#!/usr/bin/env python3
"""
PROVENANCE: EMPIRICAL

Computation 120 -- Item 1.3 (full-SM extension of the M_* cancellation):
                   the open question settled in the NEGATIVE.
=========================================================================
STATUS (v26.21+): open-research item 1.3 has stood OPEN since the v26.09
withdrawal of the sector-blindness closure (Comps 107/108). The scalar-
sector self-mass m_h^2 = (3/2) M_*^2/(16 pi^2) stands as a parameter-free
one-loop result for the Higgs self-loop in isolation; its extension to the
top/W/Z sectors -- which would let M_* = 4 pi m_h sqrt(2/3) stand as a
FULL-theory prediction -- was left as the open question:

  "Does an explicit cancellation of the EFT-layer top/W/Z quadratic
   sensitivities exist, and what partner spectrum would it require?"

This computation answers it: NO, not within PST. It quantifies the
obstruction (the Veltman residual) and the partner sector a cancellation
would require, shows that sector is both collider-excluded and absent from
PST's spectrum, and concludes that M_* is irreducibly a scalar-sector
result. Item 1.3 is thereby settled in the negative.

THE OBSTRUCTION: THE SM VELTMAN RESIDUAL DOES NOT VANISH AT M_*
==============================================================
The SM Higgs-mass quadratic sensitivity is
  delta m_h^2 = (Lambda^2 / 16 pi^2) * [ 6 lambda + (9/4) g^2 + (3/4) g'^2
                                         - 6 y_t^2 ].
A clean boson-fermion cancellation at M_* would require the bracket (the
Veltman condition) to vanish there. It does not: the top term -6 y_t^2
dominates and the bracket is large and negative (~ -3) at both the EW
scale and M_*, with no sign change or zero in between.

THE PARTNER SECTOR A CANCELLATION WOULD REQUIRE
===============================================
To cancel the dominant -6 y_t^2 one needs BOSONIC top-partners (scalar
"stop"-like states) coupling at top strength, near M_* ~ 1.3 TeV (the
SUSY-style mechanism). Such states:
  - are collider-constrained: scalar top-partners / vector-like quarks are
    excluded by LHC to ~1.2-1.4 TeV, i.e. essentially at M_* itself;
  - would generate SMEFT / EWPO signatures that PST's "no new light
    states" premise (paper sec:wilson-ewpo) explicitly forbids;
  - are ABSENT from PST's spectrum: by Proposition F4 the emergent EFT
    below M_* is exactly the Standard Model (no superpartners), and by the
    layer-disjointness of Comp 105 the substrate cancellation lives in the
    UV shell [M_*, sqrt D], disjoint from the EFT-layer top/W/Z loops, so
    it cannot supply such partners.

CONCLUSION
==========
The full-SM extension does not exist within PST: there is no mechanism to
cancel the EFT-layer top/W/Z quadratic sensitivities, and the partner
sector that would be required is both collider-disfavoured and structurally
absent. M_* = 4 pi m_h sqrt(2/3) is therefore irreducibly a SCALAR-SECTOR
prediction (the Higgs self-loop in isolation), exactly as the paper now
scopes it. Item 1.3 is settled in the negative -- the v26.09 demotion of
M_* to scalar-sector is the final word, not a temporary state.
=========================================================================
"""

import math


# --- approximate SM MSbar couplings (squared where noted) ---
# EW scale (~ m_t); standard values.
COUPLINGS_EW = dict(lam=0.126, g=0.64, gp=0.36, yt=0.94)
# At M_* ~ 1.3 TeV (one-loop-run, rough): yt and lambda decrease slightly,
# gauge couplings nearly flat. Values bracket the running; the conclusion
# is insensitive to the exact numbers.
COUPLINGS_MSTAR = dict(lam=0.11, g=0.63, gp=0.36, yt=0.91)


def veltman_bracket(c):
    """[6 lambda + (9/4) g^2 + (3/4) g'^2 - 6 y_t^2]."""
    return (6 * c["lam"] + (9.0 / 4.0) * c["g"]**2
            + (3.0 / 4.0) * c["gp"]**2 - 6 * c["yt"]**2)


def main():
    print("=" * 72)
    print("Computation 120: item 1.3 -- full-SM extension settled NEGATIVE")
    print("=" * 72)
    print()

    # ---- 1. the Veltman bracket does not vanish at M_* ----
    print("1.  THE VELTMAN BRACKET IS ~ -3 AND DOES NOT VANISH AT M_*")
    print("-" * 72)
    for label, c in (("EW scale (~m_t)", COUPLINGS_EW),
                     ("M_* ~ 1.3 TeV  ", COUPLINGS_MSTAR)):
        b = veltman_bracket(c)
        terms = (6*c["lam"], (9/4)*c["g"]**2, (3/4)*c["gp"]**2, -6*c["yt"]**2)
        print(f"    {label}: 6lam={terms[0]:+.2f}  (9/4)g^2={terms[1]:+.2f}  "
              f"(3/4)g'^2={terms[2]:+.2f}  -6yt^2={terms[3]:+.2f}")
        print(f"               bracket = {b:+.2f}   "
              f"(/16pi^2 = {b/(16*math.pi**2):+.4f})")
    print()
    print("    Top-dominated and negative at both scales; no zero crossing.")
    print("    A clean cancellation (bracket = 0) does NOT occur at M_*.")
    print()

    # ---- 2. what a cancellation would require ----
    print("2.  THE PARTNER SECTOR A CANCELLATION WOULD REQUIRE")
    print("-" * 72)
    c = COUPLINGS_MSTAR
    top_term = 6 * c["yt"]**2
    print(f"    The dominant negative term is -6 y_t^2 = {-top_term:.2f}.")
    print(f"    Cancelling it needs bosonic top-partners (stop-like scalars)")
    print(f"    at top strength near M_* ~ 1.3 TeV (the SUSY-style mechanism:")
    print(f"    two complex scalar partners restore +6 y_t^2).")
    print()

    # ---- 3. such partners are excluded / absent ----
    print("3.  THAT SECTOR IS COLLIDER-DISFAVOURED AND STRUCTURALLY ABSENT")
    print("-" * 72)
    LHC_stop_bound = 1.2     # TeV, simplified-model scalar top-partner
    LHC_vlq_bound = 1.4      # TeV, vector-like quark / top partner
    M_star = 1.285           # TeV
    print(f"    M_* = {M_star} TeV; LHC scalar top-partner bound ~ "
          f"{LHC_stop_bound} TeV; vector-like-quark bound ~ {LHC_vlq_bound} "
          f"TeV.")
    print(f"    The required partners sit AT M_* -- at or below the exclusion")
    print(f"    edge -- and would source SMEFT/EWPO signals that PST's")
    print(f"    'no new light states' premise (sec:wilson-ewpo) forbids.")
    print()
    print("    Structurally, PST does not contain them:")
    print("     - Proposition F4: the emergent EFT below M_* is EXACTLY the")
    print("       SM (no superpartners, no top-partner sector);")
    print("     - Comp 105 (layer disjointness): the substrate cancellation")
    print("       lives in the UV shell [M_*, sqrt D], disjoint from the")
    print("       EFT-layer top/W/Z loops -- it cannot reach or supply them.")
    print()

    # ---- 4. assessment ----
    print("=" * 72)
    print("ASSESSMENT: item 1.3 settled in the negative")
    print("=" * 72)
    print()
    print("  The full-SM extension does NOT exist within PST:")
    print("   - the Veltman residual at M_* is ~ -3 (top-dominated), not 0,")
    print("     so M_* is not a Veltman-natural full-theory scale;")
    print("   - cancelling it requires a bosonic top-partner sector at ~M_*,")
    print("     which is collider-disfavoured AND absent from PST's spectrum")
    print("     (F4: emergent EFT = SM) AND unreachable by the substrate")
    print("     mechanism (Comp 105: layer-disjoint).")
    print()
    print("  CONCLUSION: M_* = 4 pi m_h sqrt(2/3) is irreducibly a")
    print("  SCALAR-SECTOR prediction -- the Higgs self-loop in isolation --")
    print("  exactly as the paper now scopes it (sec:renorm, since v26.09).")
    print("  The v26.09 demotion is the FINAL word, not a temporary state.")
    print("  Item 1.3 moves from OPEN to RESOLVED (negative): there is no")
    print("  full-SM extension; the scalar-sector result is the whole of")
    print("  what the boson-fermion cancellation delivers.")
    print()
    print("  This is a negative settlement, not a positive closure: it does")
    print("  not extend M_* to the full theory; it establishes that no such")
    print("  extension exists within PST, removing the item from the open")
    print("  register with M_* correctly and finally scoped.")


if __name__ == "__main__":
    main()