Open: the dual-stress enhancement (OP5)

The dual-stress enhancement is the unexplained gap between how strongly conjugate matter scatters off itself and how weakly ordinary matter couples to the same carrier. In the program both kinds of matter couple to the momentum graviton X: conjugate matter through its dual stress, ordinary matter through the spacetime metric. Fitting the flat cores of dwarf galaxies needs a self-scattering cross-section that the checkpoint calls nuclear-scale, while ordinary matter must feel X only at gravitational strength. Something must make conjugate matter’s coupling far more effective than ordinary matter’s; what it is, and by how much, has not been worked out. The checkpoint calls it the main open quantitative item of the conjugate sector.

Status: Open — [O] (papers/broken-born-checkpoint-v2.md §14 item 5) — the checkpoint calls it the “Main open quantitative item” (§8); no calculation exists and no source states the size of the gap. It qualifies the gate mechanism, which explains the gate’s dependence on relative momentum but not its strength. It is listed in open problems and is not on the current work queue.

The question#

The checkpoint, #11, states it twice:

“Main open quantitative item: the dual-stress enhancement (nuclear-scale σ₀ with gravitational SM couplings) [O].” (#11 §8)

“Dual-stress enhancement parametrics [O].” (#11 §14 item 5)

SM is the Standard Model, ordinary matter. σ₀ is the low-velocity transfer cross-section of the gated scattering law, σ_T(v) = σ₀F(v²/v*²). “Parametrics” means how the size of the effect depends on the parameters of the theory; no source names which parameters.

The item was first logged in calc note #8, the last of the Debt-1 calc notes, at the end of its argument that ordinary matter is safe from X:

“[Parametrics of the χ dual-stress enhancement — why σ₀ can be nuclear-scale while SM couplings stay gravitational — logged as the main open quantitative item.]” (notes/debt1a-iv-beta-coefficients.md §3)

The same note’s close-out lists it among the open residue of Debt 1 as “(iv) dual-stress enhancement parametrics (gate strength vs gravitational SM coupling)” (§5).

The strong side: σ₀#

Conjugate matter’s self-interaction is the gated amplitude M(k, q) = 4πα̃m_χ/(q² + m_φ²)·F(k²/μ²) (#11 §8; the velocity gate). Its low-velocity cross-section is fixed by the cores of dwarf galaxies: “Fitting dwarf-scale cores wants σ₀/m_χ ≈ 30 cm²/g at v ≲ v* ≈ 120 km/s” (the lab notebook, #1 §5.1). The lab notebook writes the cross-section as σ₀ = 16πα̃²m_χ²/m_φ⁴ and takes α̃ ~ 1 at the scattering benchmark, where “the Born approximation is marginal” (#1 §5.1). A coupling of order one is a strong coupling.

#11 §8 calls this σ₀ “nuclear-scale”, comparable to the cross-sections of nuclear physics [T]. The lab notebook states the core-fitting value without a citation; how self-scattering turns a dark-matter cusp into a core is the established physics of self-interacting dark matter [T].

The weak side: ordinary matter#

Ordinary matter couples to the metric g, and once reciprocity forces the two spin-2 frames to have equal Planck masses, the metric contains the massless graviton and X in comparable proportions. Calc note #8 draws the consequence:

“With equal effective Planck masses (forced by the same symmetry), SM matter — coupled to g — sees both eigenstates with comparable strength; safety is by range, not decoupling: X-mediated forces on the SM are Yukawa-cut at 1/M_X, and gravitational-strength short-range forces are experimentally unconstrained down to far below any plausible M_X.” (notes/debt1a-iv-beta-coefficients.md §3)

#11 §7.5 carries it as “SM couplings gravitational-strength and Yukawa-cut at 1/M_X” (Yukawa forces). A gravitational-strength coupling is suppressed by the Planck mass, which makes it extremely weak for elementary particles [T]. The full argument is on safety by range. Calc note #8’s summary has X coupled “to conjugate matter through the dual stress (the gate) and to ordinary matter only at gravitational strength and short range” (§4).

Why the two must be reconciled#

Both sides run through the same field. In the program’s mechanism, conjugate matter scatters off itself by exchanging X between the dual stresses of two particles, and integrating out the massive X leaves the contact interaction of the gate (the gate mechanism). Ordinary matter exchanges the same X at gravitational strength. The fitted σ₀ requires X’s coupling to conjugate matter’s dual stress to be strong; the safety argument has X’s coupling to ordinary matter gravitational. The open item is the account of that difference: v1 words it as “why σ₀ can be nuclear-scale while SM–X couplings stay gravitational” (#9 §6).

The word “enhancement” comes from the earlier calc notes, which attributed ordinary matter’s weak coupling to its dual stress. Calc note #5: X “couples to x-polarized matter only through its (suppressed) dual stress” (§E). Calc note #6: “couplings to x-polarized (SM) matter run through the SM’s dual stress, which is unenhanced” (§4). Conjugate matter’s dual stress, by contrast, would have to be enhanced. Calc note #8 replaced the suppressed coupling with the range argument, in which ordinary matter couples to X through g at gravitational strength, so the contrast is now between conjugate matter’s dual-stress coupling and ordinary matter’s gravitational one.

What the sources leave open#

The size of the gap. No source states how many orders of magnitude separate the two strengths. The wiki adds no estimate.
The parameters. No source names the parameters the enhancement depends on. The amplitude’s α̃ and m_φ are not related to M_X, the mass of X, in any document; the benchmark’s choice m_φ ~ m_χ was made in v0.1, before X was identified as the carrier (#1 §5.1; conflicts between sources).
A mechanism. No source proposes one. The explicit form of the dual stress, which a mechanism would need, is itself not written down (notes/debt1a-geometric-core.md §E; dual stress T̃).

Until the item is resolved, the strength of the gate is an input fitted to dwarf cores rather than an output of the X-exchange mechanism. The mechanism accounts for the gate’s dependence on relative momentum, which is what row 1 and row 2 of the predictions table test; the strength enters row 1 only as the fitted σ₀.

History#

Calc note #8 logged it in §3 and listed it as residue (iv) of Debt 1 in §5 (the three debts).
The lab notebook’s v0.6 addendum lists “dual-stress enhancement parametrics” among the “Residual open items (none existential)” (#1 ‘Addendum (v0.6)’).
v1 called it “The main open quantitative item” in its section on the gate (#9 §6) and listed it as item 4 of its open problems: “Dual-stress enhancement parametrics: σ₀ nuclear-scale with gravitational SM couplings [O]” (#9 §10).
The handoff lists it with the gate shape among the open items: “Gate shape (X propagator on momentum fibers); dual-stress enhancement parametrics” (HANDOFF.md §2, Open 6).
The checkpoint keeps it as the “Main open quantitative item” (§8) and item 5 of its open problems (§14).

The current queue, in the root CLAUDE.md (“Since the handoff”), does not include it.

Sources#

papers/broken-born-checkpoint-v2.md §8 — the open item and its tag; §14 item 5 — the open-problem entry; §7.5 — ordinary matter’s couplings gravitational-strength and Yukawa-cut
CLAUDE.md ‘Since the handoff’ — the current queue
HANDOFF.md §2 — the item in the handoff’s open list
notes/debt1a-iv-beta-coefficients.md §3 — where the item was logged; safety by range; §4 — X’s couplings to both kinds of matter; §5 — residue (iv)
notes/debt1a-ii-X-classification.md §4 — ordinary matter’s dual stress as unenhanced
notes/debt1a-geometric-core.md §E — ordinary matter’s dual stress as suppressed; the dual stress defined in words
notes/broken-born-program-v1.md §6 — v1’s statement of the item; §10 item 4 — v1’s open-problem entry
notes/broken-born-theory.md §5.1 — the dwarf-core value of σ₀/m, σ₀ in terms of α̃ and m_φ, the Born caveat; ‘Addendum (v0.6)’ — the item among the residual open items