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Constraint Systems Institute

This archive develops a foundational constraint formalism from a premise taken seriously across quantum gravity and emergent-spacetime research, but pressed here to its full consequence: metricity is not the primitive ground of physics. Before anything can be measured, localized, evolved, or modeled, the admissible structure of determinate instantiation must already be fixed. The corpus follows that prior order outward, treating familiar mathematical and physical descriptions as consequences of constraint, exclusion, and invariant closure.

Guided Research Tours

Ten paths into the research.

Start here / The origin of AASC

Where do I fit in the universe?

AASC began with a personal puzzle: how could one experienced life fit the block universe and branching quantum descriptions? Follow the search for what stays fixed, from Lorentz invariance to the AMetric boundary.

A question about consciousness became a question about anything definite: what must a description preserve?

The big picture / Physics from below

Where the familiar laws come from

Special relativity. General relativity. Quantum dynamics. Matter and interactions.

What must physical reality support before distance and duration can describe it? Explore AASC’s premetric starting point and how a common physical source connects the familiar theories.

An interactive overview connecting the foundations to the research tours.

Four schematic views share a structural foundation: special relativity, general relativity, quantum dynamics, and matter and interactions. Explore what comes before the metric

Gravity-quantum arc / Featured capstone

Premetric Structural Unification

From the AASC Kernel to Einstein-form first-response dynamics and calibrated free-scalar Schrödinger dynamics.

A machine-checked, 49-field Lean composition connects the Kernel and downstream Kernel-faithful machinery through canonical metric licensing to both endpoints, with proved receiver maps and coverage, shared original preparations, and evolution compatibility.

The result covers the declared bounded Einstein–Hilbert response and free-scalar constructions.

Wheeler-DeWitt ten-paper branch

Standard Model / Guided Tour

Standard Model

Follow the completed eleven-paper arc from a common persistence bearer through three generation roots, matter roles, gauge and Higgs responses, to a common physical realization with gravity.

FCGS establishes the rooted fermionic structure; BCRS develops the bosonic response atlas; CSP integrates the structural, classical, and physical source constructions, culminating in the bearer-first reconstruction.

Standard Model persistence-response-realization atlas Explore the Standard Model

The complete eleven-paper arc

Earlier carrier-exhaustion sequence
Earlier support in the same arc

Neutrinos / Guided tour

One carrier. Linked signals.

Explore a proposed neutrino carrier with three light sectors and a heavy sector, and the linked observations it would require.

Follow the arc from oscillation to two completed source-qualified branches. Explore the vectorlike pairing, match the light and heavy response, and follow a possible signal through the detector.

Three light sectors and one heavy sector grouped within a common neutrino carrier. Explore the neutrino carrierReveal the pairing. Follow the detector response. Test the linked signals.
The complete sequence · 19 papers
PCR 1: Target-Fixed Physical Role Necessity for the Realized Neutrino Oscillation Interface PCR 2: Complete Physical Interface of the Neutrino Propagation Role Complex PCR 3: Source-First Exhaustion of the Physical Carrier Universe PCR 4: Simultaneous Physical Constraint Collapse of the Neutrino Carrier Universe PCR 5: Compatible Role-Occupancy Closure for the Neutrino Propagation Role Complex PCR 5A: Standing-Carrier Upper Closure for the Neutrino Propagation Role Complex PCR 5B: Exact Standing-Carrier Stratification of the Neutrino Oscillation Realization Space PCR 5C: Functorial Target Extension of Standing-Carrier Quotients PCR 5D1: Direct Kinematic-Mass Target Extension of the Neutrino Standing-Carrier Space PCR 5D2: Lepton-Number-Violating Target Extension of the Neutrino Standing-Carrier Space PCR 5D3: Heavy-State Active Closure and CLFV Extension of the Neutrino Standing-Carrier Space PCR 5D3.5: Successor Target for Quantitative Active Closure in the Neutrino Standing-Carrier Space PCR 5D4: Cosmological Population and Transport Extension of the Neutrino Standing-Carrier Space PCR 5D5: Symmetry and Charge Extensions of the Neutrino Standing-Carrier Space PCR 5E: Joint Standing-Carrier Closure for the Neutrino Sector PCR 6: Physical Nature and Minimal Identity of the Neutrino Carrier PCR 7: Observable Projection and Experimental Prediction Lock for the Neutrino Carrier PCR 7.5: Structural Stability and Degeneracy Lifting of the Neutrino Heavy Sector PCR 8: A Neutrino Carrier Prediction: Robustness and a Framework for Experimental Testing

Symmetry / Guided tour

What changes. What holds.

Turn the description, or transform the state? Explore why those are different, then change local gauge frames, test anomaly cancellation, and discover which symmetries survive extra physical terms.

The symmetry arc distinguishes domain anchors, redescription and physical action, then carries those distinctions through the Standard Model to its symmetry atlas and exhaustion closure.

same statetwo descriptions
Explore the symmetry arcFour interactions, from a turned frame to a surviving charge.

Black Holes / Guided Tour

Black Holes

What becomes of matter and energy when their connection to the outside is lost? Explore a new physical test of inward braking, then follow the arc to the limit of spacetime and a fresh interior under the completed endpoint conditions.

Nothing crosses the new boundary. The necessary foundations begin anew.

Time Pair

The arrow of time and the physical clock

Why does change have a direction, and what makes something a clock? The time pair separates these questions. The guided tour follows them into WDW 10's three different local clocks: matter, volume, and curvature.

Technically: temporal directionality is treated as standing monotonicity after primitive-arrow routes are exhausted; a physical clock is then typed as a use-relative quotient of certified same-scope clock behavior.

Mind / Agency

Consciousness, qualia, free will, and responsible authorship

What makes an experience yours, and a commitment your own? Follow a color, a memory, and a promise to distinguish what is experienced from what is reported, and what is authored from how it turns out.

Consciousness as a qualified subject-indexed referential interface; qualia as invariant qualitative differences; free will as valid authored commitment, without randomness or causal exemption.

Primary mind and agency papers

Earlier support: Mentis Umbra and the agency paper

Entanglement & quantum measurement

Entanglement & the record

Two distant measurements. One joint standing class. The Bell paper treats the two sides as local faces of a common compatibility object, admitted at the AMetric boundary before distance or clock order can supply standing authority.

Joint standing requires no later communication channel and supplies no hidden local answer sheet. Explore that argument first, then follow local measurement into physical amplification, persistent records and actual-event questions.

Paper repository

One place for each paper.

Browse the current published editions, with earlier versions and exact citations kept inside each paper's page.

Lean 4 Formalisation

Machine-checked projects that make selected structures inspectable.

Formalisation repositories

Lean 4 projects house theorem spines, certificate objects, proof-routing surfaces, and local audit scripts.

Build and audit status

Repository pages should show what builds, what scans cleanly, what axioms are expected, and what remains outside Lean.

Strong but bounded claims

The formal layer can be substantive without claiming a first-principles reconstruction of every downstream domain proof.

GitHub Project Index

Current public Lean and manuscript-linked repositories.

Foundation

Necessity of Admissibility / AMetric Boundary

Lean 4 theorem surface for the AMetric boundary, bivalence, no-repair, no-generator, and unique admissible interior consequence layer.

Open repository AMetric boundary formal surface

Lean Audit

AASC Sunflower Endpoint

Manuscript-faithful Lean A+ audit for the AASC Sunflower endpoint-transfer proof class.

Open repository Updated July 7, 2026

Lean

Standard Model Carrier Exhaustion / Generation Cardinality

AASC ARC extension Lean audit for carrier exhaustion and generation-cardinality layers.

Open repository Updated July 6, 2026

Lean

AASC Hubble Transport

Lean audit archive for downstream Hubble transport closure and endpoint-recognition work.

Open repository Updated June 23, 2026

Lean

AASC Yang-Mills Lean Audit

Dedicated Lean 4 audit archive for the AASC Yang-Mills local-net and Clay-extension endpoint.

Open repository Updated June 12, 2026
More public Lean repositories

Research Archive

A public surface for papers, code, releases, and verification notes.

Manuscripts

Papers and preprints

Downloadable manuscripts, abstracts, source packages, and revision notes for each research thread.

Submit a paper listing

Lean 4

Formalisation projects

Repository links, build targets, theorem inventories, audit scripts, and status summaries.

Add a Lean project

Releases

Evidence bundles

Versioned releases pairing manuscripts with formal artifacts, claim-boundary notes, and reproducibility checks.

Prepare a release

Metadata

Paper index for crawlers

Canonical DOI landing pages with citation metadata, Dublin Core records, and a sitemap route for academic indexing.

Open metadata index
Recommended entry fields Title, abstract, manuscript, repository, build status, audit status, claim boundary.
Review posture Readable for visitors, exact enough for technical inspection.

Next step

Send manuscripts, Lean repositories, or release material for inclusion.

Include the paper title, a short abstract, the current manuscript status, any Lean 4 repository link, and the exact claim boundary you want the archive to preserve.

amos@constraintsystemsinstitute.org