math
reading this page
This page places formulas beside values used by the reader and the site. A row changes color when the two evaluations differ. Values absent from chain remain unavailable.
A syndrome evaluates the full codeword at one field point. In a small illustration with running value 3, root 2, and next symbol 5, one Horner step is gf_mul(3, 2) exclusive-or 5. If that multiplication gives 6, the new running value is 3 because 6 exclusive-or 5 equals 3.
The reader repeats that Horner step across all 255 symbols for each of 32 roots. A valid codeword gives zero at every root. Nonzero results carry information used by the decoder.
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distance and the bound
Distance between two codewords is the number of symbol positions where their bytes differ. The minimum distance is 33. Any two valid words therefore differ in at least 33 symbol positions.
The correction bound is t = 16. A received word within that radius has one nearest codeword. At 17 unknown symbol errors, that guarantee ends.
For two independent symbol draws, the chance that the second shares the first symbol is 1/255. The chance that it lands elsewhere is 254/255. Repeating the latter probability produces the expected-damage expression.
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expected damage
Expected damage after f flips is E(f) = 255(1 − (254/255)^f). It rises quickly and then approaches 255. The current since-clean count supplies f for the marker in the figure.
The 256-bit hash is reduced modulo 2,040. Since 2^256 is not divisible by 2,040, some remainder classes receive one extra source value. The difference is negligible but defined.
The site recomputes syndromes, decoding, expectations, sums, and checks. It rounds displayed expected values to three decimal places in the table while chart coordinates use their calculated values. It takes bytes, counters, balances, and repair records from chain.
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what is rounded
Displayed percentages and expectations use limited decimal places. Replay counters and base-unit balances remain integers. Chart positions use calculated values before display formatting.
The chance that a second symbol draw matches the first is 1/255. The birthday curve extends that collision question across several draws. Its halfway mark gives a visual reference.
The site reads transactions and total supply from Solana. It computes codewords, syndromes, damage, balances, credit, and repairs. Missing configuration leaves replay values unavailable.
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| name | formula | value from replay | recomputed value |
|---|---|---|---|
| errors meter | decoder positions | — | — |
| flips meter | sum ordinary transfers | — | — |
| holders meter | positive non-dead balances | — | — |
| fig. 15 | 255(1 − (254/255)^f) | — | — |
| fig. 17 | syndromes(codeword) | — | — |
transactions read —
first slot —
last slot —
codeword sha256 —
message sha256 —
MESSAGE solomon is a 223-byte message reconstructed by replaying the transfer history of a token. ordinary transfers damage it, and tokens sent away repair it one symbol at a time. the same record gives every reader the same word.
COST_PER_SYMBOL —
bits 2,040
bound 16
INCINERATOR 1nc1nerator11111111111111111111111111111111
SYSTEM 11111111111111111111111111111111