdout benchmark reruns the initial labels on shifted, edge, and stress profiles, then checks negative controls where EML should not win.

Holdout packets

12

Retained

9

Weakened

0

Blocked

0

Negative controls

3

Case	Source	Holdout	Confidence	Profiles
exp_from_eml_v0	eml_win	`eml_win_replicated`	`retained`	3
subtraction_boundary_v0	standard_win	`standard_win_replicated`	`retained`	3
bose_boundary_expm1_v0	standard_win	`standard_win_replicated`	`retained`	3
ln_from_eml_v0	mixed	`mixed_replicated`	`retained`	3
softplus_pair_v0	standard_win	`standard_win_replicated`	`retained`	3
sigmoid_derivative_v0	standard_win	`standard_win_replicated`	`retained`	3
gaussian_energy_v0	mixed	`mixed_replicated`	`retained`	3
prime_signature_log_recovery_v0	mixed	`mixed_replicated`	`retained`	3
psi_residual_template_v0	research_only	`research_only_retained`	`retained`	1
gaussian_bumps_negative_control_v0	negative_control	`standard_win_replicated`	`control_pass`	1
arbitrary_polynomial_negative_control_v0	negative_control	`standard_win_replicated`	`control_pass`	1
logaddexp_negative_control_v0	negative_control	`standard_win_replicated`	`control_pass`	1

advantage packets

Case	Class	Compression	Runtime	Stability	Lowering	Proof	Clarity
exp_from_eml_v0	`eml_win`	same_surface_count	standard_faster_local	similar_or_mixed	lower_to_hybrid	scoped_certificate_present	eml_generator_identity
gaussian_energy_v0	`mixed`	standard_smaller_surface	standard_faster_local	similar_or_mixed	lower_to_standard	proof_obligations_open	standard_runtime_clarity
ln_from_eml_v0	`mixed`	standard_smaller_surface	standard_faster_local	similar_or_mixed	lower_to_standard	scoped_certificate_present	eml_boundary_identity
prime_signature_log_recovery_v0	`mixed`	standard_smaller_surface	not_benchmarked	identity_numeric_match_but_standard_simpler	lower_to_standard	proof_obligations_open	eml_signature_lens
bose_boundary_expm1_v0	`standard_win`	same_surface_count	standard_faster_local	standard_more_stable	lower_to_standard	scoped_certificate_present	eml_boundary_identity
sigmoid_derivative_v0	`standard_win`	standard_smaller_surface	eml_faster_local	standard_more_stable	lower_to_standard	proof_obligations_open	standard_runtime_clarity
softplus_pair_v0	`standard_win`	standard_smaller_surface	standard_faster_local	standard_more_stable	lower_to_standard	proof_obligations_open	standard_runtime_clarity
subtraction_boundary_v0	`standard_win`	standard_smaller_surface	standard_faster_local	standard_more_stable	lower_to_standard	scoped_certificate_present	eml_boundary_identity
psi_residual_template_v0	`research_only`	eml_smaller_template	not_runtime_fixture	not_finite_precision_fixture	research_only	not_a_proof_fixture	eml_search_lens

eml_winatlas_exact_identity

exp_from_eml_v0

EML

eml(x, 1)

Standard

exp(x)

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

mixedforge_efrog_fixture

gaussian_energy_v0

EML

exp(-(x * x)) + exp(-(x * x))

Standard

2 * exp(-(x * x))

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

mixedatlas_exact_identity

ln_from_eml_v0

EML

eml(1, eml(eml(1, y), 1))

Standard

ln(y)

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

mixedprime_signature_identity

prime_signature_log_recovery_v0

EML

eml(sigma(x), 1), sigma(x)=ln(ln(x))

Standard

ln(x)

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

standard_winstatistical_boundary

bose_boundary_expm1_v0

EML

eml(x, e)

Standard

expm1(x)

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

standard_winsigmoid_logistic

sigmoid_derivative_v0

EML

(1 / (1 + exp(-x))) * (1 - (1 / (1 + exp(-x))))

Standard

stable_sigmoid(x) * (1 - stable_sigmoid(x))

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

standard_winsoftplus_logsumexp

softplus_pair_v0

EML

ln(exp(a) + exp(b))

Standard

logaddexp(a, b)

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

standard_winatlas_exact_identity

subtraction_boundary_v0

EML

eml(ln(v), exp(u))

Standard

v - u

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

research_onlysymbolic_regression_frontier

psi_residual_template_v0

EML

-2 Re(x^(1/2+i gamma)/(1/2+i gamma))

Standard

sqrt(x) * (A cos(gamma log x) + B sin(gamma log x))

No general EML superiority claim.
No public performance or savings claim.
No compiler correctness claim.

non-claims

The EML Advantage Lab is a bounded comparison surface, not a proof system.
It does not claim EML is generally superior to standard mathematics.
It does not claim compiler correctness, theorem discovery, RH proof, zeta-zero discovery, hardware measurement, or public performance.
Each advantage class is local to the listed evidence and fixture.
A8.1 is a deterministic holdout benchmark, not proof of EML advantage.
A8.1 does not claim EML is generally superior to standard mathematics.
A8.1 does not claim compiler correctness, public performance, theorem discovery, RH proof, zeta-zero discovery, hardware measurement, or deployment.
Negative controls are sanity checks, not exhaustive invalidation tests.
A8.2 records discovery candidates only.
A8.2 does not test, prove, deploy, or publicly promote candidate claims.
A8.2 does not claim EML advantage, theorem discovery, compiler correctness, RH proof, zeta-zero discovery, or public performance.
A8.3 runs bounded deterministic candidate trials only.
A8.3 does not prove EML advantage, broad EML superiority, theorem discovery, compiler correctness, RH proof, zeta-zero discovery, runtime performance, public Atlas promotion, or deployment.
A8.3 confirms one runtime anti-example so standard protected math can still win.
A8.4 registers negative controls for reviewer discipline.
A8.4 does not claim the controls are exhaustive.
A8.4 does not prove EML advantage, broad EML superiority, theorem discovery, compiler correctness, runtime performance, public Atlas promotion, or deployment.
A8.5 is a deterministic deep-tree holdout, not proof of deep-tree stability.
A8.5 does not prove EML advantage, broad EML superiority, compiler correctness, runtime performance, theorem discovery, public Atlas promotion, or deployment.
Blocked deep trees are guardrail evidence, not a universal limit theorem.
A9 records compiler guard rules only; it does not modify compiler behavior.
A9 does not prove compiler correctness, EML advantage, broad EML superiority, runtime performance, theorem discovery, public Atlas promotion, or deployment.
A9 guard rules are conservative and incomplete until implemented and tested in compiler fixtures.
A9.1 records expected guard-rule fixtures only.
A9.1 does not change compiler behavior or implement guard analysis.
A9.1 does not prove compiler correctness, EML advantage, runtime performance, public Atlas promotion, or deployment.
A9.2 runs a deterministic fixture analyzer only.
A9.2 does not change compiler behavior or prove compiler correctness.
A9.2 does not claim production readiness, EML advantage, runtime performance, public Atlas promotion, or deployment.