user7: How can a node verify a transaction with a script address without the script?
I mean when i start a node months after the transaction has been minted into a block. How can my node verify that the script conditions were met since only the hash is persisted in the chain?

user88: By inspecting the current ledger CDDL specifications, you can see that each block contains a transaction_witness_sets field, where each transaction_witness_set is defined as:
transaction_witness_set =
  { ? 0: [* vkeywitness ]
  , ? 1: [* native_script ]
  , ? 2: [* bootstrap_witness ]
  }

Here, native_script, if present, contains some rules that need to be respected in order for the transaction to be valid (for instance, some minting policy):
native_script =
  [ script_pubkey
  // script_all
  // script_any
  // script_n_of_k
  // invalid_before
     ; Timelock validity intervals are half-open intervals [a, b).
     ; This field specifies the left (included) endpoint a.
  // invalid_hereafter
     ; Timelock validity intervals are half-open intervals [a, b).
     ; This field specifies the right (excluded) endpoint b.
  ]

So not only the script hash is included in the chain, but also the actual rules it contains.

7: <p>How can a node verify a transaction with a script address without the script?</p>
<p>I mean when i start a node months after the transaction has been minted into a block. How can my node verify that the script conditions were met since only the hash is persisted in the chain?</p>
 88: <p>By inspecting the current ledger <a href="https://github.com/input-output-hk/cardano-ledger-specs/blob/master/shelley-ma/shelley-ma-test/cddl-files/shelley-ma.cddl" rel="nofollow noreferrer">CDDL specifications</a>, you can see that each <code>block</code> contains a <code>transaction_witness_sets</code> field, where each <code>transaction_witness_set</code> is defined as:</p>
<pre><code>transaction_witness_set =
  { ? 0: [* vkeywitness ]
  , ? 1: [* native_script ]
  , ? 2: [* bootstrap_witness ]
  }
</code></pre>
<p>Here, <code>native_script</code>, if present, contains some rules that need to be respected in order for the transaction to be valid (for instance, some minting policy):</p>
<pre><code>native_script =
  [ script_pubkey
  // script_all
  // script_any
  // script_n_of_k
  // invalid_before
     ; Timelock validity intervals are half-open intervals [a, b).
     ; This field specifies the left (included) endpoint a.
  // invalid_hereafter
     ; Timelock validity intervals are half-open intervals [a, b).
     ; This field specifies the right (excluded) endpoint b.
  ]
</code></pre>
<p>So not only the script hash is included in the chain, but also the actual rules it contains.</p>
