Anomalon Research
10 programmes, 95 subcategories, and 388 individually named topic headings, from Pre-Genesis through finite quantum mechanics and Apeiron. These are research directions with source-specific evidence, not a blanket claim of completed results.
Pre-Genesis Research programme
Study the declared starting objects, operations, and assumptions before any derivation is claimed.
The Starting Declaration
The inert inscription
Primitive difference and supplied structure
Presentation is not an admitted carrier
What the starting language assumes
Six Operations That Must Stay Distinct
Mention and supply
Designation and admission
Retention and operation
Which event actually changes state?
Identity Before Interpretation
Tokens and occurrences
Equality as a declared relation
Repeated marks and distinct presentations
What has not yet acquired a meaning
The First Obstruction
An externally posed challenge
Unresolved distinctions
Candidate responses and their costs
Why a response may remain tied
Assumptions and Non-Claims
Imported apparatus versus object-language data
Definitions are not derived necessities
A model is not a physical observation
The boundary of an origin claim
S(n), MSS-N Research programme
Study level-indexed structure, obligations, realizations, and the maps needed to justify passage between descriptions.
Level Structure
The ground stage S(0)
What is admitted at level n?
Obstruction-indexed continuation
A level index is not elapsed time
Carriers and Presentations
Presentation counts versus carrier counts
Restricted and unrestricted lifts
The old-image recovery requirement
Refusal tokens and ground presentations
Obligation Accounting
Generated and discharged obligations
Counter vectors and combination rules
Bounded combination and definedness
What a valid terminal ledger records
Realization and Reflection
A supplied realization of S(n)
Preserving the declared operations
What must reflect back to the source?
A realization cannot authorize its own extension
MSS-N Research Boundaries
The response grammar
Candidate-class dependence
Finite stage certificates
Unresolved bridges between levels
Genesis & Genesis Ongoing Research programme
Keep the sealed derivation, separate readings, continuation histories, and later bridge obligations distinct.
The Sealed Genesis Record
The opaque seed and the blind protocol
Data, forms, instances, rules, and requirements
Supply as a no-change event
State changes through explicit admission
Readings L and F
Two genesis histories
A first separation under each reading
Cost measures and tied minima
What the terminal record actually establishes
Search, Replay, and Refusal
Enumerating a declared response space
Replaying admission histories
Branch equivalence under permitted renaming
Resource bounds and exported frontiers
Observers and Distinctions
Contexts and observable profiles
Indistinguishability versus identity
Separation capacity
A change of observer changes the question
Genesis Ongoing
Independent seeds and continuation histories
Obstruction and answer
Fewest changes under a declared grammar
Counted assertions and two relations
Admission Gates and Institutions
A reached result is not automatically admitted
Local authorization scopes
Acquisition and interpretation boundaries
Second Derivations and Higher Bridges
Stake and the first-demand question
Succession, duration, and engine classes
Finite shadows and higher-structure proposals
Missing reflection and embedding maps
The Genesis Exit Ledger
What remains endogenous-demand open
Fresh supply as a separately declared import
The Genesis-to-WDP bridge obligations
What finite quantum mechanics does not inherit for free
Finite Obstruction Calculus Research programme
Study exact finite obstruction, admissible repair, transport, and the certificates needed to support an exactness claim.
Witnessed Difference Programme
Protected questions and witnesses
Declared presentation, memory, evaluator, and policy
The degree-one window
Which witness class is being compared?
Cochains, Boundaries, and Quotients
Finite chain and cochain data
The composition condition d1 d0 = 0
Exact classes and quotient defects
Closed residuals versus closure failures
Repair Geometry
Allowed correction spaces
Weighted L1 obstruction mass
Attained minima versus infima
Tied repairs and explicit selectors
Exact Certificates
A reconstruction witness
Primal feasibility
A dual bound with the correct norm
Zero duality gap and the exactness claim
Transport and Invariants
Renaming the same finite problem
Which maps preserve the residual?
Boundary transport
Growth that changes the available repairs
Finite Decision Boundaries
What the candidate bound covers
Exact arithmetic and floating-point diagnostics
Counterexamples to stronger claims
Generality requires more than a finite census
Applications and Reference Models
Signed graphs and parity constraints
Constraint systems and incompatible records
Schema and data-migration examples
Which application bridge is actually defined?
Projection Obstruction Research programme
Ask which distinctions and answers survive a supplied projection, and what is required to recover them.
Maps and Lost Distinctions
A supplied observation map
Fibres and indistinguishable inputs
Information discarded by projection
An image label does not recover its preimage
Descent and Recovery
When an answer is constant on fibres
Recovering an answer from a quotient
Uniqueness on the image
The scope of a finite lookup rule
Local Records and Joint Descriptions
Overlapping observation contexts
Incompatible local records
The global-assignment question
Repair, Refinement, and Extension
Repair within the current carrier
Refining the observation
Extending the model
Weakening a question changes the task
Costs and Certificates Under Projection
Projected residuals
Costs on the declared domain
Transporting a feasible correction
A projected success is not automatically a source success
Semantics and Empirical Contact
Declaring a physical readout
Calibration and units
Testing a proposed correspondence
What a projection theorem leaves unobserved
Adaptive Reasoning Research programme
Study support, revision, bounded agency, host verification, and the interfaces of the proposed reasoning systems.
Claims, Supports, and Revisions
Fixed assumptions and retractable hypotheses
Explicit support dependencies
Conflicts and alternative retractions
Cascading deactivation without a truth guarantee
Local Green Global Red (LGGR)
Local acceptance versus joint compatibility
Parity and cycle witnesses
Global checks and their declared scope
Why one local repair can affect another context
Proposal Fidelity Protocol (PFP)
Mine the allowed operations
Derive and encode the candidate
Independent host verification
Bounded repair with preserved failures
Adversarial mutation controls
Source-bound records and replay
Bounded Memory and Agency
A supplied memory horizon
Retained and evicted records
Projection, envelope, and license checks
Refusal with an unchanged state
Authorization and Evidence
Permission is not execution
A receipt is not a theorem
Evidence promotion is a separate operation
Scoped authority and explicit policy inputs
Search and Selection
Retaining tied alternatives
Declared tie-breaking rules
Budgeted exploration
A stopping condition that can return open
Verification and Evaluation
Independent candidate checks
Held-out examples
Mutation rejection and recovery
Reproducible comparisons against a baseline
Anomalon Topological Processing Unit & AutoP Compiler
Proposed topological processing primitives
Typed intermediate representations
Compiler preservation obligations
Hardware realization and missing evidence
Project Codename Woland: Omega Engine
Bounded execution and continuation
Typed state transitions
Provider and budget contracts
Frozen-runtime replay and custody
Which integrations are still proposals?
Reasoning-System Research Limits
A finite host model is not universal intelligence
Metadata is not empirical validation
Runtime success versus a research claim
Failure reports that remain available for review
Mind, Body, Consciousness Research programme
Separate physical mechanisms, behavioral records, formal representations, and interpretations of experience.
The Embodied Observer
A physical substrate and a model of it
Sensing and accessible distinctions
Memory, attention, and action budgets
The environment supplies constraints
Models of Cognition
Inference and model updating
Prediction and control
Support networks and conflict resolution
What a computational model omits
Reports and Experience
First-person reports and public records
Neural correlates versus mechanisms
Behavioral evidence and its limits
Separating experience from its encoding
Structural Proposals
Observer-indexed representations
Proposed information measures
Proposed cohomological descriptions
Why a structural invariant is not itself consciousness
Competing Interpretations
Functional and biological accounts
Workspace and integration accounts
Embodied and extended accounts
Questions that distinguish rival explanations
Identity and Continuity
A system through changing states
Embodiment and substrate changes
The assumptions behind identity claims
Experimental and Ethical Boundaries
What an intervention measures
Confounds and alternative explanations
Consent and cognitive data
Which consciousness bridge remains unproved?
Cognitive Warfare: Actors, Institutions, and the Limits of Superintelligence Research programme
Study actor-specific information, institutional decisions, defensive information integrity, and the exact scope of capability bounds.
Actors and Their Views
Actor-specific observation channels
Unequal access to records
Commitments and incentives
What an actor can and cannot distinguish
Information Integrity
Provenance of a received claim
Distinguishing source identity from truth
Contradictory and incomplete records
Defensive checks against misleading context
Coordination and Disagreement
Locally acceptable but jointly incompatible plans
Common assumptions needed for agreement
Limits of aggregation
Preserving unresolved alternatives
Bounded Intelligence and Control
Channel capacity under stated assumptions
Finite memory and decision budgets
Irreducible uncertainty in a declared model
Why a finite bound is not a universal claim about every intelligence
Defensive Evaluation and Governance
Auditable decision procedures
Red-team findings and remediation records
Human review and escalation boundaries
Measuring harm reduction without invented outcomes
Open Institutional Questions
Trust without automatic authority
Incentive alignment across organizations
Accountable adaptive policies
Evidence needed for stronger capability claims
Theory of Finite Quantum Mechanics Research programme
Study exact finite constructions and their priced assumptions. Topic coverage does not imply a complete derivation of quantum mechanics or closure of the listed open questions.
The Finite-QM Assumption Ledger
The finite exact starting contract
Derived, conditional, imported, and open labels
L1 observer assumptions
What the L1-to-L2 transition still requires
Finite Carriers and State Spaces
Integer and rational models
Gaussian-rational and algebraic extensions
Finite Hilbert-space constructions
Positivity and normalization as explicit requirements
Preparation, Effects, and Probabilities
Prepared states and measurement effects
Effect-additive valuation assumptions
Born-rule representation questions
Quantum-information branches without assumed completion
Contextuality and Bell Scenarios
Classical joint-extension questions
Cabello parity configurations
Mermin–Peres constraints and their exact scope
What a Bell witness rules out under its assumptions
Composition and Local Tomography
Declared tensor-composition rules
Product measurements and local tomography
Rival combining rules
Local-unitary covariance and its hypotheses
Finite Dynamics
Discrete-time evolution rules
Commutators and conserved quantities
Generator ambiguity
What continuous time adds
Symmetry and Wigner-Type Questions
Rays and transition probabilities
The supplied probability-preservation law
Exact similarities and conjugation
When a scale can be removed
Clock, Shift, and Representation Structure
Finite clock and shift operators
Weyl commutation relations
Irreducibility over a stated field
Which scalar and phase structure is imported?
Fermion Sign Problem
Sign Structure and Cancellation
Signed weights and observable cancellations
Switching and representation changes
Positive representations with a declared cost
Instance certificates versus complexity-family claims
Meron
Involutions on a declared configuration set
Pairing and cancellation witnesses
Fixed points and leftover contributions
Which observables and parameters the construction covers
Hubbard
The supplied lattice and interaction model
Protected representations
Symmetry conditions used by a sign argument
Where the stated Hubbard result remains conditional
Sign-Problem Claim Boundaries
A failed universal dichotomy is retained as refuted
A finite witness is not an NP-hardness classification
Parameter families and input encodings
Unclosed general classification questions
Dressing Field Method
Gauge data on a declared graph
Dressing choices and retained residual symmetry
Changes of spanning tree
Which observables the dressing preserves
Limits of the comparison with other gauge descriptions
Mutually Unbiased Bases
Exact bases and projectors
Pairwise unbiasedness conditions
Prime-power constructions and their stated evidence
Tomography with a declared measurement family
Dimension six and unclosed exclusion certificates
Majorana and Stabilizer Structures
Finite parity constraints
Stabilizer and code-space data
Exact schedule and syndrome checks
Distinguishing a finite model from a hardware realization
Finite Gauge and Electroweak Programmes
Finite gauge variables and observables
Finite-QED questions
Electroweak headings with undeveloped source stages
Which continuum or field-theoretic structures are supplied?
Finite QCD and Strong Interactions
Declared finite transfer matrices
Wilson–Dirac structure
Strong-coupling assumptions
Finite-density sign obstructions
A finite gap is not a continuum mass-gap theorem
Finite Topological Models
Discrete topological data
State sums and boundary records
Which invariant survives the allowed moves?
The bridge from an exact model to a physical phase
Finite Quantum-Gravity Questions
Finite geometry and causal order
Discrete constraints and evolution choices
What a small model can establish
The missing continuum correspondence
Causal Quantum Field Theory
Finite causal order
Local observable assignments
Product-model no-signalling results
Which field-theory assumptions are imported?
AdS/CFT and Holographic Comparisons
The proposed dual descriptions
The supplied boundary dictionary
Finite analogues and their limits
A model analogy is not a derivation of the duality
Loop Quantum Gravity Comparisons
Spin-network kinematics
Imported state-space structure
Finite spin-foam questions
The scope of any proposed Genesis bridge
Genesis to Higher Structure
A finite shadow to be constructed
Truncations and path components
Horn-filling obligations
Type-theoretic models and missing soundness maps
Observer Presheaves
A declared measurement cover
Local assignment and probability data
Pushforward and marginalization
Parity holonomy in its finite setting
Support sections versus probabilistic global extensions
Computation and Constructor-Theory Comparisons
Rewriting and computation on a supplied carrier
Fresh-mark supply as an import
Halting and reachability statements with their exact scope
Constructor tasks and proposed reflection bridges
Quantum-computation viability under explicit thresholds
The Continuum Interface
Selecting a scalar field
Choosing a norm or uniformity
Completion of a finite tower
Strong-continuity and continuous-time assumptions
A conditional lift is not a free emergence claim
Implementation, Parity, and Custody
Independent Python, Rust, and Lean roles
Exact certifiers versus numerical diagnostics
Source-bound records and evidence grades
Sibling-package interfaces
Engine custody and unreplayed claims
Apeiron: The Open Atlas of Relations Research programme
Apeiron is the proposed umbrella for investigating relations, context, and representation. An overarching account of what exists, a Hilbert-space realization, or consciousness bridge requires its own definitions and evidence.
The Context Loom
Apeironic contextuality
Which local record families admit a compatible global description?
Education connections: Unit 9, Unit 22, Unit 23, Unit 69.
Local-to-global extension questions
Distinct strengths of contextual obstruction
A proposed Apeironic formal specification
The Hilbert Window
Representations and realizations
Which explicitly defined relational models admit a Hilbert-space realization, and which do not?
Education connections: Unit 5, Unit 9, Unit 69.
Explicit source and target models
Candidate realization maps
Preserved probabilities and observables
Countermodels to an overstrong representation claim
The Boundary Ledger
Obstructions and consistency
Which claimed obstruction is proved, computed on a finite case, or still conjectured?
Education connections: Unit 17, Unit 23, Unit 68.
A named obstruction and its domain
Exact reconstruction and certificate requirements
Finite tests versus general proofs
Recording open and refuted bridges
Hyperuranius
Descriptions without a preferred ambient arena
What relational data and metatheory replace an assumed embedding space?
Education connections: Unit 22, Unit 24, Unit 67, Unit 69.
Relations without preferred coordinates
Descriptions without a chosen embedding arena
The language and metatheory still in use
Consistency and comparison obligations
Omnium
An interoperable library of models
How can models exchange data while preserving their different assumptions?
Education connections: Unit 22, Unit 50, Unit 67.
A library of model contracts
Interoperable representations
Declared translations between models
What does not survive a translation?
Plenitudo
Synthesis with traceable bridges
Which cross-domain correspondences have actual maps and supporting evidence?
Education connections: Unit 25, Unit 49, Unit 66, Unit 68.
Cross-domain correspondences
A bridge with explicit maps and hypotheses
What synthesis leaves unresolved
To Pan
Whole-and-part investigations
When can local descriptions compose, and what prevents that composition?
Education connections: Unit 22, Unit 23, Unit 46, Unit 69.
Whole-and-part descriptions
Composition of local models
Failure of a common global account
Extending the atlas without a final-totality claim
The Observer Relay
Bounded observers and records
What changes when an observer has a declared memory, access policy, and action budget?
Education connections: Unit 45, Unit 53, Unit 55.
Accessible questions and records
Bounded memory and action policies
Transport between observer models
Observer changes without cosmic observer primacy
The Meaning Bridge
Semantics and empirical correspondence
How are formal symbols connected to a specified measurement procedure?
Education connections: Unit 17, Unit 35, Unit 56.
Formal symbols and intended interpretations
Measurement and calibration procedures
Empirical reference versus metadata
Tests that could reject the proposed correspondence
The Experience Question
Consciousness models
Which observations could discriminate a proposed account of experience from its rivals?
Education connections: Unit 45, Unit 54, Unit 57.
A proposed model of experience
Reports, mechanisms, and formal encodings
Rival consciousness explanations
The separate evidence needed for a mind–physics bridge
The Anomalon Workshop
Architecture and verification
Which components run, which claims have proofs, and where do integrations still fail?
Education connections: Unit 19, Unit 53, Unit 65.
A component-level architecture
Interfaces with stated preservation conditions
Implemented, tested, and proposed components
Integration failures that remain visible
The Open Horizon
Unclassified structures and future questions
How can the atlas be extended without pretending to enumerate every possible thing?
Education connections: Unit 61, Unit 67, Unit 68, Unit 69.
New structures outside the current catalogue
Questions that change the model class
A falsifiable next research target
A curriculum that can acquire new stable headings
Evidence and research boundaries
This page completes the named topic hierarchy. A heading is not a claim that its paper, proof, experiment, or implementation is complete. Read source-level evidence for the actual result and its hypotheses.
Keep supplied definitions, proved statements, bounded computations, imported assumptions, empirical records, interpretations, refutations, and open conjectures separate. A local check does not automatically settle a global claim.
Source orientation: the sealed Genesis record and the finite-QM evidence index. The source-stage navigation map covers its 36 declared stages, including stages without developed node records.
Contextuality references: the IBM CHSH example and the Abramsky–Brandenburger framework. These do not establish the proposed Apeiron structure or a consciousness bridge.