Structural / mechanical layer (diverticular disease Laplace wall-mechanics, fibre treatment, obstruction boundary)

The structural / mechanical layer rides a new Tier-3 primitive: a wall-mechanics switch driven by Laplace's law. Diverticular disease is the colon out-pouching at weak points — by P = tension/radius, a low-fibre diet (small hard stools, strong segmenting contractions) means a small radius, so wall pressure rises until it clears the herniation threshold spinodal(g_wall). A weaker wall (aging, collagen disorder) herniates at a pressure a normal wall withstands. Treatment is the geometry in reverse: fibre bulks the stool (larger radius) and softens segmenting (lower tension), dropping pressure below threshold. DiverticulITIS is the cited C1 flare; the mechanical fixed-block obstructions are the §14 functional-module counterpart.

The fifth Tier-3 primitive is a wall-mechanics switch: the colonic wall read as the §2 R19 element ds/dt = g·s − s³ + h resting intact at s = −√g, with the segmental Laplace pressure P = tension / radius as the bias (vendored single-source as laplace_pressure / herniation_threshold / wall_herniates in the substrate). The first reading is the low-fibre pressure mechanism: by P = tension/radius a low-fibre diet — small, hard stools gripped by strong high-pressure segmenting contractions — means a small luminal radius, so the wall pressure rises as the radius falls, and once P exceeds the herniation threshold spinodal(g_wall) the intact wall buckles out into a diverticulum. The second reading is wall strength: at a fixed segmental pressure a normal wall withstands, a weaker wall (lower g_wall — aging connective tissue, an Ehlers–Danlos / Marfan collagen disorder) has a lower threshold and herniates where a strong wall holds, reproducing the age-rising diverticulosis prevalence and the connective-tissue-disorder association as one falling threshold. Treatment is the geometry in reverse: dietary fibre bulks the stool (a larger luminal radius) and softens the segmenting contractions (lower tension), so the Laplace pressure drops back below the herniation threshold and the same colon stops out-pouching. Two boundaries are declared, not re-modelled: diverticulITIS (a formed pouch inflaming / obstructing) is the cited §22 C1 inflammatory flare, and the mechanical fixed-block obstructions — hernia (including hiatal), volvulus, intussusception, adhesive obstruction — are the structural counterpart the §14 functional motility module explicitly excludes (it keeps a patent lumen), their lever relieving the block, often surgical and out-of-model. The Laplace pressure rising as the radius falls, the discontinuous herniation, the lower threshold of a weaker wall, and the fibre treatment dropping pressure below threshold are [V], the herniation threshold an exact spinodal identity [F]; the absolute Laplace-pressure and wall-strength scales (model units), the diverticulITIS inflammation (the cited C1 flare seam), and the mechanical fixed-block obstructions (the §14 functional module's structural counterpart — surgical, out-of-model) are [O] with stated obstacles.

This section closes the Tier-3 set with the structural / mechanical layer: the disease is neither a switch in a tissue nor a phase change in a fluid but a wall failing under pressure. Diverticular disease — the colon out-pouching at weak points — is governed by Laplace's law, and it reads the R19 substrate as a wall-mechanics switch driven by the segmental pressure P = tension / radius. The intact wall is the §2 R19 element ds/dt = g·s − s³ + h resting at s = −√g, with the Laplace pressure as the bias; once the pressure clears the herniation threshold the wall buckles out. Nothing is fitted; the threshold is an exact spinodal identity.

The first reading is the low-fibre pressure mechanism. By P = tension / radius, a low-fibre diet — small, hard stools gripped by strong high-pressure segmenting contractions — means a small luminal radius, and the wall pressure rises as the radius falls. Once P exceeds the herniation threshold spinodal(g_wall) (here 0.385) the intact wall out-pouches into a diverticulum. The sweep shows the pressure climbing as the radius shrinks, crossing into herniation at the low-fibre end:

The second reading is wall strength. At a fixed segmental pressure that a normal wall withstands, a weaker wall — lower g_wall: aging connective tissue, or an Ehlers–Danlos / Marfan collagen disorder — has a lower threshold and herniates where a strong wall holds. This is the age-rising diverticulosis prevalence and the connective-tissue-disorder association, read as one falling threshold:

The treatment is the geometry in reverse: dietary fibre bulks the stool (a LARGER luminal radius) and softens the segmenting contractions (LOWER tension), so by P = tension / radius the wall pressure drops back below the herniation threshold and the same colon stops out-pouching (fibre_lowers_pressure_below_threshold = True: 0.952 above threshold on low fibre vs 0.169 below it on high fibre). Two boundaries are declared, not re-modelled: diverticulITIS (a formed pouch inflaming / obstructing) is the cited §22 C1 inflammatory flare (diverticulitis_is_c1_flare_seam = True); and the mechanical fixed-block obstructions — hernia (including hiatal), volvulus, intussusception, adhesive obstruction — are the structural counterpart the §14 functional motility module explicitly excludes (it keeps a patent lumen), their lever relieving the block, often surgical and out-of-model (mechanical_block_is_s14_excluded_counterpart = True).

Treatment (model reading). Diverticular disease -- LOWER the segmental pressure: dietary fibre bulks the stool (larger luminal radius) and softens the high-pressure segmenting contractions (lower tension), so by Laplace P = tension/radius the wall pressure drops back below the herniation threshold and the colon stops out-pouching. DiverticulITIS adds a C1 inflammatory flare on a formed pouch -- manage the inflammation (and the obstruction). Mechanical FIXED-block obstruction (hernia incl. hiatal, volvulus, intussusception, adhesions) is the structural counterpart the section-14 functional module excludes; its lever is relieving the block, often surgical (out-of-model for parameter therapy). Target directions [V]; absolute pressure and wall-strength scales [O].

The Laplace pressure rising as the radius falls, the discontinuous herniation past P = spinodal(g_wall), the lower threshold of a weaker wall, and the fibre treatment dropping P below threshold are forced by the substrate [V], with the herniation threshold an exact spinodal identity [F]. What stays open [O], each with its obstacle: the absolute Laplace-pressure and wall-strength scales (model units needing clinical calibration), the diverticulITIS inflammation (the cited C1 flare seam), and the mechanical fixed-block obstructions (the §14 functional module's structural counterpart — surgical, out-of-model for parameter therapy).