Pith Number

pith:TUS2TE5O

pith:2026:TUS2TE5OG7AZOJBTVQEKXE5LTP

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On the additivity of projective presentations of maximal rank

Grzegorz Bobi\'nski, Jan Schr\"oer

The modules which have a projective presentation of maximal rank are exactly the τ-regular modules.

arxiv:2605.13029 v1 · 2026-05-13 · math.RT

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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

The modules which have a projective presentation of maximal rank are exactly the τ-regular modules.

C2weakest assumption

The algebra and modules are finite-dimensional, allowing definition of module varieties and the τ functor from prior representation theory.

C3one line summary

τ-regular modules are those with projective presentations of maximal rank; they form open subsets of module varieties whose closures are generically τ-regular components, with additivity of maximal rank tied to reduction to projective dimension at most one.

References

24 extracted · 24 resolved · 1 Pith anchors

[1] T. Adachi, O. Iyama, I. Reiten, -tilting theory. Compos. Math. 150 (2014), no. 3, 415--452 2014

[2] C. Amiot, O. Iyama, I. Reiten, G. Todorov, Preprojective algebras and c -sortable words. Proc. Lond. Math. Soc. (3) 104 (2012), no. 3, 513--539 2012

[3] Asai, The wall-chamber structures of the real Grothendieck groups 2021

[4] I. Assem, D. Simson, A. Skowro\'nski, Elements of the representation theory of associative algebras. Vol1. Techniques of representation theory. London Math. Soc. Stud. Texts, 65 Cambridge University P 2006

[5] M. Auslander, I. Reiten, Representation theory of Artin algebras. V. Methods for computing almost split sequences and irreducible morphisms. Comm. Algebra 5 (1977), no. 5, 519--554 1977

Receipt and verification

First computed	2026-05-18T03:08:59.806304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d25a993ae37c1972433ac08ab93ab9bff0f8e5701162f7230730832904627c3

Aliases

arxiv: 2605.13029 · arxiv_version: 2605.13029v1 · doi: 10.48550/arxiv.2605.13029 · pith_short_12: TUS2TE5OG7AZ · pith_short_16: TUS2TE5OG7AZOJBT · pith_short_8: TUS2TE5O

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/TUS2TE5OG7AZOJBTVQEKXE5LTP \
  | 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: 9d25a993ae37c1972433ac08ab93ab9bff0f8e5701162f7230730832904627c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a8a84a5b1a375d7287984d44344865f23162b1243d9be6d6482ab8e5333e2a6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-13T05:34:06Z",
    "title_canon_sha256": "a0ddac85afb54ceb7bd19bed26c523facf0ae1430f5ff1286796822f8d5255b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13029",
    "kind": "arxiv",
    "version": 1
  }
}