Horizon Delivery-Cost Calculator

The Landauer floor at the horizon (k_B T_H ln 2) is ~10¹² below the CMB floor, but that is a disposal cost, not a delivered one. A carrier photon aimable at the horizon needs energy E_gamma ≥ hc/r_g; charging realistic delivery losses against that floor is what sets the realized gain.

🔬 Closed-form
This tool computes the delivered-cost correction, not the disposal-floor ratio. The ~10¹² CMB/horizon Landauer ratio is real but describes the marginal cost of erasure once a bit is already at the horizon. Getting it there costs at least one carrier photon of energy hc/r_g, plus engineering losses. The number this tool reports — 10⁶–10⁹ — is the realized gain after that accounting, and is the figure the MTH Paper's §4.2 says should be quoted, not the floor-to-floor ratio.
Central mass & carrier
2.0×10⁴ M☉
1.0 bit/photon

Denser coding is permitted up to the Bekenstein channel capacity, but the paper notes it yields only modest further gains at this energy scale — the slider exists to show that explicitly.

Delivery loss
2.0 dex

Pointing/capture inefficiency, error-correction overhead, and the fraction of carriers scattered rather than absorbed — charged against the ideal hc/r_g floor as one to three orders of magnitude, per the paper.

Gravitational bookkeeping (Tolman)
O(1), r ≳ 10² r_g

Energy accounted at a platform of radius r ≳ 100 r_g is redshifted at infinity by the platform's lapse factor — an O(1) correction at these radii per the paper. Not separately modeled here; it does not move the quoted range.

Floors
Gravitational radius r_g = GM/c²
Carrier floor E_gamma ≥ hc/r_g
Delivered cost per bit (E_gamma / bits)
CMB floor k_B T_γ ln 2 (T=2.7 K)
Floor-to-floor ratio (CMB / delivered)

This ratio (~4×10⁹ at the fiducial mass) is the ideal-carrier figure before delivery losses — not yet the realized gain.

Realized gain
Realized gain at current loss
Band across 1–3 dex loss
computing…
Realized gain vs. delivery loss
Realized gain = floor-to-floor ratio ÷ 10^(loss dex), swept across the paper's stated 1–3 dex loss range at the current mass and bits/photon. Shaded band marks the paper's quoted 10⁶–10⁹ realized-gain range; marker shows the current loss slider.

The correction

An event horizon lowers the Landauer erasure floor from the CMB temperature to the (far lower) Hawking temperature T_H — a ratio of ~10¹² at IMBH masses. But k_B T_H ln 2 is the marginal cost of disposal at the horizon; it is not the delivered cost from an orbiting platform. A carrier photon must be aimable at the horizon, which sets a minimum energy E_gamma ≥ hc/r_g where r_g = GM/c². At the paper's fiducial mass (2×10⁴ M☉), r_g ≈ 3×10⁷ m and E_gamma ≈ 7×10⁻³³ J — a factor ~4×10⁹ below the CMB floor of 2.6×10⁻²³ J, not the ~10¹² floor-to-floor figure.

Reproducing the paper's headline

Charging realistic engineering losses (pointing/capture inefficiency, error-correction overhead, scattered-vs-absorbed carriers) against the ideal floor — one to three orders of magnitude — leaves a defensible realized gain of 10⁶–10⁹ over the 2.7 K sky. At the default mass, bits/photon, and loss (2 dex midpoint) this tool reads ≈4×10⁷, inside that band; the slider's full 1–3 dex range spans ≈4×10⁶ to ≈4×10⁸, also inside it. Denser coding (more bits per carrier photon) is permitted up to the Bekenstein channel capacity but yields only modest further gains at this energy scale — moving the slider confirms the gain shifts by less than the loss slider does for the same log-decade change.

What this tool does not model

The Tolman/gravitational-blueshift bookkeeping is stated in the paper as an O(1) correction at platform radii r ≳ 100 r_g and is not separately computed here — modeling it further would go beyond what §4.2 states, so this tool reports the paper's qualitative conclusion (it does not change the quoted range) rather than inventing a redshift model.

OCS connection

This is the delivered-cost correction to the floor-to-floor Landauer comparison in Bekenstein-Landauer-Lloyd Limit Explorer, which quotes the ~10¹² CMB/horizon ratio as a disposal-floor figure. That figure is real and unchanged; this tool exists because the disposal floor is not the same number as the realized gain a real delivery channel achieves.

v1.0 — 2026-07-23 · Code MIT · Prose CC BY 4.0 · Swanson 2026, "The Macro Transcension Hypothesis" ("Paper A") §4.2 (sec:landauer); Bekenstein 1973/1974/1981; Hawking 1974/1975; Landauer 1961