Pith Number

pith:CRS7O6MV

pith:2026:CRS7O6MVF7BHFEKKWK5NKDHAQY

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Generalized Decidability via Brouwer Trees

Aref Mohammadzadeh, Fredrik Nordvall Forsberg, Nicolai Kraus, Tom de Jong

Using Brouwer trees, countable meets of semidecidable properties are ω²-decidable in homotopy type theory.

arxiv:2602.10844 v2 · 2026-02-11 · cs.LO · math.LO

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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

We prove that if each P(i) is semidecidable, then the countable meet ∀i∈ℕ. P(i) is ω²-decidable, and similar results for countable joins and iterated quantifiers.

C2weakest assumption

The specific definition of α-decidability via Brouwer trees captures a meaningful and useful hierarchy of decidability levels within the constructive setting of homotopy type theory.

C3one line summary

Propositions are α-decidable for Brouwer ordinals α, generalizing decidability with closure under conjunction and ω²-decidability for countable meets of semidecidable properties.

References

37 extracted · 37 resolved · 0 Pith anchors

[1] Notes on constructive set theory 2010

[2] Quotient inductive-inductive types 2018

[3] First steps in synthetic computability theory 2006 · doi:10.1016/j.entcs.2005.11.049

[4] Toward the interpretation of non-constructive reasoning as non-monotonic learning 2009

[5] Modelling general recursion in type theory 2005 · doi:10.1017/s0960129505004822

Receipt and verification

First computed	2026-05-18T02:44:31.224621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1465f779952fc272914ab2bad50ce0860cc19202bd6b776d3da1a59ada402ada

Aliases

arxiv: 2602.10844 · arxiv_version: 2602.10844v2 · doi: 10.48550/arxiv.2602.10844 · pith_short_12: CRS7O6MVF7BH · pith_short_16: CRS7O6MVF7BHFEKK · pith_short_8: CRS7O6MV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CRS7O6MVF7BHFEKKWK5NKDHAQY \
  | 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: 1465f779952fc272914ab2bad50ce0860cc19202bd6b776d3da1a59ada402ada

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2eb98fce30c3b193f756f46999c1ceadede533833590168e24ab9b2b5a444d09",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-02-11T13:31:03Z",
    "title_canon_sha256": "7495732a5c66a02602c17f68061ee20505d0146e99542adeaf853673e5fced8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.10844",
    "kind": "arxiv",
    "version": 2
  }
}