Pith Number

pith:UO3VCXF7

pith:2026:UO3VCXF77KPEPIH7TYGFA5RGBL

not attested not anchored not stored refs resolved

Monads and Distributive Laws in Substructural Contexts (Extended Version)

Ichiro Hasuo, Soichiro Fujii, Yo\`av Montacute, Yun Chen Tsai

A canonical construction produces a distributive law ST to TS for monads on sets when S is W-operadic and T is W-commutative with respect to a verbal category W.

arxiv:2605.13533 v1 · 2026-05-13 · cs.LO · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UO3VCXF77KPEPIH7TYGFA5RGBL}

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

We give a canonical construction of a distributive law ST→TS of monads on Set; it is applicable when S is W-operadic and T is W-commutative (under mild conditions). This accounts for many known and new distributive laws.

C2weakest assumption

That Tronin's verbal categories W provide a uniform and presentation-independent formalization of substructural situations, and that the mild conditions for the canonical construction hold in the intended applications.

C3one line summary

A uniform theory of W-operadic and W-commutative monads on Set yields a canonical distributive law ST to TS when S respects the structural rules in W and T is invariant under them.

References

72 extracted · 72 resolved · 0 Pith anchors

[1] 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025) , pages = 2025

[2] On Generalised Coinduction and Probabilistic Specification Formats: Distributive laws in coalgebraic modelling

[3] Seminar on Triples and Categorical Homology Theory 1969

[4] Logical Methods in Computer Science , volume= 2022

[5] Journal of Pure and Applied Algebra , volume = 1978

Receipt and verification

First computed	2026-05-18T02:44:24.196676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3b7515cbffa9e47a0ff9e0c5076260adddfb0ed8fb2ac2a6786ffba64bed897

Aliases

arxiv: 2605.13533 · arxiv_version: 2605.13533v1 · doi: 10.48550/arxiv.2605.13533 · pith_short_12: UO3VCXF77KPE · pith_short_16: UO3VCXF77KPEPIH7 · pith_short_8: UO3VCXF7

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/UO3VCXF77KPEPIH7TYGFA5RGBL \
  | 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: a3b7515cbffa9e47a0ff9e0c5076260adddfb0ed8fb2ac2a6786ffba64bed897

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "794d9be2c78acbcffbcc7e550661d597cddb4f5b0056e76aaa0f9a77b7c3555c",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-13T13:46:35Z",
    "title_canon_sha256": "3ca98074217a869b3463164726d20de20fbc218c1a93a76f2f0024b751ec2fe8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13533",
    "kind": "arxiv",
    "version": 1
  }
}