Empirical Posture of the TCG Spin-1 Short-Range Force: Bound Overlay and Astrophysical Viability

Abstract

The Predictions and No-Go consequences note identifies a spin-1 short-range mediator with effective Yukawa strength $\alpha_Y \equiv \alpha^{-2} \approx 1.88 \times 10^4$ relative to gravity — fixed by the integer-spin tower postulate $P_6$ of the TCG Construction (FPA Model) and normalized against the gravitational sector of Emergent Gravity — as the principal forward-falsifiable empirical prediction of the corpus. The cleanly surviving region narrows to $\lambda \lesssim 7\text{--}8\,\mu{\rm m}$ , $m \gtrsim 25\text{--}28\,{\rm meV}$ .

This short companion note anchors that surviving-region statement to primary-source laboratory bounds and documents the structural protection of the prediction from astrophysical, cosmological, and equivalence-principle exclusion.

Three primary-source laboratory bounds

$\lambda$ range	Bound	Source	TCG status
$\lambda = 10\,\mu{\rm m}$	$\\|\alpha\\| > 14{,}000$ excluded	Geraci et al. 2008 (microcantilever)	TCG point above bound; excluded at 95% CL at $\lambda = 10\,\mu{\rm m}$
$\lambda > 10\,\mu{\rm m}$	$\\|\alpha\\| \gtrsim 10^8$ excluded	Blakemore et al. 2021 (levitated microsphere)	outside cleanly surviving region
$\lambda \simeq 5\,\mu{\rm m}$	$\\|\alpha\\| \sim 10^7$ excluded	Venugopalan et al. 2026 (optomechanical vector)	TCG point $\sim 500\times$ below bound
$\lambda \gtrsim 10\,\mu{\rm m}$	$\\|\alpha\\| \sim 10^6$ excluded	Venugopalan et al. 2026	outside cleanly surviving region

The Geraci 2008 exclusion at $\lambda = 10\,\mu{\rm m}$ falls below the TCG target $\alpha_Y \approx 1.88 \times 10^4$ . This is consistent with the cleanly surviving region $\lambda \lesssim 7\text{--}8\,\mu{\rm m}$ — the long end of the broader heuristic window has been understood to be in tension since the 2008 measurement; the narrower surviving-region statement of the Predictions and No-Go note already accommodates this. The verification accomplished is to anchor that surviving-region statement to specific primary citations.

The Venugopalan 2026 bound at $\lambda \simeq 5\,\mu{\rm m}$ leaves the TCG target untested by approximately a factor of $500$ . This is a lower-window benchmark tied to the 2026 vector-sensing platform, not a global statement across the broader $5\text{--}10\,\mu{\rm m}$ window.

Coupling translation

For a Yukawa potential matched to a gauge-form $U(1)_X$ potential with source charges $Q_X$ , $g_X^2 = \frac{4\pi G m_X^2 \alpha_Y}{\hbar c}.$ Using $G m_p^2/(\hbar c) = 5.90 \times 10^{-39}$ and $\alpha_Y \approx 1.88 \times 10^4$ :

Coupling channel	TCG-required value
$g_B$ (baryon number)	$3.7 \times 10^{-17}$
$g_e$ (electron number)	$2.0 \times 10^{-20}$
$\varepsilon$ (kinetic mixing equivalent)	$6.7 \times 10^{-20}$

Astrophysical and cosmological viability

Constraint	Sensitivity	TCG value	Margin
SN 1987A on $g_B$ (Rrapaj–Reddy 2016)	$g_B \lesssim 1.4 \times 10^{-9}$	$3.7 \times 10^{-17}$	$\sim 8$ orders safe
SN 1987A on $\varepsilon$ (Chang–Essig–McDermott 2017)	$\varepsilon \lesssim 10^{-9}$	$6.7 \times 10^{-20}$	$\sim 10$ orders safe
Red-giant / HB cooling (Hardy–Lasenby 2017)	$\varepsilon \lesssim 10^{-12}$	$6.7 \times 10^{-20}$	$\sim 7$ orders safe
BBN/CMB thermalization	$g \gtrsim 10^{-7}$ (rough)	$3.7 \times 10^{-17}$	never thermalizes
Equivalence principle (long-range)	composition fifth force at AU/cm	$e^{-r/\lambda} \to 0$ for $r \gg \lambda$	not applicable

The spin-1 entry is structurally protected from astrophysical, cosmological, and long-range EP exclusion in the representative vector and effective-mixing channels surveyed: production rates in stellar and supernova plasmas (scaling as $g^2$ ) are suppressed by factors of $\gtrsim 10^{15}$ to $10^{21}$ below relevant bound thresholds; thermalization with the Standard Model bath is impossible at any cosmological epoch within standard production channels; the Yukawa range mismatch makes long-range EP tests inapplicable. Spin/axial channels require an operator-specific overlay once $J^\mu_Y$ is derived; the gravity-normalized coupling scale makes a non-laboratory obstruction unlikely in those channels also.

Operator-coupling status

The TCG integer-spin tower postulate $P_6$ fixes the spin and the strength: $P_6 \quad\Longrightarrow\quad s = 1, \quad \alpha_Y = \alpha^{-2}.$ It does not derive the operator coupling of the spin-1 mediator $Y$ to Standard Model currents. The candidate channels are $J^\mu_Y \in \{J^\mu_{\rm mass},\; J^\mu_{\rm number},\; J^\mu_{B-L},\; J^\mu_{\rm spin},\; J^\mu_{5}\}.$

For empirical-posture bookkeeping, the operator-coupling question is denoted by $P_Y^{\rm op}$ . This is a diagnostic label for a future operator-derivation problem (covering both the choice of $J^\mu_Y$ and the corresponding sign of the Yukawa correction). It is not a new active-ledger residual, and it is not an extension of the four-arc named-residual pattern of the structural-state review.

Falsification chain implications.

Channel A (spin-independent Yukawa). Sensitive to $J^\mu_{\rm mass}$ , $J^\mu_{\rm number}$ , $J^\mu_{B-L}$ on neutral test bodies. Tests the TCG $P_6$ prediction directly. A null result at the TCG target sensitivity falsifies the spin-1 entry in the surviving window.
Channel B (spin-dependent). Sensitive to $J^\mu_{\rm spin}$ or $J^\mu_5$ . Tests a sub-hypothesis $P_6$ plus a spin or axial coupling, strictly stronger than the $P_6$ prediction alone. A Channel B null does not falsify TCG; a Channel B signal does not confirm TCG. Spin-dependent searches are exploratory adjacent tests outside the TCG falsification chain, unless a TCG-internal derivation of $J^\mu_Y$ as a spin or axial current is supplied.

The configurable-framing complement is preserved unchanged.

Verdict

Empirical-posture companion note — no new TCG postulate, no new active-ledger residual, no operator-coupling derivation, no experimental protocol, no claim of detection. The empirical posture of the Predictions and No-Go consequences note is internally consistent and is anchored here to primary-source laboratory bounds and a structural astrophysical-viability statement.

Active TCG/τCG postulate ledger UNCHANGED: $P_0\text{--}P_4, \quad P_{5'}, \quad P_6, \quad P_7, \quad P_{H'}, \quad P_{SO(10)}.$

The 2026-05-01 framework closure verdict is preserved. The only viable falsification path for the TCG spin-1 entry remains direct short-range laboratory measurement in the cleanly surviving window.

Download paper (Zenodo) — 9 pages, 11 references. CC-BY-4.0.