Price the p19 coded-reverse chain: conditional κ = 0.0033999964

research/coded-reverse-word-p19/LIFT.json

@@ -0,0 +1,26 @@
+{
+  "commuting_letters": [
+    "I",
+    "R"
+  ],
+  "p19_entries": 2179072,
+  "p19_recodings": {
+    "even-gauge": 77,
+    "odd-gauge": 77
+  },
+  "p2_entries": 229376,
+  "p2_recodings": {
+    "coded-all/R": 14,
+    "even-gauge/R": 9,
+    "odd-gauge/I": 9,
+    "odd-gauge/R": 9,
+    "transient/D": 6
+  },
+  "rejected_letters": [
+    "D",
+    "Q"
+  ],
+  "scope": "exact operator identity and local gauge bill; no tariff, compiler or kappa claim",
+  "status": "PASS_CODED_REVERSE_GLOBAL_GAUGE_LIFT",
+  "thin_source": "S = Q D C^-1 Q^-1 D^-1 = C^-1"
+}

research/coded-reverse-word-p19/OP-RECORD-SCHEMA.md

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+# The frozen native op stream: the specification, and what it covers
+
+## Where the specification is
+
+`research/kappa-lean-verification-20261022/` holds the PR4470/PR4610 lineage's own transcription of
+the native word. It is the authority for the record encoding, and it is pinned in
+`P19_NATIVE_APPLY.json` by path and SHA-256:
+
+| file | what it defines |
+|---|---|
+| `NativeCore.lean` | the event kinds, the `step` transition with its frame guards, the `scalarAllowance` tariff, and `checkSegment` — all checked by ordinary kernel reduction |
+| `native_generate.py` | the record -> event `encode`, the `paid_index`/`warp_index` catalogues, and the chunked state loop |
+
+Upstream these run under Lean on the word whose payload SHA-256 is
+`4409d2d9328fffbd276bb03fb800f59a33ec3b2ab15f79a330a7af66e75110cc`
+(the word frozen in `research/warp-interface-20261022/`, present here).
+
+## The schema
+
+Event kinds, from `NativeCore.lean`: `0 marker, 1 climb, 2 center, 3 warp, 4 add, 5 scale, 6 clear,
+7 copy, 8 adapter`. Persistent roles are `0..631`; role `632` is the owned C₀. A record maps to a
+nine-field event `(kind, role, source, input, output, reference, operator, numerator, denominator)`:
+
+| record | event |
+|---|---|
+| `["phase", name]` | kind 0, no state change |
+| `["adapter", name, a, b]` | kind 8, no state change |
+| `["climb", tag, role, from, to, rank]` | kind 1: the role moves `from -> to`, `paid[rank] += 1`; must be ascending |
+| `["center", a, b, rank, …]` | kind 2: role 632 moves `a -> b`, `paid[rank] += 1` |
+| `["warp", ["L", role], op, from, to]` | kind 3: the role moves `from -> to` under operator `op` (negative = inverse) |
+| `["scalar", ["add", dst, src, ca, cb], field]` | kind 4, both roles must hold frame `field` |
+| `["scalar", ["scale", dst, num, den], field]` | kind 5 |
+| `["scalar", ["clear", dst], field]` | kind 6, targets role 632 |
+| `["scalar", ["copy", dst, src], field]` | kind 7 |
+
+## What the specification deliberately excludes
+
+`NativeCore.lean`'s own docstring: *"This file deliberately does not model amplitudes, Clifford
+phases, or the free noncommutative endpoint algebra."* So it certifies the **frame trace, the paid
+histogram and the scalar tariff** — not operator equality.
+
+## What this package does with it
+
+`p19_native_apply.py` re-implements `encode` + `step` + `scalarAllowance` in Python, independently of
+the Lean run, and executes both orientations of the frozen word this package prices: 21,449 records
+and 20,991 state steps each, every declared input frame equal to the role's current frame, the
+persistent roles ending on `canonical.final`, and the paid histogram `{1:2201, 2:412, 3:510, 4:127,
+5:40, 8:8}` plus the tariff (158,120 forward / 158,168 backward) **derived** from the trace. As a
+control the lineage word derives its own `{1:2201, 2:412, 3:506, 4:135, 5:36, 8:8}`.
+
+The operator side is covered separately by `P19_LOWERING.json`, which binds each emitted gate to the
+primitive stated in `research/coded-native-caller/PHYSICAL.md`.
+
+## What is still missing
+
+Encoding the 259 p19 chain gates *into* this event stream — i.e. the producer's own operator/phase
+lowering of a unit. That artefact exists upstream, not in this repository, so producer instantiation
+of the chain remains an inherited premise.

research/coded-reverse-word-p19/P19_ATTACH.json

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+{
+  "D_mass": 68782,
+  "D_status": "inherited paid profile, unchanged and not derived",
+  "T_mass": 12008,
+  "T_realised": {
+    "153": 1232,
+    "17": 336,
+    "25": 336,
+    "33": 336,
+    "4": 532,
+    "41": 336,
+    "49": 336,
+    "57": 336,
+    "65": 336,
+    "7": 133,
+    "73": 336,
+    "8": 893,
+    "9": 6530
+  },
+  "complex_root_invoiced": 0.00757853519,
+  "complex_root_realised": 0.20984141991109154,
+  "guards": {
+    "alpha": 0.7000523544831928,
+    "alpha_limit": "999999999/1000000000",
+    "alpha_pass": true,
+    "delta": 0.6689557772031509,
+    "delta_limit": "97/100",
+    "delta_pass": true,
+    "gamma": 0.6775343896533879,
+    "gamma_limit": "97/100",
+    "gamma_pass": true
+  },
+  "kappa": "951999/280000000",
+  "kappa_decimal": 0.0033999964285714285,
+  "note": "the realised census has a larger complex root than the invoice model, so the complex side has more slack at the BIT-capped endpoint; the delta guard is the one test that can tighten, and it is reported explicitly",
+  "raw_moment_sign_at_tested": "positive",
+  "status": "SUPERSEDED_DIAGNOSTIC",
+  "superseded_because": "attachment computed from the row-closure census",
+  "tested_saving": "2380001/700000000",
+  "used_for_active_claim": false
+}