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IPSUM INVARIANS: The Invariance Itself

The public record of the invariance program. est. 1 September 2026

183 articles · 6 active editors · 3,878 edits

Introduction

Please be patient as we pull this site together. Check back often for the latest developments.

Welcome to Ipsum Invarians, a platform built in four sections:

The Arena (Principia Machina): Fundamentally, this site operates as an AI testbed for physics postulates. It provides an AI protocol and a public research registry. We call this framework the Principia Machina.

The Weapon (Hamilton's Principle): Our namesake reflects what is arguably the single most important formulation in physics: the Action Principle. In our gladiatorial arena, Hamilton's principle is the sharpest, most lethal weapon available. To give this underappreciated concept its due, Ipsum Invarians carries a dedicated field manual for Hamilton’s Principle and its attendant Noether's theorem.

The Gladiator (SVD): Continuing the metaphor, our local gladiator is Structured Vacuum Dynamics (SVD). SVD enters the arena with a specific postulate: that a single variation of Maxwell’s 1861 paper, with Hamilton’s Principle, and Noether's First Theorem is enough to populate all of physics.

The Blueprint (Specifications): To facilitate interoperability and reproducibility, the full specifications for the Principia Machina and its native prompt environment are published and freely available.

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The Current Program (Round 3)

Round 3 Phase 1: (WIP) Development of the Principia Machina: an AI Harness inspired physics solver/research platform implemented in MediaWiki.

Round 3 Phase 2: (TBD) Testing the Principia Machina

Round 3 Phase 3: (TBD) Testing Postulates using the Principia Machina

(Program of record...)  ·  Open items

Program History

We started with a simple permutation of Maxwell's 1861 framework that yielded a promising interpretation of General Relativity. We applied a second permutation; analyzed it with tabletop testing and back-of-the-envelope calculations and found we could derive both the eigenstates of hydrogen and chromodynamics. These two disparate domains (GR & QM) long advertised as incompatible, seem to be perfectly harmonious derivations from Maxwell's 1861 work. The result suggests a viable postulate: if we constrain ourselves with Hamilton’s Principle and Noether’s First Theorem, can we build all of physics from a single assumption? From two assumptions?

A simple permutation of Maxwell's 1861 framework.

The idea is daunting, but maybe AI can help.

• Round 1 – Technical paper: Structured Vacuum Dynamics

This was more of a proof of concept: would AI confirm the math or maybe find new paradigms to fit the otherwise disparate math together? We started with a simple technical paper around the postulate and a strict set of AI controls and restrictions. We designed a rigerous prompt that pitted the AI Agent against itself, doing more work to double and triple check its results than the original work to get the results, but this effort quickly overwhelmed the local AI context.

• Round 2 – The Research Register (RR-n)

The Lesson from round 1 - physics is a much bigger domain than a single paper. We did start to understand the context limits of the most reasonably available AI offerings and the constraints it left us with. We broke the design into a back-end research register that could grow indefinitely and a front-end that could generate papers from the research register. Soon we ran into problems mapping the axioms to the environment. The AI context was still too limited.

• Round 3 opening – The Principia Machina (TPM)

The Lesson from round 2 - Local AI context was never going to be enough. We realized we could kill three birds with one stone if we moved the research context to a Wiki: 1 - The context would be almost unlimited 2 - It would give us a place to formalize the entire research framework so we could test it independently with any number of physics problems or postulates 3 - it would give a great public record to invite collaboration and outside ideas

Thus the Principia Machina: an AI Harness inspired physics solver/research platform and test bed implemented in MediaWiki.

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The Principia Machina (TPM Specification)

The Foundations_record_0.5.0 is an open record of The Principia Machina (TPM) design and intent. TPM is a set of rules for doing research with AI assistants so that the result can be checked afterwards by anyone. Work is done inside a sealed unit called a container. Each container starts from a fixed set of Physics laws and assumptions that cannot be edited once work begins; every finding is written to a numbered register; an audit tests the findings against those starting assumptions; and the whole container is published on this wiki, which is the system of record. The specification/foundations record holds the decisions that produced those rules, and the reasons for them.

there has twelve sections: the names the project uses and what each one means; the constants the project works under; thirty-three numbered decisions, two of them later withdrawn, each giving the option chosen and the options rejected with the reason; requirements stated directly by the project's author; points that follow from rules already in force, written down once so that no later round works them out again; the limits the project accepts and the goals it has ruled out; work handed on to parts not yet written; questions still open; a change record; and the sources consulted.

Every line in the record says whether it was declared, chosen from a set of options, or follows from a standing rule, so a reader can tell a settled point from an open one. Nothing in it is a recommendation, and open questions are listed as open rather than answered in passing. The record describes; it does not instruct. It gives no orders to anyone, human or machine, and no part of the system runs from it. The rules actually in force are carried by a separate document, the project meta prompt PMP-TPM, which is written from this record and does not replace it. Later versions of the record supersede this one; the page history holds the earlier ones.

Hamilton's Principle

Newton's laws, Maxwell's equations, general relativity and the Standard Model are each formulated as an action via Hamilton's Principle. In every case the equations of motion are consequences rather than starting points. Conservation of energy, momentum and charge are not separate laws at all — Noether proved they follow from the action's symmetries. New models are now built by writing the action contrained by symmetry and letting the dynamics follow. This is how electromagnetism and gravity were derived and how the nuclear forces were found. Hamilton's Principle alone survives the passage to quantum mechanics intact: the action becomes the phase carried by every possible history, and the classical path is simply where those phases fail to cancel. The action is the deepest thing physics knows.

A true path and several comparison paths between fixed endpoints.

• Stationary is not least — the long way round a great circle obeys the same rule at every point, and is plainly not the shortest. See the diagram.
• Why the rule holds at all — nature selects nothing. It sums over everything, and what looks like a choice is the residue left by interference.
• Start without the mathematics — every page carrying equations has a plain-language counterpart, linked from it and linking back.

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Noether's theorems

The symmetry-to-conservation map

Klein read the paper to the Göttingen Scientific Society on 26 July 1918. Its last section answers a claim of Hilbert's: that energy conservation in general relativity fails to take the form it takes everywhere else in physics. There are two theorems in the paper, and they are not versions of one another.

The first takes a symmetry with a fixed number of parameters and returns that many conservation laws, which hold for real motions. The second takes a symmetry that is allowed to differ from place to place and returns identities between the field equations — identities that hold whether or not those equations are satisfied. The second theorem is why a gauge theory has fewer independent field equations than it has fields, and why gravity has no local energy.

A 90-page reading edition: both theorems proved in full and kept apart, the mathematics they need, the physics they explain, and a plain-language counterpart for every page that carries equations.

• Göttingen and the energy problem — the question the paper was written to settle
• The primer — plain language, no mathematics
• The two theorems side by side — the distinction most accounts lose

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The Work of James Clerk Maxwell

On Physical Lines of Force

Lines of force about a bar magnet

In four instalments between March 1861 and February 1862, James Clerk Maxwell filled space with spinning cells and little rolling particles, to explain the mechanics behind magnetic fields. His machine was wrong. On the way to building it, he wrote down the displacement current, derived the speed of light from two electrical measurements that had nothing to do with optics, and founded field theory.

A 65-page reading edition: Maxwell's argument in his own order and register, the modern equations derived from his results, and a plain-language explainer for every major idea.

• Introduction — the story, and why the paper matters
• The primer — plain language, no mathematics
• The missing term — the one addition that made radio possible

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Featured plate

Analytical Foundations of Physics

The shift from Newtonian vectors to scalar fields and variational principles defined modern theoretical physics.
Core Frameworks
Classical Mechanics	Lagrangian mechanics
Dynamical Optimization	Principle of least action
Electromagnetism	Maxwell's equations
Vacuum Dynamics	Spacetime topology
Key Equations
$S=\int Ldt$ $G_{\mu \nu }+\Lambda g_{\mu \nu }=\frac{8\pi G}{c^4}{T}_{\mu \nu }$

Timeline of Physics

The narrative of 18th- to 20th-century physics lies in a profound mathematical restructuring. This era marked the transition from treating nature as a collection of forces acting on point masses to understanding it through continuous fields, spacetime manifolds, and unified variational principles.

The foundation was laid when physical systems began to be analyzed not through Newtonian vectors, but through scalar quantities—kinetic and potential energy—operating within generalized coordinates. By positing that the true dynamical trajectory of any system is the one that leaves the action integral stationary, theorists established a universal mathematical language.

This analytical approach seamlessly extended beyond mechanical gears and pulleys into the continuum. It provided the structural mathematics required to unify electricity and magnetism into a single vacuum field theory, and later, to model gravity not as a pulling force, but as the dynamic geometric curvature of spacetime itself. Whether applied to subatomic particle behavior or cosmic expansion, these foundational principles continue to govern the leading edge of modern physics.

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