Pith Number

pith:W36J7RO2

pith:2026:W36J7RO26COWURPWUXXIJXXRGP

not attested not anchored not stored refs pending

Safety by Invariance, Liveness through Refinement: Heterogeneous Contract Framework for Co-Design of Layered Control

Adnane Saoud, Alessio Iovine, Bart Besselink, Guillaume Sandou, Yoshinari Takayama

A heterogeneous contract framework enforces safety by invariance at the continuous layer and liveness by refinement at the discrete layer for layered control.

arxiv:2605.04222 v2 · 2026-05-05 · eess.SY · cs.RO · cs.SY

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\usepackage{pith}
\pithnumber{W36J7RO26COWURPWUXXIJXXRGP}

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Record completeness

1 Bitcoin timestamp

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

safety is enforced by invariance at the continuous-time layer, while liveness is achieved through refinement at the discrete-time layer, with inter-layer coordination formalized via vertical refinement and timing-compatibility conditions

C2weakest assumption

That the vertical refinement and timing-compatibility conditions can be satisfied when interconnecting an MPC planner, ISS low-level controller, and reference-governor bridge without introducing new safety violations or performance loss in the target system.

C3one line summary

A heterogeneous assume-guarantee contract framework for layered control architectures enforces safety by invariance at continuous-time layers and liveness by refinement at discrete-time layers, with vertical refinement and timing conditions, instantiated using MPC, ISS control, and a reference-gover

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-08T01:04:06.592782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6fc9fc5daf09d6a45f6a5ee84def133dc2447c64b8960856d56a6d7d463b602

Aliases

arxiv: 2605.04222 · arxiv_version: 2605.04222v2 · doi: 10.48550/arxiv.2605.04222 · pith_short_12: W36J7RO26COW · pith_short_16: W36J7RO26COWURPW · pith_short_8: W36J7RO2

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/W36J7RO26COWURPWUXXIJXXRGP \
  | 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: b6fc9fc5daf09d6a45f6a5ee84def133dc2447c64b8960856d56a6d7d463b602

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2cf6a617e8b390071691d8d2147478f650ab7bc8856b785796fdaf328b8aa67",
    "cross_cats_sorted": [
      "cs.RO",
      "cs.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-05-05T19:05:46Z",
    "title_canon_sha256": "541e96a690a8a1a5ce9db7aea481d47ce8768a3227522cda46393c9fd3e0a0b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04222",
    "kind": "arxiv",
    "version": 2
  }
}