Pith Number

pith:ZTTSBTT6

pith:2026:ZTTSBTT653F5Z573BESAEQFK6J

not attested not anchored not stored refs resolved

On the Nonexistence of Continuous Immersions for Discrete-time Systems

Eduardo Sontag, Eron Ristich, Necmiye Ozay

Discrete-time systems with countably many but more than one omega-limit sets cannot be continuously and injectively immersed into finite-dimensional linear systems.

arxiv:2605.15161 v1 · 2026-05-14 · eess.SY · cs.SY · math.DS

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations 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

we extend these results to discrete-time dynamics and show that similar obstructions exist also in discrete time.

C2weakest assumption

The immersion mapping must be continuous and one-to-one while the system has countably many but more than one omega-limit sets.

C3one line summary

Discrete-time systems with countably many but more than one omega-limit sets admit no continuous one-to-one immersion into finite-dimensional linear systems.

References

42 extracted · 42 resolved · 0 Pith anchors

[1] On the Nonexistence of Continuous Immersions for Discrete-time Systems , booktitle =

[2] Proceedings of the American Mathematical Society , volume= 1960

[3] Doklady Akademii Nauk SSSR , volume=

[4] Chaos: An Interdisciplinary Journal of Nonlinear Science , volume= 2012

[5] Koopman operator in systems and control , author=. 2020 , publisher= 2020

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T21:40:25.383484Z
Last reissued	2026-05-17T21:57:18.705392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

cce720ce7eeecbdcf7fb09240240aaf2744c29c91cccd4f4e77d5799bd9ba089

Aliases

arxiv: 2605.15161 · arxiv_version: 2605.15161v1 · pith_short_12: ZTTSBTT653F5 · pith_short_16: ZTTSBTT653F5Z573 · pith_short_8: ZTTSBTT6

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZTTSBTT653F5Z573BESAEQFK6J \
  | 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: cce720ce7eeecbdcf7fb09240240aaf2744c29c91cccd4f4e77d5799bd9ba089

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15c653479d620d61a2affcff95737ed0cc58e3127c31fbac5e27b5185ad8c743",
    "cross_cats_sorted": [
      "cs.SY",
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-05-14T17:53:56Z",
    "title_canon_sha256": "8fc42a385fc0cd45f4ce95eb3895eb32172f9d11241b1562d36c7641c7e93eab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15161",
    "kind": "arxiv",
    "version": 1
  }
}