Pith Number

pith:CUIWWH5K

pith:2025:CUIWWH5KA4WISBBH4CAIWYCFWM

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Axiomatic Foundations of Chemical Systems as Ternary $\Gamma$-Semirings

Acharya Nagarjuna University, Andhra Pradesh, Chandrasekhar Gokavarapu (Government College (Autonomous), Department of Mathematics, D. Madhusudhana Rao (Government College for Women (Autonomous), Guntur, India, India), Rajahmundry, Srinivasa Rao Thirunagari (Government College (Autonomous), Venkata Rao Kaviti (Government College (Autonomous)

Chemical systems are modeled as ternary Γ-semirings in which states and catalytic conditions interact through a mediated ternary operation.

arxiv:2511.12699 v2 · 2025-11-16 · math.RA

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Claims

C1strongest claim

We introduce an axiomatic framework in which a chemical system is modelled by a ternary Γ-semiring. The elements of the state set represent chemical states, while the parameter set encodes catalytic and environmental conditions.

C2weakest assumption

That the algebraic axioms of ternary Γ-semirings (associativity, distributivity, Γ-linearity) meaningfully capture the multi-state and multi-parameter character of real chemical processes without additional empirical validation or mapping rules.

C3one line summary

Chemical systems are axiomatized as ternary Γ-semirings whose elements and operations encode states, environmental parameters, and mediated reaction pathways.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] J. S. Golan,Semirings and Their Applications, Springer, Dordrecht, 1999 1999

[2] U. Hebisch and H. J. Weinert,Semirings: Algebraic Theory and Applications in Computer Science, World Scientific, Singapore, 1998 1998

[3] The Theory of Semirings with Applications in Mathematics, 1951

[4] N. Nobusawa, “On Ternary Semigroups,”Mathematical Journal of Okayama Univer- sity, vol. 13, pp. 1–7, 1964 1964

[5] E. Post, “Polyadic Groups,”Transactions of the American Mathematical Society, vol. 48, no. 2, pp. 208–350, 1940 1940

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:17.130203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15116b1faa072c890427e0808b6045b33b15c97bf44b6741dc415705deec7bc8

Aliases

arxiv: 2511.12699 · arxiv_version: 2511.12699v2 · doi: 10.48550/arxiv.2511.12699 · pith_short_12: CUIWWH5KA4WI · pith_short_16: CUIWWH5KA4WISBBH · pith_short_8: CUIWWH5K

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CUIWWH5KA4WISBBH4CAIWYCFWM \
  | 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: 15116b1faa072c890427e0808b6045b33b15c97bf44b6741dc415705deec7bc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74c39d462038d400e2aca6daee2072edc97dede306031b6edd6b05b1e468b309",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2025-11-16T17:35:13Z",
    "title_canon_sha256": "c92e12e2363088d9658957b66b2c4165b6edadb709d2cf9ec10684622f69c396"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.12699",
    "kind": "arxiv",
    "version": 2
  }
}