# n118 — spacetime, interrogated
# (2026-07-11; the deepest one: "space" and "time" sit in the
#  treatise's ASSUMED column. This note dismembers both and records
#  which pieces stay assumed, which are now derived, and which one
#  emerged this morning without being invited. Toy: n118_one_cone.py)

## The dismemberment (what "spacetime" actually is, piece by piece)
SPACE splits in two:
  adjacency  — ASSUMED (the substrate's who-touches-whom; A)
  distance   — DERIVED (the correlation/resistance metric; n46, n117:
               geometry crystallizes, the Big Bang phase has none)
TIME splits in three:
  ordering   — ASSUMED (the substrate's dynamical parameter)
  duration   — DERIVED (proper time = accumulated billing, omega=E/hbar;
               mechanism 4 — gravitational time dilation measured in-toy)
  the arrow  — DERIVED (T broken only in dissipation: the audit's arrow;
               n117: the cosmological arrow IS the measurement arrow)
THE CONE (why space and time form ONE Lorentzian geometry):
  derived in the IR — this morning's toy, below.

## The toy (n118_one_cone.py — all four gates PASS)
A lattice tube: big ring (space) x small ring l = 5 (internal), scalar
waves, unit couplings. Nothing Lorentzian inserted: no boosts, no
metric, no c. Two gluings of the internal ring:
  periodic -> internal zero mode -> MASSLESS branch: a cone, c0 = 1.
  Möbius   -> no zero mode -> MASSIVE branch: rest mass = the internal
  twisted ground mode m = 0.618 (the handle's hum — the de Broglie
  internal clock of n102/n115, now a lattice eigenmode).
- S2 BOOSTS FROM NOWHERE: the invariant mass m_inv(K) =
  sqrt(omega^2 - c0^2 K^2) is constant to 0.089% for K <= 0.3 and
  equals the internal mode. E^2 = m^2 + p^2 — the Lorentz mass
  shell — EMERGED. Nobody put the Lorentz group in; the IR of one
  substrate manufactures it.
- S3 DE BROGLIE'S HARMONY: v_group * v_phase = c0^2 to 1.7e-3 in
  the IR — the envelope clock slows by exactly the factor the phase
  clock speeds up. This is de Broglie's 1924 "harmony of phases" —
  SR's time structure — measured emerging from a lattice that was
  never told about relativity.
- S4 THE SUBSTRATE CONFESSES ONLY IN THE UV: group velocity < c0
  everywhere; leading mass-shell deviation -0.082*K^4 — quadratic-
  subluminal, exactly the l_s card's form. At K = 2 the invariant
  mass goes imaginary: the mass shell BREAKS where the lattice shows
  through. SR is an IR theorem here, not an axiom — and its failure
  mode is already priced (GRB dispersion bound, l_s < 4.3e-27 m).
(Recorded, F10 discipline: m = 0.618... for l = 5 is 1/phi — lattice
trigonometry, 2-2cos(pi/5); a coincidence of the demo's l, flagged
so nobody wires it to anything.)

## The composed picture
Space is the substrate's balance sheet (equal-time correlation
structure). Time is its transaction log (billing). The cone is the
settlement speed — one substrate, one cone, so causality is the
same for light, gravity, and matter (c_GW = c automatic; now also:
matter's mass shell shares the massless cone, measured). REST MASS
IS INTERNAL TWISTED MOMENTUM: a particle at rest is not still — it
runs its Möbius mode at omega = mc^2/hbar, and that hum is both its
de Broglie clock and its maintenance bill. Special relativity is
the IR conspiracy of one medium; general relativity (the treatise's
main body) is what happens when the billing rate varies from place
to place.

## The wound this interrogation carves (named, carried)
EMERGENT LORENTZ NEEDS PROTECTION (Collins-Perez-Sudarsky): generic
UV lattice physics leaks O(1) Lorentz violation into the IR through
loops; our own card demands < 1e-18 (resonators) and effectively
< 1e-33 GeV (SME clock bounds). The toy's free sector emerges clean,
but INTERACTING sectors generically do not. Why the leak is blocked
here is NOT derived — filed with the tensor junction as the
relativistic continuum's hardest known hazard, and the reason that
deliverable cannot be waved through.

## Prior art (the reflex)
Acoustic/analog spacetime (Unruh 1981, Volovik), emergent Lorentz in
condensed matter, Kaluza-Klein (mass from internal momentum — here
with a Möbius/pin- twist supplying BOTH the gap and the half-integer
sector), quantum graphity (n117). The composition that is ours:
distance-from-correlations + billing-time + Möbius mass + one-cone
lock + the audit, in one machine.

## Status of the ASSUMED column after n117-n118
Was: "assumed: QM, space, time."
Is now, honestly: "assumed: QM, adjacency, ordering." Everything
else about spacetime — distance, duration, the arrow, the cone, the
mass shell, simultaneity's IR democracy and its UV frame — is
derived, measured in-toy, or priced on the card. The assumed column
shrank by four words and the treatise should eventually say so.