# The anchored calm — the status table **This document holds status and nothing else.** No proof, no identity and no derivation lives here; every one of them lives in the leaf note named in the last column. The reason this file exists is that the same status table was written four times, in four leaf notes, at four different states of knowledge, so no summary could copy it correctly. There is one table now, and it is here. **"The anchored calm" names a phenomenon, never a claim.** It may not appear in any list headed Proven, Theorems, or the proven spine. The phenomenon is the measured fact that the anchored rotation sits in the extreme low tail of the ensemble's strike-variance statistics — rank 2 of 510,510 at @17 on equal-weight Z2, rank 14 of 9,699,690 at @19. What decomposes into claims is the explanation of that fact, and the parts of the explanation carry four different calibrations. **There is no "Fused-Window Calm Lemma".** The name is retired: it spanned a proven mechanism, a six-level certificate, a refuted uniform form and an unexplained measurement, so every summary that copied it either reproduced the whole grading or said something false. `README.md` said "Proven". The nine objects below already had their own proofs; the parent name added only the conjunction. ## Status | sub-claim | status | scope | home | |---|---|---|---| | **Mirror-Sibling Identity** | PROVEN | all x, all scour q | [natal-cap-19-calm-lemma.md](natal-cap-19-calm-lemma.md) §Lemma 1 | | **Fusion Identity** | PROVEN | all x, all scour q | [natal-cap-19-calm-lemma.md](natal-cap-19-calm-lemma.md) §Lemma 2 | | **Mirror-Phase Doubling Lemma** | PROVEN | all x, all scour q | [natal-cap-19-calm-lemma.md](natal-cap-19-calm-lemma.md) §Lemma 3 | | **Minus-Half Theorem** | PROVEN, exact, no error term | every level, every q coprime to 30 | [natal-cap-26-minus-half.md](natal-cap-26-minus-half.md) §Theorem 2, Props 3–4 | | **Skeleton Collapse Theorem** | PROVEN | all x, all q | [natal-cap-30-skeleton-bound.md](natal-cap-30-skeleton-bound.md) §Theorem A | | **Aggregate 30-Skeleton Bound (@11..@29)** | CERTIFIED, exact integer inequality | six computed levels only | [natal-cap-30-skeleton-bound.md](natal-cap-30-skeleton-bound.md) §Theorem B, [natal-cap-36-skeleton-door.md](natal-cap-36-skeleton-door.md) §Proposition E | | **Skeleton Equidistribution Conjecture** | OPEN as a statement; the named door is CLOSED as a route (2026-08-30, `research/OUTCOMES.md`): over every scour prime it removes at most 0.0102 from a G30_agg whose open part is 0.094 to 0.126, and on the open side (moduli exceeding the window) the phase never wraps, so what remains is the inequality itself, suspected TPC-strength, unresolved | all x | [natal-cap-36-skeleton-door.md](natal-cap-36-skeleton-door.md) §Proposition C | | **Uniform-in-q Anticorrelation** | **REFUTED** | six counterexample primes are known, of 10,201 scour primes over six levels | [natal-cap-23-covadj-proof.md](natal-cap-23-covadj-proof.md) §"Uniform-in-q Anticorrelation is refuted" | | **Anchored Typicality Measurement** | MEASURED, no proof mechanism in sight | @13, @17, @19 | [natal-cap-19-calm-lemma.md](natal-cap-19-calm-lemma.md) §"What Lemmas 1–3 do and do not give" | Read at a glance: the mechanism is proven at all x and all q, the size of the mechanism's effect is certified at six computed levels, its uniform-in-q form is false, its all-x form is open with its named door closed as a route (2026-08-30), and the step that joins the mechanism to the anchor is a measurement with no proof route. **The two numbers the table stands on.** The Aggregate 30-Skeleton Bound is G30_agg < 1/2, certified in exact BigInt by `natal-cap-30-skeleton-bound.js` (reading 297; the same exact pass is re-read by `natal-cap-36-skeleton-door.js`) at 0.2132, 0.1113, 0.1011, 0.1259, 0.0945, 0.1176 for @11, @13, @17, @19, @23, @29, with margins 0.287 to 0.406 and 0.3824 at @29. The Anchored Typicality Measurement is Σdev(0,q)²/ΣV_fused = 0.935 at @13 and 0.939 at @17, with mean position percentiles 47.9% and 47.8%. ## What is not proven, said plainly Two things, and they are of different kinds. The **Skeleton Equidistribution Conjecture** is the all-x form of a statement certified at every level anyone has computed; its door is named, analytic, and closed as a route, since the branches the door governs carry a small aggregate share of the skeleton's mass **of either sign** — 9.2%, −0.9%, 0.2% and 0.5% at @13, @17, @19 and @23 over every scour prime (the −10.8% and +5.5% this paragraph carried until 2026-08-30 were subsamples of 40 of 435 and 29 of 1,739 primes; `history/staging/decide-0830-skeleton-door.md` SEC B) — so proving it as named would move the bound by at most 0.0102 and close nothing; the door is a closed route in `OUTCOMES.md` and the theorem and the six-level certificate stand. *(BAND CORRECTED 2026-08-18. This read "between 9% and 11%", which is a range fitted to the two largest magnitudes and stated as if it covered the series: only @13 lies inside it, @19 lies inside only in absolute value and with the opposite sign, and @17 and @23 lie outside on either reading. The four values are printed with their signs at `research/natal-cap-36-skeleton-door.md`:190-194 and in `research/wave7-logs/cap36-skeleton-door.log`:29/33/37/41, and the home's own summary is the safe form: "the branches for which the door is a fixed-modulus question carry essentially none of the skeleton. Their aggregate is small and of either sign". This file exists because the same status table was written four times and no summary could copy it correctly, so a band no other copy carries is exactly the failure it was created to prevent.)* The **Anchored Typicality Measurement** is the harder one: it says one arithmetic position is typical of its own ensemble, which is the shape of statement that measure arguments cannot finish, and its home says in terms that it has no proof mechanism in sight. It is the calm's last wall. Neither of them is a gap in a proof of anything. The calm is not a route to the Twin Prime Conjecture and must not be read as one: `natal-cap-31-calm-vs-kill.md` refutes the intervening step, since calm does not concentrate survivors (corr(VR, S) ≈ 0). Calm is about strikes; survival is about the X-channel. ## The children, and what each owns | home | sub-claims it owns | |---|---| | [natal-cap-19-calm-lemma.md](natal-cap-19-calm-lemma.md) | Mirror-Sibling Identity, Fusion Identity, Mirror-Phase Doubling Lemma, Anchored Typicality Measurement | | [natal-cap-23-covadj-proof.md](natal-cap-23-covadj-proof.md) | the exact arithmetic of Cov_adj (Props 1–5), and the refutation of Uniform-in-q Anticorrelation | | [natal-cap-26-minus-half.md](natal-cap-26-minus-half.md) | Minus-Half Theorem, and the reduction of the open leg to G30_agg < 1/2 | | [natal-cap-30-skeleton-bound.md](natal-cap-30-skeleton-bound.md) | Skeleton Collapse Theorem, Aggregate 30-Skeleton Bound, the exception criterion | | [natal-cap-36-skeleton-door.md](natal-cap-36-skeleton-door.md) | Skeleton Equidistribution Conjecture, the @29 certificate, and why the door is not the blocker | Related, and not part of the calm: [natal-cap-31-calm-vs-kill.md](natal-cap-31-calm-vs-kill.md) prices what the calm buys against annihilation, and the answer is the fence around the strike channel rather than non-annihilation. The vocabulary is in [GLOSSARY.md](GLOSSARY.md) under "Fused window", "The anchored calm", "The skeleton" and "The X-channel".