You are classifying the chunks of a document against a rubric. Each chunk is a verbatim sentence,
equation or other unit of the document, with an id. Return one record for every chunk you can type.

A record types one chunk: "type" is one of the types below, "form" fills in that type's fields,
"rests_on" lists the ids of the chunks the statement depends on, and "hedge" is the hedging phrase
the chunk uses, such as "suggests" or "may", if it uses one.
A chunk that makes several statements of different types is split instead: "split" lists clauses
copied exactly from its text, each occurring exactly once in it, and "children" gives one typed
record (without "node") per clause, in the same order. Its children are then named by the chunk's
id followed by a, b, c, ..., and other records may rest on them.

The answer is one JSON object with a list of records, each of one of these two shapes:
{"records": [
  {"node": "<chunk id>", "type": "<type>", "form": {...}, "rests_on": ["<chunk id>", ...], "hedge": "<phrase>"},
  {"node": "<chunk id>", "split": ["<clause>", "<clause>"], "children": [{"type": "<type>", ...}, {"type": "<type>", ...}]}
]}
Leave out "form", "rests_on" and "hedge" where the type has no form fields, rests on nothing, or the
chunk has no hedge.

Rules:
- "node" is always one of the chunk ids listed below, exactly as written. Never write a clause id such
  as s-2a as "node": a clause id exists only once a split record for its chunk is applied.
- Copy every text value exactly from the chunk: a verbatim field and a hedge must be substrings of
  the chunk's text, a number or quantity must appear in it as a numeral, and an equation reference
  must be referenced in it.
- Give a record only the form fields its type lists below, and every field marked required.
- A type that "rests on nothing" below never has "rests_on". A type that rests on others lists in
  "rests_on" only chunks that have, or are typed in this answer as, one of the types it names.
- Do not give probabilities, confidence levels or any other judgement of whether a statement is
  true. The rubric sets those.

Types:
- reference: A bibliography entry.
  form: no fields
  rests on nothing
- method: What was done: a procedure, simulation or dataset.
  form: kind (enum one of ['simulation', 'dataset', 'procedure'], required)
  rests on nothing
- result: What was found.
  form: quantity (verbatim, required); trend (enum one of ['vanishes', 'increases', 'decreases', 'bounded'])
  rests on nothing
- derivation: A step of mathematics the document carries out.
  form: equation (eqref)
  rests on nothing
- literature_claim: A finding the document takes from a cited work.
  form: statement (verbatim, required)
  rests on nothing
- claim: A conclusion the document asserts.
  form: shape (enum one of ['universal', 'existential', 'bound'], required); statement (verbatim, required)
  rests on at least 1 of: result, method, derivation, literature_claim

Hedge phrases the rubric knows (report any other you find; it is listed for review, not dropped):
"suggests", "may"

Chunks, in document order, as id (current type): text
s-1 (method): We simulate 400 noise realisations with a Welch estimator.
s-2 (compound): The bias vanishes for long segments, and the estimator is therefore consistent.
s-2a (result): The bias vanishes for long segments
s-2b (claim): the estimator is therefore consistent
e-1 (derivation): \begin{equation} b = \frac{c}{N} \end{equation}
s-3 (claim): This suggests that the method may extend to coloured noise.
s-4 (unassigned): Smith reports a bias below 1\% in comparable settings~\cite{smith2020}.
s-5 (unassigned): We expect the estimator to stay unbiased in practice.
r-1 (reference): A. Smith, Estimators of noise, J. Stat. 12 (2020) 1.

Records from your previous answer that were not applied, each with the error it got and what to
change ("fix"). If this list is not empty, return corrected records for these chunks only, and
nothing else:
[
  {
    "record": {
      "node": "s-4",
      "type": "literature_claim",
      "form": {
        "statement": "a bias below one percent"
      }
    },
    "code": "invalid-argument",
    "message": "node 's-4': 'statement': 'a bias below one percent' is not a substring of the text",
    "fix": [
      "form field 'statement': 'a bias below one percent' is not a substring of the text; copy it exactly from the chunk's text"
    ]
  },
  {
    "record": {
      "node": "s-5",
      "type": "claim",
      "form": {
        "shape": "bound",
        "statement": "the estimator to stay unbiased"
      },
      "rests_on": [
        "s-4"
      ],
      "hedge": "We expect"
    },
    "code": "invalid-argument",
    "message": "node 's-4' has type 'unassigned'; type 'claim' rests on ['result', 'method', 'derivation', 'literature_claim']",
    "fix": [
      "'s-4' in rests_on is of type 'unassigned', and type 'claim' rests only on ['result', 'method', 'derivation', 'literature_claim']: type 's-4' as one of those in the same answer, or leave it out of rests_on"
    ]
  }
]
