Heat Generation

The Firechain Network is a shared resource. It is a public good that is available to all users. In order to ensure that the network is available to all users, Firechain uses a dynamic resource sharing mechanism called Heat. It's a measure of the amount of demand that an account has placed on the network recently. Accounts generate heat when they interact with the network, and that heat dissipates over time automatically. The easiest way to think about Heat is as a form of congestion control which ensures that the network remains useful to the most inclusive group of users possible by way of limiting the load that any one account can put on the network.

Understanding Heat

Most blockchains require accounts to pay some sort of fee in order to transact over the network, primarily to prevent spam and misuse of the network's resources. Firechain does not use transaction fees. Instead, we developed the concept of heat which enables the network to operate without economic barriers that can be untenable for a large percentage of the population.

To obtain heat capacity, you can:

• Stake FIRE (staking ~268 FIRE grants about 1 transaction per minute); or
• Produce a PoW solution to generate transient heat capacity when you need it.

Firechain isn't a PoW network, and PoW isn't always an option (i.e. there are limits on how much supplementary heat can be produced via PoW within a given time period, both at the account level and for the network as a whole). It's probably fine if you only intend to send one or two transactions here or there. However, it's recommended to stake rather than rely on PoW—especially if you plan to use the network on a regular basis.

Estimating Heat Generation

The table below shows the heat consumption of typical actions. You can use this to get a handle on how much heat capacity would be needed for the type of activity you expect to perform.

You'll see us refer to heat in two ways:

• Scovilles are the low-level raw units of heat generated.
• Heat Units (H) are equal to 21,000 Scovilles, which is the amount generated by a simple transfer.

Transaction Type	Scovilles	Heat Units (H)	Stake Needed
Simple asset transfer (no data)	21000	1	134
Receive a transaction (no response)	21000	1	134
Deploy a contract	31000	1.4762	267
New validator registration	168000	8	1067
Change validator registration	168000	8	1067
Unregister validator	126000	6	534
Withdraw pending rewards	147000	7	934
New governance vote	84000	4	534
Retract governance vote	52500	2.5	400
Stake	105000	5	667
Stake (w/ callback)	115500	5.5	800
Unstake	105000	5	667
Unstake (w/ callback)	115500	5.5	800
Create a new token	189000	9	1200
Change token owner	136500	6.5	934
Change token type	115500	5.5	800
Mint tokens	126000	6	800
Burn tokens	115500	5.5	800
Query token (on-chain)	31500	1.5	267

• Any data in the transaction's comment field produces 56 Scovilles per character. For example, sending a transfer transaction with the data '0x6969' (two hexadecimal characters) will consume
  $H=21000+56\ast 2=21112$ Scovilles, which translates to
  $1.0053H$.
• For contracts that require a specific global confirmation threshold, there is an additional heat consumption of
  $200\times N_{confirmations}$ applied to each response transaction.

Calculating Heat Generation

Heat consumption can be calculated using the following formulas:

$$H_{PoW}=H_{max}\times (1-\frac{2}{1+e^{H_{recent}\times \xi d\times \rho d}})$$

$$H_{Stake}=H_{max}\times (1-\frac{2}{1+e^{H_{recent}\times \xi s\times \rho s}})$$

$$H_{recent}=\{\begin{array}{ll}1,& \text{for }{H}_{avg}\le 1050000\\ 2-e^{8.260667775706495e-09\times (H_{avg}-1050000)},& \text{for }1050000<H_{avg}\le 2100000\\ e^{1.6949794096275418e-10\times (2100000-H_{avg})}-0.9,& \text{for }{H}_{avg}>2100000\end{array}$$

• $H_{PoW}$: Heat capacity earned via Proof-of-Work (PoW). (Only valid for one transaction.)
• $H_{Stake}$: Heat capacity earned via staking. Recovers at a rate of 1/75 every global block.
• $H_{max}$: Heat capacity limit =
  $1,000,000H$ (constant)
• $H_{recent}$: Heat capacity used in the current epoch
• $H_{avg}$: Global average heat generated in the current epoch
• $\xi d$: The difficulty of an accepted PoW solution
• $\rho d$: PoW solution weight =
  $6.259408129e-10$ (constant)
• $\xi s$: Account's current stake amount
• $\rho s$: Staking weight =
  $4.201037667e-24$ (constant)

$H_{sec}$ is the amount of

$H$ that an account can use in one second

$$H_{sec}=\frac{H_{Stake}}{21000}$$

$H_{epoch}$ is amount of

$H$ that an account can use in 1 epoch (75 global blocks)

$$H_{epoch}=H_{sec}\times 75$$

An account's heat capacity depends on

$H_{sec}$ and

$H_{recent}$. For example, if Alice's account earns

$1.0H_{sec}$ via staking and she hasn't sent any transactions in the last 74 blocks, she'd have

$75H$ of usable heat capacity.

However, the usable heat capacity also accounts for any added

$H_{PoW}$ value. Extending the above example, if Alice provides a PoW solution that grants

$2H$, she'd have

$77H$ of usable heat capacity.

For all transactions, a global maximum of

$47.62H$ applies, which means any transaction that would use more than

$47.62H$ will automatically fail.

For reference, here's a mapping table for determining heat from

$(\xi d\times \rho d)$ or

$(\xi s\times \rho s)$:

$(\xi d\times \rho d)$ or $(\xi s\times \rho s)$	Scovilles	$H_{sec}$	$H_{epoch}$	Stake Required (w/o PoW)	PoW Required (w/o stake)
0.0	0	0	0	0	0
$(0,0.0005600000146345639)$	280	1/75	1	134	894654
$(0.0005600000146345639,0.0011200001170773874)$	560	2/75	2	267	1789307
$(0.0011200001170773874,0.0016800003951362111)$	840	3/75	3	400	2683961
$(0.0016800003951362111,0.002240000936619286)$	1120	4/75	4	534	3578615
$(0.002240000936619286,0.002800001829335484)$	1400	5/75	5	667	4473270
$(0.0050400106687125265,0.005600014634735637)$	2800	10/75	10	1334	8946557
$(0.007840040157895736,0.008400049392522762)$	4200	15/75	15	2000	13419879
$(0.010640100380883094,0.011200117079536328)$	5600	20/75	20	2667	17893253
$(0.013440202315113498,0.01400022867338966)$	7000	25/75	25	3333	22366698
$(0.01624035693900638,0.016800395152729273)$	8400	30/75	30	4000	26840230
$(0.019040575232219203,0.019600627497492765)$	9800	35/75	35	4666	31313868
$(0.021840868175909127,0.022400936689166498)$	11200	40/75	40	5333	35787628
$(0.02464124675298827,0.025201333711046034)$	12600	45/75	45	5999	40261529
$(0.027441721948384734,0.028001829548493135)$	14000	50/75	50	6666	44735587
$(0.030242304749299606,0.030802435189193574)$	15400	55/75	55	7333	49209821
$(0.03304300614546563,0.033603161623419094)$	16800	60/75	60	7999	53684248
$(0.03584383712940819,0.036404019844283514)$	18200	65/75	65	8666	58158886
$(0.03864480869670122,0.03920502084800278)$	19600	70/75	70	9333	62633751
$(0.03920502084800278,0.039765239150590236)$	19880	71/75	71	9466	63528753
$(0.039765239150590236,0.04032546369247644)$	20160	72/75	72	9599	64423765
$(0.04032546369247644,0.04088569456168163)$	20440	73/75	73	9733	65318787
$(0.04088569456168163,0.04144593184623087)$	20720	74/75	74	9866	66213820
$(0,0.042006175634155006)$	21000	1	75	10000	67108863
$(0.042006175634155006,0.08404944434245186)$	42000	2	150	20007	134276984
$(0.08404944434245186,0.1261670961035256)$	63000	3	225	30033	201563940
$(0.1261670961035256,0.16839681732546105)$	84000	4	300	40085	269029937
$(0.16839681732546105,0.2107768956769977)$	105000	5	375	50173	336736144
$(0.382599842575369,0.4263426931297194)$	210000	10	750	101486	681123015
$(0.605878237567604,0.6521731063496397)$	315000	15	1125	155241	1041908585
$(0.8449180401302736,0.8953840470548413)$	420000	20	1500	213135	1430461202
$(1.1093075777848576,1.1664348850068706)$	525000	25	1875	277654	1863490703
$(1.4146605870070175,1.4828322881625378)$	630000	30	2250	352969	2368965656
$(1.7905932883378723,1.8790328663947373)$	735000	35	2625	447279	3001933774
$(2.3075451472522963,2.4423470353692043)$	840000	40	3000	581368	3901881752
$(2.4423470353692043,2.594395323511559)$	861000	41	3075	617561	4144793358
$(2.594395323511559,2.7694056956796604)$	882000	42	3150	659220	4424389078
$(2.7694056956796604,2.976475888792767)$	903000	43	3225	708510	4755203412
$(2.976475888792767,3.2314282909393213)$	924000	44	3300	769198	5162514130
$(3.2314282909393213,3.5656840708200748)$	945000	45	3375	848763	5696519539
$(3.5656840708200748,4.057395776090949)$	966000	46	3450	965808	6482075769
$(4.057395776090949,5.029431885090279)$	987000	47	3525	1197189	8034995932

As shown in the table above, ignoring any PoW additions, a stake of 10,000 FIRE entitles the beneficiary to

$1H_{sec}\equiv 75H_{epoch}$. The minimum stake (134 FIRE) provides just enough capacity to send one simple transfer per epoch (which is equivalent to

$\frac{1}{74}{H}_{sec}$).

Dynamic Heat Generation

In order to avoid extreme network congestion, Firechain implements a mechanism whereby the network's total heat usage over past 74 global blocks is used to estimate the current global load and dynamically adjust heat generation rates. As such, the amount of heat capacity required for any given transaction will scale with the network's load.

The following table outlines the required stake to achieve

$1H_{epoch}$ in various congestion scenarios.

Global $H_{avg}$	Congestion Factor	Stake
0-50	1	134
51	0.987079620361328125	135
52	0.97399139404296875	137
53	0.960735321044921875	139
54	0.947307586669921875	141
55	0.93370819091796875	143
60	0.8630218505859375	155
70	0.707286834716796875	189
80	0.53022003173828125	252
90	0.328899383544921875	407
100	0.0999999046325683594	1339
150	0.0869164466857910156	1541
200	0.0740036964416503906	1810
250	0.061260223388671875	2187
300	0.0486836433410644531	2752
350	0.0362710952758789062	3694
400	0.0240213871002197266	5578
410	0.0215908288955688477	6206
420	0.0191664695739746094	6991
430	0.0167486667633056641	8000
440	0.0143371224403381348	9346
450	0.0119318962097167969	11230
460	0.00953304767608642578	14056
470	0.0071404874324798584	18766
480	0.00475424528121948242	28185
490	0.00237426161766052246	56438
491	0.00213660299777984619	62716
492	0.00189901143312454224	70562
493	0.00166147947311401367	80650
494	0.00142402201890945435	94099
495	0.00118660926818847656	112926
496	0.000949271023273468018	141160
497	0.000711996108293533325	188203
498	0.000474780797958374023	282235
499	0.000237626954913139343	563908

Getting Heat Capacity

Staking (Recommended)

The recommended way to obtain heat capacity is through staking.

• The minimum staking amount is 134 FIRE. There's no maximum stake amount, but there is a
  $H_{max}=1,000,000$.
• Capacity earned via staking can be credited to any account, which is to say you may stake for the benefit of anyone you chose. The beneficiary cannot be changed until the lock-up period expires. The staker always retains title to the staked tokens, regardless of the beneficiary.
• Staked FIRE is held by the built-in staking contract for the duration of the staking period.
• Staking can be revoked and funds retrieved by the staker after ~3 days (259.2k global blocks).

One-Time PoW Solutions

If necessary, one can also get a transient heat capacity boost by solving a PoW challenge and including the solution when sending a transaction. For example, the difficulty required for a simple transfer (without any staking) is 0x3FFFFFF.

Calculating PoW Challenges

1. Derive
   $target$ from
   $difficulty$:

$$target=\frac{2^{256}}{1+\frac{1}{difficulty}}$$

• $difficulty$ is the PoW challenge difficulty (padded to a length of 256 bits).
• $target$: is the 256-bit PoW target value.

For example, given a difficulty = 0x3FFFFFF then target = 0xFFFFFFC000000000.

2. Calculate
   $nonce$ based on transaction's data. In this process, a widely range of random numbers are assigned to
   $nonce$ until the following condition is satisfied:
   
   $$blake2b(address+prevHash)+nonce<target$$

• $blake2b$: Hash function in Firechain
• $address$: User's account address
• $prevHash$: Hash of previous account block

Frequently Asked Questions

Can I stake and share my heat capacity with several accounts?

Yes. You can specify one beneficiary per staking transaction, so you would simply send one staking transaction per beneficiary address. It's currently not possible to re-assign an existing stake without first unstaking.

Can I stake multiple times for the same beneficiary?

Yes. Doing so will produce several independent staking records, each with their own expiration. Heat capacity is calculated using the total of all beneficial stakes.

Can multiple stakers provide capacity to the same beneficiary?

Yes. Heat capacity is calculated using the total of all beneficial stakes.

Can I unstake before expiration?

No, it's not possible to retrieve your stake prior to the expiration of the lock-up period.

Can heat capacity be used up?

Yes, but only transiently. It'll automatically restore at a rate of 1/75th per global block. In other words, if you exhausted your entire heat capacity right now, you'd get back to 100% in 75 global blocks. Heat is never permanent.

Do I need heat capacity to receive a transaction?

Yes, receiving a transaction generates 21,000 Scovilles.

What about transactions to or from a brand new account?

Because it's not possible for an account to stake before it exists, you'll either need to complete a PoW solution for one-time heat capacity, or have someone stake for your new account's benefit.

Can I send transactions while the network is under heavy load?

Yes, but doing so will generate more heat than normal. Unless it's urgent, we recommend waiting for the load to go down before sending the transaction. Of course this is entirely discretionary, and you are free to send transactions so long as your heat capacity allows.