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+// SPDX-License-Identifier: Apache-2.0
+; specs/policy/pr_budget.t27 -- how many PRs a port wave may open, and how many one author may hold open.
+; Closes #10067. Measured on 2026-10-17: open PRs were dmitrii-f-t27 128 and gHashTag 162 (131 of
+; them queen-*); dmitrii-f-t27 opened 6 to 9 PRs an hour around the clock; of the latest 1000 Actions
+; runs (17:34-17:59Z) 732 were master push runs, about 19 workflows per merge, and 76 were
+; dmitrii-f-t27 pull_request runs; at 18:00Z, 29 of 51 queued runs were dmitrii-f-t27's.
+; The ports are real work (Roadmap Stage 6). What filled both queues is their shape: one PR per file.
+; --
+; Rule 1, batching. A port wave PR is one whose title starts `spec(port)` or whose branch starts
+; `zcode-port-` or `port/cr-chat-`. A port wave lands one PR per ring or crate, never one per file.
+; Credit is not lost: each ported spec earns TRI_PER_SPEC in the Queen earnings ledger whatever the
+; number of PRs that carried it, so batching keeps every author's credit and drops only Actions runs.
+; Rule of thumb: a 20-file wave as 20 PRs is 20 x ~29 checks + 20 merges x ~19 push runs, about 960
+; runs; as one batch it is about 48.
+; --
+; Rule 2, budget. Each author may hold at most OPEN_CAP open non-draft PRs. Every author counts the
+; same, the owner's account and the Queen's bees included: the cap is on the queue, not on a person.
+; When the cap is full, the excess is held as a draft, and drafts are promoted in order as slots free.
+; Nothing is closed and no work is refused; a held PR only waits.
+; --
+; This card is the rule only. Wiring it into a gate that drafts the excess is a follow-up; until then
+; nothing reads this file but its own tests.
+; phi^2 + 1/phi^2 = 3 | TRINITY
+
+module PolicyPrBudget;
+
+/// Open non-draft PRs one author may hold. The starting value; tune it here, nowhere else.
+pub const OPEN_CAP : u32 = 20;
+
+/// TRI the Queen earnings ledger pays per ported spec, independent of how many PRs carried it.
+pub const TRI_PER_SPEC : u32 = 27;
+
+/// Checks one PR runs on pull_request, and workflows one merge starts on master push (2026-10-17).
+pub const CHECKS_PER_PR : u32 = 29;
+pub const PUSH_RUNS_PER_MERGE : u32 = 19;
+
+/// Verdicts of admit().
+pub const READY : u8 = 0;
+pub const HOLD_DRAFT : u8 = 1;
+
+/// The three prefixes that mark a port wave PR, with their lengths.
+pub const PORT_TITLE : str = "spec(port)";
+pub const PORT_TITLE_LEN : usize = 10;
+pub const PORT_BRANCH_ZCODE : str = "zcode-port-";
+pub const PORT_BRANCH_ZCODE_LEN : usize = 11;
+pub const PORT_BRANCH_CR_CHAT : str = "port/cr-chat-";
+pub const PORT_BRANCH_CR_CHAT_LEN : usize = 13;
+
+/// Measured 2026-10-17 on gHashTag/t27. Test data, not tuning knobs.
+pub const M_OPEN_FEDOROV : u32 = 128;
+pub const M_OPEN_GHASHTAG : u32 = 162;
+pub const M_OPEN_GHASHTAG_QUEEN : u32 = 131;
+pub const M_RATE_LOW_PER_HOUR : u32 = 6;
+pub const M_RATE_HIGH_PER_HOUR : u32 = 9;
+pub const M_RUNS_SAMPLE : u32 = 1000;
+pub const M_RUNS_MASTER_PUSH : u32 = 732;
+pub const M_RUNS_FEDOROV_PR : u32 = 76;
+pub const M_SAMPLE_MINUTES : u32 = 25;
+pub const M_QUEUED : u32 = 51;
+pub const M_QUEUED_FEDOROV : u32 = 29;
+
+/// Does buf[0..n] start with p[0..pn]?
+pub fn has_prefix(buf: []const u8, n: usize, p: []const u8, pn: usize) -> bool {
+    if (pn > n) { return false; }
+    var i : usize = 0;
+    while (i < pn) {
+        if (buf[i] != p[i]) { return false; }
+        i += 1;
+    }
+    return true;
+}
+
+/// Is this PR part of a port wave? Title `spec(port)...`, or branch `zcode-port-...` / `port/cr-chat-...`.
+pub fn is_port_pr(title: []const u8, tn: usize, branch: []const u8, bn: usize) -> bool {
+    if (has_prefix(title, tn, PORT_TITLE, PORT_TITLE_LEN)) { return true; }
+    if (has_prefix(branch, bn, PORT_BRANCH_ZCODE, PORT_BRANCH_ZCODE_LEN)) { return true; }
+    return has_prefix(branch, bn, PORT_BRANCH_CR_CHAT, PORT_BRANCH_CR_CHAT_LEN);
+}
+
+/// PRs a port wave of `files` specs across `groups` rings or crates opens: one per group when
+/// batched, one per file when not.
+pub fn wave_prs(files: u32, groups: u32, batched: bool) -> u32 {
+    if (batched) { return groups; }
+    return files;
+}
+
+/// Actions runs a wave of `prs` PRs costs: its pull_request checks plus the push runs of its merges.
+pub fn wave_runs(prs: u32) -> u32 {
+    return prs * CHECKS_PER_PR + prs * PUSH_RUNS_PER_MERGE;
+}
+
+/// TRI a wave of `files` ported specs earns its author. The PR count is not an input, on purpose.
+pub fn wave_credit(files: u32) -> u32 {
+    return files * TRI_PER_SPEC;
+}
+
+/// Can an author with `open_ready` open non-draft PRs open one more as ready, or is it held?
+pub fn admit(open_ready: u32, cap: u32) -> u8 {
+    if (open_ready < cap) { return READY; }
+    return HOLD_DRAFT;
+}
+
+/// Of `opened` new PRs from an author already holding `open_ready`, how many are held as drafts?
+pub fn held_as_draft(open_ready: u32, opened: u32, cap: u32) -> u32 {
+    if (open_ready >= cap) { return opened; }
+    const free : u32 = cap - open_ready;
+    if (opened <= free) { return 0; }
+    return opened - free;
+}
+
+/// When an author holds `open_ready` ready PRs and `drafts` held ones, how many drafts are promoted?
+pub fn promoted(open_ready: u32, drafts: u32, cap: u32) -> u32 {
+    if (open_ready >= cap) { return 0; }
+    const free : u32 = cap - open_ready;
+    if (drafts <= free) { return drafts; }
+    return free;
+}
+
+/// Whole hours until an author opening `rate` PRs an hour fills an empty cap.
+pub fn hours_to_fill(cap: u32, rate: u32) -> u32 {
+    return (cap + rate - 1) / rate;
+}
+
+/// part / whole in thousandths, rounded down.
+pub fn permille(part: u32, whole: u32) -> u32 {
+    return part * 1000 / whole;
+}
+
+test port_prs_are_named_by_title_or_branch {
+    assert is_port_pr("spec(port): port specs/port/trios-railway/crates/trios-igla-race/src/race.t27", 77, "x", 1) == true;
+    assert is_port_pr("chore: x", 8, "zcode-port-9776", 15) == true;
+    assert is_port_pr("chore: x", 8, "port/cr-chat-12", 15) == true;
+}
+
+test other_prs_are_not_port_prs {
+    assert is_port_pr("spec(t27f): spec_graph_view", 27, "claude/frosty-knuth-6faee5", 26) == false;
+    assert is_port_pr("fix(t27b): fold a constant tie-off", 34, "queen-10046", 11) == false;
+    // a near miss on each prefix, and a prefix longer than the text
+    assert is_port_pr("spec(ports)", 11, "zcode-port", 10) == false;
+    assert is_port_pr("Spec(port): x", 13, "port/cr-chat", 12) == false;
+    assert is_port_pr("spec(", 5, "port/", 5) == false;
+}
+
+test a_twenty_file_wave_costs_960_runs_unbatched_and_48_batched {
+    const prs_one_per_file : u32 = wave_prs(20, 1, false);
+    const prs_batched : u32 = wave_prs(20, 1, true);
+    assert prs_one_per_file == 20;
+    assert prs_batched == 1;
+    // 20 x 29 checks + 20 merges x 19 push runs
+    assert wave_runs(prs_one_per_file) == 20 * 29 + 20 * 19;
+    assert wave_runs(prs_one_per_file) == 960;
+    assert wave_runs(prs_batched) == 48;
+    // the saving is the file count per group
+    assert wave_runs(prs_one_per_file) / wave_runs(prs_batched) == 20;
+}
+
+test batching_keeps_the_credit {
+    // the same 20 specs earn 540 TRI whether they land as 20 PRs or 1
+    assert wave_credit(20) == 540;
+    assert wave_credit(20) == 20 * TRI_PER_SPEC;
+}
+
+test a_wave_over_three_crates_is_three_prs {
+    assert wave_prs(20, 3, true) == 3;
+    assert wave_runs(wave_prs(20, 3, true)) == 144;
+}
+
+test the_cap_admits_up_to_20_and_holds_the_21st {
+    assert admit(0, OPEN_CAP) == READY;
+    assert admit(19, OPEN_CAP) == READY;
+    assert admit(20, OPEN_CAP) == HOLD_DRAFT;
+    assert admit(21, OPEN_CAP) == HOLD_DRAFT;
+}
+
+test the_excess_is_held_as_drafts {
+    assert held_as_draft(0, 20, OPEN_CAP) == 0;
+    assert held_as_draft(15, 10, OPEN_CAP) == 5;
+    assert held_as_draft(20, 3, OPEN_CAP) == 3;
+    assert held_as_draft(25, 1, OPEN_CAP) == 1;
+}
+
+test drafts_are_promoted_as_slots_free {
+    assert promoted(20, 108, OPEN_CAP) == 0;
+    assert promoted(17, 108, OPEN_CAP) == 3;
+    assert promoted(10, 4, OPEN_CAP) == 4;
+    assert promoted(0, 0, OPEN_CAP) == 0;
+}
+
+test measured_2026_10_17_open_prs_against_the_cap {
+    // read as if every open PR were ready: the share of each queue the cap would hold back
+    assert held_as_draft(0, M_OPEN_FEDOROV, OPEN_CAP) == 108;
+    assert held_as_draft(0, M_OPEN_GHASHTAG, OPEN_CAP) == 142;
+    // the owner's account is not exempt, and most of its queue is the Queen's bees
+    assert M_OPEN_GHASHTAG_QUEEN * 2 > M_OPEN_GHASHTAG;
+    assert M_OPEN_GHASHTAG - M_OPEN_GHASHTAG_QUEEN == 31;
+}
+
+test measured_2026_10_17_rate_fills_the_cap_in_hours {
+    // 6 to 9 PRs an hour, around the clock: 144 to 216 a day
+    assert M_RATE_LOW_PER_HOUR * 24 == 144;
+    assert M_RATE_HIGH_PER_HOUR * 24 == 216;
+    // an empty cap of 20 is full within 3 to 4 hours
+    assert hours_to_fill(OPEN_CAP, M_RATE_HIGH_PER_HOUR) == 3;
+    assert hours_to_fill(OPEN_CAP, M_RATE_LOW_PER_HOUR) == 4;
+}
+
+test measured_2026_10_17_actions_runs {
+    // 732 of 1000 runs were master push runs: at about 19 a merge, about 38 merges in 25 minutes
+    assert permille(M_RUNS_MASTER_PUSH, M_RUNS_SAMPLE) == 732;
+    assert M_RUNS_MASTER_PUSH / PUSH_RUNS_PER_MERGE == 38;
+    assert permille(M_RUNS_FEDOROV_PR, M_RUNS_SAMPLE) == 76;
+    // at 18:00Z, one author held more than half of the queue
+    assert permille(M_QUEUED_FEDOROV, M_QUEUED) == 568;
+    assert M_QUEUED_FEDOROV * 2 > M_QUEUED;
+}
+
+invariant credit_does_not_depend_on_pr_count {
+    // wave_credit takes no PR count, so any batching of the same files earns the same
+    assert wave_credit(1) == TRI_PER_SPEC;
+    assert wave_credit(20) == 20 * wave_credit(1);
+    assert wave_prs(20, 1, true) < wave_prs(20, 1, false);
+}
+
+invariant batching_never_costs_more_runs {
+    // a wave never has more groups than files, so the batch is never dearer
+    assert wave_runs(wave_prs(20, 20, true)) == wave_runs(wave_prs(20, 20, false));
+    assert wave_runs(wave_prs(20, 1, true)) <= wave_runs(wave_prs(20, 1, false));
+    assert wave_runs(2) == 2 * wave_runs(1);
+    assert wave_runs(0) == 0;
+}
+
+invariant held_and_ready_add_up_and_never_exceed_the_cap {
+    // whatever is opened, ready PRs stay at or under the cap and nothing is lost
+    assert 15 + (10 - held_as_draft(15, 10, OPEN_CAP)) == OPEN_CAP;
+    assert 0 + (20 - held_as_draft(0, 20, OPEN_CAP)) == OPEN_CAP;
+    assert 17 + promoted(17, 108, OPEN_CAP) == OPEN_CAP;
+    assert READY != HOLD_DRAFT;
+}