Pith Number

pith:CD5SDPKJ

pith:2026:CD5SDPKJB7AHASBLCEUI7WEH7B

not attested not anchored not stored refs pending

Finitely Dependent Processes on Subshifts

Aditya Thorat, Nishant Chandgotia

Conway-Lagarias-Thurston height functions characterize exactly when finitely dependent processes exist on the subshift of box tilings of Z^2.

arxiv:2605.02226 v2 · 2026-05-04 · math.PR · math.DS

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Record completeness

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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 use Conway-Lagarias-Thurston height functions to characterise when there exists a finitely dependent process on the space of tilings by boxes of Z^2 answering the tiling problem posed by Gao, Jackson, Krohne and Seward in dimension 2

C2weakest assumption

The subshifts under consideration possess strong mixing properties such as the finite extension property or strong irreducibility, and the cohomology is computed via standard height functions from tiling theory.

C3one line summary

Finitely dependent processes exist densely on mixing subshifts but are obstructed by cohomology on some tiling spaces, with a characterization for Z^2 box tilings that resolves a prior open question.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-01T01:02:41.283729Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10fb21bd490fc070482b11288fd887f8586c8be460292f66f679840510a9b627

Aliases

arxiv: 2605.02226 · arxiv_version: 2605.02226v2 · doi: 10.48550/arxiv.2605.02226 · pith_short_12: CD5SDPKJB7AH · pith_short_16: CD5SDPKJB7AHASBL · pith_short_8: CD5SDPKJ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CD5SDPKJB7AHASBLCEUI7WEH7B \
  | 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: 10fb21bd490fc070482b11288fd887f8586c8be460292f66f679840510a9b627

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "140d5e5d682613c1d7318058f13f65c77a2f6bbd95b58b06ba39768fbf3fcf0e",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-04T04:57:54Z",
    "title_canon_sha256": "3066aaffdffad9015933d62bfb4ccb4eb2347cbe0a62660168bba0eb05fc7aaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02226",
    "kind": "arxiv",
    "version": 2
  }
}