14
◇ part III · meta

The published record, plus the draft/ledger context behind the newest pages

The program has two vintages. The current 4D toy model — nine preprints, from the parent action through 4PN, plus a published moving-throat derivation archive — is the backbone of the reviewed topic pages. Some newer claims also rely on draft/future-note material, especially the moving-throat, atom, and anomaly pages. An earlier round of superfluid-defect toy model papers established the ingredients that carried forward: n = 5, the throat ontology, the initial EM and 1PN derivations. The published records are indexed below.

9 current · PDE archive · 6 priorall Zenodo · open accesssearch ZenodoPDE paper draft in prep
14.1 · reading order

The canonical path through the current program

The 4D papers build a tower. A first reader should take the path below — start with the parent action, add gauge and plasma as specializations, then walk the PN ladder order by order.
01
4D · Action & Projections
4D Toy Model — Action, Projections, and Controlled Brane Limits
start here — parent action
02
4D · 1PN bridge
Deriving Key Post-Newtonian Coefficients from the Unified 4D Toy Model
bridge to optical / PN observables
03
4D · Maxwell
Maxwell from the Unified 4D Toy Model: Localized 5D Gauge Dynamics, Brane Reduction, and KK Corrections
side branch · add gauge
04
4D · Plasma / MHD
Plasma Dynamics from the Unified 4D Toy Model: A 4+1D Alternative to MHD with a Controlled MHD Limit and 4D Interaction Corrections
side branch · MHD limit
05
4D · 1PN full
A Controlled Derivation of the Full First Post-Newtonian Sector from the Unified 4D Toy Model
work out 1PN
06
4D · 2PN conservative
A Controlled Derivation of the Full Conservative Second Post-Newtonian Sector from the Unified 4D Toy Model
… then 2PN conservative
07
4D · 2.5PN conditional
A Conditional Derivation of the Point-Particle 2.5PN Sector from the Unified 4D Toy Model
conditional 2.5PN
08
4D · 3PN conservative
A Full Conservative Derivation of the Two-Body 3PN Sector from the Unified 4D Toy Model
… then 3PN conservative
09
4D · 4PN conditional
A Conditional Full Conservative Derivation of the Two-Body 4PN Sector from the Unified 4D Toy Model
conditional 4PN — same normalization gate
10
4D · PDE ledger
Moving-Throat PDE Derivation Companion Archive Ledger
derivation archive · moving-throat companion
14.2 · current 4D program

The canonical backbone — nine preprints plus one derivation archive

01
4D · Action & Projections
doi: 19449589
4D Toy Model — Action, Projections, and Controlled Brane Limits
The parent action, projection-defined brane observables, exact leakage identities, the longitudinal Poisson-hook identity, and the controlled EM reduction. It is the base file for the current 4D stack.
Parent actionZero-mode reduction
feeds topics010203040511
02
4D · 1PN bridge
doi: 19449653
Deriving Key Post-Newtonian Coefficients from the Unified 4D Toy Model
The bridge from the 4D parent theory to Newtonian, optical, and first-PN observables. This is the carry-forward paper that fixes n = 5 by weak-field optical consistency and assembles the first coefficient ledger.
Bridge paperCoefficient ledger
feeds topics01050810
03
4D · Maxwell
doi: 19449834
Maxwell from the Unified 4D Toy Model: Localized 5D Gauge Dynamics, Brane Reduction, and KK Corrections
Localized 4+1 Maxwell dynamics and the controlled far-field zero-mode reduction to brane Maxwell. Includes Kaluza–Klein/Yukawa/threshold corrections above the zero-mode limit.
Localized MaxwellZero-mode reduction
feeds topics06080911
04
4D · Plasma / MHD
doi: 19449935
Plasma Dynamics from the Unified 4D Toy Model: A 4+1D Alternative to MHD with a Controlled MHD Limit and 4D Interaction Corrections
4+1D plasma dynamics with a controlled MHD limit and explicit hidden-channel corrections/diagnostics beyond the ideal zero-mode reduction.
MHD limit4D corrections
feeds topics07
05
4D · 1PN full
doi: 19450102
A Controlled Derivation of the Full First Post-Newtonian Sector from the Unified 4D Toy Model
The full first post-Newtonian sector derived within the declared closure hierarchy. Recovers GR's 1PN two-body Lagrangian term-by-term.
Full 1PN
feeds topics0510
06
4D · 2PN conservative
doi: 19450284
A Controlled Derivation of the Full Conservative Second Post-Newtonian Sector from the Unified 4D Toy Model
The full conservative 2PN sector within the same declared hierarchy. The first major two-body test at this order in the 4D program.
Full 2PN conservative
feeds topics10
07
4D · 2.5PN conditional
doi: 19492270
A Conditional Derivation of the Point-Particle 2.5PN Sector from the Unified 4D Toy Model
A conditional derivation of the 2.5PN point-particle sector. The surviving branch is narrowed to the STF quadrupole channel; the passive/outgoing normalization remains an open branch-data gate.
Conditional 2.5PNQuadrupole gate
feeds topics10
08
4D · 3PN conservative
doi: 19501724
A Full Conservative Derivation of the Two-Body 3PN Sector from the Unified 4D Toy Model
The full conservative 3PN two-body sector within the declared hierarchy. Matches GR and closes the conservative 3PN bookkeeping.
Full 3PN conservative
feeds topics10
09
4D · 4PN conditional
doi: 19561056
A Conditional Full Conservative Derivation of the Two-Body 4PN Sector from the Unified 4D Toy Model
A conditional 4PN assembly. The local instantaneous sector is separated from the inherited tail bridge, whose remaining gate is the same passive/outgoing quadrupole normalization isolated at 2.5PN.
Conditional 4PNShared normalization gate
feeds topics10
◇ published archive
Moving-Throat PDE Derivation Companion Archive Ledger is the Zenodo derivation companion for the moving-throat PDE ledger and Topic 11 branch-realization machinery.
19699523
◇ in preparation
The full PDE paper — the moving-throat free-boundary framework underpinning Topic 11 — remains a draft/in-prep record. The published archive above is a derivation companion, not a replacement for the final paper.
14.3 · prior work

The superfluid-defect toy model — six foundational preprints

Before the unified 4D program, an earlier round of papers established the pieces that carried forward: the throat ontology, the first EM derivation, spin and vorticity, the N-body dynamics, and a hybrid 1PN calculation that motivated the full PN ladder. These records are the historical backbone, but the current status of public claims should be read from the 4D papers and audit notes above.
Newtonian and 1PN Orbital Dynamics from a Superfluid Defect Toy Model
19449058
Newtonian and 1PN orbital dynamics in the earlier superfluid-defect toy model. Historical precursor, not the current PN proof.
Gravitational Optics and Soliton Geodesics in a Superfluid Defect Toy Model
19449182
Gravitational optics and soliton geodesics. Early light-bending and null-trajectory calculations in the defect picture.
Spin, Vorticity, and N-Body Dynamics in a Superfluid Defect Toy Model
19449261
Spin, vorticity, and N-body dynamics — mechanical scaffolding behind later matter-sector ideas.
Electromagnetic Fields and Charged Defects in a Superfluid Defect Toy Model
19449355
EM fields and charged defects in the pre-4D picture. Antecedent to the current localized Maxwell paper.
Brane-Bulk Throat Ontology for a Superfluid Defect Toy Universe
19449422
The brane-bulk throat ontology. Historical source for throats-as-defects, updated by the current open-conduit audit.
Hybrid 1PN Dynamics and the Acoustic Horizon in a Superfluid Defect Toy Model
19449512
Hybrid 1PN orbital dynamics plus the acoustic-horizon construction. Precursor to the current 1PN full-sector paper.
14.4 · topic → source

Which topic pages lean on which published current 4D paper

Topic 11 additionally leans on the published moving-throat derivation archive and the in-prep PDE framework, which are not part of the nine-preprint matrix below.
topic ↓ paper →
01
Action & Projections
02
1PN bridge
03
Maxwell
04
Plasma / MHD
05
1PN full
06
2PN conservative
07
2.5PN conditional
08
3PN conservative
09
4PN conditional
01The Universe as a Fluid
02Defects
03A Hidden Direction
04Throats
05Gravity as Inflow
06EM as Puncture
07Plasma & MHD
08Light & the Speed Limit
09Atoms, g-factors
10PN Ledger
11Moving-Throat PDE
14.5 · conventions

How to cite back into the library

Every technical-track page carries one or more source: chips that link to the Zenodo record behind the claim on the page. Click any chip on this site to open the canonical preprint. Equation numbers and section references use the preprint's own numbering — if a topic page says (Eq. 3.4, 4D · Action), that means equation 3.4 of the Action, Projections, and Controlled Brane Limits preprint.
◇ a note on this site
Topic pages are written for humans; the preprints are where claims are actually defended. If a topic page says something surprising, open the cited record and check the claim in context. The claim-status badges exist precisely so this check is cheap.
◇ metaPart III pages are single-track. They describe the program itself rather than a topic within it — no plain mirror.
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