Pith Number

pith:5T7VJKKD

pith:2026:5T7VJKKD2F4WC7AIM2C4DLQGVN

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Foundational Analysis Of The Solvability Complexity Index: The Weihrauch-SCI Intermediate Hierarchy

Christopher Sorg

The unrestricted SCI model fails to be a Type-2 computability model, but restricting its base post-processing to continuous, Borel or Baire classes produces well-posed and representation-invariant intermediate hierarchies.

arxiv:2603.18955 v2 · 2026-03-19 · math.LO · cs.LO · math.SP

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\pithnumber{5T7VJKKD2F4WC7AIM2C4DLQGVN}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The unrestricted raw type-G SCI model is generally not a computability model in the Type-2/Weihrauch sense; restricting admissible base-level post-processing to regularity classes yields hierarchies that are well-posed and representation-invariant.

C2weakest assumption

That the chosen regularity restrictions (continuous/Borel/Baire) together with fixed versus adaptive query policies are sufficient to recover a robust computability model while preserving the essential separation properties of the original SCI framework.

C3one line summary

Defines the Weihrauch-SCI rank as the minimal number of iterated limit-oracles needed in the Weihrauch sense and proves that restricting SCI post-processing to continuous/Borel/Baire classes yields well-posed hierarchies with comparison theorems.

Formal links

2 machine-checked theorem links

Cited by

2 papers in Pith

From Witness-Space Sharpness To Family-Pointwise Exactness For The Solvability Complexity Index

Receipt and verification

First computed	2026-05-17T23:38:59.610170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecff54a943d179617c086685c1ae06ab6d98f5aec487467749c770fc2eb339df

Aliases

arxiv: 2603.18955 · arxiv_version: 2603.18955v2 · doi: 10.48550/arxiv.2603.18955 · pith_short_12: 5T7VJKKD2F4W · pith_short_16: 5T7VJKKD2F4WC7AI · pith_short_8: 5T7VJKKD

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ecff54a943d179617c086685c1ae06ab6d98f5aec487467749c770fc2eb339df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ef008aa133767fb41aa78f49fb32d6bca69a41ad984e1787b358e7e901e6f14",
    "cross_cats_sorted": [
      "cs.LO",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-03-19T14:24:40Z",
    "title_canon_sha256": "a8857e9ac229ecf2834f1ef935eb08bfdbad8db6df2e3a6cced350d700f66320"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.18955",
    "kind": "arxiv",
    "version": 2
  }
}