Pith Number

pith:D3WLPW5E

pith:2016:D3WLPW5E3U6ELGQB6FFPWGJCET

not attested not anchored not stored refs pending

Detecting finite flat dimension of modules via iterates of the Frobenius endomorphism

Douglas J. Dailey, Srikanth B. Iyengar, Thomas Marley

arxiv:1612.00509 v2 · 2016-12-01 · 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{D3WLPW5E3U6ELGQB6FFPWGJCET}

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	2026-05-18T00:45:19.791555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1eecb7dba4dd3c459a01f14afb192224faf1fbdfc36184560ccd2acd9e058f62

Aliases

arxiv: 1612.00509 · arxiv_version: 1612.00509v2 · doi: 10.48550/arxiv.1612.00509 · pith_short_12: D3WLPW5E3U6E · pith_short_16: D3WLPW5E3U6ELGQB · pith_short_8: D3WLPW5E

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/D3WLPW5E3U6ELGQB6FFPWGJCET \
  | 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: 1eecb7dba4dd3c459a01f14afb192224faf1fbdfc36184560ccd2acd9e058f62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "460dd3bd092321438dee818a8373c8e948a64bca9917952285543a4b6e61702d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-12-01T23:10:05Z",
    "title_canon_sha256": "d3b9f46ed6b00178e681cc17b9e70107b92c6227e4972b6bdd2010694c79a6b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00509",
    "kind": "arxiv",
    "version": 2
  }
}