Pith Number

pith:VVX6NI3A

pith:2026:VVX6NI3A2LX22Z2NCWLDJ6DFOY

not attested not anchored not stored refs pending

A Mathematical Framework for Linear Response Theory for Nonautonomous Systems

Stefano Galatolo, Valerio Lucarini

Nonautonomous systems admit explicit linear response formulas via a global transfer operator on sequence space under rapid memory loss.

arxiv:2603.19509 v3 · 2026-03-19 · math.DS · cond-mat.stat-mech · nlin.CD

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VVX6NI3A2LX22Z2NCWLDJ6DFOY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

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

Here we provide a rigorous linear response theory for a rather general class of deterministic and random nonautonomous systems satisfying a specific set of assumptions that in some sense extend the standard assumptions used in the autonomous setting.

C2weakest assumption

A central ingredient is rapid loss of memory, i.e. sufficiently fast forgetting of initial conditions along the nonautonomous evolution.

C3one line summary

Establishes rigorous linear response formulas for general deterministic and random nonautonomous systems with fast memory loss via a global transfer operator on sequence space of measures.

Formal links

2 machine-checked theorem links

Cited by

3 papers in Pith

Ulam Approximation for Nonautonomous Systems: Equivariant Measures and Linear Response

Linear response for Sinai billiards with small holes

Linear Response and Optimal Fingerprinting for Nonautonomous Systems

Receipt and verification

First computed	2026-06-25T01:17:52.067930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad6fe6a360d2efad674d159634f865763fef63c503e66374f5e323742c1761d4

Aliases

arxiv: 2603.19509 · arxiv_version: 2603.19509v3 · doi: 10.48550/arxiv.2603.19509 · pith_short_12: VVX6NI3A2LX2 · pith_short_16: VVX6NI3A2LX22Z2N · pith_short_8: VVX6NI3A

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/VVX6NI3A2LX22Z2NCWLDJ6DFOY \
  | 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: ad6fe6a360d2efad674d159634f865763fef63c503e66374f5e323742c1761d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07aadcc13d8b5935cd7dadf5a37d177f38b76c6ddfeb27d4f354eb646da65759",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "nlin.CD"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-03-19T22:32:21Z",
    "title_canon_sha256": "eec1ddedde192074f9cb5697562a8afa8a637831a7492fc26e745724b8ea9013"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.19509",
    "kind": "arxiv",
    "version": 3
  }
}