Pith Number

pith:3X44C263

pith:2023:3X44C263UANIAMM46AO3UQ356R

not attested not anchored not stored refs pending

The catastrophes of algebras

Fred Greensite

A real finite-dimensional unital associative algebra associates with a vector space of pseudo-Finsler norms linked to its normalized trace forms by an integral transform.

arxiv:2306.14995 v44 · 2023-06-26 · math.RA

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\usepackage{pith}
\pithnumber{3X44C263UANIAMM46AO3UQ356R}

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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

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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

We show that a real finite-dimensional unital associative algebra is naturally associated with a vector space of pseudo-Finsler norms whose members are linked to the algebra's space of normalized trace forms through an integral transform.

C2weakest assumption

The integral transform produces well-defined pseudo-Finsler norms to which the Hamiltonian formalism can be applied, and that repeating the procedure on the Cuntz-Quillen tower captures the full influence of the Jacobson radical to yield useful invariants (abstract, paragraph beginning 'Since components of the space of trace forms...').

C3one line summary

Finite-dimensional real unital associative algebras are linked to pseudo-Finsler norms through integral transforms from trace forms, allowing Hamiltonian formalism and Cuntz-Quillen towers to produce catastrophe-based invariants.

Receipt and verification

First computed	2026-06-09T01:04:37.154220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddf9c16bdba01a80319cf01dba437df47033f9f6a5521070aee83b4bea8f49fb

Aliases

arxiv: 2306.14995 · arxiv_version: 2306.14995v44 · doi: 10.48550/arxiv.2306.14995 · pith_short_12: 3X44C263UANI · pith_short_16: 3X44C263UANIAMM4 · pith_short_8: 3X44C263

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3X44C263UANIAMM46AO3UQ356R \
  | 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: ddf9c16bdba01a80319cf01dba437df47033f9f6a5521070aee83b4bea8f49fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca56350896e8d7833065c72e6fa43597911a6ceb3a74267890e45eb50abda138",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2023-06-26T18:23:27Z",
    "title_canon_sha256": "b1a0df92105b83b3b1330227ac25adf0d674329f74ee0d758cb1883d6cd33422"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.14995",
    "kind": "arxiv",
    "version": 44
  }
}