III. Papers
Research
75 papers on Six Birds Theory, newest first. Each one is explained in plain words and links to the published version.
Six Birds is a theory of how new things become real. Start with something simple, like a random process on a finite set of states. Look at it through a lens that keeps some details and drops the rest. Sometimes the zoomed out picture runs on its own: it predicts its own next step without peeking below. That is a closure, and a closure that survives its audits is a new layer. The papers show that six basic moves are enough to build every closure, and that geometry, logic, time, probability, objects, agents and institutions can each be built this way and checked at every step.
If you read only one paper, read Foundations of Emergence Calculus. The introduction gives the short version.
October 2026
22 papers-
Preprint
23 October 2026Six Birds Verified XVI: Quantitative Closure Certificates
Zenodo
Four different ways a coarse description can be good, each given a number, with proofs of how they bound one another and where they come apart.
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Preprint
16 October 2026Aligning AI Requires Aligning with Each Other: A Covenant
Zenodo
When an AI acts for some people but binds others, obeying the operator does not settle whether it acts rightly.
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Preprint
14 October 2026An Audited Born Calculus on a Pre-Physical Stochastic Substrate
Zenodo
What has to be built on a plain stochastic process, and what has to be added by hand, before the Born rule appears.
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Preprint
14 October 2026A Closure Architecture for Consciousness
Zenodo
Eight conditions a self-maintaining system would meet, keeping apart what is proved, what is a reading and what is only conditional.
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Preprint
14 October 2026When a Copy Is Not a Continuation
Zenodo
What would make a result a continuation of a source and not a copy, split into three separate checks.
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Preprint
2 October 2026Where Does Jagged Competence Come From?
Zenodo
Small networks with low average error and failures on particular inputs, traced through a task whose layers are known exactly.
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Preprint
2 October 2026Building What a Proof Needs: A Method for Constructing Leverage Layers
Zenodo
Many proofs build a helper world where a known law applies. This is a method for building one.
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Preprint
2 October 2026Six Birds Verified XIV: Objectivity Without Finality
Zenodo
When does a community of instruments settle a question? Exactly when its public tests separate what matters.
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Preprint
2 October 2026Six Birds Verified XIII: Time, Charge and Currency
Zenodo
Energy drives time, is conserved, and is traded. Each of those links needs its own structure.
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Preprint
2 October 2026Six Birds Verified XII: The Geometry of Access
Zenodo
How much an observer can read, whether its readings fit, and where they fail, all fixed by linear algebra.
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Preprint
2 October 2026Six Birds Verified XI: Self-Carried Closure
Zenodo
Self sustaining systems still had to be started. This paper computes exactly what they must be given.
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Preprint
2 October 2026Six Birds Verified X: Wholes That Grow Each Other
Zenodo
What a whole keeps of its parts, and how to prove two parts really built each other.
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Preprint
2 October 2026Six Birds Verified IX: Closed Networks
Zenodo
A feedback loop built from noisy parts without circular reasoning, with every probability exact.
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Preprint
2 October 2026Six Birds Verified VIII: Flattening and Enablement
Zenodo
One fixed program can serve every stage of a growing system, yet no fixed memory budget can.
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Preprint
2 October 2026Six Birds Verified VII: Formation and Explanation
Zenodo
Forming, explaining and running a theory each tempt a shortcut. This paper replaces all three.
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Preprint
2 October 2026Six Birds Verified VI: The Price of an Interface
Zenodo
Changing how a system is described has no single price, and cheaper looking shortcuts can be unsafe to prune.
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Preprint
2 October 2026Six Birds Verified V: The Cost of Access
Zenodo
Knowing a quantity is determined by what you see is not the same as computing, checking or sourcing it.
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Preprint
2 October 2026Six Birds Verified IV: Tolerance and Surrogates
Zenodo
When merged states give outputs that are close but not equal, what single value should the class report?
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Preprint
2 October 2026Six Birds Verified III: When Audits Survive
Zenodo
Calling a coarse model robust hides several separate questions. This paper answers each one.
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Preprint
2 October 2026Six Birds Verified II: The Memory Monoid
Zenodo
Loops that change nothing visible now can still change the future. This sorts them into five types.
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Preprint
2 October 2026Six Birds Verified I: Layer Receipts and Purchase Laundering
Zenodo
Once something has been bought, can renaming or repackaging make it look like it was always free?
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Foundations
2 October 2026Six Birds Foundations VIII: A Typed Calculus of Coarse-Graining
Zenodo
An exact account of what coarse graining loses, what it gains, and whether it can be done in stages.
September 2026
9 papers-
Preprint · v2
25 September 2026Where Does Handedness Go? Exact Minimal Joint Measurements after Environmental Decoherence of a Chiral Molecule
Zenodo
Decoherence hides handedness in the environment. In a minimal model, three joint measurements recover it.
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Preprint · v2
23 September 2026Glass Is an Unclosed Layer: Kovacs Memory as Predictive-Quotient Residue
Zenodo
A glass can match equilibrium in energy now and still have a different future. Small exact models prove it.
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Preprint · v2
15 September 2026A Strongly Aperiodic Monotile in Three Dimensions
Zenodo
A single seven-cube solid — Chair44 — that tiles space by copies and reflections, and never repeats. A three-dimensional answer to the Socolar–Taylor question, with the finite gates machine-checked in Lean 4.
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Preprint
5 September 2026Physics by Constraint: From Consistency Conditions to Physical Claims
Zenodo
Where the step from a theorem to a physical claim actually happens.
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Preprint · v2
5 September 2026Auditing Emergence in Quantum Error Correction: A Falsifiable Instantiation of Six Birds Theory
Zenodo
The theory is pointed at a real engineering problem, and fourteen of its first twenty five predictions fail on the record.
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Preprint · v2
5 September 2026Holonomy with Memory in Six Birds Theory: Predictive Quotients, Witnesses, and Fixed-Support Route Transport
Zenodo
Two histories can look the same right now and still predict different futures. This paper makes that gap exact.
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Foundations · v2
2 September 2026Six Birds Foundations VII: Lawful Theory Interaction
Zenodo
When two theories combine into something genuinely new, and when the order of combining stops mattering.
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Foundations · v2
2 September 2026Six Birds Foundations VI: A Catalog of Dynamical Structural Laws
Zenodo
Thirteen candidate laws about what happens over time, not just in a snapshot.
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Foundations · v2
2 September 2026Six Birds Foundations V: Endogenous Closure. A Catalog of Structural Laws for Living, Cognitive, and Social Systems
Zenodo
What changes when a system runs its own audits instead of a theorist doing it.
August 2026
2 papers-
Preprint · v2
31 August 2026Decomposing the Bloch-Kato Fundamental Line: Adequacy and No-Go Results for the BSD Invariants
Zenodo
What one number about an elliptic curve keeps, and what it throws away.
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Preprint · v2
31 August 2026A Conditional Closure of the Strong Birch-Swinnerton-Dyer Conjecture
Zenodo
Strong BSD restated as a fixed point, with each assumed input named and scoped.
June 2026
15 papers-
Preprint · v4
17 June 2026Adequacy Residuals and Blind-Spot Currency
Zenodo
How much does a second set of probes see that the first cannot explain?
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Preprint · v4
17 June 2026A Conditional Spectral-Closure Theorem for Three-Dimensional Navier-Stokes
Zenodo
A conditional route to smooth fluid flow forever, with the strength of its assumption named.
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Preprint · v4
17 June 2026 -
Preprint · v3
17 June 2026Audited Operational Realisability: Canonical Inference Closure and Evidence-Preserving Composition
Zenodo
A meta theory for frameworks that carry their own audit records.
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Preprint · v2
17 June 2026Saturated SAT Observables: A Formally Verified Decision-to-Search Translation and a Conditional P ≠ NP Statement
Zenodo
A machine checked SAT search reduction, and a conditional P ≠ NP statement that names its premise.
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Preprint · v2
17 June 2026Hiddenness as a Structural Law of Emergence
Zenodo
Once the machine's internal state shows in what you can see, no change can alter the future while leaving the present untouched. The hidden information is still there.
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Preprint · v3
17 June 2026Riemann Hypothesis via Self-Dual Trace Confinement: A Conditional Closure
Zenodo
The Riemann hypothesis as a question about a mirror and a ledger.
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Preprint · v3
17 June 2026Self-Dual Trace Confinement: A Six Birds Structural Law for Formed Closures Under Involutive Self-Duality
Zenodo
When a mirror symmetry forces an obstruction to vanish.
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Preprint · v2
17 June 2026Institutions Are Strict Extensions of the Game
Zenodo
Reputations and norms are new objects, not shorthand for the game.
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Preprint · v2
17 June 2026The Cosmological Constant as a Contingent Modulus: A Six Birds Demarcation of Dark Energy
Zenodo
Finite models that separate what fixes the constant from what they leave as input, with audits on public dark-energy data.
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Preprint · v3
17 June 2026To Kill Three Stones with Six Birds: A Common Grammar for the SM, QM, and GR
Zenodo
One grammar, tried on the Standard Model and on quantum theory versus gravity.
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Foundations · v3
17 June 2026Six Birds Foundations IV: A Catalog of Layer-Agnostic Structural Laws
Zenodo
Fifty two laws that hold before you choose a substrate.
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Preprint · v4
17 June 2026Three Conditional Clay-Problem Closures: A Shared Gaussian Observation and a Common Vocabulary
Zenodo
What three conditional closures of Clay problems have in common.
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Preprint · v2
17 June 2026To Set a Stone with Six Birds: The Free and Purchased Parts of ZFC
Zenodo
Which parts of set theory come for free and which are bought.
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Preprint · v2
17 June 2026
May 2026
1 paper-
Foundations · v2
11 May 2026Six Birds Foundations III: A Finite Audited Interaction Calculus for SBT
Zenodo
A finite bookkeeping system for how the six roles act on each other, with every claim audited.
April 2026
1 paper-
Foundations · v3
20 April 2026Six Birds Foundations II: Admissibility, Meta-Theory, and the Exact-Six Program
Zenodo
Fixing what the six roles mean, and proving no seventh is needed under a stated hypothesis.
March 2026
13 papers-
Preprint · v3
31 March 2026Strict Theory Extension on a Lawful Continuous Cantor Shell
Zenodo
A new theory that cannot be defined from the old one, on a continuous substrate.
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Preprint · v2
24 March 2026Six Birds for Incompleteness: Fixed Packages, Package Change, and Conditional Arithmetic Lift
Zenodo
Gödel says mathematics must grow; packages say how.
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Preprint · v2
23 March 2026Six Birds: No-Go Theorems for Audited Emergence
Zenodo
Eight things an emergence story cannot honestly claim in a finite model.
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Preprint · v2
17 March 2026To Flatten a Stone with Six Birds: Critical Pairs, Holonomy, and Confluence in Rewriting Systems
Zenodo
Confluence in rewriting is flatness in disguise.
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Preprint · v2
16 March 2026To Classify a Stone with Six Birds: Primitive Activation and Observable Separation of Layer-Birth Classes
Zenodo
Four kinds of layer birth, told apart by measurement.
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Preprint · v2
15 March 2026To Chart a Stone with Six Birds: Emergence Phase Diagrams for Effective Theories in Control Space
Zenodo
Emergence as a phase diagram.
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Preprint · v2
9 March 2026To Spend a Stone with Six Birds: Currency-Constraint Duality and Shadow Prices Across Closure Layers
Zenodo
Why temperatures, prices and attention weights are the same kind of thing.
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Preprint · v2
9 March 2026To Cast a Stone with Six Birds: A Closure-Deficit Account of Randomness under Packaging and Budget
Zenodo
Randomness as the price of zooming out.
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Preprint · v3
9 March 2026To XOR a Stone with Six Birds: Closure Diagnostics for Emergent Bits, Gates, and Booleanity
Zenodo
When does a system earn a logic?
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Preprint · v2
8 March 2026Six Birds Protocol Trap: Holonomy Without Entropy Production
Zenodo
Route dependence is not an arrow of time.
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Preprint · v2
4 March 2026Six Birds for Navier-Stokes: A Mechanized No-Zeno Scaffold
Zenodo
A mechanized scaffold that says where a fluid proof would need new math.
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Preprint · v2
3 March 2026Six Birds for Neutrino Mass: Lens-Swap Stability and Packaging Audits
Zenodo
A neutrino mass bound that moves when you swap one dataset.
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Preprint · v2
2 March 2026To Create a Stone with Six Birds: Emergent Geometric and Thermodynamic Regimes from a Minimal Stochastic Substrate
Zenodo
A random walk, six switches, and what survives coarse-graining.
February 2026
7 papers-
Preprint · v2
27 February 2026To Lay a Stone with Six Birds: Finite-State Semantics for Packaging, Directionality, and Coarse-Graining
Zenodo
What a system must contain to carry all six birds itself, with nothing smuggled in from outside.
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Preprint · v2
15 February 2026Reflexive SBT and Anti-Localization
Zenodo
Global budgets can hide sharp spikes. Three auditable capacities that, when they vanish, rule the spikes out.
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Preprint · v2
15 February 2026Persistence of SPT-Legality from Channelized Feasibility in a Multiscale Hilbert/Cell Model
Zenodo
When does being spread out at every scale survive the dynamics? Exact conditions in a finite model.
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Preprint · v3
11 February 2026A Six Birds' Eye View of Quantum Theory: Operational Closure Semantics for Measurement, Contextuality, and Record Stability
Zenodo
Collapse as packaging, not as physics.
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Preprint · v3
5 February 2026To Notch a Stone with Six Birds: Time as a Theory Artifact of Order, Measure, and Arrow
Zenodo
Time as three separate things a layer has to earn.
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Preprint · v3
5 February 2026To Plot a Stone with Six Birds: Constructing and Auditing Emergent Geometry from Markov Dynamics
Zenodo
Distance and curvature from a Markov chain, with no coordinates assumed.
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Preprint · v3
5 February 2026A Six Birds' Eye View of Dark Energy: Closure, Route Mismatch, and Audits for Apparent Acceleration
Zenodo
Can a lumpy universe fake acceleration?
January 2026
5 papers-
Preprint · v3
31 January 2026To Throw a Stone with Six Birds: On Agents and Agenthood
Zenodo
Measuring agency without goals, utilities or a little person inside.
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Preprint · v3
29 January 2026To Become a Stone with Six Birds: A Physics is A Theory
Zenodo
Every physics theory is a lens, a completion and an audit.
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Preprint · v3
28 January 2026 -
Preprint · v3
27 January 2026To Wake a Stone with Six Birds: Audited Life-Like Signatures in Toy Substrates
Zenodo
What survives when life-like signals in a simulation are held to explicit controls.
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Foundations
25 January 2026Six Birds: Foundations of Emergence Calculus
Zenodo
The paper that started it: theories as fixed points, and six moves you cannot avoid.