TauLib · API Book VI

TauLib.BookVI.CosmicLife.GalaxyBasin

TauLib.BookVI.CosmicLife.GalaxyBasin

Galaxy basins: galaxies as Life basins anchored by SMBHs.

Registry Cross-References

  • [VI.D62] Life Basin — LifeBasin

  • [VI.D63] Carrier Ladder — CarrierLadder

  • [VI.D64] Basin Predicate — BasinPredicate

  • [VI.T33] Galaxy–SMBH Anchor Lemma — anchor_lemma

  • [VI.L12] Basin Fusion via SMBH Merger — basin_fusion_lemma

Ground Truth Sources

  • Book VI Chapter 47 (2nd Edition): Galaxies as Life Basins

Tau.BookVI.GalaxyBasin.LifeBasin

source structure Tau.BookVI.GalaxyBasin.LifeBasin :Type

[VI.D62] Life Basin: spatial region anchored by a central carrier. Triple (B, C_anc, F) where B is basin region, C_anc is anchor, F is carrier family. Boundary at virial radius.

  • grav_bound : Bool Basin region is gravitationally bound.

  • anchor_alive : Bool Anchor carrier satisfies Distinction + SelfDesc.

  • has_carrier_family : Bool Carrier family: collection of all carriers in basin.

  • virial_boundary : Bool Basin boundary = virial radius.

Instances For

Tau.BookVI.GalaxyBasin.instReprLifeBasin

source instance Tau.BookVI.GalaxyBasin.instReprLifeBasin :Repr LifeBasin

Equations

  • Tau.BookVI.GalaxyBasin.instReprLifeBasin = { reprPrec := Tau.BookVI.GalaxyBasin.instReprLifeBasin.repr }

Tau.BookVI.GalaxyBasin.instReprLifeBasin.repr

source def Tau.BookVI.GalaxyBasin.instReprLifeBasin.repr :LifeBasin → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.GalaxyBasin.galaxy_basin

source def Tau.BookVI.GalaxyBasin.galaxy_basin :LifeBasin

Equations

  • Tau.BookVI.GalaxyBasin.galaxy_basin = { } Instances For

Tau.BookVI.GalaxyBasin.CarrierLadder

source structure Tau.BookVI.GalaxyBasin.CarrierLadder :Type

[VI.D63] Carrier Ladder: 7-level hierarchy from molecules to galaxies. X_gal[0..6] = molecular, cellular, organismal, ecosystemic, planetary, stellar, galactic. Constraints flow downward, realization flows upward.

  • level_count : ℕ Number of hierarchy levels.

  • count_eq : self.level_count = 7 Exactly 7 levels (0 through 6).

  • functorial : Bool Constraints compose functorially.

Instances For

Tau.BookVI.GalaxyBasin.instReprCarrierLadder

source instance Tau.BookVI.GalaxyBasin.instReprCarrierLadder :Repr CarrierLadder

Equations

  • Tau.BookVI.GalaxyBasin.instReprCarrierLadder = { reprPrec := Tau.BookVI.GalaxyBasin.instReprCarrierLadder.repr }

Tau.BookVI.GalaxyBasin.instReprCarrierLadder.repr

source def Tau.BookVI.GalaxyBasin.instReprCarrierLadder.repr :CarrierLadder → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.GalaxyBasin.carrier_ladder

source def Tau.BookVI.GalaxyBasin.carrier_ladder :CarrierLadder

Equations

  • Tau.BookVI.GalaxyBasin.carrier_ladder = { level_count := 7, count_eq := Tau.BookVI.GalaxyBasin.carrier_ladder._proof_1 } Instances For

Tau.BookVI.GalaxyBasin.ladder_level_names

source def Tau.BookVI.GalaxyBasin.ladder_level_names :List String

Carrier ladder names for reference. Equations

  • Tau.BookVI.GalaxyBasin.ladder_level_names = [“molecular”, “cellular”, “organismal”, “ecosystemic”, “planetary”, “stellar”, “galactic”] Instances For

Tau.BookVI.GalaxyBasin.ladder_has_7_levels

source theorem Tau.BookVI.GalaxyBasin.ladder_has_7_levels :carrier_ladder.level_count = 7 ∧ ladder_level_names.length = 7

Tau.BookVI.GalaxyBasin.BasinPredicate

source structure Tau.BookVI.GalaxyBasin.BasinPredicate :Type

[VI.D64] Basin Predicate: admissibility for a Life basin. Four conditions: (i) anchor alive, (ii) gravitational dominance, (iii) basin coherence (virialized), (iv) carrier support.

  • condition_count : ℕ Number of admissibility conditions.

  • count_eq : self.condition_count = 4 Exactly 4 conditions.

  • anchor_alive : Bool Anchor satisfies Distinction + SelfDesc.

  • grav_dominant : Bool Anchor is gravitationally dominant.

  • virialized : Bool Basin is virialized (2K + U ≤ 0).

  • carrier_support : Bool At least one carrier at level n ≤ 5.

Instances For

Tau.BookVI.GalaxyBasin.instReprBasinPredicate

source instance Tau.BookVI.GalaxyBasin.instReprBasinPredicate :Repr BasinPredicate

Equations

  • Tau.BookVI.GalaxyBasin.instReprBasinPredicate = { reprPrec := Tau.BookVI.GalaxyBasin.instReprBasinPredicate.repr }

Tau.BookVI.GalaxyBasin.instReprBasinPredicate.repr

source def Tau.BookVI.GalaxyBasin.instReprBasinPredicate.repr :BasinPredicate → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.GalaxyBasin.basin_pred

source def Tau.BookVI.GalaxyBasin.basin_pred :BasinPredicate

Equations

  • Tau.BookVI.GalaxyBasin.basin_pred = { condition_count := 4, count_eq := Tau.BookVI.GalaxyBasin.basin_pred._proof_1 } Instances For

Tau.BookVI.GalaxyBasin.AnchorLemma

source structure Tau.BookVI.GalaxyBasin.AnchorLemma :Type

[VI.T33] Galaxy–SMBH Anchor Lemma: galactic ω-germ code factors through SMBH’s ω-code. code(D^gal)[ω] = Φ_bas ∘ code(D^SMBH)[ω] Empirical grounding: M–σ relation.

  • code_factorizes : Bool Code factors through anchor.

  • code_determines_basin : Bool Same SMBH → same galactic code (up to Φ_bas).

  • eval_decomposes : Bool Evaluator decomposes through anchor.

  • m_sigma_grounding : Bool Φ_bas grounded by M–σ relation.

Instances For

Tau.BookVI.GalaxyBasin.instReprAnchorLemma.repr

source def Tau.BookVI.GalaxyBasin.instReprAnchorLemma.repr :AnchorLemma → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.GalaxyBasin.instReprAnchorLemma

source instance Tau.BookVI.GalaxyBasin.instReprAnchorLemma :Repr AnchorLemma

Equations

  • Tau.BookVI.GalaxyBasin.instReprAnchorLemma = { reprPrec := Tau.BookVI.GalaxyBasin.instReprAnchorLemma.repr }

Tau.BookVI.GalaxyBasin.anchor

source def Tau.BookVI.GalaxyBasin.anchor :AnchorLemma

Equations

  • Tau.BookVI.GalaxyBasin.anchor = { } Instances For

Tau.BookVI.GalaxyBasin.anchor_lemma

source theorem Tau.BookVI.GalaxyBasin.anchor_lemma :anchor.code_factorizes = true ∧ anchor.code_determines_basin = true ∧ anchor.eval_decomposes = true

Tau.BookVI.GalaxyBasin.BasinFusion

source structure Tau.BookVI.GalaxyBasin.BasinFusion :Type

[VI.L12] Basin Fusion via SMBH Merger: galaxy merger is basin fusion. (i) Anchor merger produces single remnant SMBH (V.D171, V.T112) (ii) Code fusion: merged code via blueprint fusion (iii) Carrier family union (with dynamical rearrangement) (iv) Ladder restructuring under new gravitational potential

  • anchor_merges : Bool SMBHs merge to single remnant.

  • code_fuses : Bool Code fuses via blueprint fusion.

  • carrier_union : Bool Carrier family is union of progenitors.

  • ladder_restructured : Bool Ladder restructured under new potential.

Instances For

Tau.BookVI.GalaxyBasin.instReprBasinFusion

source instance Tau.BookVI.GalaxyBasin.instReprBasinFusion :Repr BasinFusion

Equations

  • Tau.BookVI.GalaxyBasin.instReprBasinFusion = { reprPrec := Tau.BookVI.GalaxyBasin.instReprBasinFusion.repr }

Tau.BookVI.GalaxyBasin.instReprBasinFusion.repr

source def Tau.BookVI.GalaxyBasin.instReprBasinFusion.repr :BasinFusion → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.GalaxyBasin.basin_fusion

source def Tau.BookVI.GalaxyBasin.basin_fusion :BasinFusion

Equations

  • Tau.BookVI.GalaxyBasin.basin_fusion = { } Instances For

Tau.BookVI.GalaxyBasin.basin_fusion_lemma

source theorem Tau.BookVI.GalaxyBasin.basin_fusion_lemma :basin_fusion.anchor_merges = true ∧ basin_fusion.code_fuses = true ∧ basin_fusion.carrier_union = true ∧ basin_fusion.ladder_restructured = true