Pith Number

pith:7GTJUIRQ

pith:2026:7GTJUIRQWQHEOEI35IHFAZUNM7

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Improvements to Jacobian Arithmetic in Global Function Fields

Michael Jacobson Jr., Renate Scheidler, Vincent Macri

Two optimizations to Jacobian arithmetic in global function fields cut reduction steps for typical inputs and cache intermediates to achieve faster practical performance.

arxiv:2605.15323 v1 · 2026-05-14 · math.NT

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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

Our asymptotic analysis and empirical experiments show that our improved algorithms are significantly faster in practice than previously published methods. To the best of our knowledge, our publicly-available software implementation of Jacobian arithmetic is the first to support unique representatives of divisor classes.

C2weakest assumption

The function field contains a degree-one place (invoked for the first improvement that optimizes reduction steps for typical inputs rather than worst-case behavior).

C3one line summary

Two optimizations to Jacobian arithmetic in global function fields—optimized reductions for typical cases and caching—yield faster practical performance with the first public software supporting unique divisor class representatives.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] Bauch, J.D.: Lattices over Polynomial Rings and Applications to Function Fields. Ph.D. thesis, Universitat Autònoma de Barcelona, Bellaterra (Jul 2014) 2014

[2] Journal of Symbolic Computation24(3-4), 235–265 (Sep 1997) 1997 · doi:10.1006/jsco.1996.0125

[3] Galbraith, S.D.: Mathematics of Public Key Cryptography. 2 edn. (Oct 2018) 2018

[4] In: van der Poorten, A.J., Stein, A 2008 · doi:10.1007/978-3-540-7

[5] Free Software Foundation, Inc 2023

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:00:52.648134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9a69a2230b40e47111bea0e50668d67dd7dc9dbfefb04af30781983feea71c9

Aliases

arxiv: 2605.15323 · arxiv_version: 2605.15323v1 · doi: 10.48550/arxiv.2605.15323 · pith_short_12: 7GTJUIRQWQHE · pith_short_16: 7GTJUIRQWQHEOEI3 · pith_short_8: 7GTJUIRQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7GTJUIRQWQHEOEI35IHFAZUNM7 \
  | 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: f9a69a2230b40e47111bea0e50668d67dd7dc9dbfefb04af30781983feea71c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "864a4199cfb29672b850d1742e32cc1d2dfa30d952fcc863887bbea649576c18",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-14T18:36:12Z",
    "title_canon_sha256": "c5d83142d9c8b055789e59d1e238280e0f3217772101d2cae894419daebee69a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15323",
    "kind": "arxiv",
    "version": 1
  }
}