The first curve combines all included emitted cones through time, counting overlapping directions once. The solid curve extrapolates Arecibo/Goldstone asteroid-radar history from annual detected-target activity; the dashed curve uses recovered radar geometry. Both retain the same five spacecraft tracks and selected intentional messages. No transmissions after the cutoff are assumed. Future growth is caused by light already in flight.

The broader population is calibrated at 1.6 planets per ordinary star, limited to 5 Earth masses–10 Jupiter masses and 0.5–10 AU. The source’s quoted 0.71–2.32 occurrence endpoints give 3.9–12.9 reference planets today, before beam-history and host-population transfer uncertainty. These are sensitivity endpoints for this extrapolation, not a confidence interval for local contacts. The population is not an exhaustive count of all planets. The HZ estimate uses a separate small-planet occurrence model; the populations overlap and must not be added. Fractional values are expectations over unknown planetary systems.

“Average cone volume” is standardized as the combined reached volume divided by unique angular area expressed in full-width 2′ beam-disk equivalents. The current union is 346,457 such equivalents, averaging 0.0067 ly³ each. These are units of area, not a count of independent transmitting sessions. Wider beams correspond to many units; a moving beam creates a corridor; revisits add no new direction.

Because the beams have different ages, multiplying every direction by one average age would bias the result. Instead each direction keeps its earliest emission date. A short pulse has passed through the interior of its cone even though its photons now occupy a moving shell.

The radar model places first coverage uniformly within an empirical ±49.4° ecliptic band, covering 95% of the recovered Arecibo angular union. The annual coverage hazard uses 25.9 reference footprints per Arecibo detected target apparition and 81.4 per Goldstone apparition. Repeated radar coverage and overlap with spacecraft/message cones are subtracted. Unknown interior years are explicitly interpolated; activity before the first record is omitted. Other radar classes remain uncalibrated.

Historical hardware also changed: some Goldstone tracks used 13-cm radiation rather than 3.5 cm; Arecibo used 70 cm before its upgrade; the 1968 Icarus transmitter was 26 m. Modern area-per-target calibration cannot certify these earlier footprints. The 0.5×–2× scenarios test transfer sensitivity and do not guarantee bounds on the true total. Intentional Altair’s modeled 54′ width is an additional assumption (half/double-width alternatives), and its A7 star is outside the G/M HZ calibration.

Each new 2′ area equivalent is about 0.00087 square degrees. A useful forecast of volume is obtained by retaining the dates of the new coverage, then propagating its front; it is not a fixed volume added per transmission. The table above reports the resulting average volume through time for the cones already emitted. A continuing-transmission scenario would require a future activity schedule, which is distinct from this primary already-emitted forecast.

Only sky unilluminated in the cutoff model can become a new direction here. Repeated future coverage is removed with the same uniform-band hazard, and the remaining new-direction rate slowly falls as available sky is used. The assumed restart date follows the scheduled modernization interval; actual activity and dates may differ. No other future transmitter is introduced.

Newly emitted cones shorter than4.24 ly cannot reach another known stellar system, so their planet projection remains zero initially. Their average cumulative volume grows with time because their pulses continue crossing new space. These additional volumes occupy new angular directions in the adopted model and may be combined with the old-emission projection only at matching dates and with the same conditional assumptions. They are not included in the first curve.

“Reached” means a signal’s leading front crosses a target; it does not imply detection, communication, life, or confirmed habitability. A small planet in a modeled habitable zone (HZ) receives a suitable range of stellar energy; its atmosphere and surface conditions are unknown. In the catalogue estimator the spacecraft model predicts 4 arrived objects, and the selected intentional records add distinct Altair. Two eligible red dwarfs imply 0.32 expected small HZ planets; this conditions on known hosts and cannot be added to the volume-density estimate.

The source inventory includes five spacecraft directions in a published Deep Space Network (DSN) study, public JPL Goldstone configuration records, recovered Arecibo asteroid transmit-run pages, and selected primary-documented intentional interstellar messages. The selected intentional records add one distinct named target, Altair, with nominal arrival around 2000. Ordinary leakage, military/aircraft radars, sidelobes, lunar/planetary radar, and other message campaigns require additional histories.

The 100-year mean is 1.29 catalogue objects/year, 0.025/week, or 0.0035/day. Actual arrivals are discrete; all three immediate intervals above contain zero arrivals. Unique Gaia objects are not necessarily independent stellar systems.

Selected model: Nominal 70-m model: S-band for four probes, X-band for New Horizons; Gaia light-arrival correction, moving-star interception, continuous modeled uplinks. It assumes continuous uplinks during the adopted mission windows and omits the known 2020 Voyager 2 uplink gap. It reconstructs nominal geometry, rather than proving an uplink occurred during each alignment. All forecast rows first filter emission epochs to the past. Fresh six-hour JPL ephemerides and 15-minute refinements replace the original coarse track; spherical geometry and stellar proper-motion conventions are checked. Remaining limitations include incoming geocentric spacecraft directions instead of ground-site outgoing pointings, missing radial velocities, beam power contours, and launch-time continuous-coverage assumptions. The stellar epoch accounts for the incoming catalogue light delay and the outgoing wavefront flight; the final version solves the moving-star interception rather than keeping distance fixed.

The earlier chat’s 1,296 figure counted star–mission pairs. The author catalogue has 1,278 unique Gaia identifiers, of which 1,277 have past modeled first-emission epochs at this cutoff. Its calendar dates used rounded arrival years. Those preserved paper-reproduction files are separate from the selected reanalysis. The selected reanalysis uses New Horizons’ X-band uplink width of 0.038° for a 70-m antenna; the original paper used the 0.128° S-band width for every mission.

The 1983 record describes a one-hour Stanford 46-m transmission aimed at Altair, approximately 16.7 ly away. Date-plus-distance arithmetic puts its nominal arrival around 2000. Altair is distinct from the four current DSN-model objects, giving five named/modelled objects in the combined current inventory under their respective assumptions. The reconstructed Arecibo archive adds no current nearby-catalogue object. This bounded count cannot establish the worldwide total.

The saved intentional table contains 21 date-target sessions, 17 distinct nearby stars and the additional M13 globular-cluster target. Source-rounded arithmetic predicts three additional selected stellar targets over ten years and 16 over 100 years. These should not be added to future DSN or radar catalogue totals without identifier cross-matching. Altair is an A7V star; the Sun-like G-star and M-dwarf HZ occurrence calibrations do not apply to it.

Sónar’s actual 2017 transmissions were on October 16–18, preceding the November announcement. The source’s 12.4-ly distance places the first nominal arrival around 2030. M13’s approximately 25,000-ly travel time places the intended-cluster arrival around year 26,974; foreground beam encounters were not reconstructed here.

The four reached objects in the original model are GJ 1276 (white dwarf), GJ 1154 (M dwarf), 2MASSW J1507476-162738 (brown dwarf), and GJ 359 (M dwarf). Applying the M-dwarf calibration to the two eligible hosts gives 2 × 0.16 = 0.32 expected conservative-HZ planets; the optimistic-HZ model gives 0.48. White and brown dwarfs are excluded from these occurrence calibrations, rather than asserted incapable of planets. This remains conditional on the modeled exposure and on applying the early-M result to these hosts.

Dressing & Charbonneau’s selected cool-dwarf sample spans 2,661–3,999 K, with median 3,746 K and mostly early M dwarfs. Transferring its population mean to these M4/M4.5 hosts adds an unquantified population assumption; 0.32 is an expected planet count under that transfer, not a measurement of their planets.

The local 10-pc census yields 0.0836 ordinary stars/pc³ and 0.0609 systems containing ordinary stars/pc³. M-dwarf and F/G/K counts give a central conservative small-HZ-planet density of 0.0164 planets/pc³, equivalent to about 0.20 per ordinary star. The conservative upper median gives 0.0199/pc³. An endpoint sensitivity spans 0.0085–0.0451/pc³; this combines marginal source endpoints and is not a joint credible interval. Binary suppression, local population transfer, and incomplete classifications are unquantified limitations.

A “new direction” is defined here by the incremental union of circular half-power beam footprints. Its area divided by one 1.92-arcminute beam disk is an equivalent number of beam disks, which may be fractional. It is not a count of sessions, targets, or disjoint cones. Tracking can sweep many beam widths; repeated pointings can add no new area.

The 123 configuration windows cover 16 targets, 19 observing dates, and 30 target-days. Their total span is 71.1 hours of receive/configuration windows, not 71.1 transmitter-on hours. The angular union is 0.000346076 steradians, or 0.0028% of the sky. Monte Carlo integration standard error is 5.9e-07 sr; unresolved pulse gaps and historical pointing offsets produce additional source uncertainty.

Dividing by the 105-day calendar interval gives 13.5 equivalent new beam disks/day, or 4,914/year if that sparse sample were repeated at the same rate. This is an illustrative sample-rate scaling, not measured annual global activity. Nine windows with setup/pointing warnings remain in the nominal envelope; their exclusion is provided in the numerical sensitivity results.

Systematic retrieval recovered 75,219 raw rows from 834 advertised per-object run pages. Removing 486 identical 22-field measurement duplicates leaves 74,733 distinct measurements, of which 74,201 have verified transmitter start/end times. The other 532 rows remain in the audit. Usable intervals span August 2001–June 2020, all at 2.38 GHz. Their summed duration is 975.5 recorded window-hours; removing UTC overlaps gives 973.1 hours of window coverage. Overlapping archive representations are not counted as independent transmitter time. This retrieves 88.9% of the advertised run count; no contact estimate is scaled by that percentage.

Ground-site outgoing directions include light-time point-ahead and sample recorded transmit intervals at no more than 15″ spacing for the nominal 60″ radius. UCLA’s date is anchored at receiver start; 72 midnight-crossing transmit windows were shifted to the previous day using that documented convention. Current JPL orbit solutions reconstruct the intended tracking; original antenna offsets and power logs are unavailable. Residual simultaneous cross-target records involve 92 interval keys across 13 targets; the nominal archive envelope retains them and an exclusion sensitivity is saved separately. This cannot certify both incompatible pointings occurred. The union contains approximately 26,432 two-arcminute beam-disk equivalents. Its current cumulative volume is 8.56 ly³, giving 0.0206 expected ordinary stars and 0.00405 expected small HZ planets under the local homogeneous-density model. These are spatial expectations, rather than fractional catalogue observations.

The catalogue calculation uses 300,526 GCNS objects with median distance at most 100 pc. It predicts 0 new objects over ten years and 8 over 100 years. Eventually 168 nominal catalogue sources intersect the sampled beams; expanding the radius by 15″ gives 215 in a grazing sensitivity. That expansion diagnoses sampling at edges and is not a certified uncertainty interval. White/brown dwarfs and components are included in catalogue-object counts, so multiplying that total by an ordinary-star occurrence rate would be invalid. The density model independently gives 8.29 ordinary stars and 1.63 small HZ planets by 2126.

“New” means sky area first covered within this recovered dated inventory. A continuous tracking sweep creates a ribbon of angular coverage, so the number of cones depends on the declared beam footprint convention. The annual calculation removes angular overlap across years. Individual run counts, target counts, and beam-disk equivalents answer different questions.

The Arecibo case has 449 actual transmit windows, 9.04 transmitter-on hours, and nominal outgoing directions reconstructed with JPL Horizons. Four 2008 rows lacking transmitter times remain in the raw data and are explicitly excluded from the geometric reconstruction. The combined nominal sky union is approximately 131 two-arcminute beam disks. The current homogeneous-density expectation is only 0.00015 ordinary stars and 2.9e-05 small HZ planets; the catalogue finds zero. These values are an expectation under spatial randomization, rather than a claim of fractional observed stars.

Forecast tables provide cumulative ordinary stars, stellar systems, small-HZ planets, G-star-only HZ planets, and increments over the next day, week and calendar year. For example, at 2126 the 2025 Goldstone envelope gives 0.0086 expected new ordinary stars in its following year, 0.00016/week, or 2.3e-05/day; expected HZ planets scale by the defined population mixture. This smooth rate describes a density model, while the DSN table forecasts discrete catalogue arrivals.

The full 84,054-run Arecibo count cannot be substituted for the first column. Each run has a different time, duration and swept footprint; runs overlap and one run may traverse many beam widths. An all-source estimate needs the dated angular union, rather than a tally of radar records. Nor can one use a 12,000-ly cone as the current frontier: a 1960s signal has traveled only about 60 ly.

The JPL detection history contains 2,082 station–apparition rows across 1968–2026. Goldstone-family distinct detected targets number 55 in 2024, 41 in 2025, and one in the retrieved 2026 snapshot. These are not independent cones, and transmissions producing no echo are absent. Scheduled observations may be cancelled. The worldwide new-direction/day/year quantity remains unresolved for DSN uplinks to all spacecraft, other planetary-radar facilities, and additional radar types.

Even all 84,054 advertised UCLA asteroid runs would omit lunar/planetary targets, failed observations, and other facilities. Required fields are target, UTC transmitter-on/off times, site, frequency/power, original pointing or orbit-predicts, and beam offsets. Actual DSN uplink duty logs are needed to test its continuous-transmission model.

For a conditional estimate of continuing spacecraft beams, the next table assumes continuous tracking from October 7, 2026 to October 7, 2027. New coverage is measured against all five modeled past spacecraft tracks, with each mission’s own beam width. It is not compared with every historical human transmission.

The combined increment is approximately 0.23 square degrees/year, or 0.0006 square degrees/day. The mission footprints are widely separated. Native beam-disk equivalents have different widths and cannot simply be summed; sky area provides the common unit. This scenario assumes a 70-m antenna, continuous uplink duty, and geocentric incoming spacecraft directions. It estimates geometry under those assumptions, not a measured current operations rate.