sica-fondt/src/endocrine/etr/etr_invariants.md

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)

Each axis is bistable with five zones per pass (radial map by |v|), with unstable watersheds at 7 and 45:

 0 ─SNAP_IN─ 7 ─SOFT→─ 17 ═══BAND═══ 35 ─INCOH→─ 45 ─SNAP_OUT─ 50(≡−50)
  flip(thru 0)  weak pull    slack      firm pull   flip(over wrap)

(mirrored on the negative pole; the whole axis wraps at ±50)

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 ≤
L3 zones	C5	Five zones per pole by `
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 snap/flip	C3	A pole-flip happens only through a snap zone — inner snap across 0 (`
L8 mechanism	C3	"Opposition" = a restoring force on the drift, not an out-of-band cost. (realised by construction — the force is added alongside drift)

Constants

BAND_LO = 17, BAND_HI = 35, WRAP = 50, and the watersheds SNAP_INNER = 7, SNAP_OUTER = 45 are law (L1–L3, L7), not fitted. Fitted (so tests pass — never asserted ahead of a test):

• GAIN_SOFT = 0.25, GAIN_INCOH = 0.5 — the basin restoring is a spring toward the band centre (26); SOFT is deliberately weaker than INCOH (Anja). A centre target makes a step cross into [17,35] and stop (an edge target would asymptote onto 17 and fail L2). Valid range 0 < GAIN < ~2.
• SNAP_MARGIN = 2 — how far past the opposite watershed a snap deposits the point (inner → opposite SOFT at ±9; outer → opposite INCOH at ±43). Behaviour: [10 10 10] → +band (same pole); [5 5 5] → −band (inner snap flips); [47 47 47] → −band (outer snap flips). COUPLING (L5 strength/mapping) remains TBD — open seam, not to be invented.

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).
• zones: etr_axis_zone returns SNAP_IN/SOFT/IN_BAND/INCOH/SNAP_OUT at 5/10/25/40/47.
• L3: basin direction +sign(v) in SOFT, −sign(v) in INCOH, 0 in band; force nonzero in SOFT & INCOH, zero in snap zones; |restoring(SOFT)| < |restoring(INCOH)| (weak soft-pull).
• L2: a SOFT-zone zero-drift start settles into the band without flipping sign.
• L7: a SNAP_IN start lands in the opposite SOFT then settles in the opposite band; a SNAP_OUT start lands in the opposite INCOH then settles in the opposite band (both flip the pole).
• 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.

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 (five-zone axis fitted — 26 PASS / 0 FAIL / 1 PEND)

Green: L1 wrap; zone classification; L3 basin direction + restoring magnitudes (SOFT/INCOH, fitted) + snap-zones-carry-no-force + weak-soft-pull; L2 same-pole convergence; L7 snap/flip (inner across 0, outer over the wrap — both land just past the opposite watershed and settle in the opposite band); L4 drift-must-be-fed; L5 coupling-off identity; L8 realised by construction. Pending: L5 active coupling (C1, open seam) — the only remaining stub.