user92783: Suppose a transaction t has 5 input UTXOs each worth 1 BTC, each unlocked by a different sending address Ai. 
The outputs of that transaction are 10 UTXOs of 0.5BTC each, each locked by a different receiving address Ao.
Is it correct to posit that each of the Ai sent 0.1 BTC to each Ao? (Lets ignore the existence of transaction fee).

user7272: This kind of statement does not hold.
As RedGrittyBrick's answer mentions, bitcoin has no real concept of people, or individual contributions. Multiple inputs in a transaction might be controlled by a single entity, or multiple entities (multisig) may control a single input. There is no real relation between the number of inputs, distinct or otherwise, and the number/weight of a participant in a transaction.
This is further affected by actions such as a coinjoin, where multiple independent transactions may be combined into a single larger transaction, consisting of all the inputs of the smaller ones, and all of their outputs. In fact, coinjoins are performed because people and some tracking systems view transactions as you described, by trying to link inputs and their btc to outputs, and distribute "ownership" and responsibility proportionally to the BTC value of the input. However, as this concept does not directly translate into or accurately represent the nature of the transaction, it cannot be viewed as a "correct" interpretation.
After all, in your example tx, what stops me from saying that each input is responsible for exactly 2 of the outputs, and contributed nothing to the other 8? Or, why not say that inputs 1, 3, and 5 are responsible for outputs 1, 3, 5, 6, 7, 9, and not for 2, 4, 8, and 10? Why distribute their contributions equally to each output?

user13866: I don't think you can make that assumption with any certainty. You can fairly easily invent other explanations that are equally valid (though probably much less likely)
For example, this transaction might be created by a 23292 member club with an annual subscription of 1 BTC that sends prizes of 0.5 BTC to ten winners of their monthly competition. There would be no real-world transaction that links one specific subscriber with two specific prize-winners.
The blockchain certainly doesn't assign inputs to outputs. The only requirement is that the sum of inputs cannot exceed the sum of outputs (and usually the sum of outputs is less than the sum of inputs - the difference being the mining fee)
This may be clearer if you just think of this as a record of a fiat cash transaction. If I hand out $1 banknotes to ten people, the various five people who each gave me a couple of $1 banknotes in change have no involvement in my later transaction. The sources, sizes or sequence of the inputs are not relevant.

92783: <p>Suppose a transaction <strong>t</strong> has 5 input UTXOs each worth 1 BTC, each unlocked by a different sending address <strong>A<sub>i</sub></strong>. </p>

<p>The outputs of that transaction are 10 UTXOs of 0.5BTC each, each locked by a different receiving address <strong>A<sub>o</sub></strong>.</p>

<p>Is it <em>correct</em> to posit that each of the <strong>A<sub>i</sub></strong> sent 0.1 BTC to each <strong>A<sub>o</sub></strong>? (Lets ignore the existence of transaction fee).</p>
 7272: <p>This kind of statement does not hold.</p>

<p>As RedGrittyBrick's answer mentions, bitcoin has no real concept of people, or individual contributions. Multiple inputs in a transaction might be controlled by a single entity, or multiple entities (multisig) may control a single input. There is no real relation between the number of inputs, distinct or otherwise, and the number/weight of a participant in a transaction.</p>

<p>This is further affected by actions such as a coinjoin, where multiple independent transactions may be combined into a single larger transaction, consisting of all the inputs of the smaller ones, and all of their outputs. In fact, coinjoins are performed because people and some tracking systems view transactions as you described, by trying to link inputs and their btc to outputs, and distribute "ownership" and responsibility proportionally to the BTC value of the input. However, as this concept does not directly translate into or accurately represent the nature of the transaction, it cannot be viewed as a "correct" interpretation.</p>

<p>After all, in your example tx, what stops me from saying that each input is responsible for exactly 2 of the outputs, and contributed nothing to the other 8? Or, why not say that inputs 1, 3, and 5 are responsible for outputs 1, 3, 5, 6, 7, 9, and not for 2, 4, 8, and 10? Why distribute their contributions equally to each output?</p>
 13866: <p>I don't think you can make that assumption with any certainty. You can fairly easily invent other explanations that are equally valid (though probably much less likely)</p>

<p>For example, this transaction might be created by a 23292 member club with an annual subscription of 1 BTC that sends prizes of 0.5 BTC to ten winners of their monthly competition. There would be no real-world transaction that links one specific subscriber with two specific prize-winners.</p>

<p>The blockchain certainly doesn't assign inputs to outputs. The only requirement is that the sum of inputs cannot exceed the sum of outputs (and usually the sum of outputs is less than the sum of inputs - the difference being the mining fee)</p>

<p>This may be clearer if you just think of this as a record of a fiat cash transaction. If I hand out $1 banknotes to ten people, the various five people who each gave me a couple of $1 banknotes in change have no involvement in my later transaction. The sources, sizes or sequence of the inputs are not relevant.</p>
