Pith Number

pith:PGG2OXKE

pith:2017:PGG2OXKEO4F6DRLW7XWH7G3NSH

not attested not anchored not stored refs pending

A dichotomy for the injective dimension of $F$-finite $F$-modules and holonomic $D$-modules

Nicholas Switala, Wenliang Zhang

arxiv:1708.06481 v2 · 2017-08-22 · math.AC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PGG2OXKEO4F6DRLW7XWH7G3NSH}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T00:24:59.728267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

798da75d44770be1c576fdec7f9b6d91c1a9dcc1cb0d3efb13ccbd3fe70bccd4

Aliases

arxiv: 1708.06481 · arxiv_version: 1708.06481v2 · doi: 10.48550/arxiv.1708.06481 · pith_short_12: PGG2OXKEO4F6 · pith_short_16: PGG2OXKEO4F6DRLW · pith_short_8: PGG2OXKE

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/PGG2OXKEO4F6DRLW7XWH7G3NSH \
  | 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: 798da75d44770be1c576fdec7f9b6d91c1a9dcc1cb0d3efb13ccbd3fe70bccd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e9a70ffef31413baa657b2b197b6f7a4b09f88a19e0c782e5e097da97af1896",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-08-22T02:28:03Z",
    "title_canon_sha256": "d5cc43566951878dc07dd7340ae3e521fae97f0e80a4b84a1cc5fe0bbbf994ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.06481",
    "kind": "arxiv",
    "version": 2
  }
}