The Final Parsec Problem

The ΛCDM Tension

SMBH binaries stall at parsec separations when the stellar loss cone empties, a hundred times too far apart for gravitational waves to finish the job (Begelman 1980; Vasiliev 2014), yet pulsar timing arrays hear a background most naturally sourced by routine coalescences. The model must bridge the gap in essentially every merger using mechanisms demonstrably universal in none (Khan 2013; Merritt 2013).

The ΛCDM Assumption That Creates It

The model's only hardening agents are local: stars on intersecting orbits and circumbinary gas. When both run out, nothing remains, because constant-Λ spacetime offers no secular channel for orbital energy to leave a binary. The stall is the model's honest prediction; the observed coalescences are its embarrassment.

SCT Resolution: M5 (The Universal Decay Channel Was Already Running)

SCT carries exactly the missing ingredient as one of its founding premises: no orbit in any gravitational system is perfectly stable across time (P14). The progressive weakening of the gravitational mesh, the same secular dissipation that the lunar recession anchors at solar scale and the universe expresses as apparent expansion (P15, P16), operates on every bound pair at every separation, including a stalled parsec-scale binary. The exponential decay law of Paper 11, From Chaos to Covariant Completeness, gives the form, and the rate ladder runs from alpha_solar near 2 × 10⁻¹² per year to alpha_cluster near H₀; a galactic-nucleus binary sits on that same ladder, losing orbital energy continuously whether or not any star remains to slingshot. The stall is real in the model's inventory and absent in SCT's, because the model's inventory was missing a channel that never switches off.

The PTA chorus then requires no per-merger miracle: mesh dissipation bridges the parsec gap as a background process, slow but secular and universal, delivering binaries to the gravitational-wave regime on cosmological timescales as a matter of course. The same M5 reading carries the nanohertz background's SMBH-binary population (recid 148 territory) and the orbital-decay family across twelve orders of magnitude in scale. Expansion-side machinery is in Paper 7, From Chaos To Cosmic Expansion.

Keystone economy: P14 alone unsticks the binary; P15 and P16 are the same premise wearing larger scales. The final parsec was only final in a universe without secular mesh decay.

Falsifier

PTA spectroscopy carries the kill: the nanohertz background's spectral shape encodes how binaries traverse the sub-parsec regime, and a measured spectrum demanding stalled-then-rescued dynamics, with the turnover signature of loss-cone refilling rather than a smooth secular bridge, would refute the continuous mesh channel. Equally, a confirmed population of parsec-scale binaries stalled for longer than the mesh-decay timescale predicts would show the universal channel failing exactly where SCT requires it to operate.

Premise Grounding

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