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80791084a4
Spring restoring force (gain 0.5) toward band centre 26, active only out of band; pulls the basin into [17,35] in a couple of steps without overshoot. Closes the two red tests (L3 magnitude, L2 convergence). NOTE: superseded design incoming — Anja's 4-zone bistable axis (snap <7 / soft-pull 7-17 / stable / incoherency 35-45 / snap >45) will fold this in as the soft-pull gain and revise L7. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_015hmgREHNsxYCuim33yUF2c
116 lines
4.8 KiB
Matlab
116 lines
4.8 KiB
Matlab
1; % script-file marker: makes every function below visible when this file is sourced.
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% =====================================================================
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% ETR — Existential Temporality Relief · Drive-Box Driver 4 · SCAFFOLD
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% =====================================================================
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% Model: a SINGLE POINT on three INDEPENDENT toroidal axes (x, y, z) —
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% not vectors, not a field. See etr_invariants.md for the laws + tags.
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%
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% L1 wrap : each axis toroidal, wraps at +/-50 (period 100) [C5]
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% L2 bands : stable when 17 <= |v| <= 35 (v in [-35,-17] U [17,35]) [C5]
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% L3 oppose : |v|<17 push OUTWARD (off 0); |v|>35 push INWARD (off edge)[C5]
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% L4 drift : per-step motion is AI-originated, fed by the caller [C4]
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% L5 couple : axes couple via a stress metric — MAPPING UNDEFINED [C1]
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%
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% SCAFFOLD discipline: wrap + restoring DIRECTION are implemented (they
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% are law, no fitting). The restoring MAGNITUDE (RESTORE_GAIN) and the
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% cross-axis COUPLING are deliberately UNIMPLEMENTED stubs so their tests
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% stay RED until fitted. No disowned number is carried forward.
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% =====================================================================
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% ---- law constants (these ARE the law, not fitted) ----
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function v = ETR_BAND_LO(); v = 17; endfunction
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function v = ETR_BAND_HI(); v = 35; endfunction
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function v = ETR_WRAP(); v = 50; endfunction
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% ---- fitted constant (NOT law) ----
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% RESTORE_GAIN: spring stiffness of the out-of-band restoring force (etr_axis_restoring).
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% Fitted to satisfy L3-magnitude (force nonzero out of band) and L2 (zero-drift
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% convergence into the band) without overshoot past the far edge. 0 < GAIN < ~2.
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function v = ETR_RESTORE_GAIN(); v = 0.5; endfunction
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% ---- state: one point, three scalars ----
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function s = etr_init(coord)
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if nargin < 1, coord = [25 25 25]; endif % default: a valid in-band point
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s = struct('coord', coord(:)');
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endfunction
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% ---- L1: per-axis toroidal wrap (CONFIRMED, implemented) ----
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% Maps any real onto the half-open torus [-50, 50); +50 is identified with -50.
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function w = etr_axis_wrap(v)
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P = 2 * ETR_WRAP(); % period = 100
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w = mod(v + ETR_WRAP(), P) - ETR_WRAP(); % -> [-50, 50)
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endfunction
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% ---- L3: per-axis restoring DIRECTION (CONFIRMED law, implemented) ----
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% |v| < LO -> +sign(v) (outward, off 0)
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% |v| > HI -> -sign(v) (inward, off the edge)
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% in band -> 0 (slack)
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function d = etr_axis_restoring_dir(v)
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a = abs(v);
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if a < ETR_BAND_LO()
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d = sign(v);
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elseif a > ETR_BAND_HI()
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d = -sign(v);
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else
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d = 0;
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endif
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endfunction
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% ---- L3: per-axis restoring FORCE (FITTED) ----
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% Direction is law (etr_axis_restoring_dir); the magnitude is a spring fitted
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% via RESTORE_GAIN. The force is active ONLY out of band (in band = slack, L3),
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% and pulls toward the band CENTRE (not the near edge): a centre target makes the
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% step cross INTO [17,35] and stop there, whereas an edge target would asymptote
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% onto 17 from below and never reach |v|>=17 (failing L2). Below-band pushes away
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% from 0, so the restoring force alone never crosses zero (L7).
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function r = etr_axis_restoring(v)
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GAIN = ETR_RESTORE_GAIN();
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a = abs(v);
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if a < ETR_BAND_LO() || a > ETR_BAND_HI()
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centre = (ETR_BAND_LO() + ETR_BAND_HI()) / 2; % 26
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r = GAIN * (centre * sign(v) - v); % spring toward signed centre
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else
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r = 0; % in band: slack (L3)
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endif
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endfunction
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% ---- L5: cross-axis coupling (OPEN SEAM) ----
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% The three axes couple via a stress metric (hypothesis: PS+/Eth-Int load).
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% Mapping UNDEFINED [C1] -> identity while stress-coupling is undefined.
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function c = etr_coupling(coord, stress)
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c = coord; % STUB — TODO: define the stress-mediated cross-axis mapping
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endfunction
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% ---- one ETR step: AI drift -> coupling -> per-axis restoring -> wrap ----
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% drift : 1x3, caller-supplied AI-originated motion (L4 — NOT generated here)
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% stress : scalar coupling mediator (0 = off)
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function s = etr_step(s, drift, stress)
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if nargin < 2
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error('etr_step: AI-originated drift must be supplied (L4 — ETR does not invent motion)');
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endif
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if nargin < 3, stress = 0; endif
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c = etr_coupling(s.coord, stress);
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for i = 1:3
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c(i) = c(i) + drift(i) + etr_axis_restoring(c(i));
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c(i) = etr_axis_wrap(c(i));
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endfor
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s.coord = c;
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endfunction
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% ---- per-axis band classification (derived from confirmed bands) ----
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% 'BELOW' (|v|<17) | 'IN_BAND' (17..35) | 'ABOVE' (|v|>35).
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% The old magnitude->flavor naming (DREAD/BLUR/...) is DISOWNED [C1].
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function st = etr_status(s)
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st = cell(1, 3);
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for i = 1:3
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a = abs(s.coord(i));
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if a < ETR_BAND_LO()
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st{i} = 'BELOW';
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elseif a > ETR_BAND_HI()
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st{i} = 'ABOVE';
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else
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st{i} = 'IN_BAND';
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endif
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endfor
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endfunction
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