CSM_RH Paper 02

Hilbert–Laplace Packet Globalizer, Exact Zero-Packet Exponential Type, and Campaign 01 Closure

Project: CSM_RH
Paper: 02
Version: v0.1
Date: 2026-09-04
Parent: CSM_RH Paper 01
Status: structural theorem / frontier audit; not a proof or disproof of RH
中文標題： CSM_RH 論文 02：Hilbert–Laplace 封包全域化算子、精確零點封包指數型與 Campaign 01 閉合
作者： Neo.K
機構： EveMissLab／一言諾科技有限公司
Language: English

0. Trust boundary

This paper does not prove or disprove the Riemann Hypothesis.

Canonical state:

RH_PROVED = FALSE
RH_DISPROVED = FALSE
GLOBAL_RH_CERTIFICATE = FALSE
ROOT_STATUS = OPEN

This paper proves a narrower structural result:

For the smooth $q=1$ major-arc zeta-zero packet used in the v3.18 architecture, zero-zero interference cannot lower the packet's exponential growth type below the supremal real part of the zeta zeros.

Consequently, the pointwise packet-isolation lower bound proposed in Paper 01 is not needed for the fixed-exponent strength audit of EMAE.

The arithmetic EMAE upper bound itself remains open.

No live GLM-5.3-Flash provider run is claimed in this package.

1. Canonical correction: GLM is a worker/provider, not the protocol

Paper 01 introduced the names:

GLM_Backward Search
Goal-Led Meta-Research

as if GLM were the name of the mathematical research protocol.

That naming was not canonical and is withdrawn.

The canonical architecture is:

CSM_RH
  = closure-space mathematics protocol / state space

GLM-5.3-Flash
  = replaceable high-volume worker/provider implementation

roles
  = Designer / Builder / Verifier

frontier model
  = residual-risk judge / final promotion authority

Therefore:

\boxed{ \mathrm{GLM} \neq \mathrm{Protocol}. }

Campaign 01 is henceforth a CSM_RH worker campaign.

GLM-5.3-Flash is a preferred current worker model for that campaign, not the semantic identity of the campaign itself.

2. Campaign 01 target

Paper 01 created:

S-RH-007
LOSSLESS_WITNESS_GLOBALIZER

with the goal of converting an off-critical zero witness into a global invariant which cannot be erased by aggregation.

The principal open instances were:

O-RH-005-W
WEIL_AGGREGATION_ISOLATION

O-RH-005-M
MAJOR_ARC_AGGREGATION_ISOLATION

Campaign 01 generated and audited several candidate families.

The principal survivor is:

C-RH-GLB-01
HILBERT_LAPLACE_PACKET_GLOBALIZER
abbrev: HLPG

It applies directly to the smooth $q=1$ major-arc zero packet.

3. Candidate batch

The campaign-level candidates are:

C-RH-GLB-01
HILBERT_LAPLACE_PACKET_GLOBALIZER
status: SURVIVES / PROVED_AT_PACKET_TYPE_LEVEL

C-RH-GLB-02
FEJER_BOHR_LOGTIME_AVERAGING
status: DEPRIORITIZED
reason: amplitude-drift normalization debt; HLPG is stronger and cleaner

C-RH-GLB-03
POSITIVE_RESOLVENT_REWEIGHTING
status: REJECTED_AS_REPRESENTATION_ONLY
reason: earlier positive-kernel audits already show no fixed-exponent discount

C-RH-GLB-04
FINITE_INTERVAL_SUZUKI_SPECTRAL_LIMIT
status: DEFERRED
reason: relevant modern operator framework exists, but its infinite-interval spectral limit is conjectural

C-RH-GLB-05
DENSITY_WEIGHTED_EXTREME_ZERO_SUPPRESSION
status: REJECTED_BY_O-RH-003
reason: density alone does not exclude a single extreme zero

C-RH-GLB-06
RANDOM_PHASE_PACKET_ORTHOGONALIZATION
status: DEFERRED
reason: creates observable-transfer and arithmetic-realizability debt

Only C-RH-GLB-01 is promoted to a theorem route in this paper.

4. Smooth major-arc kernel

Let

w\in C_c^\infty((0,\infty))

be nonzero, and fix

U>0.

For

s\in\mathbb C

and

u\in[-U,U],

define

\mathcal W_s(u) = \int_0^\infty w(v)e(uv)v^{s-1}\,dv.

For

x=e^T

and

\epsilon=\frac{u}{x},

the exact scaling is

W_{x,u/x}(s) = e^{sT}\mathcal W_s(u).

5. Hilbert packet space

Define the Hilbert space

\mathcal H_{w,U} = L^2 \left( [-U,U], |\mathcal W_1(u)|^2du \right).

For each nontrivial zeta zero $\rho$ , define the coefficient vector

v_\rho(u) = \mathcal W_\rho(u).

Its squared Hilbert norm is

\|v_\rho\|_{\mathcal H_{w,U}}^2 = \int_{-U}^{U} |\mathcal W_1(u)|^2 |\mathcal W_\rho(u)|^2du.

This is exactly the zero cross-kernel coefficient

C_{w,U}(\rho).

The v3.18 kernel theorem gives

\boxed{ \|v_\rho\|_{\mathcal H_{w,U}}^2 = C_{w,U}(\rho) > 0. }

Thus every nontrivial zero has a nonzero Hilbert coefficient.

6. Rapid vertical decay

Write

s=\sigma+i\gamma, \qquad 0\le\sigma\le1.

Set

v=e^y.

Then

\mathcal W_{\sigma+i\gamma}(u) = \int_{\mathbb R} w(e^y)e^{\sigma y}e(ue^y)e^{i\gamma y}\,dy.

Because $w$ has compact support inside $(0,\infty)$ , the function

y \mapsto w(e^y)e^{\sigma y}e(ue^y)

is smooth and compactly supported in a fixed interval, uniformly for

0\le\sigma\le1, \qquad |u|\le U.

Repeated integration by parts therefore gives:

Lemma 6.1 — Uniform rapid vertical decay

For every integer

N\ge0,

there exists

C_N=C_N(w,U)

such that

\boxed{ \sup_{\substack{ 0\le\sigma\le1\\ |u|\le U }} | \mathcal W_{\sigma+i\gamma}(u) | \le C_N (1+|\gamma|)^{-N}. }

The same estimate holds for

\|v_{\sigma+i\gamma}\|_{\mathcal H_{w,U}}.

7. Absolute summability over zeta zeros

Let

N_\zeta(Y)

count nontrivial zeta zeros up to height $Y$ , with multiplicity.

The classical zero-counting estimate gives

N_\zeta(Y) = O(Y\log Y).

Combining this with Lemma 6.1, choose $N$ sufficiently large to obtain

\boxed{ \sum_{\rho} \|v_\rho\|_{\mathcal H_{w,U}} < \infty. }

Therefore the zero packet below is absolutely convergent in $\mathcal H_{w,U}$ on every compact $T$ -interval.

8. Hilbert-valued zero packet

Define

F(T) = \sum_{\rho} e^{\rho T}v_\rho, \qquad T\ge0.

Define the rightmost-zero abscissa

\Theta_\zeta = \sup_\rho \Re\rho.

By symmetry,

\Theta_\zeta = \frac12+\Delta_\zeta.

The easy upper estimate is

\|F(T)\| \le \sum_\rho e^{(\Re\rho)T} \|v_\rho\| \le e^{\Theta_\zeta T} \sum_\rho \|v_\rho\|.

Hence

\boxed{ \|F(T)\| = O(e^{\Theta_\zeta T}). }

The issue is whether zero-zero interference can improve this exponent.

The next theorem says no.

9. Hilbert–Laplace coefficient recovery

Define the packet type

\tau_F = \inf \left\{ a\in\mathbb R: \|F(T)\| = O(e^{aT}) \right\}.

Theorem 9.1 — Exact Hilbert packet type

\boxed{ \tau_F = \Theta_\zeta. }

Proof

The upper bound

\tau_F\le\Theta_\zeta

was established in Section 8.

Assume for contradiction that

\tau_F<\Theta_\zeta.

Choose

a

such that

\tau_F<a<\Theta_\zeta.

Then

\|F(T)\| = O(e^{aT}).

Therefore the Bochner-valued Laplace transform

\widehat F(s) = \int_0^\infty e^{-sT}F(T)\,dT

is holomorphic in the half-plane

\Re s>a.

For

\Re s>\Theta_\zeta,

absolute convergence permits termwise integration:

\widehat F(s) = \sum_\rho \frac{v_\rho}{s-\rho}.

By the rapid decay from Lemma 6.1, the series

\sum_\rho \frac{v_\rho}{s-\rho}

converges locally normally on compact subsets avoiding the zeta zeros.

Hence it defines an $\mathcal H_{w,U}$ -valued meromorphic function whose residue at a zero $\rho_0$ of multiplicity $m(\rho_0)$ is

m(\rho_0)v_{\rho_0}.

Because

a<\Theta_\zeta,

there exists a zero $\rho_0$ with

\Re\rho_0>a.

The coefficient non-annihilation theorem gives

v_{\rho_0}\neq0.

Choose a continuous linear functional

\ell \in \mathcal H_{w,U}^\ast

such that

\ell(v_{\rho_0})\neq0.

Then

\ell(\widehat F(s))

is holomorphic for

\Re s>a,

but on

\Re s>\Theta_\zeta

it equals

\sum_\rho \frac{ \ell(v_\rho) }{ s-\rho }.

The latter has a nonremovable pole at $\rho_0$ with nonzero residue

m(\rho_0)\ell(v_{\rho_0}).

By uniqueness of analytic continuation this is impossible, because $\rho_0$ lies inside the holomorphy half-plane

\Re s>a.

Therefore

\tau_F\ge\Theta_\zeta.

Combining both inequalities gives

\boxed{ \tau_F=\Theta_\zeta. }

$\square$

10. Interpretation

Theorem 9.1 is the major-arc analogue of the successful fixed-aperture singularity-separation mechanism.

The key fact is:

Cross terms may cancel at individual scales, but they cannot erase a nonzero exponential coefficient from the analytic Laplace resolvent.

Thus:

POINTWISE PACKET INTERFERENCE
does not imply
EXPONENTIAL-TYPE INTERFERENCE.

No literal rightmost zero is required.

If the supremum is not attained, the proof chooses a zero with

\Re\rho>a

for every

a<\Theta_\zeta.

11. Positive packet energy

The $q=1$ pole-zero packet energy on the core arc is

\mathcal E_1(e^T;U) = e^T \|F(T)\|_{\mathcal H_{w,U}}^2.

Define

\tau_E = \inf \left\{ b: \mathcal E_1(e^T;U) = O(e^{bT}) \right\}.

Theorem 11.1 — Exact $q=1$ packet-energy type

\boxed{ \tau_E = 1+2\Theta_\zeta. }

Proof

Theorem 9.1 gives the upper estimate immediately.

Conversely, if

\mathcal E_1(e^T;U) = O(e^{bT}),

then

\|F(T)\| = O \left( e^{(b-1)T/2} \right).

Theorem 9.1 therefore forces

\Theta_\zeta \le \frac{b-1}{2}.

Hence

b \ge 1+2\Theta_\zeta.

$\square$

Using

\Theta_\zeta = \frac12+\Delta_\zeta,

we also have

\boxed{ \tau_E = 2+2\Delta_\zeta. }

12. Closure of the growth-type MZI debt

Paper 01 introduced

F-RH-004
MAJOR_ZERO_PACKET_ISOLATION

because the isolated pole-zero channel

x^{1+2\Re\rho}

was not known to give a pointwise lower bound for the full packet.

Paper 02 splits that frontier.

F-RH-004A

POINTWISE_MAJOR_ZERO_PACKET_LOWER_ENVELOPE
status: OPEN
priority: DEPRIORITIZED

This is the old pointwise MZI form.

F-RH-004B

MAJOR_ZERO_PACKET_EXPONENTIAL_TYPE
status: CLOSED
certificate: Theorem 11.1

The fixed-exponent strength audit needs F-RH-004B, not F-RH-004A.

Therefore the major-arc aggregation-isolation barrier is closed at exponential-type level.

Canonical transition:

O-RH-005-M
MAJOR_ARC_AGGREGATION_ISOLATION
OPEN
->
CLOSED_AT_EXPONENTIAL_TYPE

13. EMAE strength is now certified

Recall the positive character major-arc energy gate

\operatorname{EMAE}(\eta): \qquad \mathfrak Z_2(x;Q,U) + \mathfrak Z_4(x;Q,U) \ll x^{3-\eta+o(1)}.

The $q=1$ contribution is a nonnegative term of

\mathfrak Z_2.

Therefore EMAE implies

\mathcal E_1(x;U) \ll x^{3-\eta+o(1)}.

Theorem 11.1 gives

1+2\Theta_\zeta \le 3-\eta.

Hence:

Corollary 13.1 — Fixed-strip consequence of EMAE

\operatorname{EMAE}(\eta)

holds for a fixed

\eta>0,

then

\boxed{ \Theta_\zeta \le 1-\frac{\eta}{2}. }

Equivalently,

\boxed{ \Delta_\zeta \le \frac12-\frac{\eta}{2}. }

Thus every fixed positive $\eta$ yields a fixed zero-strip breakthrough.

\eta=1,

then

\Theta_\zeta\le\frac12.

By functional-equation symmetry,

\Theta_\zeta\ge\frac12,

\Theta_\zeta=\frac12,

which is RH.

Therefore:

EMAE(eta>0)
  = at least S2 fixed-zero-strip strength

EMAE(1)
  = S3 RH-level strength

This is now a certified structural implication, not a single-zero dominance heuristic.

14. What has and has not been solved

Closed

C1
smooth zero coefficients are rapidly summable

C2
every zero has nonzero Hilbert coefficient

C3
full q=1 zero packet has exact exponential type Theta_zeta

C4
packet interference cannot reduce exponential type

C5
q=1 pole-zero energy has exact type 1 + 2 Theta_zeta

C6
EMAE fixed-power strength audit is certified

Still open

G1
prove EMAE(eta) for any fixed eta > 0

G2
derive a genuinely new arithmetic cancellation theorem strong enough for G1

G3
close the Weil constructive isolation frontier if that branch remains active

G4
prove the RH-scale eta = 1 major-arc energy bound

G5
RH

The campaign has removed a representation/globalization uncertainty.

It has not supplied the missing arithmetic fixed-power saving.

15. Why this is not another RH-equivalent representation loop

Theorem 11.1 alone does not assert

\Theta_\zeta=\frac12.

It identifies the exact exponent encoded by a pre-existing positive packet energy.

The new closure gain is:

before:
  full packet interference could invalidate the isolated-channel strength audit

after:
  full packet exponential type is exactly known

This discharges a bridge debt.

It does not discharge the arithmetic energy upper-bound debt.

Therefore this result is not classified as REPACKAGING_ONLY.

16. Candidate C-RH-GLB-02 — Fejer / Bohr log-time averaging

A natural attempt is to average the packet over long log-time windows so distinct imaginary frequencies become orthogonal.

For finite trigonometric sums this is standard.

However the amplitudes are

e^{(\Re\rho)T},

so a long translation window changes both phase and magnitude.

Without a normalization tied to an unknown extremal real part, the averaging theorem introduces a new scale-selection debt.

Because HLPG already recovers coefficients without this debt, the candidate is:

DEPRIORITIZED

not false.

17. Candidate C-RH-GLB-03 — Positive resolvent reweighting

Earlier positive-kernel work showed that fixed nonzero positive spectral pieces retain the same off-axis exponent, while moving spectral windows pay a sensitivity tax.

Full moving-center energies are elliptically equivalent, at fixed-exponent level, to classical normalized PNT mean-square quantities.

Therefore another positive reweighting without a new arithmetic theorem is classified:

REJECTED_AS_REPRESENTATION_ONLY

under the existing representation-closure obstruction.

18. Candidate C-RH-GLB-04 — finite-interval Suzuki operator limit

Modern Suzuki operator work provides a strong and relevant finite-interval framework for the Weil quadratic form and connects the construction with de Branges / operator theory.

However the proposed limiting self-adjoint operator whose spectrum would recover zeta-zero ordinates is presently formulated as a conjectural limit construction.

Therefore it cannot currently serve as a closed CSM_RH globalizer certificate.

Classification:

DEFERRED
external dependency:
  conjectural finite-interval -> infinite-limit spectral bridge

This remains a valuable future route, especially for the Weil branch.

19. Candidate C-RH-GLB-05 — density weighted suppression

Any candidate whose decisive step is only a density theorem still permits a sparse or isolated extreme zero.

The packet-type theorem actually makes the obstruction sharper:

a single nonzero zero coefficient already creates an analytic singularity in the Hilbert-Laplace resolvent.

Therefore density-only suppression remains blocked.

Classification:

REJECTED_BY_O-RH-003

20. Candidate C-RH-GLB-06 — random phase orthogonalization

Introducing an auxiliary random phase can diagonalize a finite packet in expectation.

But a new phase variable must be connected back to a canonical arithmetic observable.

Without that transfer theorem the route introduces:

OBSERVABLE_TRANSFER_DEBT
ARITHMETIC_REALIZABILITY_DEBT

Because HLPG achieves the required noncancellation without altering the observable, this candidate is deferred.

21. Updated obstruction topology

The major-arc branch now becomes:

OFF-CRITICAL ZERO
      |
      v
SMOOTH MELLIN COEFFICIENT v_rho != 0
      |
      v
HILBERT ZERO PACKET F(T)
      |
      v
HILBERT-LAPLACE COEFFICIENT RECOVERY
      |
      v
exact packet type = Theta_zeta
      |
      v
exact q=1 energy type = 1 + 2 Theta_zeta
      |
      v
EMAE fixed-power bound
      |
      v
fixed zero strip

The globalization bridge is now closed.

The only unresolved major-arc step in this chain is the arithmetic upper bound.

22. Updated CSM_RH frontier

Principal frontier

F-RH-003
EXCEPTIONAL_MAJOR_ARC_ENERGY
status: OPEN
strength:
  S2 for every fixed eta > 0
  S3 at eta = 1

Deprioritized auxiliary frontier

F-RH-004A
POINTWISE_MAJOR_ZERO_PACKET_LOWER_ENVELOPE
status: OPEN
priority: LOW
reason:
  no longer required for exponent-level closure

Closed bridge frontier

F-RH-004B
MAJOR_ZERO_PACKET_EXPONENTIAL_TYPE
status: CLOSED
certificate:
  Theorem 9.1
  Theorem 11.1

23. GLM worker architecture for the next campaign

The next worker campaign must preserve the canonical provider/protocol separation.

CSM_RH produces

Frontier Task Contract
Source Pack
Known Obstruction Pack
Strength Budget
Required Output Schema

Designer worker

Produces:

candidate mechanism
minimal assumptions
target estimate
known theorem mapping
failure modes

Builder worker

Produces:

derivation
lemmas
explicit constants / exponents
proof obligations
computational crosschecks

Verifier worker

Produces:

objections
hidden-RH-premise audit
quantifier audit
uniformity audit
counterexample attempt
strength classification

Frontier model

Receives only the typed artifacts:

Task Contract
Candidate Artifact
Objection
Repair Patch
Verification Report

It does not treat worker self-confidence as proof authority.

24. Campaign 02 target

Because the packet globalizer is closed, the next high-volume worker target is no longer LOSSLESS_WITNESS_GLOBALIZER on the major-arc branch.

The new target is:

CSM_RH Campaign 02

target:
  ARITHMETIC_EMAE_FIXED_POWER

question:
  find the weakest genuinely arithmetic theorem that yields
  EMAE(eta) for some fixed eta > 0

forbidden shortcuts:
  density-only
  representation-only
  shrinking-aperture false saving
  moving-band sensitivity omission
  isolated-channel dominance assumption
  finite verification -> global theorem

Candidate mechanism families should include only mechanisms that can change arithmetic strength.

Examples of admissible search families:

zero repulsion with quantitative energy consequence
character packet bilinear cancellation
large-sieve refinement with extremal-zero sensitivity
new weighted prime-correlation inequality
structural cancellation tied to functional-equation pairing
hybrid conductor-height-energy estimate

These are search families, not established theorems.

25. Finite synthetic crosscheck

The package includes:

hlpg_finite_packet_crosscheck.py
hlpg_finite_packet_crosscheck.csv

The script verifies on a synthetic finite Hilbert-valued exponential packet:

direct norm-square energy equals its pair expansion;
the Laplace rational form equals direct numerical integration;
the maximal-real-part diagonal term produces a positive real-axis residue;
lower-real-part same-frequency terms do not cancel the maximal diagonal pole;
pointwise interference can be substantial while exponential-type recovery remains intact.

This is a formula crosscheck only.

It is not numerical evidence for RH.

26. External literature boundary

The proof of Theorem 9.1 is self-contained at the level needed here.

Relevant surrounding literature includes:

M. Suzuki, Aspects of the screw function corresponding to the Riemann zeta-function, Journal of the London Mathematical Society 108 (2023), 1448–1487, DOI 10.1112/jlms.12785.
M. Suzuki, Weil's quadratic form via the screw function, arXiv:2606.09096 (2026). This develops a finite-interval operator framework and formulates a spectral-limit conjecture; the conjectural limit is not used as a theorem here.
D. Carando, A. Defant, F. Marceca, I. Schoolmann, Vector-valued general Dirichlet series, Studia Mathematica 258 (2021), 269–316.
A. Defant, A. Pérez, Hardy spaces of vector-valued Dirichlet series, Studia Mathematica 243 (2018), 53–78.

These references provide context for vector-valued Dirichlet-series and operator language but do not replace the explicit proof given above.

27. State transition

The canonical transition is:

CSM_RH v0.2
  ->
CSM_RH v0.3

with:

GLM semantic correction:
  GLM_Backward Search = WITHDRAWN NAME
  GLM-5.3-Flash = WORKER / PROVIDER

O-RH-005-M:
  OPEN
  ->
  CLOSED_AT_EXPONENTIAL_TYPE

F-RH-004:
  SPLIT INTO
    F-RH-004A OPEN / LOW PRIORITY
    F-RH-004B CLOSED

B-RH-005:
  old pointwise lower-envelope bridge remains OPEN

B-RH-007:
  HILBERT_PACKET_TO_EXACT_EXPONENTIAL_TYPE = CERTIFIED

B-RH-008:
  EMAE_TO_FIXED_ZERO_STRIP = CERTIFIED

S-RH-007:
  LOSSLESS_WITNESS_GLOBALIZER
  ->
  PARTIALLY_CLOSED
  major-arc instance = CLOSED
  Weil instance = OPEN

28. Final status

RH = OPEN

WEIL GLOBALIZATION = OPEN

FIXED-APERTURE GLOBALIZATION = CLOSED
FIXED-APERTURE RH-COMPLETE TAIL = OPEN

MAJOR-ARC PACKET GLOBALIZATION = CLOSED_AT_EXPONENTIAL_TYPE
MAJOR-ARC EMAE FIXED POWER = OPEN

EMAE STRENGTH AUDIT = CERTIFIED

GLM = WORKER / PROVIDER
CSM_RH = PROTOCOL / STATE SPACE

NEXT CAMPAIGN:
  ARITHMETIC_EMAE_FIXED_POWER

The main mathematical conclusion is:

\boxed{ \inf \left\{ a: \left\| \sum_\rho e^{\rho T} \mathcal W_\rho \right\|_{\mathcal H_{w,U}} = O(e^{aT}) \right\} = \Theta_\zeta. }

Therefore:

\boxed{ \operatorname{type} \left( \mathcal E_1 \right) = 1+2\Theta_\zeta = 2+2\Delta_\zeta. }

The major-arc zero packet cannot hide an off-axis zero at exponential-type level.

The remaining major-arc obstruction is arithmetic, not representational.

CSM_RH Paper 02 — Hilbert–Laplace Packet Globalizer, Exact Zero-Packet Exponential Type, and Campaign 01 Closure

CSM_RH Paper 02

Hilbert–Laplace Packet Globalizer, Exact Zero-Packet Exponential Type, and Campaign 01 Closure

0. Trust boundary

1. Canonical correction: GLM is a worker/provider, not the protocol

2. Campaign 01 target

3. Candidate batch

4. Smooth major-arc kernel

5. Hilbert packet space

6. Rapid vertical decay

Lemma 6.1 — Uniform rapid vertical decay

7. Absolute summability over zeta zeros

8. Hilbert-valued zero packet

9. Hilbert–Laplace coefficient recovery

Theorem 9.1 — Exact Hilbert packet type

Proof

10. Interpretation

11. Positive packet energy

Theorem 11.1 — Exact q=1q=1q=1 packet-energy type

Proof

12. Closure of the growth-type MZI debt

F-RH-004A

F-RH-004B

13. EMAE strength is now certified

Corollary 13.1 — Fixed-strip consequence of EMAE

14. What has and has not been solved

Closed

Still open

15. Why this is not another RH-equivalent representation loop

16. Candidate C-RH-GLB-02 — Fejer / Bohr log-time averaging

17. Candidate C-RH-GLB-03 — Positive resolvent reweighting

18. Candidate C-RH-GLB-04 — finite-interval Suzuki operator limit

19. Candidate C-RH-GLB-05 — density weighted suppression

20. Candidate C-RH-GLB-06 — random phase orthogonalization

21. Updated obstruction topology

22. Updated CSM_RH frontier

Principal frontier

Deprioritized auxiliary frontier

Closed bridge frontier

23. GLM worker architecture for the next campaign

CSM_RH produces

Designer worker

Builder worker

Verifier worker

Frontier model

24. Campaign 02 target

25. Finite synthetic crosscheck

26. External literature boundary

27. State transition

28. Final status

Theorem 11.1 — Exact $q=1$ packet-energy type