Canonical values & errata
This page is the single source of truth for every constant in the framework. Three quantities appear with divergent values across the source corpus. This page picks the canonical value for each, records the superseded value, and states the reason. Every value in the master register resolves to an entry here.
Drift is not an error. It is the normal consequence of writing a framework across many documents, in many languages, over time. The discipline is to resolve it once and record the resolution, so that every downstream artifact—HTML, JSON, code, paper—references the same number.
01 · Resolved drifts
Three quantities. Each appears with more than one value in the source documents. The canonical form is chosen for internal consistency; the superseded form is recorded so it can be recognized if encountered.
1.1 · Hubble projection factor \(P_\theta\)
| Value | Source | Status |
|---|---|---|
| 1.08308 | Monograph §4.2.1 · master register §04 · docs 1/2/5/6 | Canonical |
| 1.083086 | Step-by-step derivations paper §7 | Superseded |
Reason. The 5-decimal form appears in six of seven sources and is used consistently for the arithmetic \(67.40 \times P_\theta = 73.00\). The 6-decimal form is a higher-precision evaluation of the same expression, \((13/12)/\sqrt{2/3} = 1.0830864\), which rounds to 1.08309 at five decimals. To preserve internal consistency, 1.08308 is canonical.
1.2 · Landauer bit floor \(E_{\text{bit}}\)
| Value | Anchor T | Formula | Status |
|---|---|---|---|
| 2.606 × 10⁻²³ J/bit | \(T_{\text{CMB}} = 2.7255\) K | \(E_{\text{bit}} = k_B \cdot T \cdot \ln 2\) | Frame-Conditioned |
| 5.9051 × 10⁻³⁹ J/bit | \(T \approx 6.1706 \times 10^{-16}\) K | \(E_{\text{floor}} = k_B \cdot T \cdot \ln 2\) | Frame-Conditioned |
Both values are the same classical Landauer relation (\(E = k_B \cdot T \cdot \ln 2\)) evaluated at two declared thermal frames. Neither supersedes the other. The CMB thermal bit floor is anchored to the cosmic-microwave-background temperature; the horizon-adjacent subcoherent bit floor is anchored to the quasilocal horizon thermal noise floor.
1.3 · Planck area ceiling \(A_{\min}\)
| Value | Source | Status |
|---|---|---|
| 2.159 × 10⁻⁷⁰ m²/bit | Monograph §3.3 · master register row 9 · doc 4 normalized | Canonical |
| 7.241 × 10⁻⁷⁰ m² | Doc 4 §3 raw Bekenstein form | Superseded |
Reason. The raw Bekenstein form is \(A = 4 \ell_P^2 \ln 2 = 7.241 \times 10^{-70}\) m². The normalized per-bit form applies the standard holographic quarter factor, \(A_{\min} = \ell_P^2 \ln 2 = 2.159 \times 10^{-70}\) m²/bit. The monograph and register use the per-bit form.
Unit convention. Always express as m²/bit, not m².
02 · Consistent quantities
These values agree across all sources. Recorded here for completeness and for cross-check.
| Quantity | Value | Agreement |
|---|---|---|
| Tetrahedral apex angle \(\theta\) | 70.5288° | All sources |
| Viewer cone fraction \(S_+\) | 1/3 · 33.333% | All sources |
| Inverse cone fraction \(S_-\) | 2/3 · 66.667% | All sources |
| Boundary partition ratio \(S_-/S_+\) | 2.000000 | All sources |
| Unit triangle area \(A_{\text{area}}\) | 0.433013 · √3/4 | All sources |
| Alignment factor \(D_{\text{align}}\) | 0.707107 · 1/√2 | All sources |
| Machine closure \(R\) | 1.0000 | All sources |
| Early-universe baseline \(H_{0,A}\) | 67.4 km/s/Mpc | All sources |
| Late-universe projected \(H_{0,B}\) | 73.00 km/s/Mpc | All sources |
| Boundary flux gradient \(\Delta H\) | 5.60 km/s/Mpc | All sources |
| Inner Hubble radius \(L_0\) | 13.90 Gly | All sources |
| Outer comoving horizon \(L_1\) | 47.90 Gly | All sources |
| Effective aperture \(\Omega_{\text{eff}}\) | 31.73% | All sources |
| Cosmo readout efficiency \(\eta_{\text{budget}}\) | 0.15442 | All sources |
| Baryonic share \(\Omega_b\) | 4.90% | All sources |
| Dark matter share \(\Omega_c\) | 26.83% | All sources |
| Dark energy share \(\Omega_\Lambda\) | 68.27% | All sources |
| Planck luminosity ceiling \(L_{\max}\) | 3.628 × 10⁵² W | All sources |
| Strain readout efficiency \(\eta_{\text{strain}}\) | 0.0869 · 8.69% | All sources |
| Horizon capacity \(I_{\max}\) (62 M☉) | 1.514 × 10⁹³ bits | All sources |
| Readable capacity \(I_{\text{readable}}\) | 1.315 × 10⁹² bits | All sources |
| NEO 2019 OK warning gain | +9.0 days | All sources |
03 · Errata summary
Two corrections to apply when harmonizing the corpus. Neither changes any derivation. Each is a formatting or anchor consistency fix.
-
Step-by-step derivations paper §7. Replace
1.083086with1.08308. Alternatively, if higher precision is preferred, update all sources to1.083086and accept that \(67.4 \times 1.083086 = 73.0004\), which rounds to73.00. -
Doc 4 §3. Label the raw
7.241 × 10⁻⁷⁰ m²form as "raw Bekenstein area," distinct from the canonical per-bit2.159 × 10⁻⁷⁰ m²/bit.
04 · Precision conventions
When a value appears in the register or any generated page, it follows these formatting rules. The conventions are preserved across the corpus.
| Quantity class | Precision | Example |
|---|---|---|
| Angles | 4 decimal places | 70.5288° |
| Ratios and dimensionless factors | 6 significant figures | 0.433013 |
| Percentages | 2 decimal places | 31.73% |
| Physical constants | 4 significant figures unless source uses more | 2.606 × 10⁻²³ J/bit |
| Temperatures | 4 significant figures | 2.7255 K |
| Cosmological densities | 2 decimal places | 4.90% · 26.83% · 68.27% |
Cross-references. The taxonomy of status tags lives in register §09. Full derivations are in the proofs directory. The consolidated submission documents are in the papers directory.