Pith Number

pith:TOGCXQXD

pith:2026:TOGCXQXDHTOHU543B56QRARQE4

not attested not anchored not stored refs resolved

Remarks on diagonal dimension for algebraic stacks

Fei Peng, Pat Lank

The diagonal dimension of a variety with mild singularities is at most twice its Krull dimension in arbitrary characteristic.

arxiv:2605.13416 v1 · 2026-05-13 · math.AG · math.AC

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\usepackage{pith}
\pithnumber{TOGCXQXDHTOHU543B56QRARQE4}

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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

the diagonal dimension of a variety in arbitrary characteristic with mild singularities is at most twice its Krull dimension

C2weakest assumption

the precise definition of 'mild singularities' and the technical conditions on the Noetherian algebraic stack that allow the diagonal dimension to be defined and bounded as stated

C3one line summary

Diagonal dimension of a variety with mild singularities is at most twice its Krull dimension; explicit upper bounds are given for smooth morphisms to regular targets.

References

14 extracted · 14 resolved · 1 Pith anchors

[1] Hochschild dimensions of tilting objects.Int 2012

[2] Dimension theory of non- commutative curves

[3] Descending strong generation in algebraic geometry

[4] Approximability and rouquier dimension for noncommutative algebras over schemes

[5] Categorical characterizations of regularity for algebraic stacks · arXiv:2504.02813

Receipt and verification

First computed	2026-05-18T02:44:47.371511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b8c2bc2e33cdc7a779b0f7d088230270d5135c06583fc0333608d5c808053f2

Aliases

arxiv: 2605.13416 · arxiv_version: 2605.13416v1 · doi: 10.48550/arxiv.2605.13416 · pith_short_12: TOGCXQXDHTOH · pith_short_16: TOGCXQXDHTOHU543 · pith_short_8: TOGCXQXD

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/TOGCXQXDHTOHU543B56QRARQE4 \
  | 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: 9b8c2bc2e33cdc7a779b0f7d088230270d5135c06583fc0333608d5c808053f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11dcc565668cd2f12c53d373e6304bca0f0462872a4e94160e2baed6a3d5c3f8",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T12:10:54Z",
    "title_canon_sha256": "c5fb2237962151260fe7bb7243c34f43e654c6741adf3b09ec6c00023ef3a173"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13416",
    "kind": "arxiv",
    "version": 1
  }
}