Row 11: particles or condensate (OP9)

Row 11 asks what dark matter is made of, if the program is right. The program offers two answers: χ particles, the momentum-polarized counterpart of ordinary matter, which scatter off each other only through a velocity gate; or an X-condensate, a coherent, space-filling oscillation of the field X, the massive partner of the graviton. #11 states that the two can be told apart using rows 1–3 of its predictions table (the knee in the self-interaction, the isotropy of scattering and the shape of the knee’s tail) together with signatures of a coherent field. How to make that separation is itself open problem 9 of #11 §14, so the row is a diagnostic still to be worked out, with no kill condition. #11 counts it among the program’s predictions not previously posed. Until 2026-10-19 the question had three answers; the third, superheavy solitons, is retired.

Status: Open — [O] (#11 §14 item 9); the two-candidate framework is [D] and each candidate [O] (#11 §12) — a diagnostic row with no kill condition and nothing yet to machine-check. Listed in open problems and the queue.

The row#

Checkpoint #11 §13, row 11:

“Microstructure” is what dark matter consists of at the smallest scale on which it has structure: individual particles, or a field oscillating coherently. The open problem behind the row, #11 §14 item 9: “Discriminating the two remaining dark-sector candidates (§12) [O].”

The two candidates#

#11 §12 lists the candidates with their discriminators, tagged “[D — framework; each candidate O]”: the framework that produces them is derived, and each candidate is open (dark-sector candidates).

DM is dark matter. “The 5.4 : 1 abundance question (polarization-genesis) applies to both” (#11 §12; Open: polarization-genesis and the 5.4 : 1 ratio (OP7)).

• χ particles are the p-polarized matter of postulate P4. They gravitate like ordinary matter and scatter off each other through a gate in relative momentum, mediated by exchange of X, which makes their self-interaction strong at low collision speeds and absent at high ones (conjugate matter and the velocity gate). Their stability is assumed.
• The X-condensate is a state of the momentum graviton X, the massive, reciprocity-odd spin-2 field of the program’s geometry, coupled to ordinary matter at “gravitational-strength” and “Yukawa-cut at 1/M_X” (#11 §7.5; Yukawa forces). A field that oscillates uniformly through space behaves on average as pressureless matter [T], and the idea’s lineage is bigravity dark matter, Babichev et al. [23†], an entry of #11’s reference list that pairs one paper’s title with another’s arXiv number (flag 20 in review/wiki-build-flags.md). Its stability is “m_X-protected”, stated without an argument (the three handles).

The standard expectation#

“(not previously posed)” (#11 §13). #11 §15 counts the row, with row 3, among its progressive signs: “predictions not previously posed (rows 3, 11)”. The general distinction between particle dark matter and dark matter that behaves as a classical wave, because its occupation numbers are enormous, is established [T] (wave dark matter); what is the program’s own is the pair of candidates and the claim that rows 1–3 separate them (Assessment: a live research program).

The proposed discriminators#

Rows 1–3#

• Row 1: the knee. “Knee at v* ~ 10² km/s; zero cluster signal (particle χ)” (#11 §13). The knee is the drop in the self-interaction cross-section at the gate’s velocity scale v*. Its zero cluster signal is stated for particle χ.
• Row 2: isotropy. “Isotropic below the gate”. The argument is a two-body scattering calculation on the particle island, and the χ row of the candidate table lists “isotropic scattering”. No document states isotropy, or its absence, for a condensate.
• Row 3: the island discriminant. “Knee tail: sharp ⇒ particle; (v*/σ)⁴ ⇒ wave”, with σ the halo’s velocity dispersion. The particle law is the gate’s own cutoff; the wave law was derived in Debt 3 for very light χ, which behaves as a classical wave (#11 §9; the two laws). The candidate table assigns a “sharp tail” to χ particles and a “knee shape wave-like” to the X-condensate.

Read against the table, the three rows separate the candidates through the knee: a sharp tail with isotropic scattering is the χ-particle signature, a wave-like tail the X-condensate’s. Several links in that reading are missing from the record:

• The condensate’s knee is not derived. The (v*/σ)⁴ law belongs to wave χ, a regime of the matter field χ. No document derives a knee for a condensate of X, or relates the condensate to wave χ (caveats and open questions). A wave-like tail would therefore point away from particle χ without, on the record, separating the X-condensate from wave χ.
• The particle tail may not be sharp. Whether the gate’s tail is Gaussian or rational is open problem 4 of #11 §14. Calc note #6 calls rational gates “power-law-tailed” (notes/debt1a-ii-X-classification.md §4), so if the gate is rational, both branches have power-law tails, and no source compares them (Open: the gate shape (OP4)).
• Rows 1 and 2 have no wave form. Calc note #2 asked for rows 1–2 to be “re-derived in wave language” (notes/debt3a-stream-stability.md, ‘Consequences for the predictions table’); the (v*/σ)⁴ law answers this for the knee’s tail only (Open: rows 1 and 2 in wave language).

Coherence signatures#

The second half of the requirement, “coherence signatures”, matches the X-condensate’s handle “coherent-field signatures”. A coherent field oscillates in phase over a region, like a single standing wave, rather than as a gas of independent quanta [T]. No document says what the signatures are, at what scale they would appear, or how they would be observed (the X-condensate candidate).

What does not discriminate#

• Direct detection. Row 7’s permanent null holds for both candidates: “both dark-sector candidates SM-decoupled” (#11 §13), SM being the Standard Model.
• Gravity. Both candidates gravitate like ordinary dark matter.
• Abundance. The 5.4 : 1 question applies to both, and neither has a mechanism that produces the ratio.

Why it is open#

Telling the candidates apart needs calculations the record does not contain. For the X-condensate, no document computes how the oscillation would be produced, its amplitude, its lifetime or its coherence signatures (what is open). For χ particles, the gate’s shape and the dual-stress enhancement that would make their self-interaction large are open problems 4 and 5 of #11 §14. The row records the question and the observables that would answer it; how the answer would be read off is open problem 9 (open problems and the queue). The current work queue in the root CLAUDE.md does not include it.

The data situation#

The row has no data of its own. Its discriminators are rows 1–3, whose data situations are on their pages: the knee’s band and the cluster limits on row 1, isotropy on row 2, the knee’s tail on row 3. No coherence signature has been specified, so none has been looked for.

Superseded: the three-way question#

Until 2026-10-19 the question had three answers. #11 v2.0 listed a third candidate, superheavy topological solitons of a hidden gauge sector, and the handoff listed among the open items “Dark-sector trilemma discrimination: particles vs X-condensate vs solitons” (HANDOFF.md §2, item 8). As imported into the repository (commit 8d588f6), v2.0’s row 11 required “Particles / condensate / knots separable via rows 1–3 + compact-object lensing + coherence signatures”, and its open problem 9 read “Trilemma discrimination program (§12) [O]”. The lensing clause matches the solitons’ handle in v2.0’s candidate table, “compact-object probes (lensing) if heavy”.

Round 3 of blind review found the solitons’ abundance misnormalized, and Decision 2 retired them as a program-native proposal (review/round3-adjudication.md, ‘Decisions’):

Consequence: 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.

#11 v2.1 rewrote the row as “Particles vs condensate, separable via rows 1–3 + coherence signatures” and the open problem as “Discriminating the two remaining dark-sector candidates (§12) [O]” (commit e1c1f67). The candidate’s obituary is Obituary: superheavy conjugate solitons.

Both popular articles predate the retirement and still describe three answers: #12 says the framework “narrows the answer to three candidates” (‘Dark matter as the other polarization’), and #10 that “Dark matter’s identity, meanwhile, has narrowed to a three-way question with named experimental discriminators” (‘Dividends and daydreams’). They are not sources for the question’s status (the popular articles).

History#

• The second candidate. Calc note #6 opened the X-condensate as “A new door, deliberately left closed today: homogeneous oscillations of a massive spin-2 X are themselves a dark-matter candidate (cf. bigravity dark matter)”, logged “as an open direction, not pursued. [O]” (notes/debt1a-ii-X-classification.md §4). The lab notebook’s v0.4 addendum records it as “A new open direction: massive-X condensate as the dark matter itself”. v1 listed it as open problem 7, “X-condensate as the dark matter itself (bigravity-DM-style), potentially eliminating χ and unifying the dark sector with the geometry [O — direction, deliberately unopened]” (#9 §10), and named it beside χ in row 7.
• The row. v1’s table has no row 11. #11 v2.0 added it with three candidates; v2.1 reduced it to two; v2.2 left it unchanged (the history of the predictions table).
• The assessment. #11 §15’s italic summary lists “a two-way question about dark matter’s nature with named discriminators” among the program’s products and adds that “a third option, superheavy knots, was tested and retired”.

Sources#

• papers/broken-born-checkpoint-v2.md §13 row 11 — the row; §12 — the candidates and their handles [D — framework; each candidate O]; §14 item 9 — the open problem; §14 items 4, 5 — the gate shape and the dual-stress enhancement; §15 — “not previously posed” and the italic summary; §7.5 — X’s couplings; §8 — the gate; §9 — the island discriminant’s laws
• review/round3-adjudication.md ‘Decisions’ item 2 — the soliton option retired, two candidates left
• CLAUDE.md ‘Since the handoff’ — the current queue, which does not include the row
• HANDOFF.md §2 — the three-way question as open item 8 (superseded). #11 v2.0’s row 11 and open problem 9 are quoted from the repository’s history (commit 8d588f6; commit e1c1f67 for v2.1).
• notes/debt1a-ii-X-classification.md §4 — the X-condensate’s first appearance; rational, power-law-tailed gates
• notes/debt3a-stream-stability.md ‘Consequences for the predictions table’ — rows 1–2 to be re-derived in wave language
• notes/broken-born-theory.md ‘Addendum (v0.4)’ — “massive-X condensate as the dark matter itself”
• notes/broken-born-program-v1.md §9 — v1’s table, with the X-condensate in row 7 and no row 11; §10 — v1’s open problem 7
• popsci/universes-other-half.md ‘Dark matter as the other polarization’ and popsci/angle-of-the-mirror.md ‘Dividends and daydreams’ — the three-way question in the popular articles; not status sources
• review/wiki-build-flags.md item 20 — #11’s reference [23]†, which pairs one paper’s title with another’s arXiv number