◇ part III · meta

The program's working vocabulary, in one place

Every topic page assumes a small set of terms — throat, inflow, zero mode, closure, the bulk direction $w$ . This is the reference desk for all of them. Terms link back to the topic where they first appear.

5 sections · working entriesnotation table at the bottomsingle-track

◇ 13.1 · geometry & background

The stage and its coordinates

bulk

= 4+1 bulk · ambient

The full 4+1 dimensional space on which the parent action lives. Four spatial dimensions plus time.

→ topic 01

brane / 3-slice

= emergent 3+1

The projection-defined 3+1 subspace where ordinary physics is read off from the 4+1 parent theory.

→ topic 03

bulk direction w

= transverse direction

The extra spatial direction perpendicular to the brane. It is sampled by projection and reduced to a zero mode only in controlled far-field limits.

→ topic 03

inflow

= radial inflow

Projected flow into a positive-mass throat branch. In the controlled Newtonian regime it supplies the effective source used for the gravity analogy.

→ topic 05

throat

= bulk conduit · puncture

A finite-radius opening in the 3-slice connecting to an open brane-bulk conduit. In the effective geometry lift its surface is Σ(X,t) = r − R(Ω,w,t) = 0.

→ topic 04

defect

= vortex · topological defect

A localized nontrivial configuration of the fluid/order-parameter system. Throats are finite brane-bulk defects; vortical circulation is a separate topological sector.

→ topic 02

◇ 13.2 · dynamics & sectors

Equations of motion, sectors, and closures

parent action

= bulk action

The declared 4+1 action for the GNLS / inviscid, irrotational fluid sector, with localized Maxwell added where used. Autonomous wall dynamics require an additional promoted S_Σ action.

→ topic 01, 11

stiff polytrope

= EoS exponent n = 5

The equation of state of the bulk fluid. In the current carry-forward story, n = 5 is fixed by weak-field optical consistency rather than by downstream fitting.

→ topic 01

zero-mode closure

= zero-mode reduction

A controlled reduction in which only the lowest transverse w-mode is retained. Gives a 3+1 effective theory in the stated far-field regime.

→ topic 03

gravity sector

The projected density / velocity sector. It gives exact brane identities first, then a controlled Newtonian regime and the carried PN hierarchy within a declared closure package.

→ topic 05, 10

gauge sector

= EM sector

A localized 4+1 gauge field with profile Z(w). Its far-field zero mode gives a controlled 3+1 Maxwell reduction on the brane.

→ topic 06

matter sector

The parent complex order-parameter sector and its reduced defect / bound-state targets. Atomic precision claims remain partly open in the current source stack.

→ topic 01, 09

mixed sector

= brane-bulk mixed

Interactions between the brane zero mode and off-brane channels such as A_w, J^w, F_μw, E_w, and C_a. Source of finite-profile corrections, outgoing-normalization data, and conditional anomaly packets.

→ topic 06, 09, 10, 11

inviscid

No viscosity term in the parent fluid action. Effective dissipation, when present, belongs to reductions, collisions, leakage/work ledgers, or outgoing ports rather than parent viscosity.

→ topic 01

irrotational

∇×v = 0 except at defects. The fluid velocity is a gradient field in the bulk of the flow.

→ topic 01

◇ 13.3 · claim-status vocabulary

The badges, in formal definitions

Exactformal definition

An equality that follows from the declared action, exact definitions, or exact algebra. No discarded terms, no small-parameter expansion.

example

∂t rho_brane + ∇·j_brane = S_leak (projected continuity with leakage)

falsify

Disagreement indicates an error in the derivation — not the physics.

Within closureformal definition

An equality that follows within a named closure or declared branch. The closure is stated on the page where the claim is made.

example

The carried 1PN / 2PN / 3PN ledger inside the declared closure package.

falsify

Disagreement may indicate the closure is too restrictive at the regime in question.

Controlled reductionformal definition

A controlled reduction: an ansatz that is provably consistent at the order claimed, together with an error estimate.

example

Far-field zero-mode Maxwell reduction with higher w-modes suppressed by the profile gap.

falsify

Disagreement beyond the stated error bar falsifies the ansatz, not the program.

Effective closureformal definition

An effective identity: holds because the dropped terms are parametrically small, with the small parameter identified.

example

The Poisson hook obtained from exact brane identities in the quasi-static weak-field regime.

falsify

Disagreement points to the small parameter being less small than assumed.

Numerically locatedformal definition

Located numerically: no closed-form derivation, but a number plus uncertainty from a specific procedure.

example

A realized stationary branch returning R₀(w) or outgoing DtN data numerically.

falsify

Disagreement beyond stated uncertainty falsifies the numerical method or the closure beneath it.

Openformal definition

Unresolved: the coefficient, sign, or existence is not known. Bounds and expectations may be stated; a value is not.

example

The shared 2.5PN / 4PN outgoing normalization or the g−2 common branch packet.

falsify

Resolution — in either direction — is a result. Disagreement with an expectation is not falsification.

◇ 13.4 · results-ledger terms

Vocabulary that shows up in topic 10

PN / post-Newtonian

Expansion of GR dynamics in powers of v/c. 1PN ≡ (v/c)², 2PN ≡ (v/c)⁴, etc.

→ topic 10

kappa_rho dressing

= density dressing

A gravity-side density/mass dressing used in the Newtonian/PN ladder. kappa_rho = 1 is not electric charge.

→ topic 05, 10

quadrupole formula

= dE/dt|_2.5PN

GW power at leading order. The fluid picture narrows the surviving branch to the STF quadrupole channel, with the coefficient still gated by passive/outgoing normalization.

→ topic 10

\delta_Q

\delta_{\rm tail}

Residual diagnostics for the 2.5PN / 4PN interface:

\delta_Q

is the quadrupole-normalization miss and

\delta_{\rm tail}

is the tail-transport or scattering miss.

→ topic 10

radiation reaction

Self-force on a radiating body. The leading odd sector is isolated at 2.5PN; higher outgoing corrections remain downstream targets.

→ topic 10

ring-down / QNM

= quasi-normal modes

Characteristic oscillation modes of a perturbed throat. A realized moving-throat branch would have to return them; topic 11 does not yet publish a finished spectrum.

→ topic 11

moving-throat PDE

The free-boundary framework for R(Ω,w,t). It is an effective wall/throat closure unless the autonomous throat action S_Σ is promoted and frozen.

→ topic 11

◇ 13.5 · notation

Symbols, in one table

symbol

read as

meaning

first used

\rho

rho

Bulk fluid density.

parent action · topic 01

\rho_\infty

rho-infinity

Asymptotic / vacuum density far from defects.

topic 01

K,\; n

K, n

EoS coefficient K and exponent n. The carried weak-field branch uses n = 5.

topic 01

\psi

psi

Complex parent order parameter. The density is ρ = |ψ|².

topic 01

c

Brane-facing light/signal speed used in reductions. Its material relation is branch-dependent.

topic 08

c_s

c-sub-s

Local sound speed; in the frozen n = 5 EOS, c_s² = (1/m) dP/dρ = 5Kρ⁴/m.

topic 01, 08

w

The bulk direction — the 4th spatial dimension.

topic 03

X^\mu

X-mu

3+1 brane coordinates (t, x, y, z).

topic 03

\Sigma(X,t)

Sigma of X, t

Effective throat-surface variable: zero set of r − R(Ω,w,t).

topic 04, 11

R(\Omega, w, t)

R of Omega, w, t

Throat radius as a function of angle, bulk depth, and time. The central shape variable of the moving-throat framework.

topic 11

v^i

v-i

Bulk fluid velocity.

topic 01, 05

\varphi

varphi

Brane velocity potential in the longitudinal Helmholtz split v_brane = ∇varphi + v_T.

topic 05

\kappa_\rho

kappa-rho

Gravity-side density/mass dressing parameter. kappa_rho = 1 is not electric charge.

topic 05, 10

\eta_Q

eta-Q

Electric charge-orientation branch sign, eta_Q = ±1.

topic 04, 06

q_\star,\;q_{\rm eff}

q-star, q-eff

Microscopic branch charge and observed brane charge after localization normalization, q_eff = q_star / sqrt(Z_int).

topic 06

Z_{\rm int}

Z-int

Localization integral ∫ Z(w) dw controlling the zero-mode charge normalization.

topic 06

\delta_Q,\;\delta_{\rm tail}

delta-Q, delta-tail

Quadrupole-normalization and tail-transport residual diagnostics.

topic 10

\xi

A reduced healing/profile scale in older or auxiliary defect bookkeeping; not the final throat radius.

topic 02, 04

\alpha

alpha

Fine-structure constant. A target observable of the EM localization / mixed sector, with precision matching still branch-sensitive.

topic 06, 09

Q_{jk}

Q-j-k

Mass quadrupole tensor of a source. Appears in the GW power formula.

topic 10

◇ metaPart III pages are single-track. They describe the program itself rather than a topic within it — no plain mirror.

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