Results Results Overlay Review-Facing calibration-cascade, numerical-predictions, constants-ledger, verification Constants, couplings, mass ratios, and SI readouts from iota-tau and one dimensional anchor.
Results OverlayReview Facing

Calibration Cascade

Constants, couplings, mass ratios, and SI readouts from iota-tau and one dimensional anchor.

Results Overlay Physics E1 Directed Acyclic Cascade Registry-backed TauLib-linked External review required
Boundary. The Calibration Cascade is the Results-side overlay that shows how the Panta Rhei physics layer organizes constants. It starts with the algebraic master constant ι_τ = 2/(π+e) and one dimensional calibration anchor, the neutron mass m_n.

Dependency graph connecting the master constant, neutron-mass anchor, dimensionless couplings, mass-ratio chain, G-alpha bridge, SI readouts, prediction catalogue, falsification surfaces, Registry items, TauLib modules, and manuscript source chapters.

Directed structure. The Calibration Cascade is intentionally represented as a directed acyclic dependency structure rather than a generic graph explorer. Dependencies flow from algebraic inputs through dimensionless readouts, dimensional anchoring, SI realization, and verification comparison.
Metrology note. The modern SI is defined through exact numerical values of seven defining constants. This page therefore distinguishes τ-internal readouts, dimensional anchoring, SI expression, and external comparison datasets rather than treating SI-defining constants as ordinary measured predictions. The Book IV/V source chapters use CODATA 2018 as their comparison baseline; current CODATA 2022 / NIST and BIPM links are retained as guardrails, not recalculated Corpus claims.

This Page Is

  • a dependency cascade;
  • a public inspection overlay;
  • a map from ι_τ and m_n to readout layers;
  • a bridge between source chapters and prediction/falsification pages;
  • a Registry, TauLib, and source-chapter provenance surface.

This Page Is Not

  • a generic graph explorer;
  • a superseded one-document numerical framing;
  • a new lane or final physical ontology;
  • a substitute for expert physics or metrology review;
  • a claim that SI-defining constants are ordinary measured predictions;
  • a process-level Standard Model scattering calculation.

Cascade overview

The schematic below is intentionally compact. It gives the launch reader the finite dependency order in one pass; detailed formulas stay in the inspection sections and constant pages below.

Inputs

ι_τ + m_n

Algebraic seed and neutron-mass anchor.

L1

Dimensionless readouts

Couplings, α, α_G, and ratio terms.

L2

Mass ratios and anchoring

Mass-ratio chain plus dimensional anchoring.

L3

SI readouts

Unit-context-aware SI expression.

L4

Verification comparisons

CODATA 2018 rows and review surfaces.

Text equivalent. ι_τ = 2/(π+e) and m_n are the two visible inputs. Dimensionless readouts feed mass-ratio and G-alpha routes; anchoring and unit context then produce SI readouts; comparison rows and prediction/falsification pages provide review surfaces rather than additional dependency edges.

Inputs

L0

Master constant

Formula / role: ι_τ = 2/(π+e)

Status: τ-effective

Boundary: algebraic master constant feeding dimensionless readouts.

Source: book-iv-coupling-ledger · def:master-constant-recap

L2

Neutron-mass anchor

Formula / role: m_n = 1.674927498 × 10^-27 kg (CODATA 2018 source comparison)

Status: Established

Boundary: scale-setting anchor, not absolute mass prediction.

Source: book-v-constants-g-alpha-bridge · thm:ch71-sufficiency

Established τ-effective Conjectural Metaphorical / structural Pending unit-context review
Scope label. τ-effective means internal τ-derived or τ-effective construction/readout. Metadata keeps the stable value tau_effective.

Key constant cascades

L1 · τ-effective Fine-Structure Constant α α = (11/15)^2 ι_τ^4 This page displays the τ-internal alpha readout and comparison route. It does not establish external acceptance. Depends on: ι_τ, coupling ledger L1 · τ-effective Level 1+ Mass Ratio R1 R1 = ι_τ^-7 - (√3 + π^3α^2)ι_τ^-2 This page displays the source-mapped mass-ratio route that feeds the electron-mass readout. It is not a standalone metrology claim. Depends on: ι_τ, α L2 · τ-effective Electron Mass m_e m_e = m_n/R1 This page displays an anchored SI readout after the neutron mass enters. It does not make the neutron-mass anchor itself a prediction. Depends on: m_n, R1 L1 · τ-effective Gravitational Coupling α_G α_G = α^18√3(1 - (3/π)α) This page displays the dimensionless bridge quantity separately from the SI G readout. Depends on: α L2 · τ-effective Newton Constant G G = (ℏ c / m_n^2) · α_G This page displays the SI G readout only with explicit unit-context guardrails. It does not claim current CODATA recomputation. Depends on: α_G, m_n, ℏ, c L2 · τ-effective Planck Mass m_P m_P = sqrt(ℏc/G) This page displays a Planck-mass readout downstream of the G route. It does not make Planck units the calibration anchor. Depends on: G, ℏ, c L3 · τ-effective Rydberg Constant R_∞ R_∞ = α^2 m_e c/(2ℏ) This page displays an SI readout route downstream of alpha and electron mass. It does not update external metrology datasets. Depends on: α, m_e, ℏ, c L3 · τ-effective Bohr Radius a_B a_B = ℏ/(α m_e c) This page uses Bohr radius notation a_B and avoids ambiguous zero-subscript radius notation. Depends on: α, m_e, ℏ, c L3 · τ-effective Compton Wavelength λ_C λ_C = ℏ/(m_e c) This page displays a downstream SI readout route and preserves source-vintage comparison status. Depends on: m_e, ℏ, c

Open all seeded constant pages

Dependency edge table

This machine-readable dependency view preserves the edge list behind the overview. Acyclicity checks apply to dependency edges only; related prediction and falsification surfaces remain outside the dependency DAG.

From Relation To Edge type
ι_τ defines 10 couplings dependency
ι_τ feeds α dependency
ι_τ feeds R = m_n/m_e dependency
10 couplings supports α dependency
α holonomy_correction R = m_n/m_e dependency
R = m_n/m_e anchor_conversion m_e dependency
m_n calibrates m_e dependency
α bridge_input α_G dependency
α_G unit_context_conversion G dependency
m_n anchor_conversion G dependency
m_e feeds SI readouts dependency
G feeds SI readouts dependency
SI readouts compared_against Verification comparisons dependency
Verification comparisons public_claim_surface Numerical Prediction Catalogue related surface
Verification comparisons challenge_surface Falsification N-tests related surface

Mass-Ratio Chain

The mass-ratio chain is the clearest finite derivation path in the cascade. It shows how the neutron-to-electron mass ratio is built through a ten-link route from the τ³ fibration, torus spectral data, lemniscate capacity, and holonomy correction.

  1. 1. τ^3 fibration τ^3 = τ^1 ×_f T^2 L1 pending review

    τ^3 fibration is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    pending label review
    Registry
    I.K5
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  2. 2. Hodge Laplacian on the torus λ(k1,k2) = (2π)^2(k1^2 + ι_τ^2 k2^2) L1 mapped

    Hodge Laplacian on the torus is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    eq:laplacian-eigenvalues
    Registry
    Pending review
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  3. 3. Breathing operator B = Δ^{-1}|_{T^2} L1 pending review

    Breathing operator is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    pending label review
    Registry
    Pending review
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  4. 4. Spectral factorization Σ(s) as an Epstein zeta lattice sum L1 pending review

    Spectral factorization is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    pending label review
    Registry
    Pending review
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  5. 5. Epstein zeta at s = 4 Z(4; iι_τ) ~ C · ι_τ^-7 L1 mapped

    Epstein zeta at s = 4 is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    def:epstein-zeta
    Registry
    IV.D40
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  6. 6. Lemniscate spectral capacity sqrt(3) = |1 - ω| L1 mapped

    Lemniscate spectral capacity is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    prop:sqrt3
    Registry
    IV.P389
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  7. 7. Level 0 formula R0 = ι_τ^-7 - sqrt(3)ι_τ^-2 L1 mapped

    Level 0 formula is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    eq:R0
    Registry
    IV.T380
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  8. 8. Holonomy correction δR = π^3α^2 · ι_τ^-2 L1 mapped

    Holonomy correction is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    prop:holonomy-correction
    Registry
    IV.P236
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  9. 9. Level 1+ formula R1 = ι_τ^-7 - (sqrt(3)+π^3α^2)ι_τ^-2 L1 mapped

    Level 1+ formula is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    eq:R1
    Registry
    IV.T381
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula
  10. 10. Electron mass readout m_e = m_n/R1 L2 mapped

    Electron mass readout is retained as a finite source-mapped link in the ten-step chain.

    Source
    book-iv-mass-ratio-chain
    thm:electron-mass
    Registry
    IV.T218
    TauLib
    TauLib.BookIV.Calibration.MassRatioFormula

Coupling Ledger

The coupling ledger is one dimensionless dependency table inside the cascade. It is not a separate ontology.

  1. κ(D;1) · Temporal flow magnitude 1 - ι_τ self L1
    Value
    ≈ 0.6587
    Source
    book-iv-coupling-ledger
    def:self-couplings
    Registry
    IV.D587
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  2. κ(A;1) · Temporal arrow ι_τ self L1
    Value
    ≈ 0.3413
    Source
    book-iv-coupling-ledger
    def:self-couplings
    Registry
    IV.D587
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  3. κ(B;2) · Spatial distance scale ι_τ^2 self L1
    Value
    ≈ 0.1165
    Source
    book-iv-coupling-ledger
    def:self-couplings
    Registry
    IV.D587
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  4. κ(C;3) · Confinement coupling ι_τ^3/(1 - ι_τ) self L1
    Value
    ≈ 0.0604
    Source
    book-iv-coupling-ledger
    def:self-couplings
    Registry
    IV.D587
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  5. κ(A,B) · Electroweak coupling ι_τ^3 cross L1
    Value
    ≈ 0.0398
    Source
    book-iv-coupling-ledger
    def:cross-couplings
    Registry
    IV.D401
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  6. κ(A,C) · Weak-strong coupling ι_τ^4/(1 - ι_τ) cross L1
    Value
    ≈ 0.0206
    Source
    book-iv-coupling-ledger
    def:cross-couplings
    Registry
    IV.D401
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  7. κ(A,D) · Weak-gravity temporal consistency ι_τ(1 - ι_τ) cross L1
    Value
    ≈ 0.2248
    Source
    book-iv-coupling-ledger
    eq:temporal-multiplicative
    Registry
    IV.T02
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  8. κ(B,C) · EM-strong / Higgs-mass crossing ι_τ^3/(1 + ι_τ) cross L1
    Value
    ≈ 0.0297
    Source
    book-iv-coupling-ledger
    def:cross-couplings
    Registry
    IV.D401
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  9. κ(B,D) · EM-gravity lensing ι_τ^2(1 - ι_τ)^2 cross L1
    Value
    ≈ 0.0505
    Source
    book-iv-coupling-ledger
    prop:iv-extra-cross-couplings
    Registry
    IV.P281
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2
  10. κ(C,D) · Strong-gravity mass-curves-time relation ι_τ^3(1 - ι_τ) cross L1
    Value
    ≈ 0.0262
    Source
    book-iv-coupling-ledger
    prop:iv-extra-cross-couplings
    Registry
    IV.P281
    TauLib
    TauLib.BookIV.Calibration.DimensionlessCouplings
    TauLib.BookIV.Calibration.DimensionlessCouplings2

G-Alpha Bridge

Dimensionless identity α_G = α^18 sqrt(3)(1-(3/π)α) tau effective with unit context review dimensionless identity

G-alpha bridge keeps the dimensionless identity separate from the SI readout formula.

SI readout formula G = (ℏ c / m_n^2) · α_G si after neutron mass anchor

Dimensionless identity ≠ SI readout formula. The readout formula is rendered only with the explicit unit context shown here.

Unit context and pending alternatives si_after_neutron_mass_anchor review boundary
  • The dimensionless identity and the SI G readout are kept separate.
  • Any alternative G route without explicit unit context remains pending review.
  • This projection does not update CODATA comparisons beyond the manuscript baseline.

Constants Ledger

The constants ledger is a table of cascade outputs. Its rows should be read with their scope labels, unit context, and source vintage. The table does not by itself establish external acceptance.

Notation guardrail: the Bohr radius is rendered as a_B with the alias a_0^{Bohr} where needed, so it is not confused with acceleration-scale notation elsewhere in the physics pages.

Established 6 constants-ledger entries scope group
  1. 1. c · Speed of light L H SI defining constant · exact
  2. 2. ℏ · Reduced Planck constant M L^2 H SI defining constant · exact
  3. 3. k_e · Coulomb constant M L^3 H^2 / Q^2 Derived SI context · exact
  4. 4. ε_0 · Vacuum permittivity Q^2 / (M L^3 H^2) Derived SI context · exact
  5. 5. μ_0 · Vacuum permeability M L / Q^2 Derived SI context · exact
  6. 6. c^2 · Electromagnetic unit identity 1/(ε_0 μ_0) Derived SI context · exact
τ-effective 22 constants-ledger entries scope group
  1. 7. κ(B;2) · Electromagnetic self-coupling ι_τ^2 Dimensionless · ---
  2. 8. κ(C;3) · Strong self-coupling ι_τ^3/(1-ι_τ) Dimensionless · ---
  3. 9. κ(D;1) · Gravity-sector self-coupling 1-ι_τ Dimensionless · ---
  4. 10. κ(A;1) · Weak-sector self-coupling ι_τ Dimensionless · ---
  5. 11. α · Fine-structure constant (11/15)^2 ι_τ^4 Dimensionless · 9.8 ppm
  6. 12. sin^2 θ_W · Weak mixing readout ι_τ(1-ι_τ) Dimensionless · ~2.7%
  7. 13. α_s · Strong coupling readout 2κ(C) Dimensionless · ~2.4%
  8. 14. R · Neutron-to-electron mass ratio ι_τ^-7 - (sqrt(3)+π^3α^2)ι_τ^-2 Dimensionless · 0.025 ppm
  9. 15. m_e · Electron mass m_n/R SI after neutron-mass anchor · 0.025 ppm
  10. 16. m_p · Proton mass m_n - δ_A SI after neutron-mass anchor · ---
  11. 17. R_∞ · Rydberg constant α^2 m_e c/(2ℏ) SI readout · 0.025 ppm
  12. 18. a_B · Bohr radius ℏ/(α m_e c); alias a_0^{Bohr} SI readout · 0.025 ppm
  13. 19. λ_C · Compton wavelength ℏ/(m_e c) SI readout · 0.025 ppm
  14. 20. G · Newtonian gravitational constant G route requires explicit unit context SI after neutron-mass anchor · ~3 ppm
  15. 21. κ_τ · Temporal complement 1-ι_τ Dimensionless · ---
  16. 22. R_S · Schwarzschild-radius coefficient 2GM SI after G readout · exact
  17. 23. m_P · Planck mass sqrt(ℏc/G) SI after G readout · ~3 ppm
  18. 24. ℓ_P · Planck length ι_τ in tau-units Pending unit-context review · ~3 ppm
  19. 25. S_BH · Bekenstein-Hawking entropy readout k_B A/(4ι_τ^2) SI after G readout · ---
  20. 26. α_G · Gravitational fine-structure bridge quantity α^18 sqrt(3)(1-(3/π)α) Dimensionless · ~3 ppm
  21. 27. c_1 · Holonomy bridge coefficient 3/π Dimensionless · 0.04%
  22. 28. κ(A)+κ(D) · Temporal complement identity κ(A)+κ(D)=1 Dimensionless · exact
Conjectural 7 constants-ledger entries scope group
  1. 29. m_W · W boson mass sector-weighted Pending unit-context review · ~3%
  2. 30. m_Z · Z boson mass sector-weighted Pending unit-context review · ~3%
  3. 31. m_H · Higgs mass crossing readout Pending unit-context review · ~3%
  4. 32. m_ν · Neutrino mass scale m_e · ι_τ^15 Pending unit-context review · ~2.5%
  5. 33. κ_n · Nuclear-gravitational parameter 2sqrt(3) Dimensionless · 0.7%
  6. 34. H_0 · Hubble parameter readout cosmological readout Pending cosmological unit-context review · TBD
  7. 35. T_CMB · CMB temperature readout regime readout Pending cosmological unit-context review · TBD
Metaphorical / structural 5 constants-ledger entries scope group
  1. 36. dark-energy-status · Dark energy artifact Not a numerical constant · ---
  2. 37. dark-matter-status · Dark matter artifact Not a numerical constant · ---
  3. 38. Λ · Cosmological constant symbol regime label Not a numerical constant · ---
  4. 39. vacuum-density-status · Vacuum-energy expectation boundary capacity Not a numerical constant · ---
  5. 40. hawking-radiation-status · Hawking radiation absent Not a numerical constant · ---
  1. 1. c · Speed of light L H Established SI defining constant
    Deviation
    exact
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  2. 2. ℏ · Reduced Planck constant M L^2 H Established SI defining constant
    Deviation
    exact
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  3. 3. k_e · Coulomb constant M L^3 H^2 / Q^2 Established Derived SI context
    Deviation
    exact
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  4. 4. ε_0 · Vacuum permittivity Q^2 / (M L^3 H^2) Established Derived SI context
    Deviation
    exact
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  5. 5. μ_0 · Vacuum permeability M L / Q^2 Established Derived SI context
    Deviation
    exact
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  6. 6. c^2 · Electromagnetic unit identity 1/(ε_0 μ_0) Established Derived SI context
    Deviation
    exact
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  7. 7. κ(B;2) · Electromagnetic self-coupling ι_τ^2 τ-effective Dimensionless
    Deviation
    ---
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  8. 8. κ(C;3) · Strong self-coupling ι_τ^3/(1-ι_τ) τ-effective Dimensionless
    Deviation
    ---
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  9. 9. κ(D;1) · Gravity-sector self-coupling 1-ι_τ τ-effective Dimensionless
    Deviation
    ---
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  10. 10. κ(A;1) · Weak-sector self-coupling ι_τ τ-effective Dimensionless
    Deviation
    ---
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  11. 11. α · Fine-structure constant (11/15)^2 ι_τ^4 τ-effective Dimensionless
    Deviation
    9.8 ppm
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  12. 12. sin^2 θ_W · Weak mixing readout ι_τ(1-ι_τ) τ-effective Dimensionless
    Deviation
    ~2.7%
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  13. 13. α_s · Strong coupling readout 2κ(C) τ-effective Dimensionless
    Deviation
    ~2.4%
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  14. 14. R · Neutron-to-electron mass ratio ι_τ^-7 - (sqrt(3)+π^3α^2)ι_τ^-2 τ-effective Dimensionless
    Deviation
    0.025 ppm
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  15. 15. m_e · Electron mass m_n/R τ-effective SI after neutron-mass anchor
    Deviation
    0.025 ppm
    Layer
    L2
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  16. 16. m_p · Proton mass m_n - δ_A τ-effective SI after neutron-mass anchor
    Deviation
    ---
    Layer
    L2
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  17. 17. R_∞ · Rydberg constant α^2 m_e c/(2ℏ) τ-effective SI readout
    Deviation
    0.025 ppm
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  18. 18. a_B · Bohr radius ℏ/(α m_e c); alias a_0^{Bohr} τ-effective SI readout
    Deviation
    0.025 ppm
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  19. 19. λ_C · Compton wavelength ℏ/(m_e c) τ-effective SI readout
    Deviation
    0.025 ppm
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  20. 20. G · Newtonian gravitational constant G route requires explicit unit context τ-effective SI after neutron-mass anchor
    Deviation
    ~3 ppm
    Layer
    L2
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  21. 21. κ_τ · Temporal complement 1-ι_τ τ-effective Dimensionless
    Deviation
    ---
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  22. 22. R_S · Schwarzschild-radius coefficient 2GM τ-effective SI after G readout
    Deviation
    exact
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  23. 23. m_P · Planck mass sqrt(ℏc/G) τ-effective SI after G readout
    Deviation
    ~3 ppm
    Layer
    L2
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  24. 24. ℓ_P · Planck length ι_τ in tau-units τ-effective Pending unit-context review
    Deviation
    ~3 ppm
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  25. 25. S_BH · Bekenstein-Hawking entropy readout k_B A/(4ι_τ^2) τ-effective SI after G readout
    Deviation
    ---
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  26. 26. α_G · Gravitational fine-structure bridge quantity α^18 sqrt(3)(1-(3/π)α) τ-effective Dimensionless
    Deviation
    ~3 ppm
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  27. 27. c_1 · Holonomy bridge coefficient 3/π τ-effective Dimensionless
    Deviation
    0.04%
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  28. 28. κ(A)+κ(D) · Temporal complement identity κ(A)+κ(D)=1 τ-effective Dimensionless
    Deviation
    exact
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    mapped
  29. 29. m_W · W boson mass sector-weighted Conjectural Pending unit-context review
    Deviation
    ~3%
    Layer
    L2
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  30. 30. m_Z · Z boson mass sector-weighted Conjectural Pending unit-context review
    Deviation
    ~3%
    Layer
    L2
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  31. 31. m_H · Higgs mass crossing readout Conjectural Pending unit-context review
    Deviation
    ~3%
    Layer
    L2
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  32. 32. m_ν · Neutrino mass scale m_e · ι_τ^15 Conjectural Pending unit-context review
    Deviation
    ~2.5%
    Layer
    L2
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  33. 33. κ_n · Nuclear-gravitational parameter 2sqrt(3) Conjectural Dimensionless
    Deviation
    0.7%
    Layer
    L1
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  34. 34. H_0 · Hubble parameter readout cosmological readout Conjectural Pending cosmological unit-context review
    Deviation
    TBD
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  35. 35. T_CMB · CMB temperature readout regime readout Conjectural Pending cosmological unit-context review
    Deviation
    TBD
    Layer
    L3
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  36. 36. dark-energy-status · Dark energy artifact Metaphorical / structural Not a numerical constant
    Deviation
    ---
    Layer
    L4
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  37. 37. dark-matter-status · Dark matter artifact Metaphorical / structural Not a numerical constant
    Deviation
    ---
    Layer
    L4
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  38. 38. Λ · Cosmological constant symbol regime label Metaphorical / structural Not a numerical constant
    Deviation
    ---
    Layer
    L4
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  39. 39. vacuum-density-status · Vacuum-energy expectation boundary capacity Metaphorical / structural Not a numerical constant
    Deviation
    ---
    Layer
    L4
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
  40. 40. hawking-radiation-status · Hawking radiation absent Metaphorical / structural Not a numerical constant
    Deviation
    ---
    Layer
    L4
    Source
    book-v-constants-g-alpha-bridge
    tab:ch69-complete-ledger
    Mapping status
    pending review
# Quantity Formula Scope Deviation Unit context
1 c · Speed of light L H Established exact si_defining_constant
2 ℏ · Reduced Planck constant M L^2 H Established exact si_defining_constant
3 k_e · Coulomb constant M L^3 H^2 / Q^2 Established exact derived_si_context
4 ε_0 · Vacuum permittivity Q^2 / (M L^3 H^2) Established exact derived_si_context
5 μ_0 · Vacuum permeability M L / Q^2 Established exact derived_si_context
6 c^2 · Electromagnetic unit identity 1/(ε_0 μ_0) Established exact derived_si_context
7 κ(B;2) · Electromagnetic self-coupling ι_τ^2 τ-effective --- dimensionless
8 κ(C;3) · Strong self-coupling ι_τ^3/(1-ι_τ) τ-effective --- dimensionless
9 κ(D;1) · Gravity-sector self-coupling 1-ι_τ τ-effective --- dimensionless
10 κ(A;1) · Weak-sector self-coupling ι_τ τ-effective --- dimensionless
11 α · Fine-structure constant (11/15)^2 ι_τ^4 τ-effective 9.8 ppm dimensionless
12 sin^2 θ_W · Weak mixing readout ι_τ(1-ι_τ) τ-effective ~2.7% dimensionless
13 α_s · Strong coupling readout 2κ(C) τ-effective ~2.4% dimensionless
14 R · Neutron-to-electron mass ratio ι_τ^-7 - (sqrt(3)+π^3α^2)ι_τ^-2 τ-effective 0.025 ppm dimensionless
15 m_e · Electron mass m_n/R τ-effective 0.025 ppm si_after_neutron_mass_anchor
16 m_p · Proton mass m_n - δ_A τ-effective --- si_after_neutron_mass_anchor
17 R_∞ · Rydberg constant α^2 m_e c/(2ℏ) τ-effective 0.025 ppm si_readout
18 a_B · Bohr radius ℏ/(α m_e c); alias a_0^{Bohr} τ-effective 0.025 ppm si_readout
19 λ_C · Compton wavelength ℏ/(m_e c) τ-effective 0.025 ppm si_readout
20 G · Newtonian gravitational constant G route requires explicit unit context τ-effective ~3 ppm si_after_neutron_mass_anchor
21 κ_τ · Temporal complement 1-ι_τ τ-effective --- dimensionless
22 R_S · Schwarzschild-radius coefficient 2GM τ-effective exact si_after_g_readout
23 m_P · Planck mass sqrt(ℏc/G) τ-effective ~3 ppm si_after_g_readout
24 ℓ_P · Planck length ι_τ in tau-units τ-effective ~3 ppm pending_unit_review
25 S_BH · Bekenstein-Hawking entropy readout k_B A/(4ι_τ^2) τ-effective --- si_after_g_readout
26 α_G · Gravitational fine-structure bridge quantity α^18 sqrt(3)(1-(3/π)α) τ-effective ~3 ppm dimensionless
27 c_1 · Holonomy bridge coefficient 3/π τ-effective 0.04% dimensionless
28 κ(A)+κ(D) · Temporal complement identity κ(A)+κ(D)=1 τ-effective exact dimensionless
29 m_W · W boson mass sector-weighted Conjectural ~3% pending_unit_review
30 m_Z · Z boson mass sector-weighted Conjectural ~3% pending_unit_review
31 m_H · Higgs mass crossing readout Conjectural ~3% pending_unit_review
32 m_ν · Neutrino mass scale m_e · ι_τ^15 Conjectural ~2.5% pending_unit_review
33 κ_n · Nuclear-gravitational parameter 2sqrt(3) Conjectural 0.7% dimensionless
34 H_0 · Hubble parameter readout cosmological readout Conjectural TBD pending_cosmological_unit_review
35 T_CMB · CMB temperature readout regime readout Conjectural TBD pending_cosmological_unit_review
36 dark-energy-status · Dark energy artifact Metaphorical / structural --- not_a_numerical_constant
37 dark-matter-status · Dark matter artifact Metaphorical / structural --- not_a_numerical_constant
38 Λ · Cosmological constant symbol regime label Metaphorical / structural --- not_a_numerical_constant
39 vacuum-density-status · Vacuum-energy expectation boundary capacity Metaphorical / structural --- not_a_numerical_constant
40 hawking-radiation-status · Hawking radiation absent Metaphorical / structural --- not_a_numerical_constant

Verification Comparisons

These comparison rows preserve the manuscript baseline. Current public reference values may be tracked separately, but they should not be silently mixed with the Book IV/V CODATA 2018 comparisons.

Quantity Tau value CODATA 2018 value Deviation
Electron mass 9.10938370 × 10^-31 kg 9.10938370(28) × 10^-31 kg 0.025 ppm
Newtonian gravitational constant 6.6741 × 10^-11 6.67430(15) × 10^-11 ~3 ppm
Rydberg constant 1.097373157 × 10^7 m^-1 1.0973731568(21) × 10^7 m^-1 0.025 ppm
Bohr radius 5.291772109 × 10^-11 m 5.29177210903(80) × 10^-11 m 0.025 ppm
Compton wavelength 3.86159268 × 10^-13 m 3.8615926796(12) × 10^-13 m 0.025 ppm
Planck mass 2.176434 × 10^-8 kg 2.176434(24) × 10^-8 kg ~3 ppm
Inverse fine-structure constant 137.04 137.035999084(21) 9.8 ppm

Dataset Guardrails

Source Chapters

book-iv-coupling-ledger · Book IV complete coupling ledger coupling ledger source 31 labels pinned corpus manuscript source
Source file
manuscript-sources/book-04/part08/ch67-complete-coupling-ledger.tex
Registry range
IV.D04--D07, IV.T01--T02, IV.P01, IV.P03
Line count
573
SHA-256
702f624abc90f9fc132af6ac41e5fb1ca4f2cb8091eff4650e4bb9015c3e0786

Extracted labels:

ch:iv-coupling-ledger def:cross-couplings def:master-constant-recap def:no-running def:self-couplings eq:ab-is-weak-cubed eq:complete-ledger eq:em-is-weak-squared eq:temporal-complement eq:temporal-multiplicative fig:bookIV-ch67-coupling-ledger prop:all-couplings-positive prop:coupling-order prop:iv-alpha-ledger prop:iv-alphaG-ledger prop:iv-extra-cross-couplings sec:ch65-cross-couplings sec:ch65-derived sec:ch65-intro sec:ch65-ledger-summary sec:ch65-master-constant sec:ch65-multiplicative sec:ch65-no-running sec:ch65-positivity sec:ch65-power-hierarchy sec:ch65-self-couplings sec:ch65-temporal-complement sec:ch67-summary thm:power-hierarchy thm:temporal-complement thm:temporal-multiplicative

book-iv-mass-ratio-chain · Book IV mass-ratio chain mass ratio chain source 22 labels pinned corpus manuscript source
Source file
manuscript-sources/book-04/part08/ch70-mass-ratio-chain.tex
Registry range
IV.T10--T15, IV.P07, IV.D46--D48
Line count
448
SHA-256
7839a60e30da2ecb25fe0d85ae552ec1cda0a34313b99939cd31e89b3b2b5597

Extracted labels:

ch:iv-mass-ratio def:epstein-zeta eq:R0 eq:R1 eq:laplacian-eigenvalues fig:bookIV-ch70-mass-ratio-chain prop:holonomy-correction prop:sqrt3 sec:ch68-diagram sec:ch68-intro sec:ch68-link10 sec:ch68-link5 sec:ch68-link6 sec:ch68-link7 sec:ch68-link8 sec:ch68-link9 sec:ch68-links1-4 sec:ch68-overview sec:ch70-summary thm:electron-mass thm:level0 thm:level1

book-v-constants-g-alpha-bridge · Book V constants ledger and G-alpha bridge constants and bridge source 22 labels pinned corpus manuscript source
Source file
manuscript-sources/book-05/part07-closure/ch-closure-constants.tex
Registry range
Pending explicit range review
Line count
505
SHA-256
48773438999ae8cb1333d004c024a5183a46f55cf7a8aec5f3e1799440cfb0ce

Extracted labels:

ch:book5-ch69-constants-ledger ch:v-constants-ledger-complete ch:v-g-alpha-bridge eq:ch70-bridge eq:ch70-hierarchy-9 eq:ch71-couplings eq:ch71-iota-tau fig:bookV-closure-constants-cascade prop:ch70-hierarchy-power rem:ch69-one-anchor rem:ch71-honest sec:ch69-complete-ledger sec:ch70-bridge-statement sec:ch71-architecture tab:ch69-complete-ledger tab:ch71-architecture tab:ch71-parameter-count tab:ch71-verification thm:ch69-E1-completeness thm:ch70-bridge thm:ch70-hierarchy-exponent thm:ch71-sufficiency

Source Role Labels SHA-256
book-iv-coupling-ledger coupling ledger source 31 702f624abc90
book-iv-mass-ratio-chain mass ratio chain source 22 7839a60e30da
book-v-constants-g-alpha-bridge constants and bridge source 22 48773438999a

Limitations

  • This is a static, review-facing overlay, not a dynamic graph application.
  • The page does not recompute CODATA 2022 values or change the existing numerical prediction artifact.
  • Unresolved Registry, TauLib, and source-label mappings remain visible as pending review.
  • “SI readout / unit realization” language is used deliberately; the cascade is not presented as an unqualified SI prediction engine.
  • The prediction catalogue lists claims; this page shows dependency structure and review boundaries.

Projection Metadata

  • Public export route: /assets/data/calibration/
  • Layer count: 5
  • Dependency edges: 13
  • Coupling entries: 10
  • Mass-ratio links: 10
  • Constants-ledger entries: 40

Save or share this page for inspection

Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.

Email to expert