Pith Number

pith:6UAS4IKF

pith:2026:6UAS4IKFMU6CO35YKJDAXK3QSE

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Tropical curves with parallel rays

JuAe Song

Abstract tropical curves can now include parallel rays while maintaining a categorical equivalence to their rational function semifields.

arxiv:2605.16910 v1 · 2026-05-16 · math.AG

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Claims

C1strongest claim

We introduce a new notion of abstract tropical curves with parallel rays. Then we define the rational function semifields of these curves and give a characterization of them, and a variant of the categorical equivalence between their categories with a suitable notion of morphisms between these curves.

C2weakest assumption

The newly introduced definition of abstract tropical curves with parallel rays is assumed to be a consistent extension of the traditional definition that preserves the ability to characterize rational function semifields without introducing structural inconsistencies.

C3one line summary

Defines abstract tropical curves with parallel rays and proves a contravariant categorical equivalence between their category and the category of T-semifields with algebra homomorphisms.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] Omid Amini, Matthew Baker, Erwan Brugall´ e and Joseph Rabinoff,Lifting harmonic morphisms I: metrized complexes and berkovich skeleta, Research in the Mathematical Sciences2, Art. 7, 67, 2015 2015

[2] Omid Amini, Shu Kawaguchi and JuAe Song,Tropical function fields, finite generation, and faithful tropicalization, arXiv:2503.20611

[3] Matthew Baker and Serguei Norine,Riemann–Roch and Abel–Jacobi theory on a finite graph, Ad- vances in Mathematics215(2):766—788, 2007 2007

[4] Melody Chan,Tropical hyperelliptic curves, Journal of Algebraic Combinatorics37:331-359, 2013 2013

[5] Andreas Gathmann and Michael Kerber,A Riemann–Roch theorem in tropical geometry, Mathema- tische Zeitschrift259(1), 217–230, 2008 2008

Receipt and verification

First computed	2026-05-20T00:03:29.708669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5012e2145653c276fb852460bab70910e4556324b57d5f88677db239e65c3ac

Aliases

arxiv: 2605.16910 · arxiv_version: 2605.16910v1 · doi: 10.48550/arxiv.2605.16910 · pith_short_12: 6UAS4IKFMU6C · pith_short_16: 6UAS4IKFMU6CO35Y · pith_short_8: 6UAS4IKF

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6UAS4IKFMU6CO35YKJDAXK3QSE \
  | 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: f5012e2145653c276fb852460bab70910e4556324b57d5f88677db239e65c3ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d5e8ef6da4b8794eebe2262b8ca1bbdeb00b58a13530cad60d08fabd265f648",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-16T09:50:20Z",
    "title_canon_sha256": "4540cb0c830099844fbe4ba7d6da1f1dbf2863e1ad6beef2016aa8ab5b3b9dcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16910",
    "kind": "arxiv",
    "version": 1
  }
}