EML-A1EML_ATLAS_ANNEX_PASSEML-A7 gateevidence annexpublic Atlas remains canonical

EML Atlas Evidence Annex

Name: Monogate
Author: Monogate

A candidate-only verifier for selected Atlas identities, rewrites, and blocked claim boundaries.

Entries

35

Exact identities

9

Standard rewrites

13

Blocked

3

Review queue

35

Candidate witnesses

9

Public promotions

0

promotion gate

Safe education

7

Proof targets

3

Reviewer only

22

Blocked

3

EML_ATLAS_PROMOTION_GATE_PASSpublic promotion: falseexp_from_eml: checked_by_lake_build

annex role

This page supports the public monogate.org Atlas with generated checks. It is not a replacement Atlas and does not promote theorem, RH, physics, modular-form, quantum-group, compiler, or public SuperBEST claims.

review queue

Entry	Action	Priority	Promote
bose_boundary	`candidate_machlib_witness`	1	false
constants_zero_and_e	`candidate_machlib_witness`	1	false
euler_null_state	`candidate_machlib_witness`	1	false
exp_from_eml	`candidate_machlib_witness`	1	false
fermi_boundary	`candidate_machlib_witness`	1	false
ln_from_eml	`candidate_machlib_witness`	1	false
maxwell_boundary	`candidate_machlib_witness`	1	false
prime_signature_log_recovery	`candidate_machlib_witness`	1	false
subtraction_boundary	`candidate_machlib_witness`	1	false
bell_generating_rewrite	`keep_private_symbolic_or_numeric_verifier`	2	false
dedekind_eta_factor	`keep_private_symbolic_or_numeric_verifier`	2	false
finite_difference_heaviside	`keep_private_symbolic_or_numeric_verifier`	2	false
forward_difference_operator	`keep_private_symbolic_or_numeric_verifier`	2	false
mellin_deformation_family	`keep_private_symbolic_or_numeric_verifier`	2	false

next proof targets

bose_boundary

Bose-Einstein denominator

candidate_only_not_proved

constants_zero_and_e

constants e and 0

candidate_only_not_proved

euler_null_state

Euler null state

candidate_only_not_proved

exp_from_eml

exp(x)

candidate_only_not_proved

fermi_boundary

Fermi-Dirac denominator

candidate_only_not_proved

exact_identitypass3 checkscandidate_machlib_witness

exp(x)

standard

exp(x)

eml

eml(x, 1)

Definition-level EML identity over the real/complex exponential branch used by this verifier.

exact_identitypass3 checkscandidate_machlib_witness

ln(y) from EML

standard

ln(y)

eml

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

Requires y > 0 on the real branch.

exact_identitypass2 checkscandidate_machlib_witness

constants e and 0

standard

e, 0

eml

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

Definition-level constant identities only.

exact_identitypass3 checkscandidate_machlib_witness

Bose-Einstein denominator

standard

exp(x) - 1

eml

eml(x, e)

Boundary rewrite only; no new physics theorem is claimed.

exact_identitypass3 checkscandidate_machlib_witness

Fermi-Dirac denominator

standard

exp(x) + 1

eml

eml(x, exp(-1))

Boundary rewrite only; no new physics theorem is claimed.

exact_identitypass3 checkscandidate_machlib_witness

Maxwell-Boltzmann boundary

standard

exp(x)

eml

eml(x, 1)

Boundary rewrite only; no new statistical-mechanics theorem is claimed.

exact_identitypass3 checkscandidate_machlib_witness

linear subtraction boundary

standard

v - u

eml

eml(log(v), exp(u))

Requires v > 0 on the real branch.

exact_identitypass1 checkscandidate_machlib_witness

Euler null state

standard

exp(i*pi) + 1 = 0

eml

eml(i*pi, exp(-1)) = 0

Complex principal-branch identity; no topology or physics theorem is claimed.

exact_identitypass4 checkscandidate_machlib_witness

prime signature log recovery

standard

ln(p)

eml

eml(ln(ln(p)), 1)

Requires p > 1; signature notation does not prove prime-distribution claims.

standard_rewritepass6 checkskeep_private_symbolic_or_numeric_verifier

forward difference operator

standard

exp(d/dt) - 1

eml

eml(d/dt, e)

Operational-calculus rewrite checked on a polynomial witness; not a general operator-domain proof.

standard_rewritepass3 checkskeep_private_symbolic_or_numeric_verifier

q-integers

standard

(q^n - 1) / (q - 1), q=exp(x)

eml

eml(n*x, e) / eml(x, e)

Algebraic rewrite for q != 1; no quantum-group theorem is claimed.

standard_rewritepass3 checkskeep_private_symbolic_or_numeric_verifier

Bell exponential generating function

standard

exp(exp(x) - 1)

eml

eml(eml(x, e), 1)

Generating-function rewrite only; no combinatorics proof is claimed.

standard_rewritepass3 checkskeep_private_symbolic_or_numeric_verifier

Dedekind eta product factor

standard

1 - exp(2*pi*i*n*tau)

eml

-eml(2*pi*i*n*tau, e)

Single product-factor rewrite; no modular-form theorem is claimed.

standard_rewritepass6 checkskeep_private_symbolic_or_numeric_verifier

Mellin/polylog EML kernel

standard

Integral x^(s-1)/(exp(x)-lambda) dx = Gamma(s)*Li_s(lambda)/lambda

eml

Integral x^(s-1)/eml(x, exp(log(lambda))) dx

Includes the required division by lambda for 0 < lambda < 1; lambda -> 0 is a limiting case.

standard_rewritepass3 checkskeep_private_symbolic_or_numeric_verifier

zeta explicit-formula term

standard

x^rho

eml

eml(rho * eml(log(log(x)), 1), 1)

Grammar rewrite of a known term; not a proof of the explicit formula or RH.

conjectural_or_blockedpass2 checksblocked_public_claim

RH modulus statement

standard

|x^rho| = sqrt(x) for non-trivial zeros on Re(rho)=1/2

eml

|eml(rho * eml(log(log(x)), 1), 1)| = sqrt(x)

Blocked as a public theorem claim; verifier only demonstrates critical-line and off-critical samples.

standard_rewritepass1 checkskeep_private_symbolic_or_numeric_verifier

Chebyshev theta via prime signatures

standard

theta(x) = sum_{p <= x} ln(p)

eml

sum_{p <= x} eml(sigma(p), 1)

Finite-sum rewrite only; no prime number theorem claim.

standard_rewritepass1 checkskeep_private_symbolic_or_numeric_verifier

Chebyshev psi via prime signatures

standard

psi(x) = sum_{p^k <= x} ln(p)

eml

sum_{p^k <= x} eml(sigma(p), 1)

Finite-sum rewrite only; no explicit-formula proof.

standard_rewritepass1 checkskeep_private_symbolic_or_numeric_verifier

prime number theorem signature form

standard

pi(x) ~ x / ln(x)

eml

pi(x) ~ x / eml(sigma(x), 1)

Asymptotic theorem restatement only; no proof or improved bound.

standard_rewritepass1 checkskeep_private_symbolic_or_numeric_verifier

polylog/Lerch extension

standard

Gamma(s) Phi(z,s,a)

eml

Mellin kernel with exp/log boundary parameters

Named-function mapping only; no new special-function theorem.

heuristic_analogypass1 checkskeep_private_expository_only

statistical mechanics triad

standard

Fermi, Maxwell, Bose denominators

eml

eml(x, exp(-1)), eml(x, 1), eml(x, e)

Pedagogical boundary pattern; no new physics theorem.

standard_rewritepass1 checkskeep_private_symbolic_or_numeric_verifier

Stefan-Boltzmann zeta(4) bridge

standard

Integral x^3/(exp(x)-1) dx = pi^4/15

eml

Integral x^3/eml(x,e) dx

Classical identity restatement; no new physical derivation.

heuristic_analogypass1 checkskeep_private_expository_only

arithmetic gas partition function

standard

zeta as bosonic partition function

eml

Euler product factors as EML exponentials

Known Bost-Connes style analogy; no theorem claim.

numeric_observationpass1 checksneeds_reproduction_benchmark

Dedekind eta EML product

standard

eta(tau) product

eml

product of -eml(2*pi*i*n*tau, e) factors

Numerical/product observation; no modular-form theorem.

heuristic_analogypass1 checkskeep_private_expository_only

string eta critical-dimension note

standard

eta(tau)^-24 and zeta regularization

eml

eta factors routed through EML product factors

Pedagogical analogy; no string-theory theorem.

numeric_observationpass1 checksneeds_reproduction_benchmark

quaternionic null sphere

standard

exp(q) = -1 for pure |q| = pi

eml

eml(q, exp(-1)) = 0

Quaternionic identity candidate needs dedicated algebra verifier.

heuristic_analogypass1 checkskeep_private_expository_only

Hopf fibration null analogy

standard

division-algebra null-set dimensions

eml

EML null sets across C/H/O

Analogy only; octonionic case is blocked until formalized.

numeric_observationpass1 checksneeds_reproduction_benchmark

GUE spacing null result

standard

Delta sigma(p) vs zeta zero spacings

eml

prime-signature gap experiment

Recorded null result; no spectral correspondence claim.

numeric_observationpass1 checksneeds_reproduction_benchmark

prime signature sequence

standard

sigma(p)=ln(ln(p))

eml

zero of eml(x,p)

Coordinate projection only; no prime-distribution theorem.

standard_rewritepass1 checkskeep_private_symbolic_or_numeric_verifier

Mellin deformation family

standard

Integral x^(s-1)/(exp(x)-lambda) dx

eml

Integral x^(s-1)/eml(x, exp(log(lambda))) dx

Uses corrected polylog factor; no zero-free-region claim.

heuristic_analogypass1 checkskeep_private_expository_only

D_n operator family

standard

exp(n*x) - (ln y)^n

eml

higher-order duality engine

Exploratory family; not validated as universal algebra.

standard_rewritepass1 checkskeep_private_symbolic_or_numeric_verifier

Heaviside operational calculus

standard

exp(D) - 1 = Delta

eml

eml(D, e)

Operator-domain proof remains future work.

conjectural_or_blockedpass1 checksblocked_public_claim

SuperBEST cost boundary

standard

public tree cost vs internal DAG cost

eml

Atlas cost claims routed through evidence packets

Blocked from public promotion without cost-lab evidence.

numeric_observationpass1 checksneeds_reproduction_benchmark

symbolic regression prediction

standard

template search on psi(x)-x

eml

EML-shaped critical-line basis

Benchmark-only; no theorem or zeta-zero discovery claim.

conjectural_or_blockedpass1 checksblocked_public_claim

Riemann-EML dictionary

standard

zeta identities rewritten in EML grammar

eml

dictionary of Dirichlet, Euler product, xi, explicit formula

Dictionary is notation/grammar unless separately proved.

non-claims

The monogate.org Atlas remains the canonical public Atlas.
This annex is an internal evidence and claim-hygiene layer.
No RH proof, physics theorem, modular-form theorem, quantum-group theorem, or public SuperBEST claim is made.
No Forge/compiler behavior changes are made.
No package publish or deploy is performed by this script.