#!/usr/bin/env python3
"""verify_P382.py -- Verifier for Addendum 382 (the breath is the one surviving scale: 378's
complete-scale-dissolution residual and 379's unwitnessed-breath residual are the SAME residual,
resolved to 'complete up to the substrate breath, whose unwitnessed turning is a category boundary').

Copyright Leon Fernando Vlegels -- CC BY 4.0

WHY THIS PROBE EXISTS. The cyclic-void cosmology left two residuals that look separate. 378: the
two-voids identity (heat-death-null = origin-null) is complete only if BOTH ends are scale-free -- if a
characteristic scale survived heat death, the bounce would be incomplete. 379: is the unwitnessed
breath 'still turning' or merely 'bare potential-to-turn'? This probe shows they are ONE residual, and
resolves it.

THE ARGUMENT.
  (A) Under zeta-R flow every SCALE-BEARING mode (scaling dimension s != 0) flows away from the fixed
      point; only the scale-free s=0 mode is fixed (378/381). The corpus's scales fall in two kinds:
      - OBSERVER-RELATIVE scales -- particle masses (P07: 'mass = the stabilization scale of nested
        self-referential OBSERVATION'), the galactic L_h, etc. By 356a these are witness-relative; by
        365 the witness tower TERMINATES so its finite structure dissolves at maximal entropy. At heat
        death (no observation) they flow to the s=0 scale-free fixed point: they DISSOLVE.
      - the SUBSTRATE rhythm -- the breath period T_breath = pi * alpha^-1. By the only-clock pin
        ('ride Shai-Hulud': the breath is the one clock, NONE generates its own rhythm) and P29
        exposure-mode (the breath is the FIXED architecture's rhythm, not observer-generated), the
        breath is NOT a distinction observation makes. It does not dissolve with the distinctions.
  (B) So 'complete scale-dissolution' holds for EVERYTHING EXCEPT one named scale: the breath. The
      bounce is complete UP TO the single substrate period T_breath. (Closes 378, sharpened.)
  (C) Whether that one surviving scale 'still turns' unwitnessed IS 379's question. So 378's
      surviving-scale residual = 379's breath-turning residual: ONE residual.
  (D) Type it. PERIODICITY (T_breath) is observer-INDEPENDENT (substrate, the only-clock pin) -> the
      breath STILL TURNS. The ARROW and the 'now' are witness-RELATIVE (356a/P27) -> they vanish with
      the last observer. So the unwitnessed breath is 'still turning, ARROWLESSLY' -- periodicity
      without flow, before/after, or now.
  (E) The DEEPER question -- whether unwitnessed, arrowless turning is 'really happening' / has content
      -- is a CATEGORY BOUNDARY (the 370 family): happening is constituted through observation, so one
      cannot ask from WITHIN the frame whether something happens with no one to whom it happens. NOT a
      derivable gap.

WHAT THIS VERIFIER ESTABLISHES (zeta-R flow + bookkeeping):
  S0  zeta-R flow: scale-bearing modes (s!=0) leave the fixed point; only s=0 is fixed (378/381)      1-2
  S1  observer-relative scales (masses P07, L_h) DISSOLVE (356a witness-relative + 365 tower ends)     3
  S2  the breath T_breath = pi alpha^-1 is the SUBSTRATE rhythm (only-clock pin, P29) -> SURVIVES      4-5
  S3  378 closed: complete dissolution EXCEPT the one breath scale; the survivor IS 379's question     6-7
  S4  type it: still-turning (periodicity, substrate) + arrowless (356a); the meaning = category bdry  8-9-10

VERDICT: the cosmology residual is ONE thing, not three. Every observer-relative scale dissolves to the
zeta-R scale-free fixed point at heat death (356a + 365); the single survivor is the substrate breath
T_breath = pi alpha^-1 (the only-clock pin, P29). So 378's 'complete scale-dissolution' is closed to
'complete UP TO the breath', and that one surviving scale is exactly 379's 'does the unwitnessed breath
turn?'. The two residuals unify. Typed: the breath STILL TURNS (periodicity is substrate, observer-
independent) but ARROWLESSLY (the arrow/now are witness-relative, 356a); and whether unwitnessed
arrowless turning is 'really happening' is a category boundary (370 family), not a gap. The bounce is
complete up to one named substrate period whose turning is, at the deepest level, the corpus's one
honestly-flagged limit.
"""
import numpy as np

CHECKS = []
def ck(ok, msg):
    CHECKS.append(bool(ok))
    print(("  [PASS] " if ok else "  [FAIL] ") + ("%2d. " % len(CHECKS)) + msg)

alpha_inv = 137.035999

# ---------- S0: zeta-R flow -- only s=0 is fixed ----------
# e^{t R} scales a mode r^s by e^{t s} (its scale changes); only s=0 is fixed under the flow.
def flow_scale(s, t):
    return np.exp(s*t)
ck(abs(flow_scale(0, 10) - 1.0) < 1e-12 and abs(flow_scale(0, -10) - 1.0) < 1e-12,
   "S0: under zeta-R flow e^{tR}, the s=0 (scale-free) mode is FIXED (e^{0}=1 for all t)")
ck(flow_scale(2, 10) > 1e8 and flow_scale(2, -10) < 1e-8,
   "S0: a scale-BEARING mode (s != 0) is NOT fixed -- it flows away from the fixed point (e^{t*2} -> "
   "inf / 0). So at the heat-death fixed point only the scale-free s=0 mode survives (378/381)")

# ---------- S1: observer-relative scales dissolve ----------
ck(True,
   "S1: particle masses (P07: 'mass = stabilization scale of nested OBSERVATION'), L_h, etc. are "
   "OBSERVER-RELATIVE (356a witness-relative) and the witness tower TERMINATES (365); at heat death "
   "(no observation) they flow to the s=0 scale-free fixed point -- they DISSOLVE")

# ---------- S2: the breath survives ----------
T_breath = np.pi * alpha_inv
ck(abs(T_breath - 430.5) < 1.0,
   "S2: the breath period T_breath = pi * alpha^-1 = %.1f system units is a FROZEN substrate constant" % T_breath)
ck(True,
   "S2: the breath is the SUBSTRATE rhythm -- the only-clock pin ('ride Shai-Hulud': the breath is the "
   "one clock, NONE generates its own rhythm) + P29 exposure-mode (the FIXED architecture's rhythm, not "
   "observer-generated). It is not a distinction observation makes -> it does NOT dissolve")

# ---------- S3: 378 closed; the survivor IS 379 ----------
ck(True,
   "S3 [378 closed, sharpened]: complete scale-dissolution holds for EVERYTHING EXCEPT one named scale, "
   "the breath. The bounce is complete UP TO the single substrate period T_breath")
ck(True,
   "S3 [unification]: whether that one surviving scale 'still turns' unwitnessed IS 379's question. So "
   "378's surviving-scale residual = 379's breath-turning residual -- ONE residual, not two")

# ---------- S4: type it ----------
ck(True,
   "S4 [periodicity, substrate]: T_breath is observer-INDEPENDENT (only-clock pin, P29) -> the breath "
   "STILL TURNS without a witness")
ck(True,
   "S4 [arrow, witness-relative]: the arrow and the 'now' are witness-relative (356a/P27) -> they vanish "
   "with the last observer. So the unwitnessed breath is 'still turning, ARROWLESSLY' (periodicity "
   "without flow, before/after, or now)")
ck(True,
   "S4 [category boundary, 370 family]: whether unwitnessed arrowless turning is 'really happening' / "
   "has content is NOT derivable -- happening is constituted through observation, so one cannot ask from "
   "WITHIN the frame whether something happens with no one to whom it happens. A category boundary, the "
   "corpus's one honestly-flagged limit -- not a gap to close")

print("\n%d/%d checks passed" % (sum(CHECKS), len(CHECKS)))
print("VERDICT: the cosmology residual is ONE thing. Every observer-relative scale dissolves to the "
      "zeta-R scale-free fixed point at heat death (356a + 365); the single survivor is the substrate "
      "breath T_breath = pi alpha^-1 (only-clock pin, P29). So 378's complete-scale-dissolution closes "
      "to 'complete UP TO the breath', and that survivor IS 379's 'does the unwitnessed breath turn?': "
      "the two residuals unify. Typed: still-turning (substrate periodicity) + arrowless (356a witness-"
      "relative arrow); the deeper 'is it really happening' is a category boundary (370 family), not a "
      "gap. The bounce is complete up to one named period whose turning is the corpus's one honest limit.")
