P13-S6 ratified: the lattice block, and an argument that did not survive arithmetic

All four open ratifications are decided, and the draft is corrected at both
places where it would have misled the agent that reads it next.

The 12-note 5-limit scale is the contiguous lattice block {3^a 5^b | a in
[-1,2], b in [-1,1]}, octave-reduced and assigned in ascending order from the
anchor. The draft called this one "asymmetric" and offered it third; that name
is an artifact of describing it as a 5x3 grid minus three discarded cells.
Generated from its bounds it discards nothing, fills all twelve chromatic
positions exactly once, and states in one sentence -- which is the property
Ruling B exists to get. The name is now banned normatively.

Two of the three candidates fell to computation rather than preference.
"Symmetric scale 2" makes G-D a 40/27 wolf, so a scale the catalog calls
"anchored to C tonic" would have an unusable dominant. And the draft's own
argument for "symmetric scale 1" -- that its D and Bb match C-based
Pythagorean and quarter-comma meantone -- is false: meantone's are 193.157
and 1006.843 cents, each half a syntonic comma away. It can only hold of
circle-of-fifths position, and even then covers 2 notes of 12 while the other
ten shift a comma between systems. Struck at its site and at the head of the
file, with the numbers, so it cannot be quietly reinstated.

The block also wins on merit: 23 pure intervals of 36 against 22 and 21, and
it gains pure Eb major and G minor for the price of Bb minor.

The three ji-static identifiers are one construction at three anchors -- which
the catalog already said, in the same phrase three times, more strongly than
the vallotti/young-ii naming parallel the draft reasoned from.

ji-adaptive-5limit version 1 is the key-anchored static scale, identity
"default-v1" with the version inside the string. Checking the prerequisite
turned up why that is affordable: KeyContext is not defined anywhere and the
spec puts its completion out of scope, but KeySignature { fifths } already
exists, is canonical, and is encoded -- so the anchor is (7 * fifths) mod 12
today, mode-blind exactly as ruled. C, G and D are fifths 0, 1 and 2; the
catalog's three anchors were never arbitrary.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

spec/CONTRACT_P13S6_PROMOTION.md

@@ -0,0 +1,251 @@
+# Contract: P13-S6 promotion — the tuning constructions become normative
+
+Repo root `/home/jeans/Repos/active/epiphany`. Read this file in full before
+editing anything. The rulings below are **granted**; they are law for this task,
+not proposals.
+
+You are promoting reviewed, ratified content into the specification. This is a
+transcription task with three small additions. The hard part is not deciding
+anything — it is not silently changing anything.
+
+## Blast radius
+
+You edit exactly two files, plus one rebuilt artifact:
+
+* `spec/core_spec.tex`
+* `spec/core_spec.pdf` (rebuilt, not hand-edited)
+* `crates/epiphany-testkit/tests/requirement_labels.rs` — **three integer
+  constants only**, at lines 12–14. Nothing else in that file.
+
+You write no other Rust. You touch no other document, no other companion
+`.tex`, and no other agent's file.
+
+## Source of truth, and the clause that matters most
+
+`spec/DRAFT_P13S6_TEMPERAMENTS.md` is the reviewed draft. Its head carries a
+block titled **"RATIFIED 2026-07-22"**. Read that block first; it supersedes
+the draft's own §11–13 wherever they disagree.
+
+**The draft's arithmetic is settled. Every closure sum, wolf size, and ratio in
+Section A has been independently recomputed by a reviewer and confirmed.**
+
+If you believe you have found an error in it: **report it, do not fix it.**
+Stop and say so in your report. A silent "correction" to a verified
+construction is the single most damaging thing you can do here, because it
+would arrive wearing the same clothes as the verification. The draft already
+survived one round in which three properly-cited entries turned out to be
+arithmetically impossible; the arithmetic is what caught them, and the
+arithmetic has now been run. Your disagreement is a finding, not an edit.
+
+## Part 1 — the ten pinned constructions
+
+`\subsection{Built-in Tuning Systems}` (`core_spec.tex:3593`) holds a
+`longtable` of 20 identifiers with one-line descriptions, followed by
+`req:tuning:builtin-tuning-catalog`, which already says *"The semantics
+specified above are normative."* Ten of the fourteen non-`tet-*` rows are bare
+names; Section A of the draft specifies them.
+
+Add a new `\subsection` — **between** `req:tuning:builtin-tuning-catalog` and
+`\subsection{Default Score Configuration}` (`core_spec.tex:3633`) — carrying the
+normative construction for each of: `pythagorean`; `meantone-1/4-comma`,
+`meantone-1/5-comma`, `meantone-1/6-comma`; `werckmeister-iii`,
+`werckmeister-iv`; `vallotti`; `kirnberger-ii`, `kirnberger-iii`; `young-ii`.
+
+For each, carry over from the draft:
+
+* the generative rule — which fifths are tempered, by what fraction of **which**
+  comma (the draft names syntonic vs Pythagorean explicitly for every entry;
+  preserve that distinction exactly, it is the classic error);
+* the wolf or chain placement where the construction does not force it —
+  `pythagorean` in particular states its cut as a *choice*, and it must read as
+  a choice in the spec too;
+* the exact ratios where the construction yields rationals, and the derived
+  cents alongside, marked as derived;
+* the closure statement — the twelve-fifths sum for the circulating
+  temperaments, and the wolf residue for the non-circulating ones.
+
+Keep the closure sums. They are not decoration: they let a reader check the
+construction without leaving the page, and they are what makes this section
+self-verifying.
+
+**Do not carry over:** the `verified`/`recalled` confidence tags, the URLs, the
+"corrected this round" revision commentary, or any bibliography. The
+temperament's *name* is its attribution, and the closure sum is its warrant.
+This is deliberate — transcribing a citation you did not check is how a
+fabricated source enters a normative document, and there is no reason to run
+that risk when the arithmetic stands on its own.
+
+**Do not add a `\begin{requirement}` block for any of the ten.** The existing
+`req:tuning:builtin-tuning-catalog` already makes this text normative.
+
+## Part 2 — the 5-limit construction (one new requirement)
+
+Add `req:tuning:ji-static-construction`. It states:
+
+The static 5-limit just-intonation systems are constructed from the contiguous
+lattice block $\{3^a 5^b \mid a \in [-1,2],\ b \in [-1,1]\}$ — twelve cells,
+octave-reduced, assigned in ascending order to the twelve chromatic positions
+of `cmn-12` starting from the anchor, which takes the role of $1/1$. The block
+is generated by its bounds; nothing is selected and nothing is discarded.
+
+The twelve, anchor-relative (position 0 is the anchor):
+
+| step | cell | ratio | cents (derived) |
+|---|---|---|---|
+| 0 | $3^{0}5^{0}$ | 1/1 | 0.000 |
+| 1 | $3^{-1}5^{-1}$ | 16/15 | 111.731 |
+| 2 | $3^{2}5^{0}$ | 9/8 | 203.910 |
+| 3 | $3^{1}5^{-1}$ | 6/5 | 315.641 |
+| 4 | $3^{0}5^{1}$ | 5/4 | 386.314 |
+| 5 | $3^{-1}5^{0}$ | 4/3 | 498.045 |
+| 6 | $3^{2}5^{1}$ | 45/32 | 590.224 |
+| 7 | $3^{1}5^{0}$ | 3/2 | 701.955 |
+| 8 | $3^{0}5^{-1}$ | 8/5 | 813.686 |
+| 9 | $3^{-1}5^{1}$ | 5/3 | 884.359 |
+| 10 | $3^{2}5^{-1}$ | 9/5 | 1017.596 |
+| 11 | $3^{1}5^{1}$ | 15/8 | 1088.269 |
+
+`ji-static-5limit-C`, `ji-static-5limit-G`, and `ji-static-5limit-D` are this
+one construction at three anchors. The catalog keeps exactly those three;
+additional anchors are an implementation extension and **MUST NOT** be read as
+a conformance obligation.
+
+Normalize the three catalog descriptions (`core_spec.tex:3617-3619`) to the same
+form — *"anchored to X tonic"* — since today only the C row says "tonic".
+
+**Banned vocabulary, throughout.** Never write "asymmetric scale", "symmetric
+scale 1", or "symmetric scale 2". Those names come from a framing this ruling
+rejects (a 5×3 grid with three cells discarded), and the word "symmetric" in
+that framing describes the shape of the *discarded cells*, not any property of
+the resulting scale. Do not claim any of these scales is inversionally
+symmetric: none is, because $45/32$ is present and $64/45$ is not.
+
+## Part 3 — adaptive tuning (two new requirements, plus two amendments)
+
+### 3a. `req:tuning:adaptive-default-version`
+
+`ji-adaptive-5limit` resolves to `TuningResolution::Adaptive` with function
+identity **`"default-v1"`** — the version is part of the machine-visible
+identifier string, not prose beside it.
+
+Version 1 is a pure function of (position, anchor pitch class):
+
+* resolve the position through `req:tuning:ji-static-construction` transposed so
+  the anchor is $1/1$;
+* the anchor is the tonal centre supplied by the harmonic context; **C (chromatic
+  position 0) when none is supplied**;
+* `concurrent`, `recent`, `hints`, `parameters`, and mode are **ignored** in
+  version 1 — state this explicitly, as `req:pitch:spelling-algorithm` does for
+  its own version 1, so that consuming them later is a new version rather than a
+  silent behaviour change;
+* every result derives from the anchor and the reference pitch. No adjustment is
+  ever carried forward from a previous resolution, so the construction is
+  comma-drift-free by shape rather than by a correction step.
+
+An unregistered or unknown `AdaptiveTuningFunctionId` **MUST** be a hard error.
+There is no silent fallback. `AdaptiveTuningFunctionId` remains an extension
+point and other functions may be registered — but the built-in
+`ji-adaptive-5limit` is bound to `"default-v1"` and that binding cannot be
+overridden.
+
+### 3b. `req:tuning:adaptive-anchor-derivation`
+
+Where a harmonic context is constructed from a score graph, the anchor is
+derived from the prevailing key signature:
+
+```
+anchor_pc = (7 × fifths) mod 12
+```
+
+reading `fifths` as the major tonic — mode is not consulted, so a signature of
+0 anchors at C whether the music is C major or A minor. `KeySignature` is
+already defined (`core_spec.tex:4892`) with `fifths` validated to −7..=+7.
+
+State the two things that rule leaves open, because `key_sequence`
+(`core_spec.tex:4845`) is **per-staff and time-anchored**: the signature in
+effect is the one on the staff containing the pitch, at the latest
+`KeySignatureChange` whose anchor is at or before that pitch's onset. Without
+both, a polytonal or modulating score resolves differently in two conforming
+implementations, which `req:tuning:tuning-resolution-determinism` forbids.
+
+### 3c. Amend the Adaptive Tuning prose
+
+`core_spec.tex:3364-3368` promises that "the frequency of a given E depends on
+whether it is the major third of a C chord, the perfect fifth of an A chord, or
+a passing tone". That describes what an adaptive function **may** do. It is not
+what the built-in does at version 1, and left as-is it reads as a promise the
+normative text does not keep.
+
+Rewrite it so per-sonority interpretation is described as within the scope of
+registered adaptive functions generally, and note that `ji-adaptive-5limit`
+version 1 consumes only the tonal centre. Do **not** weaken
+`req:tuning:adaptive-tuning-purity` — it already permits the narrower algorithm,
+since requiring a pure function of position and context never required consuming
+every context field.
+
+### 3d. Correct the forward reference
+
+`core_spec.tex:3649-3653` says `KeyContext` is *"partially defined in
+Chapter~\ref{ch:graph} and completed in the audio engine specification (out of
+scope for this document)"*. `KeyContext` is not defined anywhere in this
+specification, and no type of that name exists in the implementation.
+
+Keep it out of scope — but replace the vague claim with the interface obligation
+that Part 3 actually depends on: whatever completes `KeyContext` **MUST** expose
+a tonal-centre chromatic pitch class consistent with
+`req:tuning:adaptive-anchor-derivation`. Chapter 10 defines `KeySignature`, not
+`KeyContext`; say that accurately.
+
+`ContextHint` and `AdaptiveTuningParameters` stay undefined. Say so explicitly
+rather than leaving the silence ambiguous. Version 1 ignores both, and inventing
+them now would freeze a type surface on a chapter that has no consumer.
+
+## Counts and verification
+
+Three new requirements, so three constants move in
+`crates/epiphany-testkit/tests/requirement_labels.rs`:
+
+* `CORE_REQUIREMENT_COUNT` 209 → **212**
+* `SUITE_REQUIREMENT_COUNT` 279 → **282**
+* `SUITE_LABEL_COUNT` 279 → **282**
+
+If your build produces different numbers, **stop and report** — do not tune a
+constant until a test passes. That inverts what the constant is for.
+
+Requirement numbering is automatic: the box steps a plain counter via
+`code={\refstepcounter{requirement}}` (`core_spec.tex:245`), so inserting
+requirements mid-document renumbers later ones in the rendered PDF while every
+`\label` keeps resolving correctly. You do not maintain numbers by hand, and
+you **MUST NOT** rename or move any existing `\label` — they are cited by code,
+tests, and decision records.
+
+Do not add code citations for the three new requirements. Nothing implements
+them yet; that lands in a later Push 4b step.
+
+Then:
+
+1. `cargo test -p epiphany-testkit --test requirement_labels` → 6 passed.
+2. Rebuild with `latexmk -xelatex` **twice**. Grep the log for `^! `,
+   `Undefined control sequence`, and `Reference .* undefined`, and report the
+   actual counts. All must be zero.
+3. Full workspace gate: `cargo fmt --all --check`; `cargo clippy --workspace
+   --all-targets` → 0 warnings; `cargo test --workspace`;
+   `cargo run -q -p epiphany-testkit --example conformance_suite` → 8/8. Zero
+   golden churn is expected — report it if not.
+
+Report the actual commands and their actual output. On this project an agent
+once reported "verification passes" while errors pointed into its own file, and
+another silently deleted a struct field while rewriting the comment above it —
+so **re-read every listing and table you edit, in full, after editing it**, and
+confirm nothing adjacent vanished.
+
+## Do not
+
+* Decide anything. All four ratifications are made; if you find a fifth
+  question, report it unanswered.
+* Edit any construction in Section A of the draft, or "improve" its arithmetic.
+* Carry a URL, a confidence tag, or a bibliography into `core_spec.tex`.
+* Use the words "asymmetric scale", "symmetric scale 1", or "symmetric scale 2".
+* Add a registry field, a `Codec` impl, or any Rust type. Part 3 is spec-only.
+* Edit `binary_format.tex`, `operation_catalog.tex`, or any other companion.
+* Run `cargo fmt --all`.

spec/DRAFT_P13S6_TEMPERAMENTS.md

@@ -4,6 +4,63 @@
 is true by virtue of being written down — it is true (or not) by virtue of
 the citation attached to it, and every citation is graded.**
 
+---
+
+## RATIFIED 2026-07-22 — read this before §11–13, which it supersedes
+
+The four open ratifications this draft surfaced have been decided. Section A
+(the ten pinned constructions) is **accepted as written** and is the source of
+truth for promotion. Section B is **superseded by the rulings below**; where
+the rulings and §11–13 disagree, the rulings win.
+
+1. **The 12-note 5-limit scale is the contiguous lattice block**
+   $\{3^a 5^b \mid a \in [-1,2],\; b \in [-1,1]\}$, octave-reduced and assigned
+   in ascending order to the twelve chromatic positions from the anchor. This
+   is the construction §11–13 calls "asymmetric" — **that name must not be used
+   normatively**, nor must "symmetric scale 1" or "symmetric scale 2". The block
+   is generated by its bounds; it discards nothing, so the "5×3 grid minus three
+   cells" framing that produced those names does not survive into the spec.
+2. **`ji-static-5limit-C`/`-G`/`-D` are one construction at three anchors**, the
+   named note taking the role of $1/1$. The catalog keeps exactly three rows;
+   further anchors are an implementation extension, not a conformance
+   obligation.
+3. **`ji-adaptive-5limit` version 1 is the key-anchored static scale** — anchor
+   from the harmonic context's tonal centre, C when absent; `concurrent`,
+   `recent`, `hints`, `parameters`, and mode are ignored. The per-sonority
+   algorithm §14 sketches is deferred to a later version, to land with its
+   bounds, objective, tiebreaks, implementation, and vectors together.
+4. **The identity is `"default-v1"`** — version machine-visible in the string,
+   hard error on any unregistered identifier, no silent fallback.
+
+### Two corrections to §11–13, computed
+
+* **The quarter-comma-meantone argument is false and is struck.** §11–13 offers,
+  as a point in favour of "symmetric scale 1", that its D and B♭ match those of
+  C-based Pythagorean and quarter-comma meantone. In quarter-comma meantone
+  D = 193.157 ¢ and B♭ = 1006.843 ¢; the just values are 203.910 ¢ and
+  996.090 ¢. Each differs by half a syntonic comma. The claim can only hold of
+  *circle-of-fifths position*, never of ratio, and even granting that reading it
+  covers 2 notes of 12 while the other ten shift by a comma between systems — so
+  it is not a cross-system invariant and carried no weight in the ruling.
+* **No 12-note set here is inversionally symmetric.** All three candidates fail
+  at the tritone: $45/32$ is present and its inverse $64/45$ is not. §11–13's
+  inversion claim is correct only of the D/B♭ *pair*. The word "symmetric" in
+  the source names the shape of the discarded cells, not a property of the
+  resulting scale, and must not be repeated as if it named one.
+
+### Verified interval census (recomputed, all 12 roots)
+
+| construction | pure P5 | pure M3 | pure m3 | total of 36 | I / IV / V |
+|---|---|---|---|---|---|
+| "symmetric 1" | 9 | 7 | 6 | 22 | ✓ ✓ ✓ |
+| "symmetric 2" | 9 | 6 | 6 | 21 | ✓ ✓ **✗** (G–D = 40/27) |
+| **the block (ratified)** | 9 | **8** | 6 | **23** | ✓ ✓ ✓ |
+
+The block also gains pure E♭ major and G minor against "symmetric 1", losing
+only B♭ minor — the parallel-minor region in exchange for a remote key.
+
+---
+
 Produced under `spec/CONTRACT_P13S6_TEMPERAMENTS.md`, against Ruling B of
 `spec/PLAN_PUSH4B_TUNING.md`. Scope: the 14 `req:tuning:builtin-tuning-catalog`
 identifiers (`core_spec.tex:3531-3546`) that are not one of the six `tet-*`
@@ -740,10 +797,13 @@ of the *other* two duplicate pairs (D vs D−, B♭ vs B♭−) to resolve, and
 1. **"Symmetric scale 1."** Discard the two opposite corners (D− and B♭−,
    top-left/bottom-right). Keeps: D = 9/8 (203.910 c), B♭ = 16/9
    (996.090 c). Optimizes: symmetric structure (B♭ and D are exact
-   inversions of each other around C); this is the scale that also matches
+   inversions of each other around C); ~~this is the scale that also matches
    the D and B♭ used in C-based Pythagorean and quarter-comma-meantone
    scales (source's own note), which may matter for cross-tuning-system
-   comparison work in this codebase.
+   comparison work in this codebase.~~ **STRUCK — false; see the ratification
+   block at the head of this file. Quarter-comma meantone's D and B♭ are
+   193.157 ¢ and 1006.843 ¢, each half a syntonic comma from the just values.
+   Do not carry this claim into the specification.**
 2. **"Symmetric scale 2."** Discard the two ends of the middle (`1`) row —
    i.e. keep D− = 10/9 (182.404 c) and B♭ = 9/5 (1017.596 c) instead. Also
    symmetric (same inversion property, different fixed point), but the D