T27 OS: HIVE devices page and the formula orbit (Closes #11431)

.claude/skills/t27os/SKILL.md

@@ -49,6 +49,18 @@ dashboard and back). The window only calls the decisions of `bench.t27`, `kanban
 - **Q QUEEN**: lamps (27, "not measured": `domain_pulse` cannot be linked into the window, #5980), feed, top gaps with
   why-not, the six-counter meter (links and tests from `git log` / `grep` in the space's folder once a minute),
   safety strip with STOP = GOD MODE off.
+- **H HIVE (TRI NET devices)**: `devices.t27`. One glass card per machine (host, T27 OS version + build and "behind N" against
+  the `t27os-latest` tag, `t27c` version, CPU/RAM/free disk, lanes running with model, key light and elapsed), a flow strip
+  CLAIMED -> LANE PUSHED -> TRIGIT LANDED -> BATCH PUSHED -> MERGED. Sources are git only: `git ls-remote` of
+  `refs/swarm/claims/*`, `claude/claim-*`, `claude/evolve-lane-*`, `t27os-*` tags, `refs/swarm/alive/*` fetched with their
+  committer dates, `tri golden status`. Each machine publishes `refs/swarm/alive/<host>` (subject = payload `hb1 host=.. build=..
+  lanes=issue:model:light:elapsed,..`) every 5 min from the app (`dv_publish_due`), a heartbeat older than 30 min reads OFFLINE,
+  a host with only a lane branch reads NO HEARTBEAT and n/m. Lanes of this machine come from the lanes table (the lanes feed
+  runs while the page is open and before each beat). The page widgets carry their agents in `DW_AGENTS`.
+- **Formula orbit around the home logo**: `orbit_view.t27` over `formula_orbit.t27` + `formula_table.t27`. How many of the 32
+  labels fit depends on the stage (PAD 52 is the law of formula_orbit): about 10 in a 960 x 540 window, all 32 from about
+  1440 x 800. Reduced motion (NSWorkspace) freezes the clock. formula_orbit's PAD, NONE and card_* were renamed ORB_PAD,
+  ORB_NONE, orb_card_*: t27b splices every import into one namespace and kanban/topic_reel/petal_menu own those names.
 - **Trap, measured**: `t27b` splices every imported module into one flat namespace, so a same-named private helper in
   two modules is silently the first one. The page specs prefix their internals (`kb_`, `qb_`, `bn_`); check with the
   duplicate-name script before importing a new spec into `glass_window`. The fast `t27b test` does not type-check the

.trinity/seals/t27os_T27osAgentParts.json

@@ -1,9 +1,9 @@
 {
-  "built_by": "t27c-bootstrap@0.5.2+24a3abcad",
+  "built_by": "t27c-bootstrap@0.5.2+72ddaf7ac",
   "closure": [
     {
       "spec": "specs/t27f/petal_menu.t27",
-      "spec_hash": "sha256:154e8ee093b282e51d1e8040fc7ad0fabc892f609120a50c5b0a25d7b2dae28a"
+      "spec_hash": "sha256:2d866d49ab066136006fdabfb1d6e1c4710867535c25029dee184a404af6b51e"
     },
     {
       "spec": "specs/t27os/homes.t27",
@@ -15,16 +15,16 @@
     }
   ],
   "config": "gen=c,rust,verilog,zig;tests=zig",
-  "gen_hash_c": "sha256:7ede0ad24863934e0de8867c4d4d25a52ef44bb0d764ef4e5250693b183e90c2",
-  "gen_hash_rust": "sha256:ad6998dd2706c75ed8e9aec7f796feb2cc001524d0c4cf5a1cedd6a1237cc861",
-  "gen_hash_verilog": "sha256:36ce55c255364e75ecf0c18c12d20bcd321ed94304c63415b29028c9731ea7a8",
-  "gen_hash_zig": "sha256:c68bf3d1382429f7d8ec6bd5d6be2473ce583bf5c145df1c5ac5b76f6b2c3381",
+  "gen_hash_c": "sha256:0c7e09b4e0e98371d2f8b79209a28eac552920edd9e4a2167ecf35aa2435b86e",
+  "gen_hash_rust": "sha256:d5800122192f75b8e1a7edb0b3bf3f317dccd6946662ef6a99416dbd4ee56a50",
+  "gen_hash_verilog": "sha256:f1aa990ca05be93355b8298782fe1845947f55cc70272762ca40e1abc232cc6c",
+  "gen_hash_zig": "sha256:549f51d7d6c3471e482069e55a9ea61a8a25c533867104fe0921324e60982a83",
   "module": "T27osAgentParts",
   "ring": 12,
   "seal_schema": 2,
-  "sealed_at": "2026-10-20T14:44:55Z",
+  "sealed_at": "2026-10-20T16:55:12Z",
   "sealed_by": "t27c-bootstrap@0.5.2",
-  "spec_hash": "sha256:f4d9ed2c3bd2c391f067c98eb61a2d9ae0b975b4cbe76befdd23277dd272a6d6",
+  "spec_hash": "sha256:e6b1e9e183c1a1b0192e26caf269a592b0606625904cbe29d6d25be6081ca82e",
   "spec_path": "specs/t27os/agent_parts.t27",
   "tests": {
     "failed": 0,

.trinity/seals/t27os_T27osDevices.json

@@ -0,0 +1,33 @@
+{
+  "built_by": "t27c-bootstrap@0.5.2+72ddaf7ac",
+  "closure": [
+    {
+      "spec": "specs/t27os/lanes_view.t27",
+      "spec_hash": "sha256:cf06613e5f2002ac9ca07dc8a6586b0754cc99bf1cbb75d780125c480d7b4875"
+    }
+  ],
+  "config": "gen=c,rust,verilog,zig;tests=zig",
+  "gen_hash_c": "sha256:f373497e1daf7db6665ddb21f68f24183a5ed3f5d28dc87d334a3cae07f99f0b",
+  "gen_hash_rust": "sha256:838237a1023b48e7323f595362e5eefe63db9f2d68bb892abebac7b524ee5745",
+  "gen_hash_verilog": "sha256:2e7e3d22924c35799f13ec704061c9392b5a5d5d12c1033ed9ef1cd694cccac7",
+  "gen_hash_zig": "sha256:3bce7cb61816ff322e5ab45ee29d52372a68f02a9151f61c10da439ee4cedefc",
+  "module": "T27osDevices",
+  "ring": 12,
+  "seal_schema": 2,
+  "sealed_at": "2026-10-20T16:55:08Z",
+  "sealed_by": "t27c-bootstrap@0.5.2",
+  "spec_hash": "sha256:53643c6db56c0cf3340f7f52ee550d01256877798f6be9a9af84ccf66c6afb44",
+  "spec_path": "specs/t27os/devices.t27",
+  "tests": {
+    "failed": 0,
+    "failing": [],
+    "forced": false,
+    "passed": 18,
+    "total": 18,
+    "vacuous": 0
+  },
+  "toolchain": {
+    "test_runner": "sha256:8512b80da533b79289110fca4a65f3336abd7a059ca4b72ea595d5e33ff8ad10",
+    "zig": "0.16.0"
+  }
+}

.trinity/seals/t27os_T27osOrbitView.json

@@ -0,0 +1,32 @@
+{
+  "built_by": "t27c-bootstrap@0.5.2+72ddaf7ac",
+  "closure": [
+    {
+      "spec": "specs/t27f/formula_orbit.t27",
+      "spec_hash": "sha256:8539caa8b9a6cf19a76dac9e48978c3d3491ca8b5537ac0f22adb94d6af4fee5"
+    },
+    {
+      "spec": "specs/t27f/formula_table.t27",
+      "spec_hash": "sha256:59d968f6cfd27ba742a07208fd7f0cb25c1cabf4052c9526f8fd9058e1721053"
+    }
+  ],
+  "config": "gen=c,rust,verilog,zig;tests=zig",
+  "gen_hash_c": "sha256:ad3f630947e77ad55a59fa59e8e21232dd48ade02f707b48be7915b98dab1599",
+  "gen_hash_rust": "sha256:b26400e997960a22a2b76c7a3fce79f877efa4eac99062f74ae28400239a048c",
+  "gen_hash_verilog": "sha256:388dc21a7ef33165d4888e81007903102f3f2e3794ca3cba562780679f50ad87",
+  "gen_hash_zig": "sha256:32ddfd175ab6c681a272b746e07f86a16ad0e6657d975cb74904abfb93650375",
+  "module": "T27osOrbitView",
+  "ring": 12,
+  "seal_schema": 2,
+  "sealed_at": "2026-10-20T16:55:09Z",
+  "sealed_by": "t27c-bootstrap@0.5.2",
+  "spec_hash": "sha256:0c3c4a1aad9914d4f052fd6c423b62421db02fef1357edd60bc0b7144c324558",
+  "spec_path": "specs/t27os/orbit_view.t27",
+  "tests": {
+    "blocked": "does not compile: spec.zig:247:82: error: division with 'i64' and 'comptime_int': signed integers must use @divTrunc, @divFloor, or @divExact"
+  },
+  "toolchain": {
+    "test_runner": "sha256:8512b80da533b79289110fca4a65f3336abd7a059ca4b72ea595d5e33ff8ad10",
+    "zig": "0.16.0"
+  }
+}

specs/t27f/formula_orbit.t27

@@ -10,13 +10,13 @@
 ; --
 ; How it stays calm. Each formula gets a HOME slot, fixed for a given stage: candidates walk the
 ; golden spiral (a sunflower over the stage ellipse) and a candidate is kept when
-;   (1) its label rectangle, grown by PAD on every side, stays on the stage;
+;   (1) its label rectangle, grown by ORB_PAD on every side, stays on the stage;
 ;   (2) it clears the keep-out circle (logo radius * 1.08), so it never covers the logo or a
 ;       petal's hit area;
-;   (3) it is at least PAD away, on x or on y, from every slot already kept.
-; PAD = 2 * (DRIFT_AMP + PUSH_CAP). Every moving part is capped: drift offset <= DRIFT_AMP per
+;   (3) it is at least ORB_PAD away, on x or on y, from every slot already kept.
+; ORB_PAD = 2 * (DRIFT_AMP + PUSH_CAP). Every moving part is capped: drift offset <= DRIFT_AMP per
 ; axis, pointer push <= PUSH_CAP per axis. Two labels therefore move toward each other by at most
-; PAD in total, so THEY CAN NEVER OVERLAP AND NEVER REACH THE LOGO, whatever the clock and the
+; ORB_PAD in total, so THEY CAN NEVER OVERLAP AND NEVER REACH THE LOGO, whatever the clock and the
 ; pointer do. That is a proof by bounds, and the tests below also sweep it numerically.
 ; The slowdown near the pointer is a global clock factor (time_scale_permille), not a per-label
 ; speed, so the field stays rigid and the guarantee above is untouched.
@@ -33,8 +33,8 @@
 ;      a matte glass chip; with reduced motion draw at slot_x(hx[i]) / slot_y(hy[i]) instead.
 ;   3. On pointer move:   hover = label_hit(px, py, x_i, y_i, LABEL_W, LABEL_H) per drawn label;
 ;      raise the chip, never the flight speed (the clock factor already slows it).
-;   4. On click:   i = hit_index(...) -> open the card for formula i: card_x / card_y / card_w /
-;      card_h give its frame; the text comes from formula_table.t27 (name, expression, value,
+;   4. On click:   i = hit_index(...) -> open the card for formula i: orb_card_x / orb_card_y / orb_card_w /
+;      orb_card_h give its frame; the text comes from formula_table.t27 (name, expression, value,
 ;      error, sector). A click on the logo or a petal is petal_menu's, checked first.
 ; phi^2 + 1/phi^2 = 3 | TRINITY
 
@@ -45,11 +45,11 @@ pub const DRIFT_AMP : i64 = 8;
 pub const PUSH_CAP : i64 = 18;
 pub const PUSH_RANGE : i64 = 150;
 pub const PUSH_CORE : i64 = 24;
-pub const PAD : i64 = 52;
+pub const ORB_PAD : i64 = 52;
 pub const KEEP_PERMILLE : i64 = 1080;
 pub const CANDIDATES : i64 = 1200;
 pub const MAX_SLOTS : usize = 64;
-pub const NONE : i64 = 0 - 1;
+pub const ORB_NONE : i64 = 0 - 1;
 pub const FAR : i64 = 0 - 100000;
 pub const DRIFT_MDEG_PER_S : i64 = 20;
 pub const LABEL_W : i64 = 150;
@@ -99,22 +99,22 @@ pub fn cos_pm(a : i64) -> i64 {
     return sin_pm(a + 90000);
 }
 
-/// A slot's rectangle (centre x, y; label w, h; grown by half PAD) clears the circle (cx, cy, r).
+/// A slot's rectangle (centre x, y; label w, h; grown by half ORB_PAD) clears the circle (cx, cy, r).
 pub fn clears_circle(x : i64, y : i64, w : i64, h : i64, cx : i64, cy : i64, r : i64) -> bool {
-    const dx : i64 = max_i(abs_i(x - cx) - (w / 2 + PAD / 2), 0);
-    const dy : i64 = max_i(abs_i(y - cy) - (h / 2 + PAD / 2), 0);
+    const dx : i64 = max_i(abs_i(x - cx) - (w / 2 + ORB_PAD / 2), 0);
+    const dy : i64 = max_i(abs_i(y - cy) - (h / 2 + ORB_PAD / 2), 0);
     return dx * dx + dy * dy >= r * r;
 }
 
 pub fn on_stage(x : i64, y : i64, w : i64, h : i64, sw : i64, sh : i64) -> bool {
-    const mx : i64 = w / 2 + PAD / 2;
-    const my : i64 = h / 2 + PAD / 2;
+    const mx : i64 = w / 2 + ORB_PAD / 2;
+    const my : i64 = h / 2 + ORB_PAD / 2;
     return x >= mx and x <= sw - mx and y >= my and y <= sh - my;
 }
 
-/// Two labels are apart by the full PAD margin when they clear each other on x or on y.
+/// Two labels are apart by the full ORB_PAD margin when they clear each other on x or on y.
 pub fn apart(x1 : i64, y1 : i64, x2 : i64, y2 : i64, w : i64, h : i64) -> bool {
-    return abs_i(x1 - x2) >= w + PAD or abs_i(y1 - y2) >= h + PAD;
+    return abs_i(x1 - x2) >= w + ORB_PAD or abs_i(y1 - y2) >= h + ORB_PAD;
 }
 
 /// Fill hx, hy with up to n home slots walking the golden spiral outward from the logo; returns how many fit.
@@ -207,21 +207,21 @@ pub fn label_hit(px : i64, py : i64, x : i64, y : i64, w : i64, h : i64) -> bool
     return abs_i(px - x) <= w / 2 and abs_i(py - y) <= h / 2;
 }
 
-/// Index of the label under the pointer, or NONE. The first match wins; labels never overlap, so it is the only one.
+/// Index of the label under the pointer, or ORB_NONE. The first match wins; labels never overlap, so it is the only one.
 pub fn hit_index(hx : []i64, hy : []i64, n : usize, clock : i64, px : i64, py : i64, w : i64, h : i64) -> i64 {
     var i : usize = 0;
     while (i < n) {
         if (label_hit(px, py, item_x(hx[i], hy[i], i as i64, clock, px, py), item_y(hx[i], hy[i], i as i64, clock, px, py), w, h)) { return i as i64; }
         i += 1;
     }
-    return NONE;
+    return ORB_NONE;
 }
 
 /// The card a click opens: centred on the stage, at most 520 x 300.
-pub fn card_w(sw : i64) -> i64 { return min_i(520, sw - 32); }
-pub fn card_h(sh : i64) -> i64 { return min_i(300, sh - 32); }
-pub fn card_x(sw : i64) -> i64 { return (sw - card_w(sw)) / 2; }
-pub fn card_y(sh : i64) -> i64 { return (sh - card_h(sh)) / 2; }
+pub fn orb_card_w(sw : i64) -> i64 { return min_i(520, sw - 32); }
+pub fn orb_card_h(sh : i64) -> i64 { return min_i(300, sh - 32); }
+pub fn orb_card_x(sw : i64) -> i64 { return (sw - orb_card_w(sw)) / 2; }
+pub fn orb_card_y(sh : i64) -> i64 { return (sh - orb_card_h(sh)) / 2; }
 
 test sin_cos_hit_the_quadrant_points {
     assert abs_i(sin_pm(0)) <= 2;
@@ -342,7 +342,7 @@ test hit_finds_the_label_under_the_pointer_and_none_elsewhere {
     var hx : [4]i64 = [100, 400, 700, 1000];
     var hy : [4]i64 = [100, 100, 100, 100];
     assert hit_index(hx, hy, 4, 0, 400, 100, LABEL_W, LABEL_H) == 1;
-    assert hit_index(hx, hy, 4, 0, 400, 300, LABEL_W, LABEL_H) == NONE;
+    assert hit_index(hx, hy, 4, 0, 400, 300, LABEL_W, LABEL_H) == ORB_NONE;
     assert label_hit(100, 100, 100, 100, LABEL_W, LABEL_H);
     assert !label_hit(100 + LABEL_W, 100, 100, 100, LABEL_W, LABEL_H);
 }
@@ -355,8 +355,8 @@ test a_tiny_stage_keeps_what_fits_and_drops_the_rest {
 }
 
 test the_card_is_centred_and_fits_small_stages {
-    assert card_w(1440) == 520;
-    assert card_x(1440) == 460;
-    assert card_h(300) == 268;
-    assert card_y(900) == 300;
+    assert orb_card_w(1440) == 520;
+    assert orb_card_x(1440) == 460;
+    assert orb_card_h(300) == 268;
+    assert orb_card_y(900) == 300;
 }

specs/t27f/formula_table.t27

@@ -20,8 +20,8 @@ pub const COMPLEXITY : [32]u32 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
 /// Sector names in order of first appearance: gauge-coupling, electroweak, lepton, quark, ckm, pmns, cosmology, higgs, qcd.
 pub const SECTOR_OF : [32]u32 = [0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 4, 4, 4, 5, 5, 2, 8, 6, 6];
 
-pub fn field_start(i : u32, f : u32) -> u32 { return FIELD_START[i * 4 + f]; }
-pub fn field_len(i : u32, f : u32) -> u32 { return FIELD_LEN[i * 4 + f]; }
+pub fn formula_field_start(i : u32, f : u32) -> u32 { return FIELD_START[i * 4 + f]; }
+pub fn formula_field_len(i : u32, f : u32) -> u32 { return FIELD_LEN[i * 4 + f]; }
 pub fn err_milli_pct(i : u32) -> i64 { return ERR_MILLI_PCT[i]; }
 pub fn abs_err(i : u32) -> i64 { if ERR_MILLI_PCT[i] < 0 { return 0 - ERR_MILLI_PCT[i]; } return ERR_MILLI_PCT[i]; }
 
@@ -31,10 +31,10 @@ test every_row_is_verified_and_counted {
 }
 
 test fields_tile_the_text_without_gaps {
-    assert field_start(0, 0) == 0;
-    assert field_start(31, 3) + field_len(31, 3) == 1949;
-    assert field_start(0, 1) == field_start(0, 0) + field_len(0, 0);
-    assert field_len(0, 0) > 0;
+    assert formula_field_start(0, 0) == 0;
+    assert formula_field_start(31, 3) + formula_field_len(31, 3) == 1949;
+    assert formula_field_start(0, 1) == formula_field_start(0, 0) + formula_field_len(0, 0);
+    assert formula_field_len(0, 0) > 0;
 }
 
 test errors_are_small_and_signed {

specs/t27os/agent_parts.t27

@@ -1020,13 +1020,17 @@ pub const PAGE_NONE : u32 = 0;
 pub const PAGE_BENCH : u32 = 1;
 pub const PAGE_KANBAN : u32 = 2;
 pub const PAGE_QUEEN : u32 = 3;
-pub const PAGE_KINDS : u32 = 4;
+pub const PAGE_HIVE : u32 = 4;
+pub const PAGE_KINDS : u32 = 5;
 pub const PERIOD_BENCH : u32 = 10;
 pub const PERIOD_KANBAN : u32 = 60;
 pub const PERIOD_QUEEN : u32 = 60;
+/// HIVE (H, the devices page, specs/t27os/devices.t27): its feed is DV_PERIOD_S there; the same 60 s here.
+pub const PERIOD_HIVE : u32 = 60;
 
 pub fn page_kind(l: u32) -> u32 {
     if (l == 2) { return PAGE_BENCH; }
+    if (l == 8) { return PAGE_HIVE; }
     if (l == 11) { return PAGE_KANBAN; }
     if (l == 17) { return PAGE_QUEEN; }
     return PAGE_NONE;
@@ -1037,6 +1041,7 @@ pub fn page_period(kind: u32) -> u32 {
     if (kind == PAGE_BENCH) { return PERIOD_BENCH; }
     if (kind == PAGE_KANBAN) { return PERIOD_KANBAN; }
     if (kind == PAGE_QUEEN) { return PERIOD_QUEEN; }
+    if (kind == PAGE_HIVE) { return PERIOD_HIVE; }
     return 0;
 }
 
@@ -1047,7 +1052,9 @@ pub fn page_feed_due(kind: u32, open: bool, now: u64, last: u64) -> bool {
     return now - last >= (page_period(kind) as u64);
 }
 
-test the_three_built_pages_are_the_tools_b_k_and_q {
+test the_four_built_pages_are_the_tools_b_h_k_and_q {
+    assert page_kind(8) == PAGE_HIVE;
+    assert page_of_letter(8) == "HIVE";
     assert page_kind(2) == PAGE_BENCH;
     assert page_kind(11) == PAGE_KANBAN;
     assert page_kind(17) == PAGE_QUEEN;
@@ -1066,7 +1073,7 @@ test every_other_letter_keeps_the_dashboard {
         if (page_kind(l) != PAGE_NONE) { pages = pages + 1; }
         l = l + 1;
     }
-    assert pages == 3;
+    assert pages == 4;
     assert page_kind(0) == PAGE_NONE;
     assert page_kind(28) == PAGE_NONE;
     assert page_kind(3) == PAGE_NONE;
@@ -1077,6 +1084,9 @@ test the_feeds_run_at_their_cadence_and_only_while_the_page_is_open {
     assert page_period(PAGE_KANBAN) == 60;
     assert page_period(PAGE_QUEEN) == 60;
     assert page_period(PAGE_NONE) == 0;
+    assert page_period(PAGE_HIVE) == 60;
+    assert page_feed_due(PAGE_HIVE, true, 1060, 1000);
+    assert page_feed_due(PAGE_HIVE, false, 1060, 1000) == false;
     assert page_feed_due(PAGE_BENCH, true, 1000, 0);
     assert page_feed_due(PAGE_BENCH, true, 1009, 1000) == false;
     assert page_feed_due(PAGE_BENCH, true, 1010, 1000);