Pith Number

pith:CQQOZK4P

pith:2026:CQQOZK4P4GQVFZKZ5JAJ6IRVO2

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A Linear Bound on the Projective Dimension of Height 3 Quadratic Ideals

Jason McCullough, Paolo Mantero, Zachary Greif

Height 3 quadratic ideals have projective dimension bounded linearly by the number of generators.

arxiv:2605.15992 v1 · 2026-05-15 · math.AC

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\usepackage{pith}
\pithnumber{CQQOZK4P4GQVFZKZ5JAJ6IRVO2}

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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

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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 give a nearly optimal linear upper bound on the projective dimension of height 3 ideals generated by any number of degree 2 homogeneous polynomials.

C2weakest assumption

The proof relies on the ideal having height exactly 3; if this height condition is relaxed or if the generators are not all quadratic, the linear bound may fail to hold by the same argument.

C3one line summary

A linear upper bound on the projective dimension of height 3 quadratic ideals.

References

30 extracted · 30 resolved · 0 Pith anchors

[1] Ananyan, Tigran and Hochster, Melvin , TITLE =. Math. Res. Lett. , FJOURNAL =. 2012 , NUMBER =. doi:10.4310/MRL.2012.v19.n1.a18 , URL = 2012 · doi:10.4310/mrl.2012.v19.n1.a18

[2] Ananyan, Tigran and Hochster, Melvin , TITLE =. J. Amer. Math. Soc. , FJOURNAL =. 2020 , NUMBER =. doi:10.1090/jams/932 , URL = 2020 · doi:10.1090/jams/932

[3] Ananyan, Tigran and Hochster, Melvin , TITLE =. Trans. Amer. Math. Soc. , FJOURNAL =. 2020 , NUMBER =. doi:10.1090/tran/8060 , URL = 2020 · doi:10.1090/tran/8060

[4] A conjecture of 1972 · doi:10.1215/kjm/1250523522

[5] Giulio Caviglia and Yihui Liang and Cheng Meng , year=. Explicit. 2507.19617 , archivePrefix=

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:48.087882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1420ecab8fe1a152e559ea409f223576b6bdbca9655efefdfda0e27164d8013e

Aliases

arxiv: 2605.15992 · arxiv_version: 2605.15992v1 · doi: 10.48550/arxiv.2605.15992 · pith_short_12: CQQOZK4P4GQV · pith_short_16: CQQOZK4P4GQVFZKZ · pith_short_8: CQQOZK4P

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/CQQOZK4P4GQVFZKZ5JAJ6IRVO2 \
  | 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: 1420ecab8fe1a152e559ea409f223576b6bdbca9655efefdfda0e27164d8013e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31f2c187246ad1687e0526533202095e611b137db56afa2a43bea6ff472073c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-05-15T14:23:20Z",
    "title_canon_sha256": "406b60093d54171d0100af17045e472298cff938a5377f6e8d00f6b873243076"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15992",
    "kind": "arxiv",
    "version": 1
  }
}