Pith Number

pith:HCSWGQVK

pith:2026:HCSWGQVKBNHFAT2E7SKURLFJGI

not attested not anchored not stored refs pending

Multicomponent pentagon maps

Pavlos Kassotakis

Necessary and sufficient conditions turn maps obeying associative-like conditions on n-ary magmas into pentagon maps.

arxiv:2604.07231 v2 · 2026-04-08 · nlin.SI

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\usepackage{pith}
\pithnumber{HCSWGQVKBNHFAT2E7SKURLFJGI}

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Record completeness

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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 provide necessary and sufficient conditions for maps that satisfy associative-like conditions on families of n-ary magmas to be pentagon maps.

C2weakest assumption

The maps under consideration already satisfy the stated associative-like conditions on families of n-ary magmas.

C3one line summary

Necessary and sufficient conditions are derived for maps on n-ary magmas satisfying associative-like properties to be pentagon maps, together with a procedure that produces multicomponent and entwining pentagon maps from any given pentagon map.

Receipt and verification

First computed	2026-05-28T01:04:39.713632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38a56342aa0b4e504f44fc9548aca93238438595822d20345e73e5750db7b7b0

Aliases

arxiv: 2604.07231 · arxiv_version: 2604.07231v2 · doi: 10.48550/arxiv.2604.07231 · pith_short_12: HCSWGQVKBNHF · pith_short_16: HCSWGQVKBNHFAT2E · pith_short_8: HCSWGQVK

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/HCSWGQVKBNHFAT2E7SKURLFJGI \
  | 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: 38a56342aa0b4e504f44fc9548aca93238438595822d20345e73e5750db7b7b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36a615df6f9728d7df31e52acf3b5110aee7726e28bde8d6361c573ae6533b57",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.SI",
    "submitted_at": "2026-04-08T15:54:50Z",
    "title_canon_sha256": "0c0811a434c9c6bdf35f934c2337ddd0446ab4970446942832157897f0961038"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.07231",
    "kind": "arxiv",
    "version": 2
  }
}