Pith Number

pith:RDRPNVAE

pith:2026:RDRPNVAEE366LCNO7DRDSMBEUO

not attested not anchored not stored refs pending

Derived complete intersections and polynomial growth of Betti numbers over dg-algebras

Justin Lyle, Michael K. Brown

A dg-algebra has polynomially growing Betti numbers for its modules if and only if it is a derived complete intersection.

arxiv:2605.11105 v2 · 2026-05-11 · math.AC

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\usepackage{pith}
\pithnumber{RDRPNVAEE366LCNO7DRDSMBEUO}

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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 prove a structure theorem for dg-algebras whose modules exhibit polynomial Betti growth.

C2weakest assumption

The dg-algebras are considered in a broader setting than previously known that permits existence and uniqueness of minimal models and acyclic closures of morphisms.

C3one line summary

Structure theorem for dg-algebras whose modules have polynomial Betti growth, as a derived analogue of Gulliksen's theorem.

Receipt and verification

First computed	2026-05-20T00:04:35.888823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88e2f6d40426fde589aef8e2393024a3a624d67f77defec8084e23696bf1a5d0

Aliases

arxiv: 2605.11105 · arxiv_version: 2605.11105v2 · doi: 10.48550/arxiv.2605.11105 · pith_short_12: RDRPNVAEE366 · pith_short_16: RDRPNVAEE366LCNO · pith_short_8: RDRPNVAE

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/RDRPNVAEE366LCNO7DRDSMBEUO \
  | 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: 88e2f6d40426fde589aef8e2393024a3a624d67f77defec8084e23696bf1a5d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af109187b6b286fb711d8cb760026f4c14f5e0778b3b953651f194c91adbc31e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-05-11T18:11:27Z",
    "title_canon_sha256": "ea1a185847fdf020f61d223c7bcca78b02718614b1cca2251ea30f34c020d586"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11105",
    "kind": "arxiv",
    "version": 2
  }
}