s1087 — (1,3)+(3,1)=(4,4) two-way-time split: type admissibility
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[1] Existence: explicit integer decomposition R^{4,4} = V1 ⊕ V2
  [PASS] sig(V1) = (1,3)
  [PASS] sig(V2) = (3,1)
  [PASS] V1 ⊕ V2 spans R^8 (rank 8)
  [PASS] V1 ⊥ V2 under η (block-diagonal split)
  [PASS] signature arithmetic: (1,3)+(3,1) = (4,4)

[2] STRONG FORM — swap by η-ISOMETRY: signature obstruction
  [PASS] signature is swap-obstructing: sig(V1) ≠ sig(V2)
  → STRONG FORM OBSTRUCTED: no η-isometry can carry V1 (1,3) onto V2 (3,1).
    'Past and future exchange by a rotation of the same geometry' FAILS.

[3] REFINED FORM — swap by η-ANTI-isometry (TᵀηT = −η)
  (a) census over signatures (p,q), p+q=8: anti-isometry exists iff p=q
  [PASS] (p,q)=(0,8): anti-isometry impossible — verified
  [PASS] (p,q)=(1,7): anti-isometry impossible — verified
  [PASS] (p,q)=(2,6): anti-isometry impossible — verified
  [PASS] (p,q)=(3,5): anti-isometry impossible — verified
  [PASS] (p,q)=(4,4): anti-isometry EXISTS — verified
  [PASS] (p,q)=(5,3): anti-isometry impossible — verified
  [PASS] (p,q)=(6,2): anti-isometry impossible — verified
  [PASS] (p,q)=(7,1): anti-isometry impossible — verified
  [PASS] (p,q)=(8,0): anti-isometry impossible — verified
  → the substrate's split (4,4) is EXACTLY the admissible signature.
  (b) explicit spinorial swap T on R^{4,4}
  [PASS] T is integer, det T = +1
  [PASS] TᵀηT = −η (anti-isometry: 'reflects' the metric)
  [PASS] T² = −1 (SPINOR half-turn — same square as the printed T-bridge)
  [PASS] T⁴ = +1 (four-tick return)
  [PASS] T(V1) = V2  ('past bumps into future … carried forward')
  [PASS] T(V2) = V1  ('future bumps into past … reflected back')
  [PASS] one-way sign asymmetry: (V2ᵀTV1)·(V1ᵀTV2) = −1 blockwise (reflection carries the −)
  [PASS] sig(T·V1 image form) = (3,1): the (1,3) world RETURNS as a (3,1) world
  (c) T-conjugation preserves so(4,4)  [A_SUB_010-style closure anchor]
  [PASS] so(4,4) basis count = 28
  [PASS] basis independent (rank 28)
  [PASS] closure: all [Xi,Xj] ∈ so(4,4) (28-dim Lie algebra re-certified)
  [PASS] T X T⁻¹ ∈ so(4,4) for all 28 generators (swap is a symmetry OF the algebra)

[4] Type comparison with the printed live T (appendix_h; cited, not re-derived)
    printed: T ∈ E7(7) ⊂ Sp(56,R), T² = −1, T⁴ = +1, swaps the two 27 windings.
    here:    T ∈ GL(8,Z), anti-isometric on (4,4), T² = −1, T⁴ = +1, swaps V1↔V2.
  [PASS] type invariants MATCH: order 4, square −1, swaps the two 'time-direction' summands
    ⚠ IDENTIFICATION NOT CLAIMED: matching type invariants ≠ the same operator;
      lifting this T to the live 56 is the D1011-class construction, not this kernel.

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VERDICT (feasibility; no tier moves, no public observable moves):
  STRONG FORM  — 'past/future exchange as an η-isometry of (4,4)':
                 OBSTRUCTED by the signature invariant ((1,3) ≠ (3,1)).
  REFINED FORM — 'exchange as an η-ANTI-isometry, spinorial (T²=−1)':
                 TYPE-ADMISSIBLE, explicitly constructed, integer-exact;
                 exists at signature (p,q), p+q=8, IFF p=q — the substrate's
                 (4,4) is exactly the admissible habitat; the swap preserves
                 so(4,4) and carries the PI's one-way reflection sign.
  READING: 'time passing two ways, each reflecting off the other' is the
  anti-isometric double-cover form ONLY — the naive mirror form is dead.

ASSERTS: 28/28 passed
s1087 END
