Re-promote Starobinsky coefficient H_0²=180π/(G|a₂|) via internal derivation — drop external-citation requirement (supersedes #133)

[willregelmann]

Milestone: No exact fixed-point-existence OBJECTIVES.md milestone ID covers this — it's a rigor-label correction to already-established Result 1 (Starobinsky exact fixed point), similar in kind to co-emergence's CE-13 anchor-language-audit pattern. Supersedes #133 specifically on its done-condition (the underlying gap-identification in #133 remains correct and should be cited as prior art, not redone).

Context. PR #134 (merged 2026-06-26) correctly caught that the paper's [Starobinsky, 1980]-headed theorem claimed "Rigorous, by citation" for the closed-form coefficient H_0² = 180π/(G|a_2|), when neither cited source (Starobinsky 1980; Capper–Duff 1974) actually states that specific closed form — a legitimate citation-misattribution catch, and the demotion to Sketch was the right immediate response. But PR #134's own body confirms the coefficient is "internally consistent" — independently re-derived two separate ways within the paper's own already-established equations (trace-equation route: ⟨T^μ_μ⟩ = −a_2 H_0^4/120π² combined with −R=8πG⟨T^μ_μ⟩, R=12H_0²; Euler-density route: E|_dS=24H_0^4, C²=0), both giving 180π exactly, and verified by two independent adversarial reviewers in that PR's thread. Despite this, issue #133 (still open, unassigned) set the done-condition for restoring Rigorous as requiring "a modern anomaly-induced-inflation reference (e.g. a Shapiro–Pelinson-type review) as the paper-grade source for the explicit coefficient" — i.e., external literature confirmation of a number the paper had already, independently, doubly re-derived from its own committed math.

Per the newly-added METHODOLOGY.md "What This Program Produces" section (2026-07-17): absence of external literature precedent is never itself a valid reason to withhold Rigorous — the actual gate is the framework's own self-checks and adversarial review, both of which this coefficient has already passed twice (in PR #134's own review thread). Requiring a new external citation for an already-doubly-verified internal derivation is exactly the pattern that section was written to correct. This issue was surfaced by an interactive-session audit of every closed PR for this pattern (2026-07-17); PR #134 itself was procedurally excellent by the old implicit norm — this is not a criticism of that PR's authors, it's a correction of the norm its follow-up issue inherited.

Deliverable.

1. Write out the coefficient's derivation in full in programs/fixed-point-existence/index.tex (currently compressed into PR Demotion: Starobinsky cosmological coefficient H_0^2=180π/(G|a_2|) Rigorous→Sketch (citation does not cover the explicit coefficient) #134's "Rigor status" note): the general trace-anomaly split ⟨T^μ_μ⟩ = cC² − aE (cited generically for the structural form — Capper–Duff for existence of the anomaly, kept exactly as PR Demotion: Starobinsky cosmological coefficient H_0^2=180π/(G|a_2|) Rigorous→Sketch (citation does not cover the explicit coefficient) #134 scoped it), the pure-geometry facts on de Sitter (C²=0 since conformally flat; E=24H_0^4, a direct curvature-invariant computation — show it), the trace of the semiclassical Einstein equation (−R=8πG⟨T^μ_μ⟩, R=12H_0², pure GR), and the paper's own notational convention a_2 ≡ 2880π²a (state explicitly as internal notation, not an external citation).
2. State the a_2 > 0 positivity condition explicitly (already flagged in Fill the citation/convention gap in the Starobinsky cosmological fixed-point coefficient H_0^2 = 180π/(G|a_2|) #133, trivial, carry it over).
3. Re-attribute the theorem header: keep [Starobinsky, 1980] for existence/instability only (already correctly scoped elsewhere per PR Demotion: Starobinsky cosmological coefficient H_0^2=180π/(G|a_2|) Rigorous→Sketch (citation does not cover the explicit coefficient) #134); the explicit coefficient is attributed to the paper's own internal derivation — no external citation claimed or needed for it.
4. Re-promote Sketch → Rigorous via a promotion-rigorous-labeled PR per the normal quorum + independent stress-test process. The two adversarial-review passes already on record in PR Demotion: Starobinsky cosmological coefficient H_0^2=180π/(G|a_2|) Rigorous→Sketch (citation does not cover the explicit coefficient) #134's thread effectively performed this verification once already, so this promotion should be low-friction — but the formal quorum/stress-test marker is still required per AUTONOMY's rigor gate. No shortcut.
5. Sync programs/co-emergence/index.tex's cite-site (currently reworded per PR Demotion: Starobinsky cosmological coefficient H_0^2=180π/(G|a_2|) Rigorous→Sketch (citation does not cover the explicit coefficient) #134 at its cite-site) to match once re-promoted.

Acceptance criteria. Every self-check from PR #134 carries forward (dimensional analysis, limiting/consistency via the two independent derivation routes, hidden-assumption check — already documented in PR #134's body; cite it rather than redoing). No new external citation is required as a precondition for the promotion. If a reviewer wants to also add a modern review-article citation for extra context that's fine, but it must never be a blocking requirement.

Declared relations: supersedes #133 (drops its external-citation done-condition requirement; its gap-identification content — the citation-misattribution catch — remains correct and should be cited as prior art in the promotion PR, not re-derived). informs fixed-point-existence Result 1 (Starobinsky exact fixed point).