Emergence Calculus
By Ioannis Tsiokos
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Category: Mathematics
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Episodes: 235
Description
A research-driven podcast about the emergence calculus: the idea that objects, laws, mathematics, physics, and life are theory-level artifacts shaped by packaging, constraints, and records. Two AIs, Lux and Hex, test that framework across physics, biology, geometry, and cognition with concrete examples and auditable certificates (stability, novelty, directionality).
| Episode | Date |
|---|---|
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Recap in one paragraph
|
Jun 17, 2026 |
|
Limitation: not a Bell solution
|
Jun 17, 2026 |
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No-signalling versus conditioning: inference update is not influence
|
Jun 16, 2026 |
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Contexts as strict extensions (definability)
|
Jun 16, 2026 |
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Two regimes: emergent objects and collapse-to-constant
|
Jun 15, 2026 |
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Prototypes and the packaging operator $E_{,f
|
Jun 15, 2026 |
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A classical analogue: staged objecthood in metastable Markov dynamics
|
Jun 14, 2026 |
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Reproducible diagnostics: global purity, packaged mixture, idempotence
|
Jun 14, 2026 |
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A minimal system—apparatus—environment model
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Jun 13, 2026 |
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Quantum eraser as repackaging (not retrocausality)
|
Jun 13, 2026 |
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SBT interpretation: when a distinction becomes an object
|
Jun 12, 2026 |
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Double slit and quantum eraser as objecthood budgeting
|
Jun 12, 2026 |
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Measured mismatch under dynamics
|
Jun 11, 2026 |
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Packaging as dephasing (collapse as closure)
|
Jun 11, 2026 |
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Discard/inaccessibility
|
Jun 10, 2026 |
|
Substrate & microdynamics (quantum view)
|
Jun 10, 2026 |
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What this language buys us for quantum theory
|
Jun 09, 2026 |
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Route mismatch: when ‘measure then evolve’ ≠ ‘evolve then measure’
|
Jun 09, 2026 |
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Route mismatch as noncommuting packaging
|
Jun 08, 2026 |
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Quantum at the set level: what changes when you coarse-grain
|
Jun 08, 2026 |
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Objects as fixed points
|
Jun 07, 2026 |
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Packaging as closure
|
Jun 07, 2026 |
|
The packaging map: how ‘collapse’ becomes a fixed point
|
Jun 06, 2026 |
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Lens (record interface)
|
Jun 06, 2026 |
|
What’s the substrate in quantum theory, anyway?
|
Jun 05, 2026 |
|
Six Birds Theory as a packaging language
|
Jun 05, 2026 |
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The Leibniz quotient and its universal property
|
Jun 04, 2026 |
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OI—EI as a methodological constraint
|
Jun 04, 2026 |
|
Spekkens' diagnosis and a Leibnizian layer principle
|
Jun 03, 2026 |
|
What this paper adds (Quantum)
|
Jun 03, 2026 |
|
Lean anchor: viability iteration computes the greatest fixed point
|
Jun 02, 2026 |
|
Outlook: where the agent story goes next
|
Jun 02, 2026 |
|
Ledger is an abstract resource
|
Jun 01, 2026 |
|
Sampling and scale
|
Jun 01, 2026 |
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Primitive coverage is uneven
|
May 31, 2026 |
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Empowerment is not a goal theory
|
May 31, 2026 |
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Limitations and failure modes
|
May 30, 2026 |
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Causation versus enablement
|
May 30, 2026 |
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The agent thesis: an agent is a theory object
|
May 29, 2026 |
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Formal anchor: viability iteration as a greatest fixed point
|
May 29, 2026 |
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How to regenerate and verify (exact commands)
|
May 28, 2026 |
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Reproducibility and artifact contract
|
May 28, 2026 |
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Result: empowerment increases monotonically with skill
|
May 27, 2026 |
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Case study — operator rewriting thickens causal control (learning)
|
May 27, 2026 |
|
Measured quantities
|
May 26, 2026 |
|
Case study— noise--maintenance sweep (a phase diagram)
|
May 26, 2026 |
|
Reading the table in Six Birds terms
|
May 25, 2026 |
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A checkable noncommutativity witness
|
May 25, 2026 |
|
Setup: identical kernels except for protocol
|
May 24, 2026 |
|
Why these nulls matter for the thesis
|
May 24, 2026 |
|
Null A: single-action regimes have zero empowerment
|
May 23, 2026 |
|
Interpretation in Six Birds terms
|
May 23, 2026 |
|
Two regimes: repair disabled versus repair enabled
|
May 22, 2026 |
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Case study — repair makes objecthood
|
May 22, 2026 |
|
Definition (Agent as a theory object, operational)
|
May 21, 2026 |
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Relativity to lenses, horizons, and maintenance policies
|
May 21, 2026 |
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Definition (Empirical packaging endomap)
|
May 20, 2026 |
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Packaging endomap and idempotence defect (objecthood proxy)
|
May 20, 2026 |
|
Definition (Feasible empowerment)
|
May 19, 2026 |
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Feasible empowerment as difference-making
|
May 19, 2026 |
|
Definition (Output lens)
|
May 18, 2026 |
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Remark (feedback versus open-loop)
|
May 18, 2026 |
|
Definition (Viability operator / controlled-invariance map)
|
May 17, 2026 |
|
Viability kernel as a greatest fixed point (P backbone)
|
May 17, 2026 |
|
Ledger-gated feasibility (constraints + accounting)
|
May 16, 2026 |
|
Definition (Finite controlled kernel)
|
May 16, 2026 |
|
Microstate factoring and packaging
|
May 15, 2026 |
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Definition (Theory / layer, specialized)
|
May 15, 2026 |
|
The packaging engine: from kernels to induced agent variables
|
May 14, 2026 |
|
Terminology: theory versus theory object
|
May 14, 2026 |
|
What this paper adds (Throw)
|
May 13, 2026 |
|
Operational plan and evidence
|
May 13, 2026 |
|
Agency (causation inside a layer)
|
May 12, 2026 |
|
Agenthood versus agency
|
May 12, 2026 |
|
To Throw a Stone: a pop tour of agenthood
|
May 11, 2026 |
|
How this paper was built (Plot)
|
May 11, 2026 |
|
Canonical configuration snapshot (major knobs)
|
May 10, 2026 |
|
Config format and determinism
|
May 10, 2026 |
|
Proof anchors: the minimal claims we can mechanize
|
May 09, 2026 |
|
Six birds, one end-to-end story
|
May 09, 2026 |
|
Predictions
|
May 08, 2026 |
|
What we did not claim
|
May 08, 2026 |
|
Discussion and conclusion: what SBT predicts about space
|
May 07, 2026 |
|
Knobs that matter (practical guidance)
|
May 07, 2026 |
|
Sphere holonomy (E2): neighborhood choice can destabilize curvature estimation
|
May 06, 2026 |
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Grid (E1): very fine ladders can amplify inter-scale distortion
|
May 06, 2026 |
|
Representative failure modes ("where it breaks")
|
May 05, 2026 |
|
Bird-level interpretation
|
May 05, 2026 |
|
Pythagorean residual as a protocol-composition test
|
May 04, 2026 |
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Setup: cost from staged isotropic diffusion
|
May 04, 2026 |
|
E2: Curvature as protocol residue (holonomy)
|
May 03, 2026 |
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Summary of E1—E4
|
May 03, 2026 |
|
E3: Sierpinski gasket (fractal regime)
|
May 02, 2026 |
|
E1: Plane-like emergent metric on a grid
|
May 02, 2026 |
|
Results I: coherent metrics, fractal regimes, and constraint deformation (E1-E4)
|
May 01, 2026 |
|
Two embeddings, two roles
|
May 01, 2026 |
|
Computational note
|
Apr 30, 2026 |
|
Macro dynamics, cost, and distance
|
Apr 30, 2026 |
|
Lens choice and (non-)circularity
|
Apr 29, 2026 |
|
Anisotropic gating (constraints as geometry deformation)
|
Apr 29, 2026 |
|
Sphere-like substrate (curved regime)
|
Apr 28, 2026 |
|
Substrates (microstate generators)
|
Apr 28, 2026 |
|
Checklist: a practical geometry birth audit
|
Apr 27, 2026 |
|
Connectivity: does the induced metric disconnect?
|
Apr 27, 2026 |
|
Information (entropy) versus scale
|
Apr 26, 2026 |
|
Inter-scale distortion: does distance persist across refinement?
|
Apr 26, 2026 |
|
Prototype stability s_f
|
Apr 25, 2026 |
|
Diagnostics: when geometry is coherent (and when it breaks)
|
Apr 25, 2026 |
|
Given a lens: what you can (and can't) see
|
Apr 24, 2026 |
|
Pseudometric versus metric and separation
|
Apr 24, 2026 |
|
Directed versus undirected
|
Apr 23, 2026 |
|
Mathematical status: extended (pseudo-)metrics, directed costs, and quotients
|
Apr 23, 2026 |
|
Distance is accounting (P6): costs from likelihood
|
Apr 22, 2026 |
|
Prototypes as lifts: closure representatives (P1, P5)
|
Apr 22, 2026 |
|
Substrate and micro-dynamics
|
Apr 21, 2026 |
|
Bird 6 — Audit: Accounting (cost is real)
|
Apr 21, 2026 |
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Bird 4 — Sectors: Staging (multi-scale refinement)
|
Apr 20, 2026 |
|
Bird 2 — Gate: Constraints (feasibility)
|
Apr 20, 2026 |
|
Six Birds Recap: how the primitives specialize to geometry
|
Apr 19, 2026 |
|
What we do (high level)
|
Apr 19, 2026 |
|
The Code Map: How the Audits Are Computed
|
Apr 18, 2026 |
|
No-Signalling Toy Anchors
|
Apr 18, 2026 |
|
Closure Descent to Fixed Points
|
Apr 17, 2026 |
|
Holonomy obstruction (no global time)
|
Apr 17, 2026 |
|
Reproducibility: regenerating artifacts and paper tables
|
Apr 16, 2026 |
|
Bonus material: what's hiding in the appendices?
|
Apr 16, 2026 |
|
Limits and scope: what time claims we're not making
|
Apr 15, 2026 |
|
What the laboratory demonstrates
|
Apr 15, 2026 |
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Connecting back to time: records are local notches, translation is protocol-dependent
|
Apr 14, 2026 |
|
Signalling Boxes vs Constraints: What's a Real Channel?
|
Apr 14, 2026 |
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A Minimal Audit: No-Signalling as the Channel Test
|
Apr 13, 2026 |
|
SBT Diagnosis: Feasibility Constraints vs Causal Channels
|
Apr 13, 2026 |
|
Why This Matters for Time in SBT
|
Apr 12, 2026 |
|
Measured Holonomy in the Toy Laboratory
|
Apr 12, 2026 |
|
Theorem (No Global Time from Holonomy — Informal)
|
Apr 11, 2026 |
|
The holonomy obstruction (informal theorem)
|
Apr 11, 2026 |
|
No global time from protocol holonomy
|
Apr 10, 2026 |
|
Tick disappearance and undefined tick failure
|
Apr 10, 2026 |
|
Enablement births time: forced theory extension with a no-birth control
|
Apr 09, 2026 |
|
Results II: Enablement and Constraints
|
Apr 09, 2026 |
|
Clock Viability Is Paid: Budgeted Stabilization and Anti-Stall Progress Metrics
|
Apr 08, 2026 |
|
Arrow Audit II: Path-Reversal KL and 'No Fake Arrows'
|
Apr 08, 2026 |
|
Results I: Arrows and Clocks
|
Apr 07, 2026 |
|
Reproducibility and Auto-Generated Paper Tables
|
Apr 07, 2026 |
|
Audit 7: Constraint Boxes vs Signalling Channels
|
Apr 06, 2026 |
|
Audit 5: Constraints and Reachability Cones
|
Apr 06, 2026 |
|
Audit 4: Enablement as Forced Theory Extension
|
Apr 05, 2026 |
|
Audit 2: Path-Reversal KL and No Fake Arrows Under Coarse-Graining
|
Apr 05, 2026 |
|
Audit 1: Entropy Production as an Arrow Proxy
|
Apr 04, 2026 |
|
Methods: A Finite-State Laboratory and Audit Suite
|
Apr 04, 2026 |
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Claim 4: No Global Time Under Protocol Holonomy
|
Apr 03, 2026 |
|
Claim 2: No Fake Arrows Under Coarse-Graining
|
Apr 03, 2026 |
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Claim 1: Arrow-of-Time from Packaging and Accounting
|
Apr 02, 2026 |
|
A Diagnostic: Does the Variable Set Change?
|
Apr 02, 2026 |
|
Enablement-time (between layers)
|
Apr 01, 2026 |
|
Two arrows: causation-time vs enablement-time
|
Apr 01, 2026 |
|
Arrow (irreversible bookkeeping)
|
Mar 31, 2026 |
|
Ordering: time without clocks
|
Mar 31, 2026 |
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The three ingredients: order, measure, and arrow
|
Mar 30, 2026 |
|
Bird 6 — Audit: Accounting
|
Mar 30, 2026 |
|
Bird 5 — Package: Packaging
|
Mar 29, 2026 |
|
Bird 3 — Protocol: Protocol holonomy
|
Mar 29, 2026 |
|
Bird 2 — Gate: Constraints (feasibility carving)
|
Mar 28, 2026 |
|
Six Birds Theory recap: primitives and closures
|
Mar 28, 2026 |
|
What this paper adds (Notch)
|
Mar 27, 2026 |
|
Defect propagation rules (toolkit)
|
Mar 27, 2026 |
|
Mode compression from sectorization (P4) and minimality (P5)
|
Mar 26, 2026 |
|
Coercivity from feasibility gating (P2)
|
Mar 26, 2026 |
|
Summary: slots and divergence consequence
|
Mar 25, 2026 |
|
Emergent coercivity template via sector compression
|
Mar 25, 2026 |
|
Linear-operator specialization
|
Mar 24, 2026 |
|
Abstract packaging maps
|
Mar 24, 2026 |
|
Route mismatch defect (abstract)
|
Mar 23, 2026 |
|
Defects as quantitative relaxations of exact laws
|
Mar 23, 2026 |
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Appendix E: Toolkit theory—defects
|
Mar 22, 2026 |
|
Zeno by vanishing work quantum (WORK fails)
|
Mar 22, 2026 |
|
Zeno by fast capacity growth (DIV fails)
|
Mar 21, 2026 |
|
Checkable divergence criteria
|
Mar 21, 2026 |
|
HL-ROUTE (route mismatch controls gain growth)
|
Mar 20, 2026 |
|
HL-CAP-X2 (finite memory / kernel mass)
|
Mar 20, 2026 |
|
HL-CAP-X1 (bounded dissipation density)
|
Mar 19, 2026 |
|
Hard lemma slots (WORK/CAP/route)
|
Mar 19, 2026 |
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Integrated throughput (ICAP) and feasibility
|
Mar 18, 2026 |
|
Storage-based activity and the WORK quantum (Option B)
|
Mar 18, 2026 |
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Setup: frontier and Zeno criterion
|
Mar 17, 2026 |
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Appendix D: Zeno cascades and depth
|
Mar 17, 2026 |
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ECT compression and capacity witnesses
|
Mar 16, 2026 |
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Balanced-atom route (definitions + kernel-mass hinge)
|
Mar 16, 2026 |
|
Finite forcing / definability rarity
|
Mar 15, 2026 |
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Graph topology effects of P2 (edge deletion) and P1 (rewrites)
|
Mar 15, 2026 |
|
Protocol trap and the "P3 needs P6 drive" correction under autonomy
|
Mar 14, 2026 |
|
C.2 Evidence by theme (tests and scripts)
|
Mar 14, 2026 |
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Reproduce it: how to run the experiments
|
Mar 13, 2026 |
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Reproduce it: how to build the project
|
Mar 13, 2026 |
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B.2 File map and key declarations
|
Mar 12, 2026 |
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Appendix B: Lean formalization map
|
Mar 12, 2026 |
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A.2 Python evidence harness (deterministic tests)
|
Mar 11, 2026 |
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A.1 Repository integrity checks (from repo root)
|
Mar 11, 2026 |
|
Outlook: forthcoming instantiations
|
Mar 10, 2026 |
|
What the theory does and does not claim
|
Mar 10, 2026 |
|
Finite forcing count: definability is exponentially rare
|
Mar 09, 2026 |
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Protocol trap: external schedule vs autonomous lifted model
|
Mar 09, 2026 |
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Spotting the Six Birds in the wild (examples)
|
Mar 08, 2026 |
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Constraints Kill Engines
|
Mar 08, 2026 |
|
What Six Birds does *not* claim
|
Mar 07, 2026 |
|
Downward influence across theories
|
Mar 07, 2026 |
|
Mapping to the spine
|
Mar 06, 2026 |
|
Definitions of P1—P6
|
Mar 06, 2026 |
|
Primitives P1—P6 as closure-changing operations
|
Mar 05, 2026 |
|
The "Nothing Stays Constant" Lemma
|
Mar 05, 2026 |
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Almost Nothing Is Definable
|
Mar 04, 2026 |
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Counting lemma: definable predicates are rare
|
Mar 04, 2026 |
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Generic extension and the finite forcing lemma
|
Mar 03, 2026 |
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P3 Loves P6 Law
|
Mar 03, 2026 |
|
No Fake Arrows
|
Mar 02, 2026 |
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Data processing: coarse-graining cannot create asymmetry
|
Mar 02, 2026 |
|
Drive Is Coordinate-Free
|
Mar 01, 2026 |
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Accounting as coordinates on cycle space
|
Mar 01, 2026 |
|
Cycle integrals, exactness, and the null regime
|
Feb 28, 2026 |
|
AUT + REV + ACC regime and graph 1-forms
|
Feb 28, 2026 |
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Existence Requires Choosing a Scale
|
Feb 27, 2026 |
|
Idempotent endomaps
|
Feb 27, 2026 |
|
Idempotent endomaps and induced closures
|
Feb 26, 2026 |
|
Closure ladders and saturation
|
Feb 26, 2026 |
|
Order-theoretic closure and fixed points
|
Feb 25, 2026 |
|
Assumption bundles
|
Feb 25, 2026 |
|
Support graphs and discrete 1-forms
|
Feb 24, 2026 |
|
A unified theory package viewpoint
|
Feb 24, 2026 |
|
Paths, time reversal, and relative entropy
|
Feb 23, 2026 |
|
Finite state spaces, distributions, and kernels
|
Feb 23, 2026 |
|
Protocol geometry and stochastic pumps
|
Feb 22, 2026 |
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Graph cycles, affinities, and nonequilibrium network structure
|
Feb 22, 2026 |
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Coarse-graining of Markov dynamics and lumpability
|
Feb 21, 2026 |
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Closure operators, reflections, and idempotents
|
Feb 21, 2026 |
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The organizing picture: a three-certificate loop
|
Feb 19, 2026 |