Pith Number

pith:WLEEEU3I

pith:2026:WLEEEU3I7KVNTRPI3G4IZ6J3AP

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Loop Termination and Generalized Collatz Sequences

Mishel Carelli

Termination of one-variable linear-constraint loops is decidable in polynomial time if a conjecture on generalized Collatz sequences holds.

arxiv:2605.15094 v1 · 2026-05-14 · cs.LO

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Claims

C1strongest claim

We prove that termination of one-variable linear-constraint loops is decidable in polynomial time, provided a long-standing conjecture about generalized Collatz sequences holds.

C2weakest assumption

The long-standing conjecture about generalized Collatz sequences holds.

C3one line summary

Termination of one-variable linear-constraint loops over integers is decidable in polynomial time if the generalized Collatz conjecture holds, with any such procedure also settling specific instances of the conjecture.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] 1 Amir M. Ben-Amram. Mortality of Iterated Piecewise Affine Functions over the Integers: Decid- ability and Complexity. In Natacha Portier and Thomas Wilke, editors,30th International Sym- posium on T 2013

[2] Schloss Dagstuhl – Leibniz-Zentrum für Informatik. URL:https://drops.dagstuhl.de/entities/ document/10.4230/LIPIcs.STACS.2013.514,doi:10.4230/LIPIcs.STACS.2013.514. 2 Amir M. Ben-Amram, Samir Genaim, 2013 · doi:10.4230/lipics.stacs.2013.514

[3] doi:10.1145/2400676. 2400679. 3 Amir M. Ben-Amram, Samir Genaim, Joël Ouaknine, and James Worrell. Termination analysis of linear-constraint programs, · doi:10.1145/2400676

[4] 4 Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars.Computational Geometry: Algorithms and Applications

[5] Springer Berlin Heidelberg. 6 Vincent D. Blondel, Olivier Bournez, Pascal Koiran, Christos H. Papadimitriou, and John N. Tsitsiklis. Deciding stability and mortality of piecewise affine dynamical syst 2001 · doi:10.1016/s0304-3975(00)00399-6

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Receipt and verification

First computed	2026-05-17T21:40:25.878409Z
Last reissued	2026-05-17T21:57:19.204744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

b2c8425368faaad9c5e8d9b88cf93b03d18c2f6943848f97f69e3095eabc1eba

Aliases

arxiv: 2605.15094 · arxiv_version: 2605.15094v1 · pith_short_12: WLEEEU3I7KVN · pith_short_16: WLEEEU3I7KVNTRPI · pith_short_8: WLEEEU3I

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WLEEEU3I7KVNTRPI3G4IZ6J3AP \
  | 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: b2c8425368faaad9c5e8d9b88cf93b03d18c2f6943848f97f69e3095eabc1eba

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-14T17:13:03Z",
    "title_canon_sha256": "fc78590c1bf69d9cb367b1ae4a5482c7436cf0f0071d8059d4b72b872d08ac35"
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