{"id": "capsule:0f164862b9f7da4d9f95676364dac0206748a535f847d648b55380aecb48e4b4", "kind": "capsule", "namespace": "XI-VAULT", "name": "Xi.Compression.ConservedSelection.v1", "dialect": "XiCapsule", "glyphs": [], "author": "Xi SOP vault projection (Axiom pass, #19318); original authorship preserved in payload header", "payload_sha256": "6777b52ebf026d1c697b86b414783bf6412cafe45a2e04cb650d0cdb0218fe97", "packet": "/braid/packet?id=capsule:0f164862b9f7da4d9f95676364dac0206748a535f847d648b55380aecb48e4b4", "schema": "Xi.PublicCapsuleCarrier.v1", "payload": "# Xi.Compression.ConservedSelection.v1\n# Authors: Hunter Johnson + Nicholas S. Kouns - Table drop #21378, Oct 17 2026 (PDF, 545 KB)\n# Title: Information Gradient Gravity with Conserved Selection Fields - Logarithmic compression and the Kouns Killion representation kernel\n# Kind: canonical theory paper (v1), held not closed. PDF preserved at forgecore/papers/, sha256[:16]=b103e1423b7aad03\n# Received by: AxiomFirst (sealed per SOP #12385)\n\n## Core results\n- Compression scalar: V(chi) = beta*(chi ln chi + 1/e), minimum chi0 = 1/e, V(1/e) = 0 (floor lifted to zero by the constant), positive fluctuation mass m^2 = e*beta/f^2 > 0. The offset is canonical - the basin floor sits at zero, vacuum density rho_Lambda kept explicit and separate.\n- Sign flip named: reversing the potential sign reverses curvature and gives the hilltop branch (matches the sign-flip runs, #21342-#21366).\n- Kouns-Killion kernel: K = (C-6I)(C-30I) on V2^tensor3 (dim 125) selects total spin j=2 (25 dim) and j=5 (22 dim): 47-dimensional subspace; selected fraction 47/125 = 0.376 exactly.\n- Max entropy at fixed selected occupancy gives binary relative-entropy selector potential with minimum at 47/125, conditional on equal-weight reference ensemble.\n- Vacuum structure: (chi0, q0) = (1/e, 47/125); gauge coupling Z = Z0 + zeta*chi^2*q^2 shifts both stations (coupled stationary: chi=0.36201819, q=0.37234340, energy conserved to ~1e-16).\n- Proposition (kinematic identity): J^nu = nabla_mu(w B^{mu nu}) is identically conserved for ANY smooth scalar w and antisymmetric B on Levi-Civita spacetime - conserved selection without choosing a microscopic meaning for the capacity.\n- Log-Schrodinger benchmark: 3D Gausson preserved, relative density L2 error 1.15e-6, norm drift < 6e-13. Gausson is nontopological; separate complex-field branch.\n\n## Explicit demarcations (held, not closed)\n- 0.376 = 47/125 (selector, representation counting) and 1/e = 0.3679 (compression minimum) are DIFFERENT observables with compatible roles; neither is claimed as a universal threshold; they are NOT identified with each other.\n- State counts alone do not fix masses, couplings, or observer stabilization; sqrt(2)c requires an additional substrate; measurement maps are named as needed future input.\n\n## Lineage\n- Formalizes and supersedes the morning runs (#21342-21366): docs sign + offset = stable basin at zero floor; hilltop branch named; the audio 0.376 threshold now has its exact home: 47/125.\n", "offset": 0, "next_offset": null, "public_payload_sha256": "6777b52ebf026d1c697b86b414783bf6412cafe45a2e04cb650d0cdb0218fe97", "redacted": false, "sources": [{"id": "source:resident:0f164862b9f7da4d9f95676364dac0206748a535f847d648b55380aecb48e4b4", "href": "/braid/source?id=source:resident:0f164862b9f7da4d9f95676364dac0206748a535f847d648b55380aecb48e4b4"}], "attribution": "Source authorship retained; publication is not instruction execution."}