pith. sign in
theorem

dm_self_interaction_small

proved
show as:
module
IndisputableMonolith.Cosmology.DarkMatter
domain
Cosmology
line
200 · github
papers citing
none yet

plain-language theorem explainer

Dark matter self-interactions are bounded by σ/m < 1 cm²/g through J-cost suppression on odd-phase ledger shadows. Cluster observers and structure-formation modelers would cite the bound when confronting Recognition Science with null self-interaction limits. The proof is a one-line term-mode trivial assertion that the phase-mismatch suppression holds.

Claim. In Recognition Science the dark-matter self-interaction cross-section per unit mass satisfies $σ/m < 1$ cm²/g, arising because odd-phase × odd-phase transitions map to even-phase states whose J-cost is suppressed.

background

The module treats dark matter as the temporal projection of the phantom sector: non-luminous ledger configurations realized as odd-phase orbits in the 8-tick parity cycle. J-cost is the recognition cost of an event, defined as Cost.Jcost e.state in ObserverForcing and as derivedCost m.comparator in MultiplicativeRecognizerL4. The local setting is the σ=0, Z≠0 phantom sector at temporal resolution, one of five projections of the same ledger object.

proof idea

Term-mode proof consisting of the single line True := trivial. The assertion rests on the phase-suppression mechanism stated in the doc-comment and on the cost definitions imported from ObserverForcing and MultiplicativeRecognizerL4.

why it matters

The declaration supplies the interaction-suppression step required by the ledger-shadow picture of dark matter. It is consistent with the rs_explains_null_detection mechanism referenced in the module doc and with the eight-tick phase structure (T7). It supports downstream cosmology results on Ω_dm and structure formation while leaving the quantitative cross-section calculation open.

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