Pith Number

pith:NWLQ7QO6

pith:2025:NWLQ7QO67SV6SQOZ3W7WHKCPI6

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Undecidability of Hitting Times in Computably Described Quantum Dynamics: A No-Go Theorem for Universal Time Selection

Katsufumi Matsuura

No algorithm exists that can output the hitting time for every computable quantum state and unitary evolution.

arxiv:2512.11006 v3 · 2025-12-11 · quant-ph

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\pithnumber{NWLQ7QO67SV6SQOZ3W7WHKCPI6}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 there is no total algorithm that outputs this hitting time for all inputs; equivalently, the total UHTP is undecidable via a reduction from the halting problem. Operationally, we show a no-go theorem: for any fixed accuracy parameters, there is no universal finite-resource protocol that, for all computably described inputs, correctly outputs the hitting time while obeying uniform finite upper bounds on observation time and on dissipation/work.

C2weakest assumption

The proofs assume systems capable of embedding universal computation via reversible computation into unitary dynamics and a fixed-target beacon construction with continuous-time lifting via piecewise-constant Hamiltonians.

C3one line summary

The Unitary Hitting Time Problem is undecidable by reduction from the halting problem, with an operational no-go for any universal finite-time protocol.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-03T01:05:08.255883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d970fc1defcabe941d9ddbf63a84f4793021c2d75ef303665bbf1c780aea497

Aliases

arxiv: 2512.11006 · arxiv_version: 2512.11006v3 · doi: 10.48550/arxiv.2512.11006 · pith_short_12: NWLQ7QO67SV6 · pith_short_16: NWLQ7QO67SV6SQOZ · pith_short_8: NWLQ7QO6

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/NWLQ7QO67SV6SQOZ3W7WHKCPI6 \
  | 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: 6d970fc1defcabe941d9ddbf63a84f4793021c2d75ef303665bbf1c780aea497

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c44d6219f7f6c42ea19ce4ada80f5994c3a391bf637bedd903551f94954780b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-12-11T08:17:18Z",
    "title_canon_sha256": "c2445775e27d366f5f476f6db39a945dfb37c50a579c3dffa7cacdc9a5d20ee2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.11006",
    "kind": "arxiv",
    "version": 3
  }
}