Pith Number

pith:NKAY3YMS

pith:2026:NKAY3YMSYUYKRN5XD6OTOSUTGE

not attested not anchored not stored refs pending

Shuffles of Context-Free Languages along Regular Trajectories

Corentin Barloy, Kyle Ockerlund, Micha\"el Cadilhac

Regular trajectories can force the shuffle of any two nonregular context-free languages to leave the context-free class.

arxiv:2603.26162 v2 · 2026-03-27 · cs.FL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NKAY3YMSYUYKRN5XD6OTOSUTGE}

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

This paper provides a robust toolset to show that a given trajectory would always shuffle two nonregular CFLs into a nonCFL. In the case of deterministic CFLs (DCFLs), a salient trichotomy of trajectories depending on how they shuffle DCFLs is provided.

C2weakest assumption

The lemmata on how pushdown automata invoke the stack for nonregular CFLs or DCFLs hold, and the cited result of Jančar and Šima (MFCS'2021) applies without generalization issues to the DCFL case.

C3one line summary

Regular trajectories are classified for their effect on shuffles of context-free languages, with tools to prove non-closure for nonregular CFLs and a trichotomy for DCFLs.

Receipt and verification

First computed	2026-05-18T03:10:03.382147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a818de192c530a8b7b71f9d374a933122ead8c81361f307ddf6d6177577f546

Aliases

arxiv: 2603.26162 · arxiv_version: 2603.26162v2 · doi: 10.48550/arxiv.2603.26162 · pith_short_12: NKAY3YMSYUYK · pith_short_16: NKAY3YMSYUYKRN5X · pith_short_8: NKAY3YMS

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/NKAY3YMSYUYKRN5XD6OTOSUTGE \
  | 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: 6a818de192c530a8b7b71f9d374a933122ead8c81361f307ddf6d6177577f546

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "848c4881b0351132e8fe45c39bf83a557c5e5080fdfd7488fce63d4164ec19de",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2026-03-27T08:25:56Z",
    "title_canon_sha256": "44d232c44adbe35c18b55e9bdb3d9a3d70782647e1907e17a10ba59520b92ff5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.26162",
    "kind": "arxiv",
    "version": 2
  }
}