Dark-sector candidates

The dark-sector question asks what dark matter is made of, within the program’s framework. The program gives two answers, each still open: particles of conjugate matter χ, the mirror-polarized counterpart of ordinary matter, or a coherent oscillation of X, the massive momentum graviton that the broken symmetry adds to gravity. Version 2.0 of the checkpoint listed a third answer, superheavy topological solitons of a hidden gauge sector; a review that re-ran every number in code found its abundance estimate misnormalized, and it was retired on 2026-10-19. Both remaining answers share one unsolved question: what sets the observed ratio of dark to ordinary matter, 5.4 : 1.

Stands: the χ-particle candidate, the X-condensate candidate, and two results that outlived the retired candidate, overproduction at the benchmark and W′ overclosure · Died: superheavy conjugate solitons, with its components the hidden SU(2) → U(1) proposal, the coupling α_d ≈ 34, the Kibble normalization, the √N topological floor (chat-only), the ψ relic window and Planck-suppressed adjoint mixing · Open: polarization-genesis and the 5.4 : 1 ratio (OP7)

Map#

Checkpoint #11 §12 is the current statement of the question. It lists two candidates in a table, each with its origin, what makes it stable and the observable that would single it out, and tags the table “[D — framework; each candidate O]”: the framework that produces the candidates is derived, and each candidate is open. Three pages below are established literature, one is an open problem, and the last child is a retired candidate; the two candidate pages are claims of the program.

Relic abundance mechanisms comes first because every candidate has to meet it. It is the established physics of how a relic density is set, mechanism by mechanism: the yield, a summary of thermal freeze-out, freeze-out in a sector at its own temperature, cannibal and asymmetric dark matter and the Sakharov conditions for baryogenesis, and freeze-in. It ends with the program’s uses: the argument that χ cannot freeze out, misalignment on the wave island, and the relics of the retired candidate’s hidden sector.

Thermal freeze-out works through the standard mechanism: the Boltzmann equation, why freeze-out comes near T ~ m/20, the s-wave relic formula exactly as verify/soliton_obituary.py codes it and the standard relic it is checked against, and freeze-out in a sector at its own temperature. Its program uses are the lab notebook’s argument that particle χ cannot freeze out, which leaves the ratio of dark to ordinary matter open; the freeze-out relic coupled to ordinary matter against which row 7 predicts a permanent null; and the W′ and ψ relics of the retired candidate, the first of which survives it.

The χ-particle candidate is the program’s first answer: particles of the momentum-polarized matter field χ, which no Standard Model force reaches under the strict form of postulate P4. The page sets out why χ falls, orbits and lenses like ordinary dark matter [D], summarizes the velocity gate and the knee in the scattering cross-section, and sets out its tests, rows 1, 2, 3 and 7 of the predictions table, with their kill conditions. It explains why the candidate is particle χ rather than the wave branch of Debt 3, what it no longer claims, and what is open: its stability is assumed and its abundance unexplained. The gate’s microphysics belongs to conjugate matter and the velocity gate.

Bigravity dark matter is established literature placed before the second candidate because it is that candidate’s lineage: the massive spin-2 eigenstate of a two-metric theory proposed as the dark matter by Babichev et al. [23†]. The page explains the two mass eigenstates and how the ratio of the Planck masses sets their coupling to matter, why a uniform oscillation of a massive field behaves as cold matter, the check status of the single citation, and how the program’s X differs: forced massive by the broken symmetry, restricted to the palindromic branch, and with equal Planck masses.

The X-condensate candidate is the program’s second answer: a coherent, spatially uniform oscillation of X, which would make dark matter a state of the geometry rather than a separate field. The page sets out what X is (the real part of the modular field, massive, reciprocity-odd, coupled to ordinary matter at gravitational strength with a finite range), what a condensate means here, and the three handles of #11’s table, which are stated without derivation. It records the candidate’s path from a door “deliberately left closed” in the Debt-1 notes to one of three candidates in #11 v2.0 and one of two since v2.1.

Open: polarization-genesis and the 5.4 : 1 ratio (OP7) follows the two candidates because it qualifies both. The lab notebook argues that a light, strongly self-interacting sector connected to ordinary matter only by gravity cannot get its abundance from thermal freeze-out, so the ratio Ω_χ : Ω_b = 5.4 : 1 needs an asymmetric mechanism, the program’s analog of baryogenesis. The page goes through the notebook’s sketch, heavy Grassmannian moduli decaying with a branching set by the vacuum’s tilt angle, and records that a later calc note expects most of those moduli to be eliminated; it is #11 §14 item 7.

The soliton candidate (retired) comes last. It is version 2.0’s third candidate, superheavy ’t Hooft–Polyakov monopoles of a hidden SU(2) → U(1) sector, which was written up as the standalone manuscript #14, reviewed blind three times and retired after the third review. The subsection opens with the obituary and records each failed component, the results that survive, and the published low-mass scenario the corrected candidate duplicates.

How the question changed. The handoff of 2026-10-19 still called superheavy solitons the “Current best DM candidate” (DM: dark matter) and listed “Dark-sector trilemma discrimination: particles vs X-condensate vs solitons” as open item 8 (HANDOFF.md §2). Both popular articles describe the same three-way question. After round 3, Decision 2 retired the solitons: “the trilemma becomes two program-native candidates (gated χ particles; the X-condensate), plus the remark that the framework is compatible with known PeV-scale topological dark matter” (review/round3-adjudication.md). #11 v2.1 adopted that form, and the root CLAUDE.md records the soliton candidate as “dead as a program-native proposal”.

Boundaries#

• The microphysics of χ — the velocity gate, its mechanism, the scattering law and the benchmark — is in conjugate matter and the velocity gate; the particle and wave regimes of χ are in momentum clumping.
• Telling the two candidates apart is a test, row 11: particles or condensate, which is also #11 §14 item 9. The null that both candidates predict for direct detection is row 7.
• X itself — why it is massive, its spectrum, how it couples to ordinary matter, and the open question of its stability at equal Planck masses — is in the momentum graviton X; the bimetric theory it lands on is Hassan–Rosen bimetric gravity.
• Relic production for wave χ is relic abundance by misalignment on the wave island, and the established mechanism is the misalignment mechanism. The heavy moduli of the polarization-genesis sketch belong to the field content of the broken vacuum.
• Monopole physics in general is in magnetic monopoles, and the review that retired the soliton candidate is review round 3. The program-wide registers are the graveyard and open problems.