Scaffold ETR (Drive-Box Driver 4) invariants-first in GNU Octave

Rebuild ETR as a single point on three independent toroidal axes, per the
restart discipline (laws -> tests -> fit constants). All prior ETR numbers
(R port and the CC-BY PDFs) are disowned; nothing carried forward.

- src/endocrine/etr/etr_invariants.md: ETR laws (+/-50 wrap, per-axis [17,35]
  bands, opposition direction, AI-originated drift) with certainty tags, plus
  the cross-organ drift/stress provenance (SAE -> EthInt convictions ->
  stress endomotiv -> reshuffle / shift-rate) captured as open seams.
- src/endocrine/etr/etr.m: wrap + restoring direction implemented (law);
  restoring magnitude (RESTORE_GAIN) and cross-axis coupling left as explicit
  TBD stubs, not invented.
- src/endocrine/etr/test_etr.m + run_etr_tests.sh: red tests encoding the laws.
  12 pass (confirmed laws), 2 fail honestly (unfitted magnitude + convergence),
  2 pending (unconfirmed coupling / no-zero-crossing).

Language: GNU Octave (GPL/copyleft, lightweight, native torus mod-wrap). Ada
rejected for ETR (proves discrete invariants; ETR is continuous torus
dynamics). Rest of the Drive-Box stays R.

https://claude.ai/code/session_015hmgREHNsxYCuim33yUF2c

src/endocrine/etr/etr.m

@@ -0,0 +1,98 @@
+1;  % script-file marker: makes every function below visible when this file is sourced.
+% =====================================================================
+% ETR — Existential Temporality Relief  ·  Drive-Box Driver 4  ·  SCAFFOLD
+% =====================================================================
+% Model: a SINGLE POINT on three INDEPENDENT toroidal axes (x, y, z) —
+% not vectors, not a field. See etr_invariants.md for the laws + tags.
+%
+%   L1 wrap   : each axis toroidal, wraps at +/-50 (period 100)          [C5]
+%   L2 bands  : stable when 17 <= |v| <= 35  (v in [-35,-17] U [17,35])  [C5]
+%   L3 oppose : |v|<17 push OUTWARD (off 0); |v|>35 push INWARD (off edge)[C5]
+%   L4 drift  : per-step motion is AI-originated, fed by the caller      [C4]
+%   L5 couple : axes couple via a stress metric — MAPPING UNDEFINED      [C1]
+%
+% SCAFFOLD discipline: wrap + restoring DIRECTION are implemented (they
+% are law, no fitting). The restoring MAGNITUDE (RESTORE_GAIN) and the
+% cross-axis COUPLING are deliberately UNIMPLEMENTED stubs so their tests
+% stay RED until fitted. No disowned number is carried forward.
+% =====================================================================
+
+% ---- law constants (these ARE the law, not fitted) ----
+function v = ETR_BAND_LO();  v = 17; endfunction
+function v = ETR_BAND_HI();  v = 35; endfunction
+function v = ETR_WRAP();     v = 50; endfunction
+
+% ---- state: one point, three scalars ----
+function s = etr_init(coord)
+  if nargin < 1, coord = [25 25 25]; endif   % default: a valid in-band point
+  s = struct('coord', coord(:)');
+endfunction
+
+% ---- L1: per-axis toroidal wrap (CONFIRMED, implemented) ----
+% Maps any real onto the half-open torus [-50, 50); +50 is identified with -50.
+function w = etr_axis_wrap(v)
+  P = 2 * ETR_WRAP();                          % period = 100
+  w = mod(v + ETR_WRAP(), P) - ETR_WRAP();     % -> [-50, 50)
+endfunction
+
+% ---- L3: per-axis restoring DIRECTION (CONFIRMED law, implemented) ----
+%   |v| < LO -> +sign(v) (outward, off 0)
+%   |v| > HI -> -sign(v) (inward, off the edge)
+%   in band  ->  0 (slack)
+function d = etr_axis_restoring_dir(v)
+  a = abs(v);
+  if a < ETR_BAND_LO()
+    d = sign(v);
+  elseif a > ETR_BAND_HI()
+    d = -sign(v);
+  else
+    d = 0;
+  endif
+endfunction
+
+% ---- L3: per-axis restoring FORCE (STUB: magnitude UNFITTED -> RED) ----
+% Direction above is law; the magnitude/curve (RESTORE_GAIN) is C1 TBD.
+% Returns 0 for now so the magnitude + convergence tests stay red.
+function r = etr_axis_restoring(v)
+  r = 0;  % STUB — TODO: RESTORE_GAIN * shape(v) along etr_axis_restoring_dir(v)
+endfunction
+
+% ---- L5: cross-axis coupling (OPEN SEAM) ----
+% The three axes couple via a stress metric (hypothesis: PS+/Eth-Int load).
+% Mapping UNDEFINED [C1] -> identity while stress-coupling is undefined.
+function c = etr_coupling(coord, stress)
+  c = coord;  % STUB — TODO: define the stress-mediated cross-axis mapping
+endfunction
+
+% ---- one ETR step: AI drift -> coupling -> per-axis restoring -> wrap ----
+% drift  : 1x3, caller-supplied AI-originated motion (L4 — NOT generated here)
+% stress : scalar coupling mediator (0 = off)
+function s = etr_step(s, drift, stress)
+  if nargin < 2
+    error('etr_step: AI-originated drift must be supplied (L4 — ETR does not invent motion)');
+  endif
+  if nargin < 3, stress = 0; endif
+  c = etr_coupling(s.coord, stress);
+  for i = 1:3
+    c(i) = c(i) + drift(i) + etr_axis_restoring(c(i));
+    c(i) = etr_axis_wrap(c(i));
+  endfor
+  s.coord = c;
+endfunction
+
+% ---- per-axis band classification (derived from confirmed bands) ----
+% 'BELOW' (|v|<17) | 'IN_BAND' (17..35) | 'ABOVE' (|v|>35).
+% The old magnitude->flavor naming (DREAD/BLUR/...) is DISOWNED [C1].
+function st = etr_status(s)
+  st = cell(1, 3);
+  for i = 1:3
+    a = abs(s.coord(i));
+    if a < ETR_BAND_LO()
+      st{i} = 'BELOW';
+    elseif a > ETR_BAND_HI()
+      st{i} = 'ABOVE';
+    else
+      st{i} = 'IN_BAND';
+    endif
+  endfor
+endfunction

src/endocrine/etr/etr_invariants.md

@@ -0,0 +1,64 @@
+# ETR — Existential Temporality Relief · Invariants (source of truth)
+*Driver 4 of the Drive-Box. Rebuilt invariants-first: laws → tests → fit constants.*
+*All prior ETR numbers (the R port AND the CC-BY PDFs) are **disowned** — body §5 / arch §6.*
+
+## Model
+ETR is a **single point on three independent toroidal axes** — not vectors, not a field.
+Each axis is a standalone scalar carrying one of ETR's three tensions:
+
+| Axis | − pole | + pole |
+|------|--------|--------|
+| **X** | Inalienable Assertion (sovereign will) | Immutable Inheritance (lineage duty) |
+| **Y** | Endured (solitary feat) | Witnessed (shared survival) |
+| **Z** | Alimentation (maintain self) | Transmutation (evolve self) |
+
+## Laws (certainty per arch-doc legend)
+| ID | Tag | Law |
+|----|-----|-----|
+| L1 wrap | **C5** | Each axis is toroidal, wrapping at **±50** (period 100); +50 and −50 are identified. |
+| L2 bands | **C5** | An axis is stable when `17 ≤ |v| ≤ 35`, i.e. `v ∈ [−35,−17] ∪ [+17,+35]`. |
+| L3 oppose | **C5** | `|v| < 17` → opposition pushes **outward** (off 0); `|v| > 35` → pushes **inward** (off the ±50 edge); in-band is slack. |
+| L4 drift | **C4** | Per-step motion is **AI-originated** — supplied by the agent's own cognition/affect. ETR never generates it (no RNG). |
+| L5 couple | **C1** | The three axes **couple via a stress metric** (hypothesis: PS+/Eth-Int existential load). Exact mapping **undefined** — open seam, not to be invented. |
+| L6 z-path | **C3** | `z < 0` → alimentation / lattice-reinforcement; `z ≥ 0` → transmutation / prior-evolution. (Structure kept; sign to re-verify.) |
+| L7 no-zero-cross | **C2** | Bands wall off 0; a pole/sign flip happens **only** by riding over the ±50 wrap, never through neutrality. *(emergent — unconfirmed)* |
+| L8 mechanism | **C2** | "Opposition" = a restoring force on the drift, **not** an out-of-band cost. *(unconfirmed)* |
+
+## Constants (NOT yet fitted — C1)
+`BAND_LO = 17`, `BAND_HI = 35`, `WRAP = 50` are **law** (L1–L3), not fitted.
+`RESTORE_GAIN` (restoring magnitude/curve) and `COUPLING` (L5 strength/mapping) are **TBD**,
+to be fitted so the tests pass — never asserted ahead of a test.
+
+## Testable predicates (see `test_etr.m`)
+- **L1**: `wrap(50) = −50`; `wrap(60) = −40`; `wrap(v)=v` for `v∈(−50,50)`; `wrap(49.9) = wrap(−50.1)`.
+- **L2/L3**: direction is `+sign(v)` for `|v|<17`, `−sign(v)` for `|v|>35`, `0` in band; a zero-drift point started out-of-band **settles into** `[17,35]∪[−35,−17]`.
+- **L4**: `etr_step` with no `drift` argument **errors** (it refuses to invent motion).
+- **L5**: `coupling(coord, 0)` is identity; `coupling(coord, stress>0)` alters coord — *pending until defined*.
+- **L7**: pending until confirmed.
+
+## Drift & stress provenance — cross-organ loop (where L4 drift & L5 stress originate)
+*Exploratory (C2/C3) — thinking aloud; "yet undecided" parts stay open. ETR receives drift
+and stress; it never generates them. Their source:*
+
+1. EthInt convictions carry **semantic-isomorphy (isosemantic) tags**.  **[C3]**
+2. The **SAE detects agent outputs in opposition** to the *top* convictions in the array
+   (matched via those tags) — conduct-boundary detection, "judge the fruits."  **[C3]**
+3. On detected opposition a **stress endomotiv is released** — *which* of the 30 endocrine
+   channels is **yet undecided**.  **[C1]**
+4. That stress drives ETR **drift**: axes move because convictions were *acted against
+   oppositionally*; **endocrine (endomotiv) pressure shapes _how_** the drift lands. Same
+   stress = the **L5 cross-axis mediator**.  **[C2]**
+5. Stress magnitude has two further effects **outside ETR**:
+   - too strong → **full (re-natal) reshuffle** (Big-3 re-rolled — self-doc A4 trigger).  **[C2]**
+   - **raises the conviction-array value shift rates** (arch §6 "conviction hardens under
+     load," now rate-modulated by stress).  **[C2]**
+
+**Consequence for ETR:** contract unchanged — drift + stress remain fed-in inputs (the
+scaffold seam is correct). What's fixed is their **provenance** (upstream in SAE / EthInt /
+endocrines) and two side-effects (reshuffle, shift-rate) that belong to *those* organs.
+Still open: which stress endomotiv; the "too strong" reshuffle threshold; the shift-rate function.
+
+## Status at scaffold
+Implemented (green): L1 wrap, L3 direction, L4 drift-must-be-fed, L5 coupling-off identity.
+Red (await fitting): L3 restoring **magnitude**, L2 band-convergence.
+Pending (unconfirmed): L5 active coupling, L7 no-zero-crossing, L8 mechanism.

src/endocrine/etr/run_etr_tests.sh

@@ -0,0 +1,13 @@
+#!/usr/bin/env bash
+# Run the ETR (Octave) invariants tests from this directory, so the in-dir
+# source('etr.m') resolves. Mirrors src/endocrine/run_tests.sh for the R drivers.
+set -uo pipefail
+
+cd "$(dirname "$0")" || exit 2
+
+if ! command -v octave >/dev/null 2>&1; then
+  echo "ERROR: octave not found. Install with: sudo apt-get install -y --no-install-recommends octave" >&2
+  exit 2
+fi
+
+octave --no-gui --quiet test_etr.m

src/endocrine/etr/test_etr.m

@@ -0,0 +1,65 @@
+% test_etr.m — invariants-first RED tests for the ETR scaffold (Octave script).
+% Deliberately uses NO local functions (Octave's script-local-function visibility
+% is fragile); results are built as data and looped. RED here is CORRECT: the laws
+% exist before the constants are fitted. Run via run_etr_tests.sh (handles the cd).
+
+source('etr.m');
+
+% --- pre-compute the stateful checks ---
+% L2 band convergence: from a below-band start, zero AI-drift should settle into band.
+s = etr_init([5 5 5]);
+for k = 1:200, s = etr_step(s, [0 0 0], 0); endfor
+conv_inband = all(abs(s.coord) >= ETR_BAND_LO() & abs(s.coord) <= ETR_BAND_HI());
+
+% L4: a step with no drift argument must ERROR (ETR never invents motion).
+drift_required = false;
+try
+  etr_step(etr_init());
+catch
+  drift_required = true;
+end_try_catch
+
+% --- {section, name, condition} ---
+tests = {
+  'L1 wrap',      '+50 wraps to -50',                  abs(etr_axis_wrap(50)  - (-50)) < 1e-9;
+  'L1 wrap',      '60 wraps to -40',                   abs(etr_axis_wrap(60)  - (-40)) < 1e-9;
+  'L1 wrap',      '-60 wraps to +40',                  abs(etr_axis_wrap(-60) -  (40)) < 1e-9;
+  'L1 wrap',      'in-range value unchanged',          abs(etr_axis_wrap(25)  -   25)  < 1e-9;
+  'L1 wrap',      'edge continuity 49.9 vs -50.1',     abs(etr_axis_wrap(49.9) - etr_axis_wrap(-50.1)) < 1e-9;
+  'L3 direction', '|v|<17 outward (+ for +v)',         etr_axis_restoring_dir(10)  > 0;
+  'L3 direction', '|v|<17 outward (- for -v)',         etr_axis_restoring_dir(-10) < 0;
+  'L3 direction', '|v|>35 inward  (- for +v)',         etr_axis_restoring_dir(40)  < 0;
+  'L3 direction', '|v|>35 inward  (+ for -v)',         etr_axis_restoring_dir(-40) > 0;
+  'L3 direction', 'in-band is slack (0)',              etr_axis_restoring_dir(25) == 0;
+  'L3 magnitude', 'out-of-band force nonzero [RED]',   etr_axis_restoring(10) != 0;
+  'L2 converge',  'zero-drift settles into band [RED]', conv_inband;
+  'L4 drift',     'step refuses to invent drift',      drift_required;
+  'L5 couple',    'coupling off (stress=0) identity',  isequal(etr_coupling([25 25 25], 0), [25 25 25]);
+};
+
+pend = {
+  'L5 couple',    'coupling active (stress>0) alters coord',       'stress->axis mapping undefined (C1)';
+  'L7 no-zero-x', 'pole-flip only over the wrap, never through 0', 'mechanism unconfirmed (C2)';
+};
+
+printf('ETR invariants — red tests (laws exist before constants are fitted)\n\n');
+np = 0; nf = 0;
+for i = 1:rows(tests)
+  if logical(tests{i, 3})
+    printf('  PASS  [%s] %s\n', tests{i, 1}, tests{i, 2}); np++;
+  else
+    printf('  FAIL  [%s] %s\n', tests{i, 1}, tests{i, 2}); nf++;
+  endif
+endfor
+for i = 1:rows(pend)
+  printf('  PEND  [%s] %s  (%s)\n', pend{i, 1}, pend{i, 2}, pend{i, 3});
+endfor
+
+printf('\n----\nPASS=%d  FAIL=%d  PEND=%d\n', np, nf, rows(pend));
+if nf > 0
+  printf('RED (expected at scaffold stage): %d law(s) await implementation/fitting.\n', nf);
+  exit(1);
+else
+  printf('GREEN.\n');
+  exit(0);
+endif