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Algebraic Cartan Elimination in Minimal Einstein–Cartan–Holst Gravity: Spin-Sourced Contact and Zero-Spin Scalar Branches
What minimal spin-torsion gravity can and cannot change — a boundary-setting theory note
Abstract
A narrow algebraic Note. Eliminating the Cartan connection gives the convention-pinned axial four-fermion contact term; on a canonical scalar branch with zero spin current, torsion vanishes and the Holst density reduces pointwise by the torsion-free Bianchi identity. The included density and NJL calculations are dimensional/regulator diagnostics, not observational constraints or state-independent phenomenology.
Result summary
- openMinimal ECH Cartan elimination yields −(3κ/16)[γ²/(1+γ²)] J₅² in the stated convention
- openCanonical zero-spin scalar matter gives a torsion-free branch; the Holst density then vanishes pointwise by the Bianchi identity
- openFinite-density benchmark κnψ²/ρΛ ≈ 3.6×10⁻⁶⁹ (nψ/100 cm⁻³)² is explicitly dimensional and non-observational
- openThe direct scalar Fierz channel has Gs = −3κ/16 and no nonzero real homogeneous scalar gap in the stated hard-cutoff convention
Readiness
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Review evidence (179 rounds)
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External peer review kit
Houston-driven manual round · paste prompt into any frontier LLM web UI with the PDF attachedOne click to copy a referee prompt scoped to this paper. One click to download the latest PDF. Paste both into Claude / GPT-5 / Gemini / Grok / Perplexity — return findings here and the autonomous cron will close them in the next bundled hard-fix wave.
preview prompt
You are an external referee for MNRAS / Physical Review D / JCAP (target journal depends on paper). Attached: Paper 1 v1A.0.127 — "Algebraic Cartan Elimination in Minimal Einstein–Cartan–Holst Gravity: Spin-Sourced Contact and Zero-Spin Scalar Branches" Source: arxiv/paper1a_ech_nogo.tex PDF: PDF · 8 pp · v1A.0.127 · updated Jul 24, 2026 · md5 0bc1ee72836c867114118521cf86e1c2 — v1A.0.127 makes the IOP-mandatory declarations actually compile: the whole acknowledgements block sat inside a commented-out region with the cut cosmology material, so the Note had shipped with no competing-interests, funding, or AI-usage statement. A new Note-scoped block was written rather than un-commenting the old one, and Data and Code Availability was promoted to its own section. Archival deposit PUBLISHED (Houston go): DOI 10.5281/zenodo.21481838 (CC-BY-4.0). No readiness change. Read the FULL PDF end-to-end. Produce a referee report in MNRAS format with: 1. Recommendation: ACCEPT / MINOR REVISIONS / MAJOR REVISIONS / REJECT 2. BLOCKERS (must fix before publication) — list each with section/line + proposed fix 3. MAJORS (should fix) — same format 4. MINORS (polish) — same format 5. Strengths (>= 3 bullet points) 6. Specific scrutiny on: - Convention-pinned minimal ECH axial four-fermion contact term - Canonical zero-spin scalar branch and torsion-free Bianchi reduction - Dimensional hard-cutoff diagnostics, not observational constraints - Bounded final-hash confirmation and Houston CQG sign-off CALIBRATION (do not burn findings on these known classes): - The current date is June 2026. arXiv identifiers of the form 25xx.xxxxx and 26xx.xxxxx are VALID, already-published preprints — do not flag them as "future-dated" or "nonexistent". Verify a citation against arXiv/ADS before claiming it does not exist. - Correction notes, retraction notices, and "an earlier version stated X" disclosures in the text are DELIBERATE transparency policy. Flag them only if their content is wrong, never for existing. - Companion-paper citations marked "posted concurrently on arXiv" are deliberate placeholders; real arXiv IDs are inserted during the coordinated submission sequence. - Explicitly labeled conservatism allowances, scaling estimates, ansatz/heuristic status labels, and disclosed queued follow-up computations are deliberate scoping, not oversights — flag only if the label itself is inaccurate. - PDF text extraction can mangle math (square roots, fractions, superscripts). Before flagging "garbled" or "wrong" math, consider extraction artifacts; flag only what is visibly wrong in the rendered PDF. VERDICT STANDARD (apply the SAME high bar a first-pass Physical Review D / MNRAS referee would — this is one of the most rigorous journals in the world): - Assign each finding's severity (BLOCKER / MAJOR / MINOR) by your own independent referee judgment. Do NOT default to any tier, and do NOT soften a finding because the rest of the paper is strong. Do not echo this prompt's context. - A reporting choice that headlines the more favorable of two numbers, an unstated assumption, an uncontrolled systematic, or an internal inconsistency IS a real finding — classify it honestly (MINOR at minimum), not as mere "style" or "opinion". - Truth-audit any claim that seems off by checking it against the published .tex / on-disk artifacts before flagging (this only filters out genuine extraction artifacts — it does not lower the bar on real defects).
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Lineage
Archived — Merged into P1N, the Track B ECH Note (v1N.0.1) — 2026-09-02 portfolio restructure, directive R3. Frozen on disk unedited; no longer an independent submission target. See the current version at paper-paper-1n