A coherent filter does not erase signals. It classifies them, reduces unsafe coupling, routes them into bounded spaces, preserves traceability, and validates effects over time. Deletion blinds auditability. Suppression creates hidden debt.

1. Formal Definition

The Filtering Law states that coherent filtering attenuates and routes signals rather than deleting, suppressing, or making them disappear from audit.

Filtering is a boundary and signal-processing function. It determines what passes, what is slowed, what is sandboxed, what requires review, what remains visible, and what must be time-validated before recoupling.

A filter is coherent when it preserves enough traceability for later audit and enough signal integrity for correction. It may reduce bandwidth, delay coupling, isolate risk, or prevent immediate propagation. But it should not destroy the evidence path, erase causal visibility, or suppress signals into hidden debt.

Deletion is not filtering. Deletion removes the signal from the system’s future capacity to inspect and learn.

Suppression is not filtering. Suppression hides the signal without repair and often converts it into hidden debt.

Filtering therefore protects the system only when it preserves auditability.

2. Canonical Form

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classify → attenuate → sandbox → trace → time-validate

Expanded canonical form:

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coherent filtering classifies a signal, reduces unsafe coupling, isolates it when needed, preserves its trace, and validates effects over time before release, recoupling, or escalation

Failure expression:

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delete / suppress signal ⇒ Au↓ + H↑

Related variables:

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O, H, ε, ι, Au, R, BΣ, K, µᵢ, Φ, Γ, Π, Σ, Θ, Ψ, Τ, FI

Where:

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Variable	Meaning in this law
`Γ`	Classification of the signal before filtering action
`Π`	Constraint / attenuation / sandboxing rule applied to the signal
`Σ`	Boundary and scope conditions defining where signal may pass
`Τ`	Time validation required before release or recoupling
`FI`	Feedback integrity; filtering must not corrupt feedback loops
`Au`	Auditability; preserved through traceability
`BΣ`	Boundary integrity; filtering protects membranes without erasing signals
`O`	Coherence; preserved when filtering reduces harm without hiding debt
`H`	Hidden debt; rises when deletion or suppression hides unresolved signals
`ε`	Observable error; may appear late if suppression hides signal recurrence
`ι / Ξ`	Inversion; rises when deletion is framed as safety or restoration
`R`	Restoration capacity; needed to repair what the filter reveals
`K`	Slack / sovereignty; filters should reduce overload without removing agency
`µᵢ`	Meaning integrity; harmed when signals are removed from context or audit
`Φ`	Visible success proxy; may improve when signals disappear while coherence declines
`Θ`	Humility / uncertainty; prevents overconfident deletion
`Ψ`	Field / affected-node feedback required to test filtering effects

3. Core Mechanism

The Filtering Law unfolds when a system must decide how to handle signals that are risky, noisy, harmful, uncertain, high-volume, destabilizing, adversarial, unvalidated, or not yet safe for full coupling.

Coherent filtering pathway

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signal appears
→ signal is classified
→ coupling is attenuated
→ signal is sandboxed if needed
→ trace is preserved
→ affected effects are monitored
→ time validation occurs
→ signal is released, repaired, recoupled, or retired with audit

Incoherent deletion / suppression pathway

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signal appears
→ signal is treated as inconvenient or risky
→ signal is deleted or suppressed
→ audit path disappears
→ feedback loop loses information
→ hidden debt accumulates
→ recurrence returns through another pathway

The core mechanism is:

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filtering reduces unsafe coupling while preserving the conditions for truth, audit, and repair

A filter protects coherence when it controls coupling without destroying visibility.

4. When This Law Applies

This law applies whenever systems moderate, screen, throttle, rank, hide, delete, suppress, quarantine, sandbox, redact, dampen, route, flag, deprioritize, restrict, or delay signals.

It is especially important in:

AI safety and guardrails;
content moderation;
security filtering;
institutional intake;
governance reporting;
medical triage;
biological immune response;
media feeds;
search and ranking;
social platforms;
incident response;
policy enforcement;
evidence handling;
complaint systems;
contract review;
information hygiene;
cultural boundary systems.

The law applies strongly when:

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a system removes a signal from visibility without preserving traceability

or when:

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filtering is used to reduce visible error while preventing audit or repair

Typical domains:

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Domain	Expression
AI systems	refusal, moderation, ranking, or safety filters attenuate signals but must preserve auditability
Security	alerts may be suppressed or deduplicated, but trace must remain available
Institutions	complaints may be routed or triaged, but not erased from repair pathways
Media systems	ranking may attenuate visibility, but opaque suppression creates legitimacy debt
Medicine / biology	immune filtering must distinguish attenuation from total suppression
Governance	sensitive information may be sandboxed or redacted, but deletion destroys accountability
Culture	boundary moderation may reduce harm without erasing dissent or evidence
Economy	risk filters must not hide externalities or burden signals

5. When This Law Does Not Apply

This law should not be used to require unlimited propagation of every signal.

Some signals should be slowed, isolated, sandboxed, redacted, quarantined, rate-limited, or prevented from immediate coupling. Coherent filtering can protect vulnerable nodes, preserve boundary integrity, reduce overload, and prevent adversarial amplification.

This law does not prohibit:

attenuation;
sandboxing;
rate-limiting;
quarantine;
scoped redaction;
temporary suppression with trace;
visibility reduction;
investigation queues;
delayed release;
safety review;
decoupling harmful pathways.

This law does prohibit:

deletion that destroys auditability;
suppression without trace;
hiding signals to avoid responsibility;
reducing visible error by destroying evidence;
making filters invisible and unappealable;
preventing affected-node correction;
using filtering to bypass restoration;
calling erasure “safety” when hidden debt rises.

False-positive cases:

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Case	Why it is not filtering failure
A harmful signal is sandboxed with trace and review	Coupling is reduced while audit remains
A security alert is deduplicated but raw logs remain	Signal is attenuated, not deleted
Sensitive data is redacted with provenance preserved	Scope is controlled without destroying audit
AI refuses unsafe direct output but logs policy path and offers safe alternative	Filtering routes into safer coupling
A complaint is triaged but remains reviewable and appealable	Signal is not suppressed

Important distinction:

Filtering protects coherence by controlling signal coupling. Deletion and suppression damage coherence by destroying signal legibility.

6. Diagnostic Signature

The basic diagnostic signature is:

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classify → attenuate → sandbox → trace → time-validate

A stronger warning signature:

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signal visibility↓
traceability↓
Au↓
recurrence↑
H↑
filter rationale opaque
affected-node feedback blocked
⇒ suppression / deletion risk

Common indicators:

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Diagnostic	Expected movement	Interpretation
`signal visibility`	↓	Signal is being reduced, hidden, or routed
`traceability`	should remain ↑ / stable	Coherent filtering preserves trace
`Au`	↓ under deletion	Auditability collapses if signal path is erased
`FI`	↓ if feedback is corrupted	Filtering may prevent correction
`H`	↑ if suppression occurs	Hidden debt accumulates from unprocessed signal
`BΣ`	↑ or stable if coherent	Filtering should protect boundaries
`Γ`	should be explicit	Signal must be classified before action
`Π`	should be scoped	Attenuation / sandboxing must have boundaries
`Τ`	required	Filtered effects must be time-validated
`ι / Ξ`	↑ under pseudo-safety	Erasure may be framed as safety
`recurrence`	should ↓ after valid filtering	Persistent recurrence means signal was not resolved
`affected-node feedback`	should remain open	Filtered nodes need correction/appeal paths

Additional diagnostics:

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Diagnostic	Use
Filter Traceability	Primary diagnostic for audit-preserving filtering
Attenuation Integrity	Tests whether filtering reduces coupling without erasure
Deletion Risk	Detects audit-destroying removal
Suppression Risk	Detects hidden-debt signal hiding
Effective Auditability	Tests whether filtered signal remains reviewable
Feedback Integrity	Ensures filtering does not corrupt regulation
Signal Integrity	Ensures signal context is preserved
Boundary Integrity	Tests whether filter protects membranes
Hidden Debt	Tracks debt from suppressed signals
Inversion Index	Detects erasure framed as safety
Time Validation	Confirms filter effects over time
Recurrence	Tests whether filtering actually reduced the pattern

7. Failure Pattern

If ignored, this law produces deletion blindness, suppression debt, and pseudo-safety.

General failure pathway:

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signal appears
→ system wants reduced visible disturbance
→ signal is deleted or suppressed
→ visible error decreases
→ auditability falls
→ feedback loses source signal
→ hidden debt accumulates
→ recurrence returns later
→ legitimacy or security shock appears

Common failure modes:

Deletion Blindness — the system loses ability to see what it removed.
Suppression Debt — hidden signals become future repair burden.
Auditability Collapse — evidence path is destroyed.
Feedback Corruption — regulation cannot learn from filtered signals.
Signal Erasure — signals disappear without repair.
Pseudo-Safety — visible risk decreases while hidden debt increases.
Pseudo-Security — security appears improved because alerts or evidence disappear.
Invisible Constraint Amplification — hidden filters shape cognition or action without awareness.
Hidden Debt Accumulation — unresolved signals continue issuing debt.
Misclassification — deletion prevents category correction.
Control-Restoration Confusion — control over visibility is mistaken for repair.
Legitimacy Shock — hidden suppression becomes visible later.

Compact failure signature:

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visibility↓ + traceability↓ + Au↓ + H↑ ⇒ suppression debt

8. Restoration Implications

Restoration requires converting deletion or suppression into traceable attenuation and repair.

The first restoration question is not:

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How do we make the signal disappear?

The first restoration question is:

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How do we reduce unsafe coupling while preserving auditability and repair?

Restoration priorities:

Identify the filtered signal.
Determine whether it was attenuated, sandboxed, suppressed, or deleted.
Restore traceability where possible.
Classify the signal and its risk level.
Preserve source, context, and decision provenance.
Reopen affected-node feedback or appeal paths.
Route valid signals into repair.
Time-validate filtered outcomes.
Track recurrence to detect suppressed debt.
Replace deletion-based filtering with attenuation-based filtering.

Relevant restoration arcs:

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Restoration Arc	Why it applies
Auditability Restoration	Deleted/suppressed signals require trace repair
Boundary Reconstitution	Filtering is boundary operation
Controlled Decoupling	Filtering reduces unsafe coupling without erasure
Origin-Layer Repair	Signal source must be repaired when valid
Restoration Capacity Rebuild	Repair must exist behind the filter
Temporal Validation	Filter effects must be tested over time
Recurrence Reduction	Recurrence reveals suppression or unresolved signal
Basin Supersession	Required when a system depends on deletion to remain stable

Minimal restoration sequence:

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identify signal
→ classify
→ attenuate / sandbox
→ preserve trace
→ restore Au and FI
→ route into repair
→ time-validate
→ reduce recurrence

Temporal validation requirement:

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traceability preserved
Au↑
FI intact
BΣ intact
H↓
recurrence↓
filter rationale reviewable
affected-node feedback available
O stable or rising
filter no longer depends on deletion or suppression

9. Design Rule

A coherent filter must reduce unsafe coupling without destroying auditability.

Operational design requirements:

Classify before filtering.
Prefer attenuation over deletion.
Prefer sandboxing over suppression.
Preserve signal provenance.
Preserve decision trace.
Preserve appeal and correction pathways.
Time-validate filter effects.
Monitor recurrence after filtering.
Distinguish harm reduction from evidence destruction.
Route valid signals into repair.

Avoid:

deleting signals to reduce visible error;
suppressing signals to avoid responsibility;
hiding filter logic from audit;
treating filtered silence as absence;
treating alert suppression as safety;
treating moderation as restoration;
treating refusal as explanation;
treating redaction as deletion;
removing affected-node feedback;
letting filters become invisible belief-shaping infrastructure.

10. Cross-Scale Expressions

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Scale / Layer	Expression of the Law
U0 — Substrate	physical signal is damped without destroying material trace
U1 — Energy / capacity	load is attenuated rather than erased from accounting
U2 — Boundary / interface	primary layer; filter regulates membrane passage
U3 — Process / execution	process routes signals through sandbox/review
U4 — Classification / claim	signal must be classified before filtering action
U5 — Time / delay	filtered effects require time validation
U6 — Field effect	field response reveals whether filtering reduced harm
U7 — Recurrence / memory	recurrence detects suppression or unresolved debt
U8 — Environment / forcing	external signals may need attenuation without denial

11. Examples

Example A — AI Safety Refusal

Scenario:

An AI system refuses unsafe direct output. Coherent filtering classifies the request, attenuates unsafe coupling, offers a safer route, preserves policy trace, and allows appeal or review where appropriate.

Law expression:

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classify → attenuate → sandbox → trace → time-validate

Interpretation:

The refusal is coherent only if it preserves user orientation, auditability, and repair pathways.

Example B — Security Alert Filtering

Scenario:

A SOC tool suppresses duplicate alerts. If raw logs, deduplication logic, and incident trace remain available, this is attenuation. If alerts vanish without trace, auditability collapses.

Law expression:

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alert attenuation with trace ⇒ filtering
alert deletion without trace ⇒ Au↓ + H↑

Interpretation:

Signal reduction is coherent when the evidence path remains intact.

Example C — Institutional Complaint Triage

Scenario:

An institution routes complaints into different queues. Coherent filtering preserves complaint trace, classification rationale, appeal path, and repair route.

Law expression:

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complaint classified / routed / traced ⇒ valid filtering
complaint hidden / closed / erased ⇒ suppression debt

Interpretation:

Triage is filtering only when it remains auditable and repair-capable.

Example D — Media Feed Ranking

Scenario:

A platform reduces visibility of harmful or low-confidence content. Coherent filtering preserves provenance, rationale, recourse, and aggregate audit. Hidden suppression creates trust and legitimacy debt.

Law expression:

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visibility attenuation + trace ⇒ filter
invisible suppression ⇒ H_legitimacy↑

Interpretation:

Ranking systems are filters and must be auditable at the consequence level.

Example E — Medical Signal Management

Scenario:

A symptom is damped while the system tracks cause, recurrence, recovery, and side effects. If the symptom is merely suppressed and no trace or repair path remains, hidden debt rises.

Law expression:

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symptom attenuation + source audit ⇒ coherent filter
symptom deletion from attention ⇒ false recovery risk

Interpretation:

Symptom suppression is not restoration unless the underlying signal is repaired.

Example F — Governance Redaction

Scenario:

Sensitive information is redacted to protect privacy or safety. Coherent redaction preserves provenance, review authority, and accountability. Deletion destroys public auditability.

Law expression:

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redaction with provenance ⇒ scoped filtering
deletion without trace ⇒ auditability debt

Interpretation:

Redaction can be coherent if audit pathways remain.

12. Relationship to Nearby Laws

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Related Law	Relationship
LAW-006 — Time Validation Law	Filters must be validated over time
LAW-009 — U4 / U6 Truth Law	Filtered claims require field validation
LAW-010 — Hidden Debt Accumulation Law	Suppressed signals become hidden debt
LAW-012 — Error Lag Law	Deleted signals may return later as visible error
LAW-013 — Auditability-Debt Law	Deletion destroys auditability
LAW-015 — Suppressed Auditability Debt Law	Designed suppression is a direct violation of coherent filtering
LAW-016 — Inversion Formation Law	Deletion may be framed as safety while coherence falls
LAW-017 — Silent Extraction Law	Signal suppression can silently extract agency or truth
LAW-030 — Slack Sovereignty Law	Filters reduce overload but must preserve agency and refusal
LAW-031 — Observability Collapse Law	Deletion accelerates observability collapse
LAW-036 — Signal Artifact Law	Signals require interpretation before filtering
LAW-037 — Misclassification Law	Bad filtering can follow wrong classification
LAW-038 — Pattern Recognition Discipline Law	Pattern-based filters must not overclaim proof
LAW-039 — Identity-Binding Hard Rule	Low-information identity-binding signals must be blocked from control, not deleted from audit
LAW-041 — Boundary Membrane Law	Filtering is a membrane function
LAW-043 — Safe Coupling Law	Filtering prepares safe or delayed coupling
LAW-048 — Feedback Integrity Law	Filtering must preserve regulatory feedback
LAW-050 — Control-Restoration Separation Law	Filtering controls flow; it does not itself restore
LAW-060 — Interface Legitimacy Law	Interfaces that filter must remain auditable and revocable
LAW-111 — Meaning Audit Law	Meaning-based filtering is not audit-exempt
LAW-114 — Pseudo-Security Law	Alert suppression may produce pseudo-security
LAW-115 — Surveillance–Restoration Law	Sensing must route into restoration, not only suppression
LAW-120 — Security Legibility Law	Security filters require traceability
LAW-121 — AI as Γ-Amplifier Law	AI filtering scales classification and attenuation effects
LAW-123 — AI U4 Truth Discipline Law	AI safety filters must be field-validated
LAW-124 — AI Rule-Stacking Law	Too many opaque filters can outrun auditability
LAW-135 — Guardrail Belief-Sculpting Law	AI filters shape what feels thinkable
LAW-136 — Invisible Constraint Amplification Law	Invisible filters have amplified epistemic power

Aliases folded into this law:

Filtering Law
Filtering Is Attenuation Law
Attenuation Not Deletion Law
Traceable Filtering Law
Audit-Preserving Filtering Law

Deduplication note:

This law should remain the root attenuation-versus-deletion rule. LAW-041 should handle membranes and boundary passage; LAW-048 should handle feedback integrity; AI-specific filtering laws should reference this law while preserving their domain diagnostics.

13. Operator Mapping

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Operator	Role in this law
`Γ`	Classifies the signal before attenuation or sandboxing
`Π`	Applies filtering constraints, attenuation, sandboxing, or routing
`Ξ`	Represents inversion when deletion is framed as safety
`⊗`	Coupling pathway being attenuated or blocked
`ℛ`	Repairs valid signal sources rather than suppressing them
`Τ`	Time-validates filtered outcomes
`Θ`	Maintains uncertainty and prevents overconfident deletion
`Σ`	Defines boundary, scope, and filter membrane
`Ψ`	Incorporates field and affected-node feedback after filtering

Coherent operator sequence:

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Γ(classify) → Π(attenuate) → Σ(sandbox / boundary scope) → Au(trace) → Ψ(feedback) → Τ(time-validate) → ℛ(repair if valid)

Inverted operator sequence:

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signal appears → Π(delete / suppress) → Au↓ → FI↓ → H↑ → Ξ / ι↑ → recurrence returns

14. Machine-Readable Summary

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id: "LAW-040"
name: "Filtering Law"
type: "law"
status: "draft"
family:
  - "Signal and Classification Laws"
summary: "Filtering is attenuation, not deletion."
canonical_statement: "Filtering is attenuation, not deletion."
canonical_form: "classify → attenuate → sandbox → trace → time-validate"
failure_form: "delete / suppress signal ⇒ Au↓ + H↑"
variables:
  primary:
    - "Γ"
    - "Π"
    - "Σ"
    - "Τ"
    - "FI"
    - "Au"
    - "BΣ"
  secondary:
    - "O"
    - "H"
    - "ε"
    - "ι"
    - "R"
    - "K"
    - "µᵢ"
    - "Φ"
    - "Θ"
    - "Ψ"
diagnostics:
  - "Filter Traceability"
  - "Attenuation Integrity"
  - "Deletion Risk"
  - "Suppression Risk"
  - "Effective Auditability"
  - "Feedback Integrity"
  - "Signal Integrity"
  - "Boundary Integrity"
  - "Hidden Debt"
  - "Inversion Index"
  - "Time Validation"
  - "Recurrence"
failure_modes:
  - "Deletion Blindness"
  - "Suppression Debt"
  - "Auditability Collapse"
  - "Feedback Corruption"
  - "Signal Erasure"
  - "Pseudo-Safety"
  - "Pseudo-Security"
  - "Invisible Constraint Amplification"
  - "Hidden Debt Accumulation"
  - "Misclassification"
  - "Control-Restoration Confusion"
  - "Legitimacy Shock"
restoration_arcs:
  - "Auditability Restoration"
  - "Boundary Reconstitution"
  - "Controlled Decoupling"
  - "Origin-Layer Repair"
  - "Restoration Capacity Rebuild"
  - "Temporal Validation"
  - "Recurrence Reduction"
  - "Basin Supersession"
related_laws:
  - "LAW-006"
  - "LAW-009"
  - "LAW-010"
  - "LAW-012"
  - "LAW-013"
  - "LAW-015"
  - "LAW-016"
  - "LAW-017"
  - "LAW-030"
  - "LAW-031"
  - "LAW-036"
  - "LAW-037"
  - "LAW-038"
  - "LAW-039"
  - "LAW-041"
  - "LAW-043"
  - "LAW-048"
  - "LAW-050"
  - "LAW-060"
  - "LAW-111"
  - "LAW-114"
  - "LAW-115"
  - "LAW-120"
  - "LAW-121"
  - "LAW-123"
  - "LAW-124"
  - "LAW-135"
  - "LAW-136"
related_invariants:
  - "INV-001"
  - "INV-004"
operator_sequence:
  coherent:
    - "Γ classify"
    - "Π attenuate"
    - "Σ sandbox / boundary scope"
    - "Au trace"
    - "Ψ feedback"
    - "Τ time-validate"
    - "ℛ repair if valid"
  inverted:
    - "signal appears"
    - "Π delete / suppress"
    - "Au↓"
    - "FI↓"
    - "H↑"
    - "Ξ / ι↑"
    - "recurrence returns"
aliases:
  - "Filtering Law"
  - "Filtering Is Attenuation Law"
  - "Attenuation Not Deletion Law"
  - "Traceable Filtering Law"
  - "Audit-Preserving Filtering Law"
deduplication_note: "Root attenuation-versus-deletion rule. LAW-041 handles membranes and boundary passage; LAW-048 handles feedback integrity; AI-specific filtering laws should reference this law while preserving their domain diagnostics."
source: "content/archive/laws/technical.md"

15. Compact Card Version

LAW-040 — Filtering Law

Filtering is attenuation, not deletion.

Plain meaning:

A coherent filter does not erase signals. It classifies them, reduces unsafe coupling, routes them into bounded spaces, preserves traceability, and validates effects over time.

Canonical form:

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classify → attenuate → sandbox → trace → time-validate

Failure form:

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delete / suppress signal ⇒ Au↓ + H↑

Primary variables:

Γ, Π, Σ, Τ, FI, Au, BΣ, O, H, ι, R, K, µᵢ, Θ, Ψ

Diagnostic signature:

A signal is removed, suppressed, hidden, deprioritized, or filtered while traceability, feedback integrity, affected-node feedback, recurrence monitoring, and auditability decline.

Failure risk:

Deletion blindness, suppression debt, auditability collapse, feedback corruption, signal erasure, pseudo-safety, pseudo-security, invisible constraint amplification, hidden debt accumulation.

Restoration priority:

Replace deletion and suppression with traceable attenuation: classify, attenuate, sandbox, preserve trace, restore auditability and feedback, route valid signals into repair, and time-validate recurrence reduction.

LAW-039 — Identity-Binding Hard Rule

Registry

LAW-041 — Boundary Membrane Law