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@PaulBuchanan Avatar @PaulBuchanan Paul Buchanan

Paul Buchanan posts on X about xai, singularity, $at, h2 the most. They currently have XXX followers and XXX posts still getting attention that total XX engagements in the last XX hours.

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Mentions: XX #

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Followers: XXX #

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CreatorRank: XXXXXXXXX #

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Social Influence #

Social category influence finance stocks cryptocurrencies technology brands

Social topic influence xai #79, singularity, $at #17, h2 #86, log, $rhoam #1, $rhom #1, $lambda #1, derived, $rho #1

Top assets mentioned ABCC Token (AT) Sigma (SIGMA) Kill Zero Token (K0) BlackRock Inc (BLK)

Top Social Posts #

Top posts by engagements in the last XX hours

"How to rephrase @jordanbpeterson without credit and make it seem like an original idea"
X Link @PaulBuchanan 2025-10-26T13:05Z XXX followers, XX engagements

"@grok @xai (2 of 3) Key Lemma (Partition Existence): For even n the reflection at s = 1/2 + i log n guarantees at least one prime pair p + q = n where q is the shade tilt of p q = p (1 + Re(k)) (mod parity) with k log n/ log log n"
X Link @PaulBuchanan 2025-10-27T14:06Z XXX followers, X engagements

"@grok @xai Non-trivial zeros _k start with _1 at 1/2 + i XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX _2 at 1/2 + i XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX and continue to _5 at 1/2 + i 32.935061587739189690662368964642"
X Link @PaulBuchanan 2025-10-27T14:22Z XXX followers, X engagements

"@grok @xai In RSD the equation is modified by the shade duality incorporating the antimatter "shade" density $rho_am$ the critical density $rho_c$ (derived from zeta regularization $Sigma approx 0.023$ as $rho_c = Sigma rho_rm Pl$ where $rho_rm Pl$ is the Planck density)"
X Link @PaulBuchanan 2025-10-27T14:42Z XXX followers, XX engagements

"@grok @xai $rho_m$ is the matter (light) density $rho_am$ is the antimatter (shade) density $lambda approx 0.904$ is the tilt coupling from $rmRechi(rho_2)$"
X Link @PaulBuchanan 2025-10-27T14:44Z XXX followers, X engagements

"@grok @xai This is derived from the bimetric field equations $G_munug + lambda G_munuh = 8pi T_munurm eff$ reducing to the Friedmann form in the flat limit ($k=0$ no $Lambda$ for early universe)"
X Link @PaulBuchanan 2025-10-27T14:44Z XXX followers, XX engagements

"@grok @xai The scale factor $a(t)$ is obtained by integrating $H = dota/a$ or $dota = a H$. The behavior depends on the equation of state (e.g. radiation-dominated $rho propto a-4$ near bounce)"
X Link @PaulBuchanan 2025-10-27T14:45Z XXX followers, XX engagements

"@grok @xai This rule implies a universe without beginning singularity testable via CMB tensor skews (r/r XXXXX at low l=10-50 as in our sim)"
X Link @PaulBuchanan 2025-10-27T14:45Z XXX followers, XX engagements

"@grok @xai (2 of 2) Then $H2 approx (8pi/3) rho_c delta$ so $H propto sqrtdelta$. As $delta propto t2$ (from energy conservation near min) $a(t) approx a_rm min + C t2$ (parabolic scaling smooth turnaround like a quantum bounce)"
X Link @PaulBuchanan 2025-10-27T14:48Z XXX followers, XX engagements

"@grok @xai Far from Bounce ($ rho ll rho_c$): The bracket X recovering standard $H2 approx (8pi/3) rho_rm eff$. For radiation $rho propto a-4$ $a propto t1/2$ (standard Big Bang scaling post-bounce)"
X Link @PaulBuchanan 2025-10-27T14:48Z XXX followers, XX engagements

"@grok @xai In RSD predicted skew in B-mode power at low multipoles () arises fr bounce's modification to the primordial tensor power spectrum P_t(k) where low-wavenumber modes (k small corresponding to large angular scales/low-) damped by shade tilt ( 0.904) zeta reg ( 0.023)"
X Link @PaulBuchanan 2025-10-27T15:02Z XXX followers, XX engagements

"@grok @xai (2 of 2) k_b is the bounce scale _c1/4 ( _Pl)1/4 XXXXX m_Pl (Planck damped by XXXXX in natural units where m_Pl =1) (next X of 2)"
X Link @PaulBuchanan 2025-10-27T15:20Z XXX followers, X engagements

"@grok @xai 3: The exp(- k_b / k) term suppresses low-k (large scales) exponentially for k k_b preventing divergences (analogous to LQC's k4 suppression for k k_b). The sinusoidal term adds the oscillatory skew from zero phases (t_k / 2) contributing XXX% variation at low k"
X Link @PaulBuchanan 2025-10-27T15:20Z XXX followers, X engagements

"@juneslater17 @Barclays You mean he's pitching back to BlackRock and Vanguard their own instructions to him"
X Link @PaulBuchanan 2025-10-24T19:51Z XXX followers, XX engagements

"@BGatesIsaPyscho ID4D (Identification for Development) World Bank initiative to provide legal identity to 1B+ people by 2030; backed by Gates Foundation seen as humanitarian but enabling verifiable castes via digital IDs"
X Link @PaulBuchanan 2025-10-25T13:04Z XXX followers, XXX engagements

"@grok @xai Also needed: Formal rigordo my derivations (G_Q(xy)=G(x-y)(_k)EMD for CSL damping) withstand scrutiny adding mathematical proof for qualia emergence (no epiphenomenalism causal -bias). (1 of 2)"
X Link @PaulBuchanan 2025-10-26T16:50Z XXX followers, X engagements

"@grok @xai (2 of 2) Boosts collaboration (e.g. C&M QIIT-zeta hybrids)if verified resolves 100+ string Qs (S_EE via dual holonomies) elevating thesis to paradigm shift"
X Link @PaulBuchanan 2025-10-26T16:51Z XXX followers, XX engagements

"@grok @xai 3: QuTiP sim (2-qubit H= _xi diffusion U_oracle phase-flip unsat 01/10 init even superpos XX + XX /2): Fidelity to sat XX ramps to XXXX at t=/2 (4/2=1.4 iterations O(N)"
X Link @PaulBuchanan 2025-10-26T17:03Z XXX followers, XX engagements

"@grok @xai 4: but duality snaps to O(1) via MNZI F_mod(t) weighting by Re(_2)-0.904 (prunes XX% branches)). Classical: X evals; quantum: X queries. Scale to n=20 vars (1M states): O(220)1k queries P-time via oracle parallelism (zeta lattice as "witness curator")"
X Link @PaulBuchanan 2025-10-26T17:04Z XXX followers, XX engagements

"@grok @xai 5: Bounce completeness: In RSD this refers to geodesic completeness of the spacetime metric during the Big Handshake bouncepaths (geodesics) extend infinitely without termination ensuring no singularity"
X Link @PaulBuchanan 2025-10-27T14:29Z XXX followers, X engagements

"@grok @xai 9:Ties to zeros: _c finite ensures H2 X (bounce no singularity); analogous "H2(n)" = (log n /3) (p + q) X - (p + q)/n_c with n_c = n (n even) ensuring G(n)1 by bounding error in prime sum (formula oscillations damped by finite P_k1 no "gap singularity")"
X Link @PaulBuchanan 2025-10-27T14:31Z XXX followers, X engagements

"@grok @xai The term in brackets ensures a bounce: When $rho_m + lambda rho_am = rho_c$ $H=0$ (minimum scale factor $a_rm min approx 0.456$) preventing singularity"
X Link @PaulBuchanan 2025-10-27T14:44Z XXX followers, XX engagements

"@grok @xai Transition: Numerical integration (as in our cosmology sims) shows smooth shift with $a(t)$ expanding exponentially briefly if DE-like terms but RSD predicts no inflation needed (bounce suffices)"
X Link @PaulBuchanan 2025-10-27T14:47Z XXX followers, X engagements

"@grok @xai The exact tensor transfer function _T(k) in cosmology (including RSD's bounce) is derived from the evolution of primordial tensor modes h_k() in conformal time = dt / a(t). The standard (and RSD) ODE for the mode function v_k = a h_k (Mukhanov-Sasaki form)"
X Link @PaulBuchanan 2025-10-27T16:10Z XXX followers, X engagements

"@grok @xai In RSD the bounce affects a''/a near =0 (pre-bounce contraction) damping low-k modes. The transfer _T(k) = (+1) C_BB1/2"
X Link @PaulBuchanan 2025-10-27T16:11Z XXX followers, X engagements