Programme Status: Complete and sealed (2026-01-07).
All formal papers archived. All interpretive boundaries explicit.

TL;DR
This repository presents a research programme on structural semantics in recursive systems. It establishes:

• a formal impossibility result proving necessary conditions for exact memory revocation in recursive systems, and
• a domain-agnostic interpretive grammar for recognising bounded recursion patterns.

The work defines structural and semantic limits only. It does not propose algorithms, mechanisms, policies, or physical or universal laws.

This is a research reference and reading hub, not a software project. It documents work on bounded recursion, structural stability, and semantic well-formedness in feedback-driven systems, with particular relevance to agentic AI architectures and governance-facing claims.

This work clarifies when claims about control, reset, forgetting, or containment are structurally well-defined in recursive systems — and when they are not.

In systems where present state feeds back into future behaviour, influence often persists even when intervention is intended to remove it. This research provides tools to:

• distinguish apparent reset from structurally persistent influence,
• recognise when containment must be designed prospectively rather than retrofitted, and
• identify cases where governance or safety claims are ill-posed at the semantic level, prior to questions of feasibility, ethics, or implementation.

• Primary Contribution: The Revocation Barrier
• Supporting Framework: Structural Grammar
• Scaffolding Papers
• How to Read This Work
• Why This Work Exists
• Interpretive vs Formal Components
• Relationship Between Papers
• Relation to Existing Work
• Scope and Non-Claims
• Transparency Notes
• Contact

Why Memory Reset Is Not a Well-Defined Operation in Many Agentic AI Systems

Role: Primary research contribution — formal semantic impossibility result
Status: Complete, standalone paper
Claim type: Necessity-only (proven theorem)

Singh, S. (2026). The Revocation Barrier: Why Memory Reset Is Not a Well-Defined Operation in Many Agentic AI Systems. Zenodo.

This paper proves a necessary-condition impossibility result:

Exact revocation under observational equivalence is semantically undefined unless all cross-episode influence paths are dominated by a single prospectively controllable cut-point.

Key contributions:

• Graph-theoretic formalization of influence propagation
• Mechanically checkable architectural criterion
• Implications for AI governance and system design
• Architecture-agnostic result (applies to any recursive system)

This result:

• does not propose an algorithm or implementation
• does not claim sufficiency (only necessity)
• does not depend on any interpretive framework for validity

Applications: AI memory systems, data governance (GDPR "right to erasure"), system auditing, privacy-preserving architectures.

Signal, Collapse, Containment, and Proportional Delay

Role: Supporting interpretive framework
Status: Canonical grammar definition (fixed for this programme)
Claim type: Descriptive / interpretive (non-causal, non-mechanistic)

Singh, S. (2026). A Structural Grammar for Bounded Recursion: Signal, Collapse, Containment, and Proportional Delay. Zenodo.

Defines the structural grammar:

S → R → C_in → C_out(1 − δᴰ) → σ

This grammar is:

• interpretive rather than explanatory
• architecture-agnostic and domain-neutral
• non-predictive and non-causal

It provides a compact descriptive language for recognising escalation, containment, and stabilisation patterns in recursive systems.

Not a theory of mechanism, optimisation, or physical law.

Prospective Containment in Recursive Systems: A Structural Synthesis of Stability and Revocation

Role: Bridge connecting formal result to interpretive framework
Status: Published synthesis (derivative; no new claims)

Singh, S. (2026). Prospective Containment in Recursive Systems: A Structural Synthesis of Stability and Revocation. Zenodo.

Makes explicit the shared structural constraint:

Both stability and meaningful revocation require prospective containment of influence through explicit, governable boundaries.

Introduces no new primitives, theorems, or claims.

A Companion Guide to Structural Grammar: How to Read Bounded Recursion Without Overreach

Role: Pedagogical introduction
Status: Published guide (no new claims)

Singh, S. (2026). A Companion Guide to Structural Grammar: How to Read Bounded Recursion Without Overreach. Zenodo.

Purpose:

• Explain how to interpret the structural grammar responsibly
• Clarify scope and non-applicability
• Prevent metaphysical or causal overreach
• Safe entry point for non-technical readers

Recommended starting point for new readers.

On the Applicability Limits of a Structural Grammar for Bounded Recursion

Role: Normative scope governance
Status: Published boundary specification (no new claims)

Singh, S. (2026). On the Applicability Limits of a Structural Grammar for Bounded Recursion. Zenodo.

Provides formal boundary specification:

• Defines necessary conditions for applicability
• Identifies classes of non-applicability
• Treats misuse as category error, not limitation
• Stabilises grammar's meaning across applications

The companion guide is pedagogical; this paper is normative.

Stability in Recursive Systems: An Interpretive Clarification

Role: Final interpretive seal
Status: Published clarification (non-contributory)
Programme Status: Complete and sealed (2026-01-08)

Singh, S. (2026). Stability in Recursive Systems: An Interpretive Clarification. Zenodo.

Purpose:

• Makes explicit what the programme characterises
• Clarifies that stability (not survival, optimization, or teleology) is the central object
• Establishes final interpretive boundaries
• Introduces no new claims

Status: Closed.

For researchers interested in the formal result:

1. Start with: The Revocation Barrier (main theorem)
2. Then read: Prospective Containment in Recursive Systems (connection to stability)
3. Optionally: A Structural Grammar for Bounded Recursion (interpretive context)

For readers new to the programme:

1. Start with: A Companion Guide to Structural Grammar (pedagogical introduction)
2. Then read: On the Applicability Limits (scope boundaries)
3. Then read: Prospective Containment in Recursive Systems (structural overview)
4. Then read: The Revocation Barrier (main result)
5. Then read: A Structural Grammar for Bounded Recursion (interpretive framework)

For governance/policy audiences:

1. Focus on: The Revocation Barrier
2. Reference: Stability in Recursive Systems: An Interpretive Clarification

Modern discussions of AI safety, memory, privacy, and control often treat these properties as policy choices, optimisation targets, or ethical preferences. This work begins from a different premise:

In recursive systems, many desirable properties are not matters of choice at all, but consequences of structural constraints.

When a system's present state feeds back into future behaviour, influence does not disappear simply because we wish it to. Claims about "reset," "forgetting," or "clean intervention" are meaningful only if the system's architecture makes them well-defined.

The purpose of this research programme is to clarify:

• What kinds of control are structurally possible
• What kinds of claims are semantically ill-posed
• Where containment must be designed prospectively rather than retrofitted

The papers identify limits before prescriptions. They aim to replace hope-based engineering with structural honesty.

This programme contains two distinct kinds of contributions that operate at different epistemic levels:

The Revocation Barrier is a formal semantics paper with a proven theorem.

It defines revocation as prospective denial of influence under observational equivalence, introduces an influence-graph model, and proves a necessary structural condition.

This result is:

• Model-conditional
• Architecture-agnostic
• Necessity-only (no sufficiency claim)
• Independently valid

The Structural Grammar is a descriptive framework.

It provides compact notation for recognising bounded recursion patterns but:

• Is interpretive rather than explanatory
• Makes no causal or mechanistic claims
• Does not assert necessity or optimality
• Gains credibility from connection to formal result

The two are structurally aligned but serve different functions.

The Revocation Barrier (formal theorem)
↓ proves necessity of prospective dominance
↓
Synthesis (connects result to stability theory)
↓ shows shared structural requirement
↓
Grammar (interpretive framework)
↓ provides descriptive language
↓
Companion Guide (pedagogical)
↓ prevents misuse
↓
Applicability Limits (normative)
↓ defines scope boundaries
↓
Interpretive Clarification (closure)
→ seals programme

Papers are non-overlapping in claims and may be cited independently.

Core dependency: Only the Revocation Barrier stands alone as a complete formal contribution.

This programme does not replace:

• Control theory
• Stability analysis
• Unlearning and privacy theory
• Non-interference semantics
• Safety-engineering practice

Instead, it operates upstream at the level of:

• Semantic well-formedness (when claims are structurally meaningful)
• Structural description (compact notation for bounded recursion)

It clarifies when certain claims — such as "reset" or "revocation" — are even semantically well-defined, before implementation questions arise.

This research:

• Defines structural and semantic limits
• Does not claim physical, biological, or ontological laws
• Does not guarantee safety, alignment, or correctness
• Does not provide implementations or policy prescriptions

Purpose: To clarify what is structurally possible before engineering or governance decisions are made.

The novelty of this work lies in:

• Proving necessary conditions for exact revocation in recursive systems
• Separating formal semantics from interpretive description
• Showing both rely on prospective containment through explicit boundaries

No claims are made about: physical law, universality, sufficiency, or causal mechanism.

This programme emerged from an exploratory phase documented separately. Early manuscripts (2025) are preserved on Zenodo for provenance but are not part of the canonical programme. See Method Note for full developmental history.

AI language models were used as drafting and editorial aids during development.

Their role was limited to:

• Iterative editing and refinement
• Clarification of language and structure
• Stress-testing formulations for ambiguity or overclaiming

All theoretical content, definitions, claims, scope boundaries, and final decisions are the author's own.

No results, proofs, or conceptual frameworks were generated autonomously by AI systems.

Full transparency documentation: See 📄 Method Note — Provenance and AI Use (provided separately for audit purposes).

For formal correspondence, critique, or academic discussion:

Email: shivsingh555@outlook.com

ORCID: 0009-0004-0368-1988