forge: add patch 13 — quadratic hop delay growth

bias = hop * step + hop^2 * BOT_HOP_GROW_MILLIS

Bumps hop_step 3000->2000, adds BOT_HOP_GROW_MILLIS=400, raises cap
15000->50000 and TTL 75000->95000. Forces re-default of hop_step on
existing bots via BOT_PREFS_VERSION 5->6.

Gap between adjacent hops now grows with hop count (3200ms at hop 1
all the way to 8000ms at hop 8), so a far bot reliably has time to
hear a near bot's reply through the mesh before its own scheduled
fire time -- previous linear bias kept the gap constant at 3000ms,
which wasn't enough at 6+ hops where reply propagation takes ~5-10s.

patches/meshcore/0001-Add-companion-radio-firmware-bot-command-parity.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Fri, 15 May 2026 11:44:21 -0600
-Subject: [PATCH 01/12] Add companion radio firmware bot command parity
+Subject: [PATCH 01/13] Add companion radio firmware bot command parity
 
 ---
  .../companion_radio/BotCommandRegistry.cpp    |  121 ++

patches/meshcore/0002-Harden-firmware-bot-response-coordination.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Fri, 15 May 2026 19:58:42 -0600
-Subject: [PATCH 02/12] Harden firmware bot response coordination
+Subject: [PATCH 02/13] Harden firmware bot response coordination
 
 ---
  examples/companion_radio/BotCommands.cpp      |   2 +-

patches/meshcore/0003-Allow-prefixless-firmware-bot-DMs.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Fri, 15 May 2026 20:09:58 -0600
-Subject: [PATCH 03/12] Allow prefixless firmware bot DMs
+Subject: [PATCH 03/13] Allow prefixless firmware bot DMs
 
 ---
  examples/companion_radio/BotPolicy.cpp | 2 +-

patches/meshcore/0004-Align-firmware-bot-commands-with-upstream-behavior.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 04:12:02 +0000
-Subject: [PATCH 04/12] Align firmware bot commands with upstream behavior
+Subject: [PATCH 04/13] Align firmware bot commands with upstream behavior
 
 ---
  .../companion_radio/BotCommandRegistry.cpp    |  25 +-

patches/meshcore/0005-Add-hop-aware-bot-coordination-utility-commands-and-.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 12:38:13 -0600
-Subject: [PATCH 05/12] Add hop-aware bot coordination, utility commands, and
+Subject: [PATCH 05/13] Add hop-aware bot coordination, utility commands, and
  bounded delays
 
 Adds new utility commands (TIME, LORA, ID, NEIGHBORS), neighbor tracking,

patches/meshcore/0006-Mark-bot-adverts-speed-up-initial-advert-default-con.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 18:58:28 -0600
-Subject: [PATCH 06/12] Mark bot adverts, speed up initial advert, default
+Subject: [PATCH 06/13] Mark bot adverts, speed up initial advert, default
  contacts auto-overwrite
 
 Three coordination/discoverability fixes:

patches/meshcore/0007-Prefix-bot-responses-with-request-token-for-inter-bo.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 19:33:04 -0600
-Subject: [PATCH 07/12] Prefix bot responses with request token for inter-bot
+Subject: [PATCH 07/13] Prefix bot responses with request token for inter-bot
  suppression
 
 Adds a 4-hex request token (low 16 bits of the request fingerprint) as a

patches/meshcore/0008-Drop-MCBOT-advert-suffix-and-auto-learn-known-bot-pa.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 19:55:36 -0600
-Subject: [PATCH 08/12] Drop [MCBOT] advert suffix and auto-learn known-bot
+Subject: [PATCH 08/13] Drop [MCBOT] advert suffix and auto-learn known-bot
  path
 
 Removes BOT_ADVERT_MARKER / writeBotAdvertName / isBotAdvertName from

patches/meshcore/0009-Widen-hop-step-drop-ack-prefix-from-test-response.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 20:05:19 -0600
-Subject: [PATCH 09/12] Widen hop-step + drop "ack " prefix from test response
+Subject: [PATCH 09/13] Widen hop-step + drop "ack " prefix from test response
 
 Two changes:
 

patches/meshcore/0010-Widen-coordinator-delays-a-tiny-bit-more.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 20:31:12 -0600
-Subject: [PATCH 10/12] Widen coordinator delays a tiny bit more
+Subject: [PATCH 10/13] Widen coordinator delays a tiny bit more
 
 ~25% bump across the main coordination knobs:
 - BOT_RESPONSE_DELAY_BASE_MILLIS   1200 -> 1500

patches/meshcore/0011-Auto-advert-on-startup-initial-flood-at-5s-instead-o.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 20:49:51 -0600
-Subject: [PATCH 11/12] Auto-advert on startup (initial flood at 5s instead of
+Subject: [PATCH 11/13] Auto-advert on startup (initial flood at 5s instead of
  120s)
 
 BOT_PREFS_INITIAL_FLOOD_ADVERT_MILLIS 120000 -> 5000. The bot now sends

patches/meshcore/0012-Spell-out-hops-byte-in-test-path-drop-channel-name-f.patch

@@ -1,7 +1,7 @@
 From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
 From: cj-vana <cj@depth23.online>
 Date: Sat, 16 May 2026 21:32:04 -0600
-Subject: [PATCH 12/12] Spell out hops/byte in test+path; drop channel name
+Subject: [PATCH 12/13] Spell out hops/byte in test+path; drop channel name
  from test ack
 
 Test response (writeAckResponse):

patches/meshcore/0013-Hop-delay-grows-quadratically-wider-gaps-at-higher-h.patch

@@ -0,0 +1,94 @@
+From 0000000000000000000000000000000000000000 Mon Sep 17 00:00:00 2001
+From: cj-vana <cj@depth23.online>
+Date: Sat, 16 May 2026 22:18:02 -0600
+Subject: [PATCH 13/13] =?UTF-8?q?Hop=20delay=20grows=20quadratically=20?=
+ =?UTF-8?q?=E2=80=94=20wider=20gaps=20at=20higher=20hop=20counts?=
+MIME-Version: 1.0
+Content-Type: text/plain; charset=UTF-8
+Content-Transfer-Encoding: 8bit
+
+New formula: bias = hop * step + hop^2 * BOT_HOP_GROW_MILLIS
+
+Constants:
+  BOT_HOP_STEP_MILLIS_DEFAULT  3000 -> 2000
+  BOT_HOP_GROW_MILLIS           NEW = 400
+  BOT_HOP_BIAS_MAX_MILLIS    15000 -> 50000
+  BOT_RESPONSE_PENDING_TTL_MILLIS 75000 -> 95000
+  BOT_PREFS_VERSION              5 -> 6
+
+Hop -> bias / gap from previous:
+  1 ->  2400ms /   --
+  2 ->  5600ms / +3200
+  3 ->  9600ms / +4000
+  4 -> 14400ms / +4800
+  5 -> 20000ms / +5600
+  6 -> 26400ms / +6400
+  7 -> 33600ms / +7200
+  8 -> 41600ms / +8000
+  9+-> 50000ms (cap)
+
+Previous linear bias gave the same gap between every adjacent hop. At
+higher hop counts that wasn't enough: a 7-hop bot's scheduled delay was
+only one step longer than the 6-hop bot's, but the 6-hop bot's reply
+needed ~5-10s of mesh airtime to propagate one extra hop to the 7-hop
+bot. Result: the further bot fired before the closer bot's reply
+arrived -> token suppression never triggered.
+
+Now an N-hop bot has roughly 2*N*400ms more spacing than an (N-1)-hop
+bot, which keeps growing as the mesh gets deeper.
+---
+ examples/companion_radio/BotTypes.h              | 9 +++++----
+ examples/companion_radio/ResponseCoordinator.cpp | 6 +++++-
+ 2 files changed, 10 insertions(+), 5 deletions(-)
+
+diff --git a/examples/companion_radio/BotTypes.h b/examples/companion_radio/BotTypes.h
+index 08fe8bc7..f3afa21f 100644
+--- a/examples/companion_radio/BotTypes.h
++++ b/examples/companion_radio/BotTypes.h
+@@ -30,14 +30,14 @@
+ #define BOT_NEIGHBOR_RECENT_MILLIS (60UL * 60UL * 1000UL)
+ #define BOT_RESPONSE_DELAY_BASE_MILLIS 1500UL
+ #define BOT_RESPONSE_DELAY_JITTER_MILLIS 2200UL
+-#define BOT_RESPONSE_PENDING_TTL_MILLIS 75000UL
++#define BOT_RESPONSE_PENDING_TTL_MILLIS 95000UL
+ #define BOT_RESPONSE_RECENT_TTL_MILLIS 30000UL
+ #define BOT_KNOWN_BOT_FLAG_SUPPRESS_NORMAL 0x01
+ #define BOT_SENDER_KEY_PREFIX_LEN 6
+ #define BOT_MIN_AUTH_SENDER_KEY_PREFIX_LEN 4
+ #define BOT_KNOWN_BOT_LABEL_LEN 12
+ #define BOT_PREFS_MAGIC 0x31504642UL
+-#define BOT_PREFS_VERSION 5
++#define BOT_PREFS_VERSION 6
+ #define BOT_PREFS_DEFAULT_LOCAL_ADVERT_MILLIS (24UL * 60UL * 60UL * 1000UL)
+ #define BOT_PREFS_DEFAULT_FLOOD_ADVERT_MILLIS (24UL * 60UL * 60UL * 1000UL)
+ #define BOT_PREFS_INITIAL_LOCAL_ADVERT_MILLIS 60000UL
+@@ -45,9 +45,10 @@
+ #define BOT_PREFS_MAX_DELAY_MILLIS 60000U
+ #define BOT_PREFS_MAX_ADVERT_MILLIS (7UL * 24UL * 60UL * 60UL * 1000UL)
+ #define BOT_PREFS_SERIALIZED_SIZE 296
+-#define BOT_HOP_STEP_MILLIS_DEFAULT 3000U
++#define BOT_HOP_STEP_MILLIS_DEFAULT 2000U
+ #define BOT_HOP_STEP_MILLIS_MAX 30000U
+-#define BOT_HOP_BIAS_MAX_MILLIS 15000UL
++#define BOT_HOP_GROW_MILLIS 400UL
++#define BOT_HOP_BIAS_MAX_MILLIS 50000UL
+ 
+ enum BotChannelKind : uint8_t {
+   BOT_CHANNEL_DM = 0,
+diff --git a/examples/companion_radio/ResponseCoordinator.cpp b/examples/companion_radio/ResponseCoordinator.cpp
+index 3640f8b6..837b3f12 100644
+--- a/examples/companion_radio/ResponseCoordinator.cpp
++++ b/examples/companion_radio/ResponseCoordinator.cpp
+@@ -23,7 +23,11 @@ uint32_t channelDelayBias(BotChannelKind kind) {
+ 
+ uint32_t hopDelayBias(BotChannelKind kind, uint8_t path_hash_count, uint16_t hop_step_millis) {
+   if (kind == BOT_CHANNEL_DM) return 0;
+-  uint32_t bias = (uint32_t)path_hash_count * (uint32_t)hop_step_millis;
++  // Linear + quadratic growth: gap between consecutive hops widens with hop
++  // count, so a far bot always has more slack than a near bot to receive
++  // the near bot's reply before its own scheduled fire time.
++  uint32_t hop = (uint32_t)path_hash_count;
++  uint32_t bias = hop * (uint32_t)hop_step_millis + hop * hop * BOT_HOP_GROW_MILLIS;
+   if (bias > BOT_HOP_BIAS_MAX_MILLIS) bias = BOT_HOP_BIAS_MAX_MILLIS;
+   return bias;
+ }

tests/firmware_bot/test_firmware_bot.cpp

@@ -1533,8 +1533,13 @@ static void test_response_coordinator_hop_count_ranking() {
                                                           base_delay, jitter, hop_step);
   uint32_t d2 = ResponseCoordinator::responseDelayMillis(two_hop, BOT_COMMAND_PING, request, 0x01020304UL, 0, 0,
                                                           base_delay, jitter, hop_step);
-  assert(d1 == d0 + hop_step);
+  // Linear + quadratic growth: bias(h) = h*step + h*h*grow
-  assert(d2 == d0 + (uint32_t)hop_step * 2);
+  assert(d1 == d0 + (uint32_t)hop_step + BOT_HOP_GROW_MILLIS);
+  assert(d2 == d0 + (uint32_t)hop_step * 2 + 4 * BOT_HOP_GROW_MILLIS);
+  // Gap between hops widens as hop count rises:
+  uint32_t gap_0_to_1 = d1 - d0;
+  uint32_t gap_1_to_2 = d2 - d1;
+  assert(gap_1_to_2 > gap_0_to_1);
 
   uint32_t alt_step = 2000;
   uint32_t d0_alt = ResponseCoordinator::responseDelayMillis(near, BOT_COMMAND_PING, request, 0x01020304UL, 0, 0,
@@ -1542,7 +1547,7 @@ static void test_response_coordinator_hop_count_ranking() {
   uint32_t d1_alt = ResponseCoordinator::responseDelayMillis(one_hop, BOT_COMMAND_PING, request, 0x01020304UL, 0, 0,
                                                               base_delay, jitter, alt_step);
   assert(d0_alt == d0);
-  assert(d1_alt == d0 + alt_step);
+  assert(d1_alt == d0 + alt_step + BOT_HOP_GROW_MILLIS);
 
   BotMessage dm = make_message("dm", "!ping");
   dm.channel_kind = BOT_CHANNEL_DM;
@@ -1570,7 +1575,8 @@ static void test_response_coordinator_hop_bias_cap() {
   uint32_t dmany = ResponseCoordinator::responseDelayMillis(many_hops, BOT_COMMAND_PING, request, 0x01020304UL, 0, 0,
                                                              base_delay, jitter, hop_step);
   assert(dmany == d0 + BOT_HOP_BIAS_MAX_MILLIS);
-  assert((uint32_t)many_hops.path_hash_count * hop_step > BOT_HOP_BIAS_MAX_MILLIS);
+  uint32_t hop_u32 = (uint32_t)many_hops.path_hash_count;
+  assert(hop_u32 * (uint32_t)hop_step + hop_u32 * hop_u32 * BOT_HOP_GROW_MILLIS > BOT_HOP_BIAS_MAX_MILLIS);
   assert(dmany + BOT_RESPONSE_DELAY_JITTER_MILLIS < BOT_RESPONSE_PENDING_TTL_MILLIS);
 }