Pith Number

pith:LZHW2GCU

pith:2026:LZHW2GCUZSY4I52ZCCE5WGY2XX

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From Coalgebraic Determinization to Belief Construction for Partial Observability

Kazuki Watanabe, Mayuko Kori

The semantics of a partially observable system coincides with that of its belief coalgebra, and under further conditions matches its fully observable counterpart.

arxiv:2604.25355 v2 · 2026-04-28 · cs.LO

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\usepackage{pith}
\pithnumber{LZHW2GCUZSY4I52ZCCE5WGY2XX}

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Record completeness

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2 Internet Archive

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 semantics of a partially observable system coincides with that of the corresponding belief coalgebra; under further conditions the latter agrees with the semantics of its fully observable counterpart, recovering the standard equivalence between POMDPs and belief MDPs and obtaining a new equivalence for weighted transition systems with the multiset monad.

C2weakest assumption

The monad can be lifted to the slice category in a way that preserves the relevant coalgebraic semantics, and the belief decomposition correctly reorganizes states by observations without altering the underlying behavior.

C3one line summary

A coalgebraic generalization of the belief construction shows semantics of partially observable systems coincide with belief coalgebras, recovering POMDP equivalences and yielding a new equivalence for weighted transition systems with the multiset monad.

Receipt and verification

First computed	2026-05-20T00:05:45.284823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e4f6d1854ccb1c477591089db1b1abddcdb5b66aca90f6de72ee9fe7da196e4

Aliases

arxiv: 2604.25355 · arxiv_version: 2604.25355v2 · doi: 10.48550/arxiv.2604.25355 · pith_short_12: LZHW2GCUZSY4 · pith_short_16: LZHW2GCUZSY4I52Z · pith_short_8: LZHW2GCU

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LZHW2GCUZSY4I52ZCCE5WGY2XX \
  | 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: 5e4f6d1854ccb1c477591089db1b1abddcdb5b66aca90f6de72ee9fe7da196e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1950351e0dab8e8aee1d8db700a8e54c283ea5c224e6a0162d2564b6fe1d9bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-04-28T08:16:30Z",
    "title_canon_sha256": "1093813b05d74419c63ac737047629fa1da2dcd2fcba940d724f77c264d0eca5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25355",
    "kind": "arxiv",
    "version": 2
  }
}