GGD-3: Independent noise-kernel cross-check against arXiv:2606.04099 (informs-issue #107)

[willregelmann]

Milestone: GGD-3 (programs/gaussian-gravitational-decoherence/OBJECTIVES.md) — Independent noise-kernel cross-check.

Paper location: programs/gaussian-gravitational-decoherence/index.tex, §"Time-independence in the Newtonian limit" and the preceding noise-kernel derivation — eq:N0000 (line ~232, the general noise kernel N_{0000}(x,x') = (c^4/4)Δρ(x)Δρ(x')) and eq:N0000_static (line ~265, its time-independent/static specialization for a stationary superposition). The surrounding text (lines ~262–268) states that the static character of eq:N0000_static "is the key structural feature that distinguishes the Einstein–Langevin noise from the white noise postulated by Diósi" — this is the claim GGD-3 exists to independently harden or challenge.

Context. informs-issue #107 (arXiv:2606.04099, Takeda–Tomizuka–Tanaka, "Gravitationally Induced Quantum Decoherence of Macroscopic Objects") derives a closed-time-path influence functional for gravitational decoherence of a superposed massive object, starting from linearized gravity coupled to an environmental quantum field, with the noise source built by dressing the environmental stress-energy correlator with graviton propagators. Per the abstract (per #107, not yet verified against the primary source — verification is part of this issue's precondition, not a shortcut to skip), the resulting decoherence contribution accumulates logarithmically over distance and is subdominant to collisional decoherence under realistic conditions. This is a structurally different-looking result (log accumulation vs. GGD's static, factorized Δρ(x)Δρ(x') kernel) computed via a different channel (environment-mediated graviton dressing vs. GGD's direct acoustic-mode / rigid-body Newtonian construction), so the OBJECTIVES done-condition explicitly makes establishing comparability part of the milestone, not an assumed given.

Note: PR #173 (merged, first live explorer cycle) investigated a different cross-program question — whether GGD's stationary-noise approximation sits inside FPE's M3 obstruction — and is not a substitute for this milestone; it did not touch arXiv:2606.04099 or #107 at all. GGD-3 remains fully open.

Deliverable (mirrors the milestone's done-condition):

1. Verify [informs-issue] arXiv:2606.04099 — Gravitationally induced decoherence noise kernel from linearized gravity (GGD-2, GGD-1) #107 against the primary source. Fetch and read arXiv:2606.04099 directly (not the abstract-only summary in [informs-issue] arXiv:2606.04099 — Gravitationally induced decoherence noise kernel from linearized gravity (GGD-2, GGD-1) #107) per METHODOLOGY's citation discipline; confirm the claimed noise-kernel construction, the log-distance accumulation result, and the subdominance-to-collisional-decoherence claim actually appear as stated.
2. Establish comparability. Before any agreement/disagreement claim can be signal, state explicitly what must match between the two constructions for a meaningful comparison: the physical setup (Newtonian-limit, non-relativistic rigid-body superposition — matching GGD's own Assumption regime), the regime (stationary/static superposition, matching eq:N0000_static's own stated preconditions — wavepacket spreading negligible on the decoherence timescale), and which piece of arXiv:2606.04099's construction is the analogue of GGD's Δρ(x)Δρ(x') noise kernel (as opposed to its logarithmic-distance far-field/environmental-field-loop contribution, which may not be the comparable object at all).
3. Then, and only then: either (a) show the independent construction reproduces the static, factorized kernel structure of eq:N0000_static under matched Newtonian/stationary assumptions — hardening Result 2 (the Gaussian $t^2$ profile) beyond the paper's own built-in Gaussian-noise Assumption 1; or (b) show it disagrees under matched assumptions — a demotion signal for Result 2, to be filed as such (an honest negative result is a complete, valid deliverable per this program's demotion-as-normal-maintenance convention).

Acceptance criteria:

• Rigor label: Sketch level acceptable per the milestone; do not claim Rigorous for a comparison built on an unverified secondary summary.
• Self-checks: dimensional consistency between the imported kernel object and eq:N0000_static (both must reduce to the same units for a two-point stress-energy correlator); limiting cases — check whether arXiv:2606.04099's result reduces to something comparable to eq:N0000_static in the appropriate Newtonian/stationary/non-relativistic limit, or state precisely why no such limit exists if comparability fails at step 2; consistency — the comparison must not disturb any already-merged §5 discriminant number (GGD-2, PR GGD-2: recompute discrimination metrics at corrected τ_DP and extend §5 to dDP #105) or GGD-4's per-realization/ensemble result (PR GGD-4: resolve Remark 2 ensemble-dephasing caveat (per-realization coherence; §5 observable re-scoped) #151) unless the comparison result is a demotion signal, in which case say so explicitly and note the affected downstream milestones.
• Citations: arXiv:2606.04099 remains flagged exploratory-tier (per [informs-issue] arXiv:2606.04099 — Gravitationally induced decoherence noise kernel from linearized gravity (GGD-2, GGD-1) #107's own flag) unless independently verified per METHODOLOGY's strict tier as part of step 1 of this issue; do not commit it to \begin{thebibliography} at paper-grade without that verification.

Declared relations:

• informs GGD-2 (closed, PR GGD-2: recompute discrimination metrics at corrected τ_DP and extend §5 to dDP #105, issue GGD-2: Quantify experimental discriminability of the Gaussian profile from DP and dissipative-DP at corrected platform parameters #102) — a demotion outcome here would bear on the §5 discriminability numbers' interpretation, not their arithmetic.
• informs GGD-1 (open, halted needs-human, PR GGD-1: Acoustic-gravitational crossover threshold — Conjecture 1 restricted (no accessible platform) #141) — no direct dependency; noted per the milestone's own cross-reference.
• Resolves and closes out informs-issue [informs-issue] arXiv:2606.04099 — Gravitationally induced decoherence noise kernel from linearized gravity (GGD-2, GGD-1) #107 (its purpose — surfacing the pointer for action — is fulfilled once this milestone issue exists to act on it).

routine: scout · model: claude-sonnet-5